University of Southern California Dissertations and Theses

Media access control for optical CDMA networks through interference avoidance

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Media access control for optical CDMA networks through interference avoidance

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Content MEDIA ACCESS CONTROL FOR OPTICAL CDMA NETWORKS
THROUGH INTERFERENCE A VOIDANCE
by
Purushotham V . Kamath
A Dissertation Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(COMPUTER ENGINEERING)
December 2006
Copyright 2006 Purushotham V . Kamath
Dedication
To my parents, Venkatesh and Vatsala Kamath
ii
Acknowledgments
I have had the opportunity to work with several excellent researchers during the course of my
doctoral research. I would like to take this opportunity to express my gratitude to them and
acknowledge their contribution in shaping me as a researcher. My advisers, Profs. Joseph
Bannister and Joseph Touch, supported and advised me through the doctoral process. Their
feedback and commentary has greatly influenced my work. Prof. Alan Willner gave me the
opportunity to collaborate and work with researchers at USC’s Optical Communication Lab-
oratory. Prof. P. Vijay Kumar provided significant feedback on my work and its relationship
to coding theory. Prof. Ramesh Govindan provided valuable feedback on the presentation of
the work.
This work would not have been possible without the help of several collaborators. In par-
ticular, Poorya Saghari, Reza Gholizadeh, Saurabh Kumar, Deniz Gurkan and Paniz Ebhrahimi
of the Optical Communications Laboratory at USC helped me significantly in my experimen-
tal work. I am grateful to them for discussions concerning the behavior of the optical physical
layer. Reza Omrani of the coding theory group at USC provided me with inputs on coding
theory, codeset design and tools for generating codesets. Sumit Mediratta provided me feed-
back on VLSI design and hardware implementation issues. I would also like to thank several
graduate students at ISI for time spent in interesting discussions on networks, engineering
iii
and many other topics. Among them were Lars Eggert, Panagiotis Galiotis, Amy Hughes,
Kashyap Merchant, Venkata Pingali, Aatash Patel, Josh Train, Yu-shun Wang and Edward
Yang.
Finally, I would like to thank my friends and family without whom the last few years
would not have been as memorable. Krishna Chintalapudi, Aparna Ram, Rishi Sinha, Ramya
Balasundaram, Divya Devaguptapu, Sangram Tidke, Alefiya Hussain, Debojyoti Dutta, Vidya
Navalpakkam, Narayanan Sadagopan, the Fettucini gang, Iftikhar Burhanuddin, Shiva Kin-
tali and Spundun Bhatt: thank you all for making the last few years such a great experience
in every possible way. My parents, my sister Sadhana and her family constantly supported
me in every way possible. I certainly would not have completed my doctoral studies without
their support. Finally, I would like to thank my wife Roopa for her constant encouragement
and belief in me.
iv
Table of Contents
Dedication ii
Acknowledgments iii
List of Figures xi
List of Tables xxii
Abstract xxiv
1 Introduction 1
1.1 Optical CDMA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 The problem: Interference . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3 The solution: Interference Avoidance . . . . . . . . . . . . . . . . . . . . . . 8
1.3.1 State of an optical CDMA network . . . . . . . . . . . . . . . . . . 10
1.3.2 State estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.3.3 Transmission scheduling . . . . . . . . . . . . . . . . . . . . . . . . 11
1.4 Optical CDMA and the future of optical access networks . . . . . . . . . . . 12
1.4.1 Utilization of the capacity of an optical fiber . . . . . . . . . . . . . . 13
1.4.2 Role of optical CDMA in optical access networks . . . . . . . . . . . 14
1.5 Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2 A primer on optical CDMA 16
2.1 Optical CDMA channel characteristics . . . . . . . . . . . . . . . . . . . . . 17
2.1.1 Intensity modulation and unipolar encoding . . . . . . . . . . . . . . 17
2.1.2 Guided, low noise medium . . . . . . . . . . . . . . . . . . . . . . . 19
2.2 Optical CDMA codeset design . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.3 Optical CDMA transmitter and receiver design . . . . . . . . . . . . . . . . 25
2.3.1 Optical CDMA transmitters . . . . . . . . . . . . . . . . . . . . . . 25
2.3.2 Optical CDMA receivers . . . . . . . . . . . . . . . . . . . . . . . . 26
2.4 Optical CDMA errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
v
3 Interference and Interference Avoidance 31
3.1 Interference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.1.1 Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.1.2 Condition for a bit error . . . . . . . . . . . . . . . . . . . . . . . . 33
3.1.3 Condition for a packet error . . . . . . . . . . . . . . . . . . . . . . 38
3.2 State of the line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.2.1 State of the line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.2.2 State observations . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.2.3 State transitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.3 Properties of an optical CDMA network . . . . . . . . . . . . . . . . . . . . 42
3.3.1 Non mutually destructive nature of interference . . . . . . . . . . . . 42
3.3.2 Correlation of state . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.4 Comparison of state and its properties to other physical layers . . . . . . . . 47
3.4.1 Wired networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.4.1.1 Interference . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.4.1.2 Correlation of state . . . . . . . . . . . . . . . . . . . . . 48
3.4.2 Wireless networks . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.4.2.1 Interference . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.4.2.2 Correlation of state . . . . . . . . . . . . . . . . . . . . . 51
3.5 Interference Avoidance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.5.1 Transmission scheduling . . . . . . . . . . . . . . . . . . . . . . . . 54
3.5.2 State estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4 Network architecture 56
4.1 Network topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.2 Node architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.3 Physical layer design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.3.1 Codeword assignment . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.3.2 Codeset design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.4 Link layer design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.4.1 Addressing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4.4.2 Address to codeword mapping . . . . . . . . . . . . . . . . . . . . . 63
4.4.3 Frame synchronization . . . . . . . . . . . . . . . . . . . . . . . . . 64
4.4.4 Frame format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
4.5 Upper layer protocol design issues . . . . . . . . . . . . . . . . . . . . . . . 66
5 Transmission scheduling 68
5.1 The transmission scheduling problem . . . . . . . . . . . . . . . . . . . . . 69
5.2 Transmission scheduling strategies . . . . . . . . . . . . . . . . . . . . . . . 69
5.2.1 Selfish strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
5.2.2 Cooperative strategies . . . . . . . . . . . . . . . . . . . . . . . . . 71
5.2.3 Pseudo-cooperative strategies . . . . . . . . . . . . . . . . . . . . . 72
5.3 Transmission scheduling algorithms . . . . . . . . . . . . . . . . . . . . . . 73
5.3.1 Pure selfish scheduling . . . . . . . . . . . . . . . . . . . . . . . . . 74
vi
5.3.2 Threshold scheduling . . . . . . . . . . . . . . . . . . . . . . . . . . 75
5.3.3 Overlap section scheduling . . . . . . . . . . . . . . . . . . . . . . . 76
5.4 Performance study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
5.4.1 Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
5.4.2 Performance metrics . . . . . . . . . . . . . . . . . . . . . . . . . . 78
5.4.2.1 Normalized offered load . . . . . . . . . . . . . . . . . . . 78
5.4.2.2 Normalized network throughput . . . . . . . . . . . . . . . 79
5.4.3 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
5.4.4 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
5.4.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
5.5 Performance limits of transmission scheduling algorithms . . . . . . . . . . . 87
5.5.1 Centralized perfect scheduling . . . . . . . . . . . . . . . . . . . . . 88
5.5.2 Distributed perfect scheduling . . . . . . . . . . . . . . . . . . . . . 89
5.5.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
5.6 Sensitivity analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
5.6.1 Effect of varying the length of the codeset . . . . . . . . . . . . . . . 93
5.6.2 Effect of varying the weight of the codeset . . . . . . . . . . . . . . 94
5.6.3 Effect of varying the cross correlation parameter . . . . . . . . . . . 96
5.6.4 Effect of varying the number of wavelengths . . . . . . . . . . . . . 98
5.6.5 Effect of varying the threshold scheduling algorithm parameter . . . . 98
5.6.6 Effect of packet size distribution . . . . . . . . . . . . . . . . . . . . 100
5.6.7 Performance with real network traffic . . . . . . . . . . . . . . . . . 106
5.7 Conclusions and future work . . . . . . . . . . . . . . . . . . . . . . . . . . 107
6 State estimation 108
6.1 The state estimation problem . . . . . . . . . . . . . . . . . . . . . . . . . . 109
6.2 State estimation algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
6.2.1 Distribution of the state . . . . . . . . . . . . . . . . . . . . . . . . . 112
6.2.2 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
6.2.2.1 Observation parameters . . . . . . . . . . . . . . . . . . . 115
6.2.2.2 Estimation parameters . . . . . . . . . . . . . . . . . . . . 116
6.2.3 State estimation algorithms . . . . . . . . . . . . . . . . . . . . . . . 116
6.3 Causes for packet loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
6.3.1 Interference because of erroneous transmission scheduling . . . . . . 119
6.3.2 Interference because of collisions . . . . . . . . . . . . . . . . . . . 120
6.3.3 Interference because of erroneous state estimation . . . . . . . . . . 121
6.4 Performance study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
6.4.1 Perfect state estimation, a = 0 . . . . . . . . . . . . . . . . . . . . . 123
6.4.2 Perfect state estimation, a> 0 . . . . . . . . . . . . . . . . . . . . . 125
6.4.3 Realistic state estimation, a> 0 . . . . . . . . . . . . . . . . . . . . 128
6.5 Sensitivity analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
6.5.1 Effect of varying the codeset length . . . . . . . . . . . . . . . . . . 130
6.5.2 Effect of varying the codeset weight . . . . . . . . . . . . . . . . . . 131
6.5.3 Effect of varying the cross correlation parameter . . . . . . . . . . . 131
vii
6.5.4 Effect of varying the number of wavelengths . . . . . . . . . . . . . 131
6.5.5 Effect of varying threshold . . . . . . . . . . . . . . . . . . . . . . . 133
6.5.6 Effect of different estimation algorithms . . . . . . . . . . . . . . . . 134
6.5.7 Effect of varying the number of state observations collected . . . . . 135
6.5.8 Effect of varying the average distance from the coupler . . . . . . . . 136
6.5.9 Effect of varying the packet length . . . . . . . . . . . . . . . . . . . 138
6.5.10 Performance with real network traffic . . . . . . . . . . . . . . . . . 138
6.5.11 Performance under very high load . . . . . . . . . . . . . . . . . . . 139
6.6 Conclusions and future work . . . . . . . . . . . . . . . . . . . . . . . . . . 142
7 Implementation 143
7.1 Experimental demonstration and measurement of transmission scheduling . . 143
7.1.1 Optical CDMA transmitter component . . . . . . . . . . . . . . . . . 146
7.1.1.1 Modulator . . . . . . . . . . . . . . . . . . . . . . . . . . 147
7.1.1.2 Encoders . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
7.1.2 Optical CDMA receiver . . . . . . . . . . . . . . . . . . . . . . . . 150
7.1.3 Measurement instruments . . . . . . . . . . . . . . . . . . . . . . . 152
7.1.4 Limitations of the testbed . . . . . . . . . . . . . . . . . . . . . . . 153
7.1.5 Objective of the experiment . . . . . . . . . . . . . . . . . . . . . . 154
7.1.6 Experimental procedure . . . . . . . . . . . . . . . . . . . . . . . . 155
7.1.6.1 Preliminary checks . . . . . . . . . . . . . . . . . . . . . 155
7.1.6.2 Measurements . . . . . . . . . . . . . . . . . . . . . . . . 156
7.1.7 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
7.2 Implementation of a network interface card . . . . . . . . . . . . . . . . . . 161
7.2.1 Bus interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
7.2.2 State observation collection module . . . . . . . . . . . . . . . . . . 164
7.2.3 State estimation module . . . . . . . . . . . . . . . . . . . . . . . . 166
7.2.4 Controller module . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
7.2.5 Transmission scheduling module . . . . . . . . . . . . . . . . . . . . 169
7.2.6 Optimizing the state observation collection and state estimation module172
7.2.7 Ranging and synchronization modules . . . . . . . . . . . . . . . . . 173
7.2.8 Optical CDMA transmitter . . . . . . . . . . . . . . . . . . . . . . . 174
7.2.9 Optical CDMA receiver . . . . . . . . . . . . . . . . . . . . . . . . 176
7.2.10 Timing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
7.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
8 Related work 180
8.1 Wired networks with a single channel . . . . . . . . . . . . . . . . . . . . . 181
8.1.1 Contention protocols . . . . . . . . . . . . . . . . . . . . . . . . . . 181
8.1.2 Reservation protocols . . . . . . . . . . . . . . . . . . . . . . . . . . 183
8.2 Wired networks with multiple orthogonal channels . . . . . . . . . . . . . . 184
8.3 Wired networks with pseudo-orthogonal channels . . . . . . . . . . . . . . . 185
8.4 Wireless networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
8.4.1 Channel load sensing . . . . . . . . . . . . . . . . . . . . . . . . . . 186
viii
8.4.2 Multi-user interference estimation . . . . . . . . . . . . . . . . . . . 187
8.4.3 MIMO and CSIT . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
8.4.4 Other related work in transmission scheduling . . . . . . . . . . . . . 188
8.5 Other relevant work in optical CDMA networks . . . . . . . . . . . . . . . . 189
8.5.1 Codeset design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
8.5.2 Bit error rate performance analysis . . . . . . . . . . . . . . . . . . . 190
8.5.3 Forward error correction . . . . . . . . . . . . . . . . . . . . . . . . 190
9 Conclusions and future directions 192
9.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
9.2 Future directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
9.2.1 Analysis of Interference Avoidance . . . . . . . . . . . . . . . . . . 195
9.2.1.1 Optimal transmission scheduling algorithms . . . . . . . . 195
9.2.1.2 Delay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
9.2.1.3 Fairness and quality of service . . . . . . . . . . . . . . . 196
9.2.1.4 Error control . . . . . . . . . . . . . . . . . . . . . . . . . 196
9.2.2 Architectural issues . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
9.2.2.1 Other areas . . . . . . . . . . . . . . . . . . . . . . . . . . 197
9.2.3 Power control in optical CDMA LANs . . . . . . . . . . . . . . . . 198
9.2.4 Optical CDMA switch design . . . . . . . . . . . . . . . . . . . . . 198
Reference List 199
Appendix A
State representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206
Appendix B
Packet error rate and number of codewords multiplexed on the line . . . . . . . . . 210
B.1 Packet error rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210
B.2 Number of codewords multiplexed on the line . . . . . . . . . . . . . . . . . 211
Appendix C
Equilibrium state probabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
C.1 Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
C.2 Admissible transmissions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
C.2.1 Aloha-CDMA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
C.2.2 Pure selfish scheduling . . . . . . . . . . . . . . . . . . . . . . . . . 215
C.2.3 Threshold scheduling . . . . . . . . . . . . . . . . . . . . . . . . . . 215
C.2.4 Overlap section scheduling . . . . . . . . . . . . . . . . . . . . . . . 215
C.3 Arrival state transition probabilities . . . . . . . . . . . . . . . . . . . . . . . 216
C.4 Departure state transition probabilities . . . . . . . . . . . . . . . . . . . . . 217
C.5 Balance equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
Appendix D
Arrival state transition diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
ix
Appendix E
Throughput of Centralized Perfect Scheduling . . . . . . . . . . . . . . . . . . . . 221
E.1 N
offered
N(w 1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
E.2 N
offered
< N(w 1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224
Appendix F
Interference Avoidance is a generalization of Carrier Sensing and CDMA . . . . . 227
x
List of Figures
1.1 A typical optical CDMA network. The network consists of M nodes. The
nodes are connected by transmit and receive fibers to a passive star coupler
forming a shared medium LAN. . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 An example of multi-user interference showing three codewords C0, C1, and
C2. The two codewords (C1 and C2) interfere with another codeword (C0).
(a) shows the line (fiber) when C0 is OFF (transmitting a 0 bit) and (b) shows
the line when C0 is ON (transmitting a 1 bit). In (a), C0 experiences an
interference error. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.3 The normalized network throughput vs. normalized offered load for Aloha-
CDMA. The results are based on simulation. The traffic model is Poisson ar-
rivals with exponentially distributed packet lengths. The codeset is (10;3;3).
The destination of a packet is chosen uniform randomly from all the nodes
and codewords are allocated to nodes by choosing them randomly from the
codeset. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.4 The effect of Interference Avoidance. The codewords are the same as in Fig-
ure 1.2. C0 has been transmitted one chip time later compared to Figure 1.2.
(a) shows the line (fiber) when C0 is OFF and (b) shows the line when C0 is
ON. In either case, C0 does not have an interference error. . . . . . . . . . . 9
2.1 The ON-OFF keying of codewords. The lower line shows the signal on the
optical fiber when a single codeword (0100011) is being transmitted. The
upper line shows the corresponding data. . . . . . . . . . . . . . . . . . . . . 18
2.2 Packet, codeword and chip overlaps. This figure depicts chip synchronous
transmission. The effect of chip synchronous and asynchronous transmission
is discussed in Chapter 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.3 Three codewords of an optical CDMA codeset whose parameters are codeset
length N = 25, weight w = 3 and maximum crosscorrelation parameter κ = 1. 23
xi
2.4 An optical CDMA receiver. It is a hard-limiting correlation detector that
consists of a hard-limiter, decoder, a photodetector, and a threshold detector.
The receiver is tuned to the codeword 1110000. The power in the 1
st
;2
nd
and
3
rd
chip positions is summed by the decoder. The photodetector converts the
signal to current and the threshold detector detects a 1 bit. . . . . . . . . . . 26
3.1 A bit error. The figure shows four codewords on the optical fiber. In (a)
codeword C0 is OFF. A false positive error occurs at the receiver due to in-
terference from C1 and C2 or C3. . . . . . . . . . . . . . . . . . . . . . . . 33
3.2 Four codewords multiplexed on an optical fiber. The figure shows the receiv-
ing codeword, interfering codewords, the error generating codeset and the
error generating delays. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.3 The different cases that can occur when codewords overlap. (a) shows the
case when all members of the EGC are ON and the receiving codeword is
OFF (causes a bit error). (b) shows the case when all members of the EGC are
ON and the receiving codeword is ON (does not cause a bit error). (c) shows
the case when one member of the EGC is OFF and the receiving codeword is
OFF (does not cause a bit error). (d) shows the case when one member of the
EGC is OFF and the receiving codeword is ON (does not cause a bit error). . 36
3.4 Four overlapping packets on an optical fiber. Each packet may be divided
into sections at instants where a packet has arrived or departed. . . . . . . . . 37
3.5 The state of the line at a point on a receiver fiber. The state of the line at time
t at distance d is [2 2 1 2 2 3 0 1]. The second bit of codeword C1 is OFF. To
calculate the state, C0 is assumed to be ON and the codewords are added. . . 39
3.6 The four possible packet transmission events that are a consequence of the
non-mutually destructive nature of interference. . . . . . . . . . . . . . . . . 43
3.7 Examples of the four packet transmission events. In each example, the dif-
ferent transmission time of codeword C0 has caused a different transmission
event. The circled chips mark the ‘1 chips’ that do not have overlaps and the
corresponding codewords are preserved. . . . . . . . . . . . . . . . . . . . . 44
3.8 The correlation between the state at the estimation point at estimation time
and the merging point at merging time for an optical CDMA network as the
diameter of the network increases. The network has 100 nodes distributed
uniformly over the length of the network. The network uses Aloha-CDMA.
Packet arrivals are Poisson with offered load 1 and packet lengths are expo-
nentially distributed with an average length of 1000 bytes. . . . . . . . . . . 45
xii
3.9 Interference Avoidance prevents occurrence of a bit error. No error is caused
when the same codewords in Figure 3.1 are sent with a different set of trans-
mission delays. The figure shows the same codewords with codeword C0
delayed by 1 chip time. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.1 A typical Fiber to the Home (FTTH) network topology. It shows the upstream
link where Interference Avoidance may be used as a media access mechanism. 59
4.2 Block diagram of an Interference Avoidance Network Interface Card. . . . . 60
4.3 The frame format for Interference Avoidance frames. The synchronization
sequence is used for the frame synchronization operation, the length field is
used to determine the size of the payload, and the checksum field is used for
error detection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
5.1 The transmission scheduling strategies and the events that they attempt to
achieve. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
5.2 Normalized network throughput vs. normalized offered load for different
transmission scheduling algorithms based on analysis. The traffic model is
Poisson arrivals with exponentially distributed packet lengths. The codeset
is (10;3;3). For the threshold scheduling algorithm, the threshold parame-
ter was set to 0.5. The destination of a packet is chosen uniform randomly
from all the nodes and codewords are allocated to nodes by choosing them
randomly from the codeset. . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
5.3 This graph shows the normalized network throughput vs. normalized offered
load for different transmission scheduling algorithms. The results are based
on simulation. The traffic model is Poisson arrivals with exponentially dis-
tributed packet lengths. The codeset is (10;3;3). For the threshold scheduling
algorithm, the threshold parameter was set to 0.5. The destination of a packet
is chosen uniform randomly from all the nodes and codewords are allocated
to nodes by choosing them randomly from the codeset. . . . . . . . . . . . . 83
5.4 The average number of codewords multiplexed at a point on a receiver fiber
vs. normalized offered load for different transmission scheduling algorithms.
The results are based on simulation. The traffic model is Poisson arrivals
with exponentially distributed packet lengths. The codeset is (10;3;3). For
the threshold scheduling algorithm, the threshold parameter was set to 0.5.
The destination of a packet is chosen uniform randomly from all the nodes
and codewords are allocated to nodes by choosing them randomly from the
codeset. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
xiii
5.5 Packet error rate vs. normalized offered load for different transmission schedul-
ing algorithms. The results are based on simulation. The traffic model is
Poisson arrivals with exponentially distributed packet lengths. The codeset
is (10;3;3). For the threshold scheduling algorithm, the threshold parame-
ter was set to 0.5. The destination of a packet is chosen uniform randomly
from all the nodes and codewords are allocated to nodes by choosing them
randomly from the codeset. . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5.6 The normalized throughput vs. normalized offered load for the Centralized
and Distributed Perfect Scheduling algorithms and threshold scheduling. The
results are based on both simulation and analysis. The parameters are detailed
in the text. The codeset is (10;3;3). The threshold algorithm used a threshold
of 0.5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
5.7 The normalized network throughput at normalized offered load of 1 vs. the
codeset length N for different transmission scheduling algorithms. The re-
sults are based on simulation. The traffic model is Poisson arrivals with expo-
nentially distributed packet lengths. The codeset weight is 3 and κ = 3. For
the threshold scheduling algorithm, the threshold parameter was set to 0.5.
The destination of a packet is chosen uniform randomly from all the nodes
and codewords are allocated to nodes by choosing them randomly from the
codeset. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
5.8 Normalized network throughput at normalized offered load of 1 for different
transmission scheduling algorithms. The results are based on simulation. The
traffic model is Poisson arrivals with exponentially distributed packet lengths.
The codeset length is 100 and κ = 3. For the threshold scheduling algorithm,
the threshold parameter was set to 0.5. The destination of a packet is chosen
uniform randomly from all the nodes and codewords are allocated to nodes
by choosing them randomly from the codeset. . . . . . . . . . . . . . . . . . 96
5.9 Normalized network throughput at normalized offered load of 1 for different
transmission scheduling algorithms. The results are based on simulation.
The traffic model is Poisson arrivals with exponentially distributed packet
lengths. The codeset length N = 42 and weight w = 6. The cross correlation
parameter κ is varied from 1 to 6. For the threshold scheduling algorithm,
the threshold parameter was set to 0.5. The destination of a packet is chosen
uniform randomly from all the nodes and codewords are allocated to nodes
by choosing them randomly from the codeset. . . . . . . . . . . . . . . . . . 97
xiv
5.10 Normalized network throughput at normalized offered load of 1 vs. the num-
ber of wavelengths for different transmission scheduling algorithms. The
results are based on simulation. The traffic model is Poisson arrivals with
exponentially distributed packet lengths. The codeset length is 10, weight is
3 and κ = 3. For the threshold scheduling algorithm, the threshold parame-
ter was set to 0.5. The destination of a packet is chosen uniform randomly
from all the nodes and codewords are allocated to nodes by choosing them
randomly from the codeset. . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
5.11 Normalized network throughput at normalized offered load of 1 vs. threshold
parameter α for different transmission scheduling algorithms. The results are
based on simulation. The traffic model is Poisson arrivals with exponentially
distributed packet lengths. The codeset is (100;3;3). The destination of a
packet is chosen uniform randomly from all the nodes and codewords are
allocated to nodes by choosing them randomly from the codeset. . . . . . . . 100
5.12 Normalized network throughput vs. average packet size at a normalized of-
fered load of 1. The results are based on simulation. The traffic model is
Poisson arrivals and exponentially distributed packet sizes. The codeset is
(100;3;3). The algorithm was threshold scheduling; the threshold parame-
ter was set to 0.5. The destination of a packet is chosen uniform randomly
from all the nodes and codewords are allocated to nodes by choosing them
randomly from the codeset. . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
5.13 Normalized network throughput vs. normalized offered load for different
transmission scheduling algorithms. The results are based on simulation. The
traffic model is Poisson arrivals with a trimodal packet size distribution (70%
40 bytes, 20% 1500 bytes and 10% 500 bytes). The codeset is (100;3;3). For
the threshold scheduling algorithm, the threshold parameter was set to 0.5.
The destination of a packet is chosen uniform randomly from all the nodes
and codewords are allocated to nodes by choosing them randomly from the
codeset. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
5.14 The squeeze through effect. The throughput is maximized when the fraction
of short packets is 0.9. The graph shows both analytical and simulation re-
sults. The transmission scheduling algorithm is pure selfish. The packet sizes
are 50 bytes and 1000 bytes. The codeset is (100,3,3). . . . . . . . . . . . . . 105
5.15 Normalized network throughput vs. normalized offered load for different
transmission scheduling algorithms. The results are based on simulation.
The traffic model was based on real network traffic traces (see description).
The codeset is (100;3;3) and codewords are allocated to addresses. For the
threshold scheduling algorithm, the threshold parameter was set to 0.5 . . . . 107
xv
6.1 The points on the optical fiber where state is estimated and transmissions
merge. The state is estimated by a node at its estimation point at the estima-
tion time. The node transmits a packet at the transmission time and it merges
with other packets at the merging point (coupler) at the merging time. . . . . 109
6.2 Observations of the state at a point. The state estimation algorithm calculates
a state estimate from the state observations. . . . . . . . . . . . . . . . . . . 111
6.3 The mean number of bits between a state change for different codeset lengths
at an offered load of 1. The network is an Aloha-CDMA network with Pois-
son arrivals and exponentially distributed packet lengths. The average packet
length is 1000 bytes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
6.4 The state estimation parameters. The figure shows 10 state observations. The
collection of state observations begins at t
s
. Estimation is run after n
e
= 5
observations are collected at time t
e
. . . . . . . . . . . . . . . . . . . . . . . 117
6.5 Collisions on an optical CDMA network. Transmissions from nodes A and
B collide because neither can see the others’ transmission. . . . . . . . . . . 120
6.6 Normalized network throughput vs. normalized offered load for perfect state
estimation, normalized propagation delay a = 0. The results are based on
simulation. The codeset length is 10. All other parameters are as specified in
Table 6.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
6.7 Normalized network throughput vs. normalized offered load for perfect state
estimation, normalized propagation delay a = 0. The results are based on
simulation. The codeset length is 100. All other parameters are as specified
in Table 6.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
6.8 Normalized network throughput vs. normalized offered load for perfect state
estimation, normalized propagation delay a = 0. The results are based on
simulation. The codeset length is 200. All other parameters are as specified
in Table 6.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
6.9 Normalized network throughput vs. normalized offered load for perfect state
estimation, normalized propagation delay a > 0 (average distance from the
coupler is 1000m). The results are based on simulation. The codeset length
is 10. All other parameters are as specified in Table 6.2 . . . . . . . . . . . . 125
xvi
6.10 Normalized network throughput vs. normalized offered load for perfect state
estimation, normalized propagation delay a > 0 (average distance from the
coupler is 1000m). The results are based on simulation. The codeset length
is 100. All other parameters are as specified in Table 6.2 . . . . . . . . . . . 125
6.11 Normalized network throughput vs. normalized offered load for perfect state
estimation, normalized propagation delay a > 0 (average distance from the
coupler is 1000m). The results are based on simulation. The codeset length
is 200. All other parameters are as specified in Table 6.2 . . . . . . . . . . . 125
6.12 Normalized network throughput vs. normalized offered load for continuous
state estimation, normalized propagation delay a> 0 (average distance from
the coupler is 1000m). The results are based on simulation. The codeset
length is 10. All other parameters are as specified in Table 6.2 . . . . . . . . 127
6.13 Normalized network throughput vs. normalized offered load for continuous
state estimation, normalized propagation delay a> 0 (average distance from
the coupler is 1000m). The results are based on simulation. The codeset
length is 100. All other parameters are as specified in Table 6.2 . . . . . . . . 127
6.14 Normalized network throughput vs. normalized offered load for continuous
state estimation, normalized propagation delay a> 0 (average distance from
the coupler is 1000m). The results are based on simulation. The codeset
length is 200. All other parameters are as specified in Table 6.2 . . . . . . . . 127
6.15 Normalized network throughput vs. codeset length N for different transmis-
sion scheduling algorithms and on-demand state estimation. The results are
based on simulation. The traffic model is Poisson arrivals with exponentially
distributed packet lengths. The codeset is (N;3;3). For the threshold schedul-
ing algorithm, the threshold parameter was set to 0.3. All other parameters
are specified in Table 6.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
6.16 Normalized network throughput vs. codeset weight w for different transmis-
sion scheduling algorithms and on-demand state estimation. The results are
based on simulation. The traffic model is Poisson arrivals with exponen-
tially distributed packet lengths. The codeset is (100;w;w). For the threshold
scheduling algorithm, the threshold parameter was set to 0.3. All other pa-
rameters are specified in Table 6.2 . . . . . . . . . . . . . . . . . . . . . . . 130
xvii
6.17 Normalized network throughput at normalized offered load of 1 for different
transmission scheduling algorithms. The results are based on simulation. The
traffic model is Poisson arrivals with exponentially distributed packet lengths.
The codeset length N = 42 and weight w= 6. The cross correlation parameter
κ is varied from 1 to 6. For the threshold scheduling algorithm, the threshold
parameter was set to 0.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
6.18 Normalized network throughput vs. number of wavelength for different trans-
mission scheduling algorithms and on-demand state estimation. The results
are based on simulation. The traffic model is Poisson arrivals with exponen-
tially distributed packet lengths. The codeset is (10;3;3). For the threshold
scheduling algorithm, the threshold parameter was set to 0.3. All other pa-
rameters are specified in Table 6.2 . . . . . . . . . . . . . . . . . . . . . . . 132
6.19 Normalized network throughput vs. threshold for the threshold scheduling
algorithms and on-demand state estimation. The results are based on sim-
ulation. The traffic model is Poisson arrivals with exponentially distributed
packet lengths. The codeset lengths are 10;100 and 200. All other parameters
are specified in Table 6.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
6.20 Normalized network throughput vs. threshold vs. offered load for the thresh-
old scheduling algorithms and on-demand state estimation. The results are
based on simulation. The traffic model is Poisson arrivals with exponentially
distributed packet lengths. The codeset length is 100. All other parameters
are specified in Table 6.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
6.21 Normalized network throughput vs. normalized offered load for on demand
state estimation, normalized propagation delay a> 0 (average distance from
the coupler is 1000m). The codeset length is N = 200. The results are based
on simulation. All other parameters are specified in Table 6.2 . . . . . . . . . 135
6.22 Normalized network throughput vs. state estimation window (in bits) for
the transmission scheduling algorithms and continuous and on-demand state
estimation. The results are based on simulation. All other parameters are
specified in Table 6.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
6.23 Normalized network throughput vs. average distance from coupler (uniform
distribution) for the transmission scheduling algorithms and continuous state
estimation. The results are based on simulation. The codeset length is 10.
All other parameters are specified in Table 6.2 . . . . . . . . . . . . . . . . . 137
xviii
6.24 Normalized throughput vs. average distance from coupler (uniform distribu-
tion) for the transmission scheduling algorithms and continuous state estima-
tion. The results are based on simulation. The codeset length is 100. All
other parameters are specified in Table 6.2 . . . . . . . . . . . . . . . . . . . 137
6.25 Normalized throughput vs. average distance from coupler (uniform distribu-
tion) for the transmission scheduling algorithms and continuous state estima-
tion. The results are based on simulation. The codeset length is 200. All
other parameters are specified in Table 6.2 . . . . . . . . . . . . . . . . . . . 137
6.26 Normalized network throughput vs. average packet length (in bytes) for the
transmission scheduling algorithms and on-demand state estimation. The re-
sults are based on simulation. The traffic model is Poisson arrivals with ex-
ponentially distributed packet lengths. The codeset is (100;3;3). For the
threshold scheduling algorithm, the threshold parameter was set to 0.3. All
other parameters are specified in Table 6.2 . . . . . . . . . . . . . . . . . . . 138
6.27 Normalized network throughput vs. normalized offered load for the trans-
mission scheduling algorithms and continuous state estimation with realistic
network traffic. The results are based on simulation. All other parameters are
specified in Table 6.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
6.28 Normalized network throughput vs. normalized offered load for the threshold
scheduling transmission scheduling algorithms and continuous state estima-
tion with Poisson arrivals, exponentially distributed packet sizes. The codeset
length is 10. The results are based on simulation. All other parameters are
specified in Table 6.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
6.29 Normalized network throughput vs. normalized offered load for the threshold
scheduling transmission scheduling algorithms and continuous state estima-
tion with Poisson arrivals, exponentially distributed packet sizes. The codeset
length is 100. The results are based on simulation. All other parameters are
specified in Table 6.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
6.30 Normalized network throughput vs. normalized offered load for the threshold
scheduling transmission scheduling algorithms and continuous state estima-
tion with real traffic. The codeset length is 100. The results are based on
simulation. All other parameters are specified in Table 6.2 . . . . . . . . . . 141
7.1 A block diagram of the optical CDMA experimental testbed constructed at
the USC Electrical Engineering department’s Optical Communications Lab-
oratory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
xix
7.2 A block diagram of the modulator part of the Optical CDMA testbed. . . . . 145
7.3 A block diagram of the four encoders of the Optical CDMA testbed. . . . . . 145
7.4 The optical CDMA encoders. The tunable delay lines (TDLs) of the encoder
encode an optical CDMA codeword. . . . . . . . . . . . . . . . . . . . . . . 149
7.5 The receiver of the optical CDMA testbed. . . . . . . . . . . . . . . . . . . . 151
7.6 The decoder of the optical CDMA receiver. The figure shows how the Tun-
able Delay Lines (TDLs) of the receiver decode the optical CDMA codeword. 151
7.7 Experimental results: The transmission scheduling algorithm results in the
best case BER. It occurred under cases when there were zero overlaps. The
worst case BER is the worst possible bit error rate that was measured. It
occurred in cases when the number of overlaps was the maximum possible.
Aloha-CDMA does not control the number of overlaps. Its BER is the aver-
age over all the measured cases. . . . . . . . . . . . . . . . . . . . . . . . . 160
7.8 A block diagram of an Interference Avoidance Network Interface Card. . . . 163
7.9 State observation collection module. The input to the state observation col-
lection module is a multivalued optical signal that arrives at the chipping rate.
The output is an electronic digital value, a chip observation, which changes
at the chipping rate. Each chip observation represents the magnitude of the
multivalued signal in a chip time. The figure shows 4 threshold detectors,
enough to detect up to 4 different chip magnitudes. The number of detectors
can be modified based on the accuracy desired. Section 7.2.6 discusses why
a minimum of 3 is needed. . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
7.10 State estimation module. The input is a stream of chip observations arriving
at the chipping rate. The output is a state estimate that is output at the clock
rate of the hardware. The figure also shows the width of the data lines in the
hardware. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
7.11 Transmission scheduling hardware. There are two inputs: the codeword that
arrives on packet arrival and the state estimate, which changes every clock
cycle. The output is the delay in terms of number of chips from the start of
the hardware clock cycle. This delay is used to delay the transmission. The
width of the data lines is also shown in the figure. . . . . . . . . . . . . . . . 170
xx
7.12 Optical CDMA transmitter hardware implementation. The input is a stream
of bits. It modulates a stream of codewords being transmitted by the laser
and encoder. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
7.13 Optical CDMA receiver hardware. The input is the signal on the optical fiber
at the chipping rate and the output is the received data at the bit rate. . . . . . 176
7.14 Timing diagram (not to scale). The diagram shows the timing of events on a
NIC for a 10Gc/s network using a codeset of length N = 100, weight w = 3.
The hardware clock speed is 100MHz. The hardware design is as described in
this section. A new state estimate is generated every 10ns. On packet arrival,
the transmission scheduling hardware operates on its input and produces its
result in 50ns. After tuning delays and the calculated delay (t
d
), the packet is
transmitted. The residual chip time (the time between the delay line tuning
and the start of the next hardware clock cycle) is also shown. . . . . . . . . . 178
A.1 State can be represented mathematically by a pair (n
0
, n
1
) where n
0
is the size
of the zeros section and n
1
is the size of the ones section. . . . . . . . . . . . 207
A.2 The initial few states of a state transition diagram. . . . . . . . . . . . . . . . 209
F.1 The performance of Interference Avoidance vs. codeset length and codeset
weight. The results are based on simulation. The graph shows the normalized
network throughput at a normalized offered load of 1 and normalized prop-
agation delay of a = 0. The traffic model is Poisson arrivals, exponentially
distributed packet sizes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228
xxi
List of Tables
3.1 Comparison of the state of the network in three shared medium networks:
Single channel wired networks, single channel wireless networks, and optical
CDMA networks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.2 Comparison of the properties of the state of the network in three shared
medium networks: Single channel wired networks, single channel wireless
networks, and optical CDMA networks. . . . . . . . . . . . . . . . . . . . . 52
5.1 The Pure selfish transmission scheduling algorithm. . . . . . . . . . . . . . . 74
5.2 The Threshold transmission scheduling algorithm. . . . . . . . . . . . . . . . 76
5.3 The Overlap section transmission scheduling algorithm. . . . . . . . . . . . . 77
5.4 The Centralized Perfect Scheduling algorithm. . . . . . . . . . . . . . . . . . 88
5.5 The Distributed Perfect Scheduling algorithm. . . . . . . . . . . . . . . . . . 89
5.6 Parameter list and default values for the transmission scheduling sensitivity
study. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
6.1 The Sample means state estimation algorithm. . . . . . . . . . . . . . . . . . 117
6.2 Parameter list and default values for the state estimation performance and
sensitivity study. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
7.1 Codewords for the 4 nodes in the experimental testbed. The codewords are
from a 2 D codeset (more than one wavelengths is used) with parameters (11,
6, 6, 1). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
7.2 Testbed bit error rate in the presence of 1 interfering user. . . . . . . . . . . . 157
xxii
7.3 Testbed bit error rate in the presence of 2 interfering users. . . . . . . . . . . 158
7.4 Testbed bit error rate in the presence of 3 interfering users. . . . . . . . . . . 159
F.1 Reduction of Interference Avoidance to the Aloha, Aloha-CDMA, and CSMA
protocols. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227
xxiii
Abstract
This work proposes Interference Avoidance, a contention media access control protocol for
optical Code Division Multiple Access (CDMA) Local Area Networks (LANs). Optical
CDMA is a direct sequence spread spectrum technology for multiplexing transmissions on
an optical fiber. When used as the physical layer of a LAN, its throughput tends to zero
at high offered load because of multiuser interference. Interference Avoidance prevents this
throughput collapse of optical CDMA networks at high offered load.
An optical CDMA LAN exhibits two unique properties: non-mutually destructive inter-
ference and correlation of state. Interference Avoidance exploits these properties to reduce
packet loss because of interference. It extends the Carrier Sensing mechanism to high speed,
shared medium, optical networks. Interference Avoidance consists of state estimation and
transmission scheduling. This work proposes algorithms for transmission scheduling and
state estimation. The transmission scheduling algorithms stabilize the throughput at around
30% of the maximum at high offered load, under the assumption of perfect state estimation.
Under identical conditions, throughput without transmission scheduling tends to zero. The
algorithms achieve throughput within 10% of optimal codeword scheduling algorithms. The
complexity of the algorithms is linear in codeset length, enabling low complexity hardware
xxiv
implementation. The performance of the state estimation algorithms approaches that of per-
fect state estimation as the codeset length increases and weight decreases, with a low number
(< 100) of estimation samples. The complexity of the algorithms is linear in the number of
estimation samples, allowing for low complexity hardware implementation. This work also
demonstrates the feasibility of transmission scheduling using a laboratory testbed. Measure-
ments from the testbed show that transmission scheduling reduces the bit error rate in the
presence of severe physical layer noise and potentially improves throughput performance as
load is increased.
xxv
Chapter 1
Introduction
Optical CDMA is a multiplexing technology for optical fiber. When used as the physical layer
of a Local Area Network (LAN), the throughput without media access control collapses at
high offered load. Interference Avoidance is a contention media access control protocol for
optical CDMA LANs that prevents throughput collapse. This dissertation proposes Interfer-
ence Avoidance and shows that it prevents throughput collapse in optical CDMA LANs.
This chapter introduces the concepts of optical CDMA, interference, and Interference
Avoidance. Section 1.1 provides a brief description of optical CDMA. Section 1.2 discusses
the problem of interference. Section 1.3 discusses the contribution of this thesis: the solution
of the throughput collapse problem at high offered load through Interference Avoidance.
Section 1.4 discusses the role that optical CDMA may play in future optical access networks.
Section 1.5 describes the organization of the thesis.
The discussion in this chapter is brief and informal. Subsequent chapters provide formal
definitions and in-depth discussions of topics covered here.
1
2
1
Node
Receive fiber Transmit fiber
3
M
13101021 (Line)
01001010 (C2)
11100000 (C0)
01000011 (C1)
Figure 1.1: A typical optical CDMA network. The network consists of M nodes. The
nodes are connected by transmit and receive fibers to a passive star coupler forming a shared
medium LAN.
1.1 Optical CDMA
Optical CDMA is a multiplexing technology for optical fiber. This work considers a packet
switched, shared medium, multiple access Local Area Network that uses optical CDMA as
the physical layer.
This work considers optical CDMA based on intensity modulation and unipolar encod-
ing. Data is encoded using optical CDMA codewords. An optical CDMA codeword is a
distinct sequence of 0s and 1s (the 0s and the 1s are called chips)
1
A node transmits data by
ON-OFF keying of the codeword, i.e., to send a 1 bit, the nodes sends the codeword and to
send a 0 bit, an all zeroes codeword is sent. In intensity modulation an optical pulse is a ‘1
1
This work uses single quotes to distinguish between the magnitude and quantity of chips. The term ‘1 chip’
refers to a chip of magnitude 1.
2
chip’, while the absence of a pulse is a ‘0 chip’. Unipolar encoding refers to the encoding of
data using sequences of ‘0 chips’ and ‘1 chips’. Figure 1.1 shows three nodes transmitting
1 bits using three codewords C0, C1 and C2. Multiple nodes transmit simultaneously using
different codewords.
The network consists of several nodes connected by optical fiber to a passive star coupler
as shown in Figure 1.1. The fibers and the coupler form a low noise, guided medium. Signals
transmitted on the inputs enter the coupler, merge, and are transmitted on all outputs. The
star coupler is passive, i.e., the input power is split equally among the receive fibers and is
transmitted to all nodes on the receive fibers. The signal at the output of the coupler on any
receive fiber at time t is given by:
r(t) = (1=K)
K
∑
i=1
s
i
(t)
where K is the number of input (or output) ports of coupler and s
i
(t) is the signal entering
on the i
th
transmit fiber at time t. The signals on the transmit fibers s
i
(t) are binary optical
signals and the signal on a receive fiber r(t) is a multilevel optical signal. The signal on the
receive fiber may be amplified or attenuated after the coupler. In Figure 1.1 the merged signal
is [1 3 1 0 1 0 2 1]
1
.
The network is based on a Tunable Transmitter-Fixed Receiver (TT-FR) architecture. A
receiver chooses a codeword to receive on and a transmitter that needs to communicate with a
1
The figure indicates that transmission is chip synchronous, i.e., chip boundaries are aligned in time. In reality
this need not be true. However, it is assumed for simplicity of explanation. Chapter 3 justifies this as a reasonable
assumption for analysis. This work also assumes that there are amplifiers on every receive fiber after the coupler
which amplify the signal K times.
3
receiver tunes to the receiver’s codeword. The network uses codeword sharing. If the number
of nodes is greater than the codewords, the codewords are shared among receivers. Packets
sharing a codeword are demultiplexed using a higher layer unique identifier such as a link
layer address. Every node runs a frame synchronization algorithm [29] that allows the node
to identify that a frame destined for it has arrived and where the first bit of the frame begins.
Chapter 4 discusses these three architectural choices.
Every node has a hard-limiting correlation receiver [57]. The receiver is tuned to a par-
ticular codeword. It consists of an optical hard-limiter, a decoder, a photodetector, and a
threshold detector. The signal on the optical fiber is a multilevel optical signal. It is first
passed through an optical hard-limiter. The hard-limiter limits the energy in each chip posi-
tion. The decoder consists of a splitter and delay lines. It collects energy in the chip positions
where it expects to see ‘1 chips’. The energy is then sent to a photodetector that converts it
to a multilevel electrical signal. The signal is then sent through a threshold detector whose
threshold is set proportional to the weight w of the codeset, i.e., to the number of ‘1 chips’ in
the codeword. If the energy is equal to or greater than the threshold, a 1 data bit is detected,
else a 0 bit is detected. Let R be the received signal (a vector of length N whose components
are nonnegative integers), and C the codeword being received (a vector of length N whose
components are binary values). Let R = [r
0
r
1
r
2
:::r
N1
] and C = [c
0
c
1
c
2
:::c
N1
]. Then the
received bit b is given by:
b = 1 if (C h(R) w)
= 0 otherwise
4
where ‘’ represents the dot product defined as
UV = [u
0
u
1
:::u
N1
][v
0
v
1
:::v
N1
] =
N1
∑
i=0
u
i
v
i
and h() is the hard-limiting operation defined as
h(R) = [s
0
s
1
::::::s
N1
]
where s
i
= 0 if 0 r
i
< 1
s
i
= 1 if r
i
1
Chapter 4 discusses the architecture of the network in detail.
1.2 The problem: Interference
The throughput of an optical CDMA LAN at high offered load collapses because of interfer-
ence between multiplexed codewords.
Figure 1.2 is a snapshot of data bits on the receive fiber of an optical CDMA LAN. It
shows three codewords sent by three nodes (codewords C0, C1, and C2). The figure also
shows the signal on the line (any receive fiber) which is also called the state of the line (state
is defined formally in Chapter 3). A node on the network has a receiver tuned to codeword
C0 and is receiving transmissions sent using codeword C0. The time t = 0 on the time scale
shown in the figure marks the start of a bit of codeword C0. Figure 1.2(a) shows a case where
a 0 bit is being received and Figure 1.2(b) shows a case where a 1 bit is being received.
5
0 1 0 1 0 0 1 0
1 1 0 0 0 1 0 0
0 1 0 1 0 0 1 0
1 1 0 0 0 1 0 0
C2
C1
0 0 0 0 0 0 0 0
C0 (0 bit)
0 1 0 1 0 0 1 0
1 1 0 0 0 1 0 0
C2
C1
t=0 1 2 3 4 5 6 7 8 9 10
0 0 1 1 0 3 2 2
Line
(a)
(b)
0 0 0 0 0 1 1 1
C0 (1 bit)
0 1 0 1 0 0 1 0
1 1 0 0 0 1 0 0
t=0 1 2 3 4 5 6 7 8 9 10
0 0 1 1 0 2 1 1
Line
Figure 1.2: An example of multi-user interference showing three codewords C0, C1, and
C2. The two codewords (C1 and C2) interfere with another codeword (C0). (a) shows the
line (fiber) when C0 is OFF (transmitting a 0 bit) and (b) shows the line when C0 is ON
(transmitting a 1 bit). In (a), C0 experiences an interference error.
In Figure 1.2(a) the codewords C1 and C2 add up such that there is power in the 1st, 2nd,
and 3rd chips, among others. Because of codewords C1 and C2, the receiver tuned to C0
detects a 1 bit whether the transmitter sends a 1 bit or a 0 bit. As shown in Figure 1.2(a),
when a 0 bit is sent, the receiver detects a 1 bit. The packet would have an error and be
lost. The overlap of chips is termed multi-user interference or multi-access interference or
simply interference. The error is called an interference error. Note that interference does not
necessarily cause interference errors, i.e., there can be chip overlaps without any interference
errors. Chapter 3 formalizes the conditions for an interference error. At high offered load in-
terference leads to throughput collapse. Figure 1.3 shows the throughput of an optical CDMA
6
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Normalized network throughput
Normalized offered load
Aloha-CDMA
Figure 1.3: The normalized network throughput vs. normalized offered load for Aloha-
CDMA. The results are based on simulation. The traffic model is Poisson arrivals with ex-
ponentially distributed packet lengths. The codeset is (10;3;3). The destination of a packet
is chosen uniform randomly from all the nodes and codewords are allocated to nodes by
choosing them randomly from the codeset.
network without media access control (Aloha-CDMA) as the offered load is increased. At
high offered load (near or above 1), the throughput tends toward zero.
The problem of throughput collapse in optical CDMA LANs is conceptually similar to the
problem of throughput collapse in single channel, shared medium networks. Single channel,
shared medium networks without media access control (Aloha networks) suffer throughput
collapse at high offered load because of collisions between packets. Carrier Sensing Multi-
ple Access (CSMA) and its variants [68] have been proposed as solutions to this problem.
They have been shown both analytically and experimentally to prevent throughput collapse
by reducing packet collisions. However, the throughput of CSMA at high offered load de-
creases as the speed of the network increases for a network of fixed diameter and packet size.
For typical packet sizes (1500 bytes) and network diameters (1000m), CSMA is limited to
7
network speeds of less than 100 Mb/s. At high speeds (in the range of 10 Gb/s) CSMA is
ineffective.
The problem statement of this dissertation is: Can Carrier Sensing-like protocols prevent
throughput collapse in high speed optical CDMA LANs?
This dissertation answers this question by proposing Interference Avoidance, a contention
media access control protocol that extends Carrier Sensing to high speed networks.
1.3 The solution: Interference Avoidance
Interference Avoidance is a contention media access control protocol that prevents throughput
collapse at high offered load by estimating the state of the network and scheduling packet
transmissions to reduce interference errors.
Consider the codewords shown in Figure 1.4. The codewords C0, C1, C2 are the same
as in Figure 1.2. The figure also shows the signal on the line (fiber) which is also called the
state of the line. The state at a point on the line at a time is informally defined as the sum of
the codewords on the line at that point, e.g., the state of the line at t = 0 in Figure 1.2(a) is [
1 1 2 0 1 1 0 0 ]. Chapter 3 defines state formally and discusses its properties.
Codeword C0 has been transmitted one chip time later compared to Figure 1.2. Now a
receiver tuned to C0 detects correctly whether the transmitter sends a 0 bit or a 1 bit. This is
because when the transmitter transmits C0 with a delay of one chip time, C0 has at least one
chip that does not interfere with codewords C1 and C2. Therefore, a false positive error does
not occur and the receiver receives the 0 or 1 bit correctly.
8
(b)
0 1 0 1 0 0 1 0
1 1 0 0 0 1 0 0
C2
C1
t=0 1 2 3 4
5
6 7 8 9 10
1 0 0 1 1 1 3 2
Line
(a)
0 0 0 0 0 1 1 1
C0 (1 bit)
0 1 0 1 0 0 1 0
1 1 0 0 0 1 0 0
0 1 0 1 0 0 1 0
1 1 0 0 0 1 0 0
C2
C1
t=0 1 2 3 4 5 6 7 8 9 10
1 0 0 1 1 0 2 1
Line
0 0 0 0 0 0 0 0
C0 (0 bit)
0 1 0 1 0 0 1 0
1 1 0 0 0 1 0 0
Figure 1.4: The effect of Interference Avoidance. The codewords are the same as in Fig-
ure 1.2. C0 has been transmitted one chip time later compared to Figure 1.2. (a) shows the
line (fiber) when C0 is OFF and (b) shows the line when C0 is ON. In either case, C0 does
not have an interference error.
This principle can be translated into a media access control protocol. The resulting pro-
tocol is called Interference Avoidance. Each node on the network contends for access to
the medium using the Interference Avoidance protocol. This work shows that Interference
Avoidance can prevent throughput collapse at high offered load. It may be viewed as an ex-
tension of carrier sensing to high speed optical CDMA LANs. The thesis statement of this
dissertation is:
Throughput collapse in high speed optical CDMA LANs can be prevented by Interference
Avoidance, a Carrier Sensing-like protocol.
The following sections give an overview of the properties of an optical CDMA network
and how they make Interference Avoidance feasible.
9
1.3.1 State of an optical CDMA network
The state of an optical CDMA LAN is the sum of several overlapping codewords. The state
is used to show that optical CDMA LAN possesses two properties:
Non-mutually destructive interference: Interference can cause errors in a subset of the
codewords on the line. The subset depends on the codewords and their delays. This
property allows transmissions to be scheduled to reduce interference loss (transmission
scheduling).
Correlation of state: State at point (on a receive fiber) and time is correlated to the
state at some other point and time. This property allows state to be estimated (state
estimation).
There are two reasons for discussing these properties: First, these two properties make
transmission scheduling and state estimation feasible. Secondly, these properties differentiate
the problem of throughput collapse in optical CDMA LANs from the corresponding problem
in other physical layers. Chapter 3 describes the state, its properties and these reasons in
detail.
1.3.2 State estimation
State estimation is the process by which a node estimates the state of the line.
Chapter 6 formulates the state estimation problem. It demonstrates how correlation of
state is a necessary condition for accurate state estimation. It discusses the distribution of the
10
state and proposes a state estimation procedure consisting of collecting observations and esti-
mation. The performance of state estimation is analyzed under different topology conditions,
codeset parameters and traffic conditions. In particular, this work shows that as the codeset
length increases the performance of state estimation approaches optimal performance.
1.3.3 Transmission scheduling
Transmission scheduling is the process by which a node schedules a packet transmission
based on the estimated state and the codeword to be used for encoding. The objective is to
improve throughput at high offered load by reducing packet loss because of interference.
Chapter 5 formulates the transmission scheduling problem. It discusses strategies for
transmission scheduling. The strategies are used to define three scheduling algorithms: pure
selfish, threshold and overlap section. The algorithms differ in how transmissions are sched-
uled to avoid interference loss. The algorithms are analyzed and simulated under different
codeset parameters and traffic conditions under the assumption of perfect state estimation.
Chapter 5 shows that the proposed transmission scheduling algorithms prevent throughput
collapse when used with low codeset weights. They improve throughput to around 30% of
the maximum at high offered load. Under identical conditions, systems with no transmis-
sion scheduling have close to zero throughput. The algorithms perform within 10% of an
optimal codeword scheduling algorithm. This study demonstrates that when all the config-
urable parameters (codeset, transmission scheduling and state estimation) are chosen cor-
rectly, throughput collapse can be prevented at high offered load.
11
Finally, the performance of Interference Avoidance under laboratory conditions is mea-
sured. Chapter 7 describes a laboratory testbed that is used to measure the performance of
transmission scheduling. Measurements from the testbed show that transmission scheduling
improves the bit error rate (BER) by two orders of magnitude in the presence of physical
layer noise.
1.4 Optical CDMA and the future of optical access networks
This section discusses the role that optical CDMA may play in the evolution of access net-
works. The term access network refers to networks that connect residential users to a service
provider. Shared medium access networks such as the cable network are currently being con-
verted from hybrid fiber coaxial networks to all-fiber networks (Fiber To The Home (FTTH)
networks) to take advantage of their large capacity and provide a diverse range of services.
There are limitations on how much capacity of an optical fiber may be utilized. This
means that in the near future (5-10 years) optical access networks may evolve to use a mixture
of switching, multiplexing and media access control technologies. Applications will use the
most appropriate switching, multiplexing or media access control technology that satisfies
their performance requirements. Optical CDMA with Interference Avoidance is a packet
switched, CDMA, contention protocol with low latency, low packet error rates and moderate
throughput at high offered load. It is particularly suited to the needs of delay sensitive, loss
tolerant applications.
12
1.4.1 Utilization of the capacity of an optical fiber
Optical fiber is well suited for the transmission of data because of its large bandwidth (up to
15THz) and low attenuation (0.2dB/km). Studies have shown that the transmission capacity
of this bandwidth could be around 100 Tb/s [43]. Currently, only about 40 GHz (around 40
Gb/s) of this bandwidth can be used for communication. The maximum rate at which a single
stream of data can be transmitted today is around 40 Gb/s (OC-768) although experiments
have shown it can be increased to 160 Gb/s [37]. This is the maximum rate at which a
laser can be modulated, i.e., the electronic processing speed. So current hardware can utilize
only a fraction of the capacity of an optical fiber. Slow progress in the development of laser
technology means that this may be the status for the next 5-10 years. Therefore, in the near
term, optical networks will need to share the capacity through some form of multiplexing
and/or media access control.
Multiplexing in current optical access networks is by Wavelength Division Multiplexing
(WDM), Time Division Multiplexing (TDM) or reservation media access control protocols.
In WDM, the bandwidth of the fiber is divided and several nodes transmit in parallel by
intensity modulation of different wavelengths. In TDM systems such as SONET, time is di-
vided into slots, and different nodes transmit in different slots. In reservation protocols such
as DOCSIS [19], nodes request transmission slots from a centralized controller. WDM is
characterized by low access latency, high throughput and low packet error at the cost of ex-
pensive equipment such as tunable lasers. TDM is characterized by high access latency, high
throughput and low hardware costs. Reservation protocols are characterized by moderate
access latency, moderate throughput and low hardware costs.
13
1.4.2 Role of optical CDMA in optical access networks
Different applications that share the optical access shared medium have different performance
requirements. This means they may require different multiplexing/media access control tech-
nologies. Current Internet traffic is primarily composed of six applications: web, file sharing,
file transfer, email, streaming media (video and audio) and multi-user games. Each of these
has different performance requirements. Optical CDMA with Interference Avoidance is a
multiplexing and media access control technology with characteristics of low access latency
(compared to TDM/reservation protocols [50]), low packet error rate (Chapter 5 and 6), the
ability to coexist with other multiplexing technologies [12] and the potential for low cost
transmitters and receivers [60]. These characteristics are well suited for delay sensitive, loss
tolerant applications such as voice and video. They make Optical CDMA a suitable access
technology for specific applications on shared medium networks.
1.5 Organization
The following chapters justify the assertion of this dissertation, i.e., that a generalization of
carrier sensing can exploit the properties of optical CDMA to prevent throughput collapse.
Chapter 2 is a primer on Optical CDMA. It discusses the characteristics of optical CDMA
LANs, optical CDMA codeset design, transmitter and receiver design and network architec-
ture. Chapter 3 is the problem statement of this work. It discusses the problem of interference,
the concept of state and its properties and why they differ from problems studied before. It
defines Interference Avoidance and shows that optical CDMA possesses properties that make
14
Interference Avoidance feasible. Finally, it shows that Interference Avoidance is a general-
ization of Carrier Sensing. The next three chapters discuss the functionality of Interference
Avoidance. Chapter 4 provides an overview of the architecture of an optical CDMA Local
Area Network. Chapter 5 discusses transmission scheduling strategies and algorithms. It
analyzes the algorithms and compares their performance to optimal codeword scheduling al-
gorithms. The sensitivity of the algorithms to network and traffic parameters is discussed.
Chapter 6 defines state and state estimation algorithms. Performance of the system under dif-
ferent network and traffic parameters is discussed. Chapter 7 discusses the implementation
of a prototype and presents measurements taken from a laboratory testbed. Chapter 8 is a
survey of related work. Chapter 9 discusses conclusions and open areas of research.
15
Chapter 2
A primer on optical CDMA
This chapter is an introduction to optical CDMA. Optical CDMA is a direct sequence spread
spectrum technology [55] used for multiplexing optical transmissions on an optical fiber.
An optical CDMA network in this work refers to an all-optical, packet switched, shared
medium, Local Area Network (LAN) [58] [57] that uses optical CDMA as the physical layer.
The network consists of several nodes connected by optical fiber to a star coupler to form a
low noise, guided medium. The optical signal is modulated using intensity modulation and
encoding is unipolar encoding. The receiver is a hard-limiting correlation receiver.
Section 2.1 discusses the characteristics of the optical CDMA physical layer (intensity
modulation and unipolar encoding) and the physical medium (low noise, guided medium).
Section 2.2 discusses optical CDMA codesets, their design parameters and construction
methods. Section 2.3 discusses the design of optical CDMA transmitters and receivers. Other
architectural and design issues at the physical and link layer (topology, codeword allocation,
addressing, frame format and link layer error correction/detection) are discussed in Chapter 4.
16
2.1 Optical CDMA channel characteristics
This section describes the characteristics of the physical layer. The intensity modulation and
unipolar encoding differentiate optical CDMA from other multichannel physical layers such
as TDM, WDM or wireless orthogonal CDMA. The low noise, guided medium differentiates
optical CDMA from the other physical medium where CDMA has been applied before, i.e.,
the electromagnetic field on the wireless medium.
2.1.1 Intensity modulation and unipolar encoding
Optical CDMA is based on unipolar encoding (also called time domain encoding) [54] [57]
[58] [36]. Data is encoded using a codeword sequence. An optical CDMA codeword is a
sequence of 0s and 1s. The 0s and 1s are transmitted by binary intensity modulation, i.e.,
a pulse of light is a 1 and no pulse of light is a 0. Each 0 or 1 of a codeword is called a
chip, and the codeword represents a data bit. Bits are transmitted by ON-OFF keying of the
codeword, i.e., to transmit a 1 bit, the codeword is sent and to transmit a zero bit, a codeword
of all zero chips is sent. The term ON refers to the transmission of a 1 bit and OFF refers to
the transmission of a 0 bit. The term intensity modulation refers to the transmission of binary
signals using pulses of optical light. The term unipolar encoding refers to the use of ON-OFF
keying of codeword sequences to encode bits. Intensity modulation and unipolar encoding
are illustrated in Figure 2.1. The data is 10010110. The codeword is 0100011.
Unipolar encoding has been widely studied due to simplicity in construction of the trans-
mitters and receivers. Other encoding techniques such as spectral phase encoding [59] and
Code Cyclic Modulation (CCM) [35] have been proposed. In spectral phase encoding, an
17
0 1 0 0 1 0 1 1
Data
0 1 0 0 0 1 1
Codeword
Figure 2.1: The ON-OFF keying of codewords. The lower line shows the signal on the
optical fiber when a single codeword (0100011) is being transmitted. The upper line shows
the corresponding data.
optical pulse is decomposed in the spectral domain. Data is transmitted by encoding each
spectral component using a phase shift. In Code Cyclic Modulation, symbols are encoded
using rotations of code sequences. Both forms of encoding require complex transmitter and
receiver design. As a result, unipolar encoding has been more widely studied and is better
understood. For the remainder of this work, it is assumed that unipolar encoding is used.
Unipolar encoding in optical CDMA differs from conventional CDMA encoding in wire-
less networks. Wireless networks use different modulation and encoding formats. Coherent
modulation (phase, amplitude, or frequency) and bipolar encoding are most frequently used.
In bipolar encoding codewords use +1 and -1 signals, thereby allowing the construction of
orthogonal codewords. In contrast, optical CDMA codewords use 0 and +1, transmitted
18
asynchronously, and therefore cannot be designed to be orthogonal. They are called pseudo-
orthogonal.
2.1.2 Guided, low noise medium
The optical CDMA LAN consists of several nodes connected by optical fiber to a passive star
coupler. The optical fiber is single mode dispersion compensated optical fiber. The passive
star coupler multiplexes the optical signals from all the nodes. It consists of several inputs and
output ports. Each node is connected to one input and one output port by an optical fiber. The
nodes and the passive star coupler form a shared medium network. The fiber connected to
the input port is called the transmit fiber and the other is the receive fiber. Signals transmitted
on the inputs enter the coupler, merge, and are transmitted on all outputs. This work assumes
that the power transmitted by each node on the network is the same. The star coupler is
passive, i.e., input signals pass through without any electronic processing. The coupler is a
divide-by-N coupler [28]. When data enters the coupler on several transmit fibers, the optical
power from all transmit fibers is merged. The power is then split equally among the receive
fibers. The same signal emerges on all the receiver fibers of the coupler and is transmitted to
all nodes. Figure 1.1 shows a typical optical CDMA network topology. Three codewords are
shown entering the coupler and the merged signal emerges. The signal at an output port of
the coupler is given by the equation:
r(t) = (1=K)
K
∑
i=1
s
i
(t)
19
1 1 0 0 0 1 0 0
P1
Packet
overlap
P0
0 0 1 1 0 0 0 1
C1
Codeword
overlap
C0
Chip overlap
Figure 2.2: Packet, codeword and chip overlaps. This figure depicts chip synchronous trans-
mission. The effect of chip synchronous and asynchronous transmission is discussed in Chap-
ter 3.
where K is the number of input (or output) ports of the coupler and s
i
(t) is the signal
entering on the i
th
transmit fiber. The signal on the receive fiber can be amplified or atten-
uated after the coupler to obtain a required power level. Therefore, for ease of explanation,
diagrams and explanations in this work may indicate that the signal on a receive fiber is:
r(t) =
K
∑
i=1
s
i
(t)
The fiber and the coupler form a guided medium. A guided medium is a medium where all
nodes on the network see the same signal (perhaps after different propagation delays) [28].
A packet overlap occurs when two or more packets are at the same point in space on
the optic fiber (line) at the same time. Figure 2.2 shows a packet overlap on the line. When
20
a packet overlap occurs, the codewords of the packets overlap. When a codeword overlap
occurs, two or more ‘1 chips’ of different codewords may overlap. This is termed a chip
overlap. Codeword overlaps and chip overlaps are also shown in Figure 2.2. When a chip
overlap occurs, the power of the optical pulses are added in the coupler. The chip length l is
the length of a chip on the fiber. It is given by l = c=B where c is the speed of light in fiber
and B is the chipping rate in chips per second (c/s). The chip magnitude at a point on a fiber
at a time is the number of chips at that point at that time. Any point on the fiber where the
chip magnitude is greater than 1 is chip overlap.
The medium is a low noise medium, i.e., it exhibits the following properties:
Low noise: Physical layer noise such as thermal, ASE and shot noise can cause bit er-
rors. However, these effects are negligible compared to the effects of multi-user inter-
ference at high loads. Other work [57] has explored these effects in detail. Therefore,
this work neglects these effects.
Low attenuation: The optical fiber has relatively low attenuation (0.2 dB/km) [28]
compared to the other media such as copper or wireless. The effects of attenuation can
be eliminated by placement of amplifiers at suitable points in the network. Therefore,
this work assumes that there is no attenuation in the optical fiber.
Low dispersion of the fiber: Dispersion in single mode optical fiber is low (1 ps/nm
km). This work neglects dispersion because it can be reduced to a negligible effect by
using dispersion compensated fiber.
21
The low noise, guided medium characteristic distinguishes the optical CDMA medium
from the wireless medium where CDMA has been traditionally applied. The wireless medium
is an unguided noisy medium. Transmissions from a node follow different paths to different
receivers. As a result, different nodes on the network see different signals. This contrasts
with optical CDMA where every node sees the same signal. Further, the wireless medium is
noisy. The power of signals attenuate as the square of the distance and the signal experiences
random fluctuations because of slow and fast fading [55]. The next few chapters will show
how this low noise, guided medium property of optical CDMA may be exploited.
2.2 Optical CDMA codeset design
An Optical Orthogonal Codeset (OOC) [10] is a set of (0,1) sequences of length N that
satisfies certain autocorrelation and crosscorrelation constraints. The term codeset refers to
the set of sequences, and a codeword is a member of the set. The number w of ‘1 chips’ of
a codeword of the codeset is called its Hamming weight or just weight. Codesets with all
codewords having the same weight are called constant weight codesets.
The rate at which individual chips are transmitted is called the chipping rate. The rate at
which the data bits are transmitted is called the data rate. The chipping rate is N times the
data rate. The chip time t
c
is the time required to transmit a chip. It is given by t
c
= 1=B. The
bit time t
b
is the time required to transmit a bit. It is given by t
b
= Nt
c
= N=B.
OOCs are constructed such that the interference between pairs of codewords is con-
strained (interference is discussed in detail in Chapter 3). This is done by constructing the
codeset such that the codewords obey auto and crosscorrelation constraints. These constraints
22
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1
0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0
Figure 2.3: Three codewords of an optical CDMA codeset whose parameters are codeset
length N = 25, weight w = 3 and maximum crosscorrelation parameter κ = 1.
limit the number of overlapping chips between pairs of codewords. For any two codewords
in the codeset, the correlation constraints are:
N1
∑
n=0
s(i;n+ τ)s( j;n)
= w when i = j;τ = 0
κ otherwise
where s(i;n) is the n
th
chip of the i
th
codeword, 0 τ N 1 and addition is modulo N.
A codeset designed under these constraints is said to be pseudo-orthogonal. κ is called the
Maximum Collision Parameter. A particular codeset is specified by the parameters (N;w;κ).
Figure 2.3 shows 3 codewords of a (25, 3, 1) codeset.
23
The size of a codeset is the number of codewords in the codeset. The size S of a con-
stant weight codeset constructed under the pseudo-orthogonality constraints can be shown to
satisfy the Johnson bound [23]:
S(N;w;κ)

1
w

N 1
w 1

N 2
w 2

:::::

N κ
w κ

::::

Codeset design for optical CDMA has been studied extensively [10] [9] [11]. Algo-
rithms for codeset design methods include projective geometry, greedy and iterative con-
structions [10]. These methods differ in how closely they approach the Johnson bound. The
choice of the algorithm to generate a codeset depends on the codeset parameters. Different
algorithms may be closer to the bound for different codeset parameters. Codesets described
in this work have been designed using the greedy algorithm.
Codesets can be extended by using other orthogonal dimensions such as wavelength or
polarization [67] for encoding. A codeset that uses multiple dimensions is called a mul-
tidimensional codeset. A multidimensional codeset with multiple wavelengths is specified
by the parameters (N;Λ;w;κ). In this work, when three parameters are specified as part of
codeset description, it may be assumed to be a one dimensional codeset. When four or more
parameters are specified as part of the codeset description, it may be assumed to be a multi-
dimensional codeset. Construction methods for one dimensional codesets can be extended to
multidimensional codesets [52].
The use of unipolar encoding (0/1 signals) makes it impossible to construct asynchronous
optical CDMA codewords that are orthogonal (having a cross correlation parameter equal to
24
zero). As a result, optical CDMA codewords are pseudo-orthogonal. Note that the cross-
correlation constraint limits interference between pairs of codewords. Therefore, when more
than two codewords are multiplexed on a fiber there may still be interference between the
codewords. This problem is much more severe than wireless CDMA which can use bipolar
orthogonal codesets [38]. Chapter 3 discusses the problem of interference in detail.
2.3 Optical CDMA transmitter and receiver design
The transmitter and receiver design determines how packet transmissions, interference, packet
errors, and packet receptions happen. Optical CDMA systems are Intensity Modulation-
Direct Detection (IM-DD) systems [28]. This means that data is transmitted by using power
to represent a chip. Data is received by conversion of the optical power to electrical energy
using a photo detector.
2.3.1 Optical CDMA transmitters
Optical CDMA transmitters (also called encoders) are intensity modulation based transmit-
ters. The transmitter modulates the data using the optical CDMA codeword and transmits
the modulated data on the fiber. An optical CDMA transmitter design is described in [57]. It
consists of a laser source that is externally modulated at electronic speeds by the data. The
encoder is built from passive optical components (delay lines, splitters, and couplers).
25
Control
TDL
TDL
TDL
Splitter
Coupler
Threshold
detector
Photo-
detector
Hard-
limiter
Receive
fiber
1
1
1
1 1 1
3
2
3
1 1 1 1 0 1 1 1 1 1
Figure 2.4: An optical CDMA receiver. It is a hard-limiting correlation detector that consists
of a hard-limiter, decoder, a photodetector, and a threshold detector. The receiver is tuned to
the codeword 1110000. The power in the 1
st
;2
nd
and 3
rd
chip positions is summed by the
decoder. The photodetector converts the signal to current and the threshold detector detects a
1 bit.
2.3.2 Optical CDMA receivers
The optical CDMA receiver (also called a decoder or threshold detector) is a hard-limiting
correlation receiver [57]. The receiver decodes the codeword in the received signal and
regenerates the transmitted data. Figure 2.4 depicts the operation of a receiver. The input
signal from the coupler is a multilevel optical signal. The receiver converts it to a digital
optical signal by hard-limiting the power in each chip of the received signal. It then decodes
the signal to detect a 1 or 0 bit.
26
The receiver consists of an optical hard-limiter, a decoder, a photodetector, and a thresh-
old detector. The multilevel signal is first passed through the optical hard-limiter. The hard-
limiter limits the energy in each chip position. The decoder consists of a splitter and delay
lines. It collects energy in the chip positions where it expects to see 1 chips. The energy
is then sent to a photodetector that converts it to a multilevel electrical signal. The signal is
then sent through a threshold detector whose threshold is set proportional to the weight of the
codeset, i.e., in the figure this is an electrical power proportional to 3 chips. If the energy is
equal to or exceeds the threshold, a ‘1’ data bit is detected, else a ‘0’ bit is detected.
In Figure 2.4, the receiver is tuned to codeword C0 = 11100000. The power in the 2nd
chip is 3 units before the hard-limiter. After the hard-limiter, it is reduced to 1 unit. The
decoder collects the energy in the 1st, 2nd, and 3rd chip. The threshold detector detects a 1
bit.
Let R be the received signal (a vector of length N whose components are nonnegative
integers), and C be the codeword being received (a vector of length N whose components are
binary values). Let R = [r
0
r
1
r
2
:::r
N1
] and C = [c
0
c
1
c
2
:::c
N1
]. Then the received bit b is
given by the equation:
b = 1 if (C h(R) w)
= 0 otherwise
27
where represents the dot product defined as
UV = [u
0
u
1
:::u
N1
][v
0
v
1
:::v
N1
] =
N1
∑
i=0
u
i
v
i
and h() is the hard-limiting operation defined as
h(R) = [s
0
s
1
:::s
i
:::s
N1
]
where s
i
= 0 if 0 r
i
< 1
s
i
= 1 if r
i
1
The discussion so far has assumed that the receiver has acquired both chip and bit syn-
chronization. In practice, before a frame is received, there needs to be a frame synchroniza-
tion phase where the receiver detects where the frame begins. The frame synchronization
sequence and phase is discussed in more detail in Chapter 4.
Other optical CDMA receiver designs such as the multi-user detector [49] and the bal-
anced detector [14] have been proposed. The complexity (number of components) of the
multi-user detector increases exponentially as the length of the codeset. The hard-limiting
correlation based receiver is widely accepted as the receiver with the lowest implementation
complexity and this work assumes that it is the receiver design.
28
2.4 Optical CDMA errors
This section defines all possible optical CDMA errors and specifies which of those errors this
work deals with. An optical CDMA error is an error that occurs in a packet due to a property
of optical CDMA. The following are a list of optical CDMA errors:
Physical layer errors: Errors can occur due to characteristics of the optical fiber medium
(such as thermal noise, shot noise, Amplifier Spontaneous Emission (ASE), beat noise).
Other work [28] discusses these effects in detail. Moreover, at high offered load, these
effects are negligible compared to the effect of multi-user interference. Therefore,
these errors are not discussed in this work.
Interference errors: An interference error occurs when the sum of the codewords on
the line adds up to another codeword. An interference error causes a false positive
detection at a receiver. If this error occurs when the receiver is receiving a frame,
it causes an error in the frame and loss of the packet. This work deals exclusively
with interference errors. Interference errors have been handled through FEC [47] or
centralized control of codeword allocation [63]. This work does not assume the use
of any forward error correction. This work studies the use of media access control to
handle these errors.
Synchronization errors: Synchronization [29] is the process of detecting the start of
a frame. It is usually done by detection of a synchronization sequence in the pream-
ble of the frame. A synchronization error occurs when the sum of the codewords on
the line adds up to the initial bit of the synchronization sequence of some receiver on
29
the network. Because of this, the receiver inadvertently enters the frame synchroniza-
tion phase. Synchronization and synchronization errors in an optical CDMA network
have been studied and quantified in [29]. That work proposes a serial search synchro-
nization algorithm and quantifies the synchronization errors. This work assumes that
synchronization is instantaneous and that there are no synchronization errors to sim-
plify the analysis of the network under heavy load. To determine overall throughput
of the network, the effect of synchronization errors must be added to the interference
losses.
Receiver contention errors: A receiver contention error occurs when two packets are
simultaneously sent to the same node. If the receiving node has only one receiver
then it can receive only one of the packets. It synchronizes to the first packet that
reaches it and the other packet is lost. Receiver contention errors have been studied
and quantified in [74]. This work assumes that there is no receiver contention loss
to simplify analysis. This work assumes that if receiver contention occurs, then all
the packets destined to the receiver are received without error (provided they are not
subject to interference error). To determine the overall throughput of the network, the
effect of receiver contention errors must be added to the interference losses.
30
Chapter 3
Interference and Interference Avoidance
Interference between multiplexed optical CDMA codewords can cause errors in reception of
packets. This chapter defines the conditions for a bit error and packet error due to interfer-
ence. It shows that optical CDMA networks exhibit two properties: non-mutually destructive
interference and state correlation. The properties distinguish the optical CDMA medium
from other media. The properties can be exploited to design a media access control protocol,
Interference Avoidance.
Section 3.1 defines interference and the conditions for a bit error and a packet error.
Section 3.2 defines the state of the line. Section 3.3 uses the state definition to demonstrate
that optical CDMA LANs possess the properties of non-mutually destructive interference and
state correlation. Section 3.4 compares the properties to those in other media. Section 3.5
defines Interference Avoidance.
31
3.1 Interference
Interference, multi-user interference or multi-access interference in an optical CDMA net-
work is the overlapping of chips when codewords are multiplexed on an optical fiber. In-
terference can result in packet errors and a consequent degradation in network throughput at
high offered load. This section defines the conditions for a bit error and packet error due to
interference
1
.
3.1.1 Assumptions
This work assumes that the codewords on the receive fiber are chip synchronized, i.e., the
chip boundaries are aligned in time. In reality that may not be true. Salehi [57] studied
the effect of both chip synchronous and chip asynchronous transmission on a correlation
receiver (both non-hard-limiting and hard-limiting). Using an argument based on varying the
offset between two codewords continuously from zero to one chip time, it was shown that
the chip synchronous case is a reasonable approximation for the Bit Error Rate (BER) of the
system. This work uses that result. Analysis, simulations, and explanations assume that the
codewords are chip synchronized.
32
(a)
t=0 1 2 3 4 5 6 7 8 9 10
0 0 0 0 0 0 0 0 C0 (0 bit)
0 1 0 1 0 0 1 0
1 1 0 0 0 1 0
0 1 1 1 0 3 1 2
0
Line
0 0 1 0 1 0 1 0
0 1 0 1 0 0 1 0
1 1 0 0 0 1 0 0
0 0 1 0 1 0 1 0 C3
C2
C1
0 0 0 0 0 1 1 1 C0 (1 bit)
0 1 0 1 0 0 1 0
1 1 0 0 0 1 0
0 1 1 1 0 4 2 3
0
Line
t=0 1 2 3 4 5 6 7 8 9 10
0 0 1 0 1 0 1 0
0 1 0 1 0 0 1 0
1 1 0 0 0 1 0 0
0 0 1 0 1 0 1 0 C3
C2
C1
(b)
Figure 3.1: A bit error. The figure shows four codewords on the optical fiber. In (a) codeword
C0 is OFF. A false positive error occurs at the receiver due to interference from C1 and C2 or
C3.
3.1.2 Condition for a bit error
A bit error is an error in the reception of a codeword that is caused by interference. It occurs
because a receiver falsely detects its codeword due to interference caused by other codewords
on the line.
When several codewords are multiplexed on the line, a codeword on the line that has a
chip overlap with the codeword being received is called an interfering codeword of the code-
word being received. Figure 3.1 shows how a bit error occurs due to interfering codewords.
1
Interference is not a measurable quantity nor is it a metric that measures network performance. Interfer-
ence results in packet errors which results in a fall in network throughput. This work uses normalized network
throughput (defined in Chapter 5) as a measure of network performance.
33
The figure is a snapshot of data bits sent by four nodes (codewords C0, C1, C2, C3) multi-
plexed on an optical fiber. The codewords are from an (8, 3, 3) codeset. A receiver tuned to
codeword C0 expects to receive ‘1 chips’ in the 1st, 2nd and 3rd chip slot. The time scale
shown in the figure indicates the start of a bit of codeword C0. Figure 3.1(a) shows a case
where a 0 bit is being received on C0 and Figure 3.1(b) shows a case where a 1 bit is being
received. The codewords C1 and C2 add up such that there is power in the 1st, 2nd and 3rd
chips. The receiver tuned to C0 detects a 1 bit whether a 0 bit is sent or a 1 bit is sent. So if
a 0 bit were sent, it would be detected as a 1 bit. The packet would have an error and be lost.
The errors are false positive errors, i.e., a one bit is detected when a zero bit was transmitted.
This work assumes that an error refers to a false positive error. The necessary and sufficient
condition for a bit error is:
A bit is received with error if every ‘1 chip’ of its codeword has at least one chip overlap
with other codewords multiplexed on the line.
Conversely, a bit is received without error if at least one of the ‘1 chips’ of its codeword
does not have a chip overlap with any other codeword multiplexed on the line.
An Error Generating Codeset (EGC) of a codeword being received is a minimal subset
1
of the codewords on the line that have chip overlaps with all the ‘1 chips’ of the codeword
being received. Its members are called error generating codewords. The transmission delays
of the codewords are the delays (expressed in number of chips) of codewords from the start
of the codeword being received (the reference time). The transmission delays of the error
generating codewords are called error generating delays. Transmission delays are always
1
A minimal subset for a given set and property is the subset with the minimum number of members that
satisfies the property, i.e., if any one member of the subset is removed, the subset no longer satisfies the property.
34
Receiving codeword: C0
Interfering codewords: {C1, C2, C3}
An error generating codeset: {C1, C2}
and its error generating delays: {3, 4}
0 0 0 0 0 1 1 1 C0
0 1 0 1 0 0 1 0
1 1 0 0 0 1 0
0 1 1 1 0 4 2 3
0
C2
C1
Line
t=0 1 2 3 4 5 6 7 8 9 10
0 0 1 0 1 0 1 0
C3
0 1 0 1 0 0 1 0
1 1 0 0 0 1 0 0
0 0 1 0 1 0 1 0
Figure 3.2: Four codewords multiplexed on an optical fiber. The figure shows the receiv-
ing codeword, interfering codewords, the error generating codeset and the error generating
delays.
specified as positive quantities, i.e., time after the reference time in the interval (0, N]. Fig-
ure 3.2 shows the same codewords on the line. In this example, codeword C0 is the receiving
codeword. CodewordsfC1, C2, C3g are interfering codewords. CodewordsfC1, C2g form
an error generating codeset. CodewordfC3g in the figure is an interfering codeword, but is
not a member of this error generating codeset. However, it could be the member of another
error generating codeset. With respect to the codeword C0, the transmission delay of code-
word C1 is 3 and the transmission delay of codeword C2 is 4. The error generating delay set
for the error generating codesetf C1, C2g isf3, 4g. The condition for a bit error may be
restated as follows: A bit error occurs in a codeword being received if there exists an error
generating codeset with error generating delays.
35
0 0 0 0 0 0 0 0
0 1 0 1 0 0 1 0
1 1 0 0 0 1 0 0
C2
C1
C0
(a)
0 0 0 0 0 1 1 1
0 1 0 1 0 0 1 0
1 1 0 0 0 1 0 0
C2
C1
C0
(b)
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
1 1 0 0 0 1 0 0
C2
C1
C0
(c)
0 0 0 0 0 1 1 1
0 0 0 0 0 0 0 0
1 1 0 0 0 1 0 0
(d)
C2
C1
C0
Figure 3.3: The different cases that can occur when codewords overlap. (a) shows the case
when all members of the EGC are ON and the receiving codeword is OFF (causes a bit error).
(b) shows the case when all members of the EGC are ON and the receiving codeword is ON
(does not cause a bit error). (c) shows the case when one member of the EGC is OFF and the
receiving codeword is OFF (does not cause a bit error). (d) shows the case when one member
of the EGC is OFF and the receiving codeword is ON (does not cause a bit error).
The codeword being received may span two bits of an error generating codeword. For
example, in Figure 3.1(a) two bits of codeword C1 span the receiving codeword C0. From
the figure, it can be seen that only the first bit needs to be ON for it to contribute to the false
positive error. Similarly, only the first bit of codeword C2 needs to be ON. However, that may
not be the case in general. Four possible cases can occur when a receiving codeword has an
error generating codeset on the line:
The error generating codeset has all its codewords ON and the receiving codeword is
OFF. This causes a false positive error.
36
Direction of propagation
P2
P0
P3
P1
S4 S2 S1 S6 S0 S5
S3
Figure 3.4: Four overlapping packets on an optical fiber. Each packet may be divided into
sections at instants where a packet has arrived or departed.
The error generating codeset has all codewords ON and the receiving codeword is ON.
This does not cause an error.
The error generating codeset has at least one codeword OFF and the receiving code-
word is OFF. This does not cause an error
The error generating codeset has at least one codeword OFF and receiving codeword
is ON. This does not cause an error.
The cases are shown in Figure 3.3.
37
3.1.3 Condition for a packet error
A packet is received with an error if at least one of its codewords has been received with a bit
error. This work assumes that if a packet is received with at least one error then the packet is
lost. This loss is called an interference error packet loss.
Figure 3.4 shows packets on a receive fiber. The packet (P0) is being received by a node.
During the time when P0 is on the line, there are arrivals and departures of other packets. The
figure shows the overlapping of several other packets (P1, P2, P3). The packet being received
P0 can be divided into sections. A section is defined as a portion of the received packet when
a unique set of packets overlap with the packet being received. In Figure 3.4, packet P0 has
three sections: S0, S1, and S2. The new section may contain an error generating codeset
for the codeword being received. The occurrence of an error in a packet being received
depends on both the interfering codewords and delays in every section of the packet. This
work assumes that if a packet has a section that has interfering codewords that form an error
generating codeset, then the packet being received is lost. A section is generated when a
packet arrives on the line or when a packet departs form the line.
3.2 State of the line
The state of the line (also called state of the network) at a point in time and space on a shared
medium is a variable that can be used to predict the result (success or failure) of transmitting
a packet at that point at that time. The prediction assumes that the state does not change
during the transmission of the packet. The state at a point on a CSMA/CD based network
38
State span = N chips
3 1 2 1 2 2 S(t) =
Direction of
propagation
1 0
0 1 0 1 0 0 1 0
1 1 0 0 0 1 0 0
C2
C1
0 0 0 0 0 1 1 1
0 0 0 0
0 0 0 0 0
C3
0 0 1 0 1 0 1 0
C0
Line = 3 1 2 1 2 2 0 0
Figure 3.5: The state of the line at a point on a receiver fiber. The state of the line at time t at
distance d is [2 2 1 2 2 3 0 1]. The second bit of codeword C1 is OFF. To calculate the state,
C0 is assumed to be ON and the codewords are added.
such as 10 Mb/s Ethernet could be idle, busy or collision. The state can be used to predict the
result of transmitting a packet at that point. If the state is busy, then the result of transmitting
a packet is a failure. In the case of an optical CDMA LAN, the state is a variable that can be
used to predict the result of transmitting a codeword at that point at that time. The following
sections define state of an optical CDMA network. The conditions for a state transition are
also discussed.
39
3.2.1 State of the line
The state of the line at a time t, at a distance d from the coupler on the receive fiber is a
vector of length N whose elements are the chip magnitudes at distance d at times t;t +t
c
;t +
2t
c
;::::t +(N1)t
c
from the coupler assuming that all codewords at d are transmitting 1 bits.
S(d;t) = [s
0
s
1
s
2
::::s
N1
]
where s
n
= chip magnitude at distance d at time t + nt
c
(t
c
is the chip time) assuming all
codewords at d are transmitting 1 bits.
The transmission delays of the codewords with respect to the state are the delays (in chip
times) of codewords from the start of the state (the reference time). The state is the sum of
codewords each shifted by different transmission delays due to the different packet arrival
times. In Figure 3.5, the second bit of codeword C1 is OFF. To calculate the state, assume
that it is ON and add the codewords. The state in Figure 3.5 is S(d;t) = [2 2 1 2 1 3 0 1]. The
state at the same distance from the coupler on different receive fibers is the same because all
receive fibers carry the same signal. This is a consequence of the low noise, guided medium
characteristic of the physical medium.
40
3.2.2 State observations
The signal that reaches a node on the receive fiber is a multilevel optical signal. A node
receive this signal and can determine the chip magnitude at each chip time. Chapter 7 dis-
cusses the hardware design for a module that can perform this function. Using these chip
observations, it can construct an observation of the state.
A state observation at time t, and distance d from the coupler on the receive fiber is a
vector of length N whose elements are the chip magnitudes at distance d at times t;t +t
c
;t +
2t
c
;::::t +(N 1)t
c
from the coupler.
S
observation
(d;t) = [s
0
s
1
s
2
::::s
N1
]
where s
n
= chip magnitude at distance d at time t + nt
c
(t
c
is the chip time).
3.2.3 State transitions
The state consists of N chips. It follows that state at a point is measured over an interval of Nt
c
where t
c
is the time to transmit a chip. Therefore, state at a point is measured at intervals of
Nt
c
(or integral multiples of Nt
c
) to avoid overlapping two consecutive state measurements.
Similarly, state at a time is measured at points that are separated by distance of Nt
d
(or
integral multiples of Nt
d
). The times when state is measured at a point are called the state
measurement instants. The points where state is measured are called the state measurement
points.
41
A state transition is defined as the change of state at a point on the line from one state
measurement instant to the next. A state transition occurs due to a packet arrival or departure.
State transitions are significant because a state transition can trigger an interference error in a
packet on the line. The state measurement instants between which the state transition occurs
depend on the codeword that arrives/departs and its arrival/departure time with respect to the
state measurement instants.
State observations at a point change between state measurement instants due to ON-OFF
keying of codewords. However, the state does not change due to ON-OFF keying.
3.3 Properties of an optical CDMA network
An optical CDMA network has two properties that distinguish it from other physical lay-
ers: the non-mutually destructive nature of interference and the correlation of state. The
non-mutually destructive nature of interference makes transmission scheduling feasible. The
correlation of state makes state estimation feasible.
3.3.1 Non mutually destructive nature of interference
The non-mutually destructive nature of interference is the property by which interference can
cause errors in a subset of the codewords on the line. The subset can be controlled by varying
the transmission delays of the codewords.
The non-mutually destructive nature can be illustrated by considering a packet arrival at
the output of the coupler. A packet arrival triggers a state transition at the coupler. The state
transition may trigger an interference error in the arriving packet or in any packet that overlaps
42
Preserve self,
Preserve others
Preserve self
Destroy others
Destroy self
Preserve others
Destroy self
Destroy others
Figure 3.6: The four possible packet transmission events that are a consequence of the non-
mutually destructive nature of interference.
with the arriving packet. As a result, one of four possible events (transmission events) could
occur:
The arriving packet may not have an interference error, (i.e., it preserves itself), but
may cause interference errors in one or more other packets on the line (it destroys
others). This case is called Preserves self/Destroys others (PS/DO).
The arriving packet may preserve itself and also preserve all other packets on the line.
This case is called Preserves self/Preserves others (PS/PO).
The arriving packet may destroy itself but preserve all other packets on the line. This
case is called Destroys self/Preserves others (DS/PO).
43
0 1 0 1 0 0 1 0
1 1 0 0 0 1 0 0
0 0 0 0 0 1 1 1
0 0 1 0 1 0 1 0
Preserves self
Preserves
others
0 1 0 1 0 0 1 0
1 1 0 0 0 1 0 0
0 0 1 0 1 0 1 0 C3
C1
C0
C2
0 1 0 1 0 0 1 0
1 1 0 0 0 1 0 0
0 0 0 0 0 1 1 1
0 0 1 0 1 0 1 0
Preserves self
Destroys
others
0 1 0 1 0 0 1 0
1 1 0 0 0 1 0 0
0 0 1 0 1 0 1 0
C3
C1
C0
C2
0 1 0 1 0 0 1 0
1 1 0 0 0 1 0 0
0 0 0 0 0 1 1 1
0 0 1 0 1 0 1 0
Destroys self
Destroys
others
0 1 0 1 0 0 1 0
1 1 0 0 0 1 0 0
0 0 1 0 1 0 1 0
0 1 0 1 0 0 1 0
1 1 0 0 0 1 0 0
0 0 0 0 0 1 1 1
0 0 1 0 1 0 1 0
Destroys self
Preserves
others
0 1 0 1 0 0 1 0
1 1 0 0 0 1 0 0
0 0 1 0 1 0 1 0 C3
C1
C0
C2
C3
C1
C0
C2
Figure 3.7: Examples of the four packet transmission events. In each example, the different
transmission time of codeword C0 has caused a different transmission event. The circled
chips mark the ‘1 chips’ that do not have overlaps and the corresponding codewords are
preserved.
The arriving packet may destroy itself and destroy one or more other packets on the
line. This case is called Destroys self/Destroys others (DS/DO).
The condition for a bit error can be applied to every codeword on the line to determine which
event occurs. Figure 3.6 shows the four different transmission events. Figure 3.7 shows
examples of all four events. The codewords are the same as in Figure 3.2. C0 is the arriving
codeword and C1, C2, C3 are codewords on the line. The offset of codeword C0 is different
in each case. The codewords with circled ‘1 chips’ are the codewords that are preserved
(the circled ‘1 chips’ do not have overlaps and hence the codewords satisfy the condition for
correct reception). All other codewords are destroyed.
44
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 500 1000 1500 2000 2500 3000 3500 4000
Pearson’s correlation coefficient
Diameter of network in m
N=100
N=50
N=10
Figure 3.8: The correlation between the state at the estimation point at estimation time and the
merging point at merging time for an optical CDMA network as the diameter of the network
increases. The network has 100 nodes distributed uniformly over the length of the network.
The network uses Aloha-CDMA. Packet arrivals are Poisson with offered load 1 and packet
lengths are exponentially distributed with an average length of 1000 bytes.
The codewords that are destroyed by interference are a subset of the codewords on the
line. The events do not specify how many other packets are destroyed. When a packet arrives,
the state transition could result in the destruction of up to w other codewords. Each ‘1 chip’ of
the arriving codeword could contribute to an interference error in one of the other packets on
the line. If the arriving codeword preserves itself, it can destroy up to w1 other codewords.
3.3.2 Correlation of state
Correlation of state is a property by which state at a state measurement point and instant is
correlated to the state at other state measurement points and instants.
45
The correlation between two states is measured using the Pearson correlation coeffi-
cient [2]. The Pearson correlation coefficient between two vector samples X and Y is defined
below:
r =
∑
N
i=1
(x
i
X)(y
i
Y)
q
∑
N
i=1
(x
i
X)
2
∑
N
i=1
(y
i
Y)
2
where x
i
are the elements of a vector X, and X is the mean of the elements. It is a number
between -1 and 1 and indicates the extent of a linear relationship between two measured
quantities. A value of 0.8 and above generally indicates a strong degree of linear correlation.
A simple experiment shows that an optical CDMA network exhibits correlation. Con-
sider an Aloha-CDMA optical CDMA network, i.e., an optical CDMA network without any
media access control. Packet arrivals are Poisson and the offered load is 1. The packet size
is exponentially distributed with average size 1000 bytes. The chipping rate is 10 Gc/s. The
offered load is 1. The number of nodes on the network is 100 and the nodes are at uniformly
distributed distances from the coupler. The distance between the nodes and the coupler are
integral multiples of the length of the state on the line. Figure 3.8 shows the average correla-
tion between the state at a node and the state at the output of the coupler as the diameter of the
network is increased. The graphs are plotted for different codeset lengths. The graph shows
that as the diameter of the network increases, the correlation between the state at the node
and at the coupler decreases. As the codeset length increases the correlation increases. For
diameters of up to 4000m, a codeset length of N = 100, shows a reasonable amount of cor-
relation. This indicates that under certain conditions the state of the optical CDMA network
exhibits correlation.
46
Several factors affect the correlation including the diameter of the network, packet lengths,
chipping rate and the codeset length. Consider the states (S(d
1
;t) and S(d
2
;t)) measured at
two different points (d
1
;d
2
from the coupler) at the same time t. There are two reasons why
the correlation increases as N increases and w decreases.
The probability of a chip remaining the same increases: As N increases, the physical
length of the packet on the line increases. To illustrate this, consider the k
th
chips
c
k1
;c
k2
in the two states S
0
and S
1
. If the chip is a 1, then the probability that it remains
a 1 increases as N increases. This is because the length of packets are longer and
therefore it is likely that the same codeword is present in both S
1
and S
2
.
The probability of a chip changing decreases: A chip can change only if a packet
arrival or departure occurs between the two state measurement points. As N increases,
the probability that a change occurs in any particular chip of the state reduces,e.g., if
N = 10, and a change occurs in the state, the probability of a change in any particular
chip is 1=10. However if N = 100, this probability reduces to 1=100.
The consequence of both of these is that there is higher correlation between the states.
3.4 Comparison of state and its properties to other physical layers
This section compares the properties of an optical CDMA LAN with the properties of two
other physical layers that use contention media access control: the single channel, shared
medium, wired network (such as CSMA/CD based 10 Mb/s Ethernet) and the single channel,
shared medium, wireless network (such as CSMA/CA based 802.11 wireless networks). This
47
section focuses on the differences in three areas: the state definition, the destructive/non-
destructive nature of interference and the correlation/non-correlation of state. Tables 3.1
and 3.2 summarize these differences.
3.4.1 Wired networks
Early work on state in single channel shared medium wired networks considered state at a
point as a scalar that could take on one of three values: Idle, Busy, Collision. Idle is the state
when there is no packet transmission at that point. Busy is the state when there is exactly one
packet transmission at that point. Collision is the state when more than one packet is being
transmitted at that point.
3.4.1.1 Interference
Collisions on wired networks are mutually destructive, i.e., a collision destroys all packets
involved in the collision. In terms of transmission events, the only possible events are Pre-
serves self/Preserves others and Destroys self/Destroys others. This model has been used
to analyze shared medium, wired networks with Aloha [32] and carrier sensing [68] media
access control.
3.4.1.2 Correlation of state
The state in single channel, shared medium, wired networks exhibits the property of correla-
tion. [32] showed that the mechanisms of Carrier Sensing and Collision Detection depend
on this property (though the term correlation was not used in that work). It showed that the
48
performance of carrier sensing depended on the normalized propagation delay a, i.e., the ra-
tio of the propagation delay to the packet transmission time. As a increases, the correlation
of the state decreases and the efficiency of carrier sensing as a predictor of the state of the
network decreased. a depends on three parameters: the length of the packets, the diameters
of the network and the transmission rate.
a = t
p
=t
x
= (d=c)=(L=B) = dB=cL
where c is the speed of light, d is the diameter of the network, L is the packet length and B
is the transmission rate. For certain values of a (0:01 < a < 0:2) it was shown that carrier
sensing and collision detection can significantly improve throughput in single channel shared
medium networks. For a network of speed 100Mb=s, packet length 1000 bytes, diameter
4000m the value of a = 0:1. However for a high speed network, such as a 10Gb/s network, the
value of a = 10. In comparison, for an optical CDMA network the normalized propagation
delay reduces by a factor of N, because the codeword length increases the length of the packet
on the line. For a network of diameter 4000m, chipping rate 10 Gc/s, packet length 1000 bytes
and codeset length N = 100, the value of a = 0:25. This low value of a, is responsible for the
high correlation of state in an optical CDMA network.
3.4.2 Wireless networks
In a single channel, shared medium, wireless network the state depends on the channel con-
ditions. The wireless medium is much noisier than the wired medium due to fading (slow and
49
fast), multipath effects, and frequency selective fading [55]. These conditions vary greatly
depending on the location of a node within a network. Early work in wireless MAC proto-
cols [6] uses a scalar state that can take on three values: idle, busy or collision. Recent work
in the area of Channel State Estimation [56] uses a scalar value with a limited number of
levels to describe the channel state.
3.4.2.1 Interference
Initial work on contention protocols such as packet radio and 802.11 considered packet colli-
sions to be mutually destructive. The effect of carrier sensing in this model has been studied
using both theoretical [6] and experimental [22] techniques. The model has been extended
to consider the effect of capture [72]. Capture is the ability of a receiver to receive a packet
despite interference from another transmitter (even if it overlaps with other packets). It is not
just a property of the medium but also depends on the implementation of the radio, modula-
tion scheme, and decoding scheme. In a network that exhibits capture, destruction may be
controlled by varying the power levels of the transmitter [65]. A node can preserve itself by
raising its transmission power, while possibly destroying other transmissions. A multi-packet
reception model [69] has been proposed for modeling the reception of a subset of packets.
The model has been used for cross layer design of signal processing and MAC protocols to
improve throughput.
Although capture is similar to the non-mutually destructive optical CDMA interference,
the difference is that it is controlled by power rather than delay. Moreover, the subset of
packets being destroyed cannot be controlled.
50
Property Single channel Single channel Optical CDMA
wired medium wireless medium
State representation Scalar Scalar Vector
State values Idle, Busy Good/Bad Vector of
Collision length N
Components are
non-negative integers
State transitions Packet arrival, Attenuation, Packet arrival,
departure noise departure
ON-OFF keying
Table 3.1: Comparison of the state of the network in three shared medium networks: Single
channel wired networks, single channel wireless networks, and optical CDMA networks.
3.4.2.2 Correlation of state
The wireless medium exhibits low correlation of state. In a wireless medium, transmissions
follow different paths from transmitters to a receiver. Every node on the network sees a
different state because the propagation distances between different nodes are different and
transmissions follow a straight line propagation path. In addition, multipath and mobility of
nodes can make propagation delays dynamic. The limited range of transmitters can cause hid-
den and exposed terminals [6]. As a result, the wireless medium has low correlation of state.
These four conditions mean that the state of the network appears different at different points
on the network and correlation is low. Studies of carrier sensing in wireless networks [6]
confirm this.
51
Property Single channel Single channel Optical CDMA
wired medium wireless medium
Correlation of state Yes No Yes
Depends on: Depends on: Depends on:
Packet length Noise Packet length
Network diameter Attenuation Network diameter
Transmission rate Mobility Chipping rate
Codeset length
Nature of interference Mutually Non-mutually Non-mutually
destructive destructive destructive
(Capture) (PS/PO, PS/DO,
(DS/DO, DS/PO)
Table 3.2: Comparison of the properties of the state of the network in three shared medium
networks: Single channel wired networks, single channel wireless networks, and optical
CDMA networks.
C3
(a)
t=0 1 2 3 4 5 6 7 8 9 10
0 0 0 0 0 0 0 0 C0 (0 bit)
0 1 0 1 0 0 1 0
1 1 0 0 0 1 0
2 0 1 1 1 0 3 1
0
Line
0 0 1 0 1 0 1 0
0 1 0 1 0 0 1 0
1 1 0 0 0 1 0 0
0 0 1 0 1 0 1 0
C2
C1
C3
0 0 0 0 0 1 1 1 C0 (1 bit)
0 1 0 1 0 0 1 0
1 1 0 0 0 1 0
2 0 1 1 1 1 4 2
0
C2
C1
Line
t=0 1 2 3 4 5 6 7 8 9 10
0 0 1 0 1 0 1 0
0 1 0 1 0 0 1 0
1 1 0 0 0 1 0 0
0 0 1 0 1 0 1 0
(b)
Figure 3.9: Interference Avoidance prevents occurrence of a bit error. No error is caused
when the same codewords in Figure 3.1 are sent with a different set of transmission delays.
The figure shows the same codewords with codeword C0 delayed by 1 chip time.
52
3.5 Interference Avoidance
Interference Avoidance is a distributed, contention based Media Access Control (MAC) pro-
tocol for broadcast shared medium optical Code Division Multiple Access (CDMA) Local
Area Networks (LANs). It improves network throughput at high offered load by estimating
the state of the line and scheduling transmissions to reduce packet loss due to interference
errors.
From Sections 3.1 and 3.3:
A packet is received correctly if at least one ‘1 chip’ of its codeword does not overlap
with any other ‘1 chip’ on the line over the entire packet length (Condition for a packet
error).
Varying the transmission time of a packet can cause or prevent errors in any codeword
on the line (The non-mutually destructive nature of interference).
The state exhibits correlation, i.e., the state at points on the fiber at the estimation time
is correlated to the state at the output of the coupler (The state correlation).
Interference Avoidance exploits these properties. It consists of two procedures: State
estimation and Transmission scheduling. State estimation is the process by which a node
estimates the state of the line. Transmission scheduling is the process by which a node, given
an estimate of the line state and the codeword for encoding, calculates when to transmit the
codeword such that packet loss due to interference errors is reduced. Interference Avoidance
is a distributed, contention based protocol, i.e., nodes perform state estimation and transmis-
sion scheduling independent of each other. Each node on the network contends for access
53
to the medium using the Interference Avoidance protocol. There is no centralized scheduler
arbitrating access to the network.
3.5.1 Transmission scheduling
Transmission scheduling is defined as the process by which a node, given an estimate of
the state and the codeword to transmit, calculates when to transmit the codeword such that
packet loss due to interference errors is reduced. The objective of transmission scheduling is
to schedule the transmission time of codewords to reduce false positive errors. Figures 3.1
and 3.9 show this effect. In the second figure, codeword C0 has been delayed by one chip
time. The first case has an interference error and the second case does not. If Interference
Avoidance was used, before transmitting C0 the node would estimate the state and see that it
was [ 2 1 3 0 1 1 1 0 ]. By applying the condition for correct reception of its own codeword,
the transmission scheduling algorithm would calculate that by delaying the transmission by
1 chip time, an interference error in its own packet could be eliminated. As a result, the
node would transmit as indicated in Figure 3.9. By delaying the transmission the event has
be changed from a Destroys self/Destroys others to a Preserve self/Preserve others event.
There are several ways to schedule a transmission such that any one of the four transmission
events could occur. Chapter 5 formulates the transmission scheduling problem and discusses
transmission scheduling algorithms and their performance.
54
3.5.2 State estimation
State estimation is the process by which a node estimates the state of the line at the point/time
where packets merge. The objective of state estimation is to use state samples at the estima-
tion point and estimation time to calculate a value as close as possible to the state at the
output of the coupler. Chapter 6 formulates the state estimation problem and discusses state
estimation algorithms and their performance in detail.
The performance of state estimation algorithms is compared to Perfect state estimation.
Perfect state estimation is an ideal, unrealizable state estimation with the following proper-
ties:
The nodes can estimate the state at any point on the line and time without error.
All nodes see the same state at the same time.
State estimation is instantaneous.
There is no delay between state estimation and transmission scheduling.
Perfect state estimation is not possible in a real network. However, it simplifies the study
of transmission scheduling. The study of transmission scheduling in Chapter 5 assumes a
perfect state estimation process. When state is estimated using a state estimation algorithm
that collects state observations it is called Realistic state estimation.
55
Chapter 4
Network architecture
This chapter discusses the architecture of an optical CDMA Local Area Network. The ar-
chitectural designs discussed in this chapter neither are a limitation nor are enforced by In-
terference Avoidance. Interference Avoidance may also be used with alternate designs. This
section discusses these designs to provide the context within which Interference Avoidance
may be discussed.
The base features of the optical CDMA Local Area Network proposed in this work are:
Shared medium with multiple access: The network consists of several nodes connected
by optical fiber to a passive optical coupler. The fiber and the coupler form a shared
medium. The multiple access mechanism is optical CDMA using one or more wave-
lengths. Its typical use is in a shared medium, optical access network such as a Fiber
To The Home (FTTH) Passive Optical Network (PON).
Packet switching: The unit of data transmission is a packet. Nodes on the network do
not maintain connection state (for any protocol layer below the transport layer).
56
Contention media access control: The media access control is Interference Avoidance.
It is a distributed media access control protocol based on contention [5].
This chapter specifically looks at the following issues:
Network topology: The physical layout of the network.
Physical layer design: Codeword assignment.
Link layer design: Addressing, address to codeword mapping, frame format and frame
synchronization.
Node design: How the physical, link and MAC layer are integrated in a node.
4.1 Network topology
The topology of the network is a star topology. The optical CDMA LAN is constructed
using single mode fiber and a passive optic coupler. Single mode fiber is used for most
FTTH deployments today [31] because of low attenuation and dispersion. The passive optic
coupler [28] links all the nodes on the network. The passive star coupler is an integrated star
coupler based on free space optics. The coupler has low loss (< 3dB) and can have up to
128 ports. The network has amplifiers placed along the fiber at points where signal strength
degrades below receiver sensitivity. The placement of amplifiers is significant because of their
contribution to noise. Erbium Doped Fiber Amplifiers (EDFAs) [28] are the most suitable
amplifiers for this purpose. The effect of EDFAs on signal propagation in a long haul fiber
carrying optical CDMA has been studied [42]. The results indicate that for long networks
57
noise due to EDFA can affect the signal to interference ratio. They also show that the effects
can be reduced for by using dispersion compensation and EDFA gain equalization. Based on
this conclusion, this work assumes that signal distortions can be compensated for in an FTTH
network.
Chapter 6 shows that the performance of Interference Avoidance is dependent on the dis-
tance of nodes from the point where transmissions are multiplexed, i.e., the coupler. There-
fore the performance analysis presented here this applies only to a star topology
1
. This work
assumes that the maximum diameter of the network (the distance between the two furthest
nodes) is 4000m. This is a limitation of Interference Avoidance. It is discussed in Chapter 6.
The choice of a star topology and a passive optic coupler was influenced by the archi-
tecture of Fiber to the Home networks. Most FTTH networks are Passive Optical Networks,
which are based on a star topology. The head end of the network and the residential nodes
are connected by fiber to the coupler. Typical FTTH networks generally have much larger
diameters than 2000m. The head end is usually 10-15 km away from the end users. However,
most of the home users are within close proximity of each other (1000 users within 5 square
km). The end users contend for access to the upstream link to the head end. Optical CDMA
with Interference Avoidance can be used as the media access technology in such a topology.
End users can contend for the upstream link using Interference Avoidance. The downstream
link between the head end and the end users can use other access technology (it does not need
multiple access). Figure 4.1 shows a diagram of the future FTTH network.
1
Some topologies such as a bus topology can be reduced to a star topology. However there are several topolo-
gies for which such a mapping may not exist.
58
Head end
(Service provider)
Upstream link
(Interference Avoidance)
Downstream link
H
2
1
M
End users
(Homes)
1000m
10000m
Coupler
(Curb)
Figure 4.1: A typical Fiber to the Home (FTTH) network topology. It shows the upstream
link where Interference Avoidance may be used as a media access mechanism.
4.2 Node architecture
Interference Avoidance is a contention media access control (MAC) protocol. Each node on
the network contends for access to the medium using the Interference Avoidance protocol.
Figure 4.2 shows a block diagram of an Interference Avoidance Network Interface Card. It
consists of an optical CDMA transmitter, optical CDMA receiver, state estimation module,
and transmission scheduling module.
The state estimation module performs two functions: receiving and estimation. It receives
the multilevel optical signal on the receive fiber and collects observations of the state of the
line. It uses a series of state observations to calculate a state estimate. The state estimation
algorithm is always active. It is run continuously in a loop, collecting state observations
59
Bus
(from node
processor)
Optical CDMA
Receiver
Transmit
buffer
State
estimation
module
Transmission
scheduling
module
State
observation
module
Optical CDMA
Transmitter
Receive
buffer
Transmit
fiber
(to coupler)
Receive
fiber
(from
coupler)
Bus
(to node
processor)
Figure 4.2: Block diagram of an Interference Avoidance Network Interface Card.
and calculating a state estimate. The state estimation module consists of both optical and
electronic components.
The transmission scheduling module uses the state estimate and the codeword to be used
for encoding to calculate an appropriate delay to transmit the packet. Transmission schedul-
ing is invoked on arrival of a packet from the node processor. It reads the current state esti-
mate and the codeword for encoding and calculates the delay. The optical CDMA transmitter
encodes the data and begins transmission after the delay.
Chapter 5 defines the transmission scheduling algorithms. Chapter 6 defines different
state estimation algorithms. Chapter 7 describes the hardware implementation of the individ-
ual blocks of this NIC.
60
4.3 Physical layer design
This section deals with the issue of codeword assignment, i.e., how a node chooses a code-
word to transmit or receive on.
4.3.1 Codeword assignment
Codeword assignment is the scheme by which nodes decide which codewords to receive on
and which to transmit on. Every node on the network is equipped with at least one transmitter
and one receiver.
This work assumes a Tunable Transmitter-Fixed Receiver (TT-FR) architecture. This
means that a node receives on a fixed codeword. A node that wants to transmit tunes its
transmitter to the receiver’s codeword and transmits. Networks based on the (TT-FR) archi-
tecture as well as other architectures (TT-TR, FR-TT, FT-FR) have been studied before in the
context of single hop WDM networks [48]. Each architecture has its advantages and limi-
tations. The TT-FR architecture is chosen for the optical CDMA LAN because it requires
only one transmitter/receiver pair per node and it eliminates the need for pre-transmission
coordination. The TT-FR architecture works well when every node has a unique codeword
to receive on. However, if the number of nodes is greater than the number of codewords in a
codeset, then codewords are shared.
4.3.2 Codeset design
Chapter 2 shows that for a given set of optical CDMA codeset parameters (N;w;κ), the
number of codewords in the codeset is constrained to a value below the Johnson bound.
61
Any one of the parameters N, w or κ can be varied to increase the number of codewords in a
codeset. However Chapter 5 shows that varying N affects the data rate of the individual nodes
and varying w affects the aggregate network throughput. Therefore to increase the number of
codewords in the codeset, κ is the only parameter that can be varied. Chapter 5 shows that
varying κ does not affect the throughput.
If κ = 1, then the number of codewords in the codeset is low. If the number of nodes
on the network is greater than the number of codewords, then the network shares codewords
among nodes. This is called codeword sharing or codeword reuse. Multiple nodes tune their
receivers to the same codeword and receive their packets on the same codeword. They de-
multiplex their packets based on a unique higher layer address such as a link layer address.
The number of codewords generated can be increased by increasing κ and each node on the
network can be allocated a unique codeword to receive on. If κ = w, a large number of code-
words may be generated. However, some codewords may be rotations of other codewords.
The codesets in this work are generated using κ = w with a greedy algorithm [10]. Code-
words that are rotations of each other were removed from the codeset. To understand the
effect of κ on performance, some experiments use codesets with κ < w, generated by other
methods such as prime sequences, BCH [10]. In such cases, the number of codewords may
be less than the number of nodes on the network. Such experiments use codeword sharing.
For a given N, w and κ, the different codeset methods generate a different codeset size. The
performance at high offered load is not affected by the choice of codeset design method. This
will be demonstrated in the next chapter by varying all three codeset parameters: N, w and κ
and the codeset size.
62
The mechanism that a node uses to choose the codeword to receive on is out of the
scope of this work. Alternatives for the allocation mechanism include permanent allocation
at manufacture, a centralized server based allocation (such as DHCP) or selection from a
codeset based on the hash function of a higher layer address.
4.4 Link layer design
4.4.1 Addressing
Every node has a unique node address that is unrelated to the codewords in the codeset. The
node address is a higher layer (link or network) address. It is an identifier that uniquely
identifies the node on the LAN. A network layer address (IP address) or a link layer address
(Ethernet address) may be used.
4.4.2 Address to codeword mapping
It is assumed that there is a mapping function from the destination node address to the code-
word that the destination node is receiving on. The mapping function allows any node on
the network to determine the codeword that any other node is receiving on. When a node
wants to transmit to another node, it uses the mapping function to determine the codeword to
transmit on.
The mechanism for mapping is out of the scope of this work. Alternatives for the mapping
function include a centralized server (a DNS like mechanism), a broadcast codeword (an ARP
63
like mechanism), or a hash function that maps the higher layer address to a codeword. Traffic
due to the mapping function is not included in analysis of the system.
4.4.3 Frame synchronization
Frame synchronization is the process by which a receiving node determines the exact time
when data transmission of the packet has begun. The objective of synchronization is to allow
the receiver to determine where the first chip of the header of the frame starts.
Several frame synchronization algorithms for optical CDMA have been proposed [29] [30].
The serial search synchronization mechanism uses a synchronization sequence in the header
of the packet. The receiving node continuously listens for the synchronization sequence.
When a receiver detects that the frame synchronization sequence has started, the receiver
enters a synchronization phase where it receives the remainder of the frame synchronization
sequence (usually a series of 1 data bits) and attempts to acquire synchronization with the
start of the packet. This is called the synchronization phase. When it detects the sequence,
it knows that data will arrive after the sequence. After acquiring synchronization, it starts
detection of the bits of the packet.
This work assumes that the frame synchronization is instantaneous, i.e., the receiver
knows where the frame starts.
4.4.4 Frame format
The frame has the following fields:
Synchronization sequence: The frame synchronization sequence.
64
Checksum Payload
Length
of frame
Synchronization
sequence
Figure 4.3: The frame format for Interference Avoidance frames. The synchronization se-
quence is used for the frame synchronization operation, the length field is used to determine
the size of the payload, and the checksum field is used for error detection.
Length: The length of the link layer payload.
Link layer payload
Error detection: A checksum or other error detection mechanism.
Details of the synchronization sequence, synchronization algorithm, error detection and
correction mechanism, and link layer error control protocols are out of the scope of this work.
65
4.5 Upper layer protocol design issues
The main concern about optical CDMA is its high bit error rate, which causes a high packet
error rate. Interference Avoidance prevents throughput collapse at loads up to 100%. How-
ever, the packet error rates can still be fairly high. At such high error rates, transport protocols
such as TCP have been shown to provide very low throughput. Moreover, at offered loads
higher than 100%, Interference Avoidance shows a degradation in throughput. Therefore,
some mechanism is required to reduce packet error at high load and beyond. There are four
possible methods that can be used. The interaction of these mechanisms with Interference
Avoidance is an open area of research.
Forward Error Correction: Muckenheim [47] studied the performance of block FEC
codes with optical CDMA and suggested the use of suitable codes. They showed that
error codes can reduce error rates at high load.
Link layer Automatic Repeat Request (ARQ): A link layer ARQ may be used to initiate
retransmission of packets in which errors are detected.
Randomized delay before transmission: Nodes can delay the execution of the schedul-
ing algorithm by a random interval after the packet arrival. In single channel networks
persistence algorithms (non, p and 1 persistent) are used to generate a random delay
before transmission. This can improve throughput by reducing collisions [68].
Interference detection: If a node aborts transmission of a packet when it sees that it has
been destroyed due to interference, then packet throughput may improve. However,
66
this is at the cost of additional optical components needed to perform the error detection
during transmission.
67
Chapter 5
Transmission scheduling
Transmission scheduling is the process by which a node, given an estimate of the state of
the line and a codeword to transmit, calculates when to transmit the codeword such that
packet losses due to interference errors are reduced. This chapter formulates the transmis-
sion scheduling problem and discusses strategies for transmission scheduling. The chapter
assumes that all nodes can perform perfect state estimation and the network has a propaga-
tion delay of zero. It proposes three algorithms for transmission scheduling. The algorithms
stabilize throughput at around 30% of the maximum throughput at high offered load. Under
similar conditions, non-scheduled systems have almost zero throughput.
Section 5.1 formulates the transmission scheduling problem. Section 5.2 discusses strate-
gies for transmission scheduling. Section 5.3 defines and explains the algorithms. Section 5.4
presents a performance study of transmission scheduling. It analyzes performance using
mathematical modeling and simulation. Section 5.5 shows that the performance of the al-
gorithms is within 15% of the performance of an optimal codeword scheduling algorithm.
68
Section 5.6 presents a sensitivity study that shows how transmission scheduling algorithms
perform over a wide range of codeset parameters and traffic conditions.
5.1 The transmission scheduling problem
The transmission scheduling problem is:
Given a state estimate S
e
and a codeword to be used for encoding c
tx
, determine a trans-
mission delay t
d
in chips such that the aggregate network throughput Th
norm
is maximized.
The input to the transmission scheduling algorithm is the state estimate and the codeword
to be used for encoding
1
. If the packet can be scheduled, the algorithm returns a transmission
delay t
d
(0 t
d
< N) and the node transmits its codeword after t
d
chips
2
. If not the packet is
returned to a higher layer for a retransmission attempt.
The transmission scheduling problem is an online scheduling problem. Nodes on the net-
work schedule their packet transmissions taking local decisions with the objective of maxi-
mizing the global aggregate network throughput.
5.2 Transmission scheduling strategies
A transmission scheduling strategy is a subset of the transmission events that a node tries to
achieve when it schedules its transmissions. Chapter 3 defined the four possible transmis-
sion events that could occur when a packet is transmitted (PS/PO, PS/DO, DS/PO, DS/DO).
1
This chapter assumes Perfect state estimation, as defined in Chapter 3. Chapter 6 discusses the state estima-
tion problem.
2
The transmission delay t
d
is measured from the first chip of the estimated state. Chapter 6 discusses the
effect of timing differences between the state estimate and the state of the line.
69
Transmission scheduling controls which of the four events occurs when a packet is transmit-
ted.
A transmission scheduling algorithm is an implementation of a strategy, e.g., a node’s
strategy may be to transmit only if the resulting event is Preserves self/Preserves others.
There may be several possible algorithms that achieve this goal.
The objective of transmission scheduling is maximization of the network throughput. The
throughput is maximized when interference errors are minimized. Therefore, the transmis-
sion scheduling strategy should prevent transmissions where a node Destroys self or Destroys
others. In other words, a node must schedule such that it Preserves self/Preserves others.
Achieving this in a distributed algorithm is not straightforward. Given the state and a code-
word and its transmission delay, it is possible to apply the condition for correct reception to
determine whether it Preserves self. However, as the next three sections demonstrate, it is not
possible to determine whether the transmission will destroy any codewords already on the
line or how many codewords it will destroy. Therefore, it is not possible to apply the condi-
tion for correct reception and determine whether it Preserves others. The following sections
discuss selfish, cooperative, and pseudo-cooperative strategies in detail.
5.2.1 Selfish strategies
An algorithm follows a selfish strategy if the node schedules its packet transmission such
that the resulting event is either Preserves self/Preserves others or Preserves self/Destroys
others. A selfish strategy guarantees that the packet that the node transmits is preserved
if the state does not change after the packet is transmitted. It can be implemented using the
70
condition for correction reception to choose a delay that guarantees that the line state does not
cause an error in the codeword being transmitted. The delay should be chosen such that the
codeword being transmitted has at least one ‘1 chip’ that does not have a chip overlap. Note
that this strategy does not guarantee that packets will be received correctly. Errors in state
estimation or subsequent scheduling by other nodes may cause an error in the packet. The
selfish strategy defines a class of algorithms that are significant because there is no incentive
for a node to attempt non-selfish scheduling. If an algorithm is non-selfish, a node schedules
a transmission even if it knows its packet may be lost due to interference. Therefore, there is
no motivation for a non-selfish algorithm.
5.2.2 Cooperative strategies
An algorithm follows a cooperative strategy if the node schedules its transmission such that
the resulting event is either Preserves self/Preserves others or Destroys self/Preserves others.
A cooperative strategy guarantees that the packet that the node transmits does not destroy
other packets multiplexed on the line if the state does not change after the packet is transmit-
ted.
It is not easy to design a cooperative strategy. The previous chapter discussed the condi-
tion for a packet error. A decision on whether all the codewords are preserved can be made
only if all the codewords on the line are known. However, a node only knows the state of the
71
line and not the individual codewords multiplexed on the line. It is not possible to decompose
the line state into its constituent codewords in general for all codesets.
1
.
Another way of implementing a cooperative strategy is to schedule transmissions such
that the number of chip overlaps in the resulting state is below the weight of the codeset.
This guarantees that no codeword on the line can be destroyed (the condition for error is not
satisfied). However, this strategy limits the number of codewords multiplexed on the line to a
very low number. Section 5.6 shows that this strategy results in low network throughput. The
difficulty of implementing a cooperative strategy is the motivation for the pseudo-cooperative
strategy, discussed in the next section
2
.
5.2.3 Pseudo-cooperative strategies
An algorithm follows a pseudo-cooperative strategy if it schedules transmission such that
it increases the probability that the resulting event is either Preserves self/Preserves others
or Destroys self/Preserves others. It is a best effort strategy that reduces the probability of
destroying other codewords on the line. A node speculatively schedules its transmission
because of insufficient information about the codewords on the line.
Figure 5.1 shows the strategies along with the transmission events that they cause. Intu-
itively a good transmission scheduling algorithm should incorporate both selfish and pseudo-
cooperative strategies, so that both its own and other packets are preserved. This strategy is
1
It may be possible to decompose the line state into its constituent codewords under certain conditions. How-
ever, to accomplish this decomposition, the codewords in the codeset and all their rotations must be linearly
independent. It can be shown that this property is not satisfied by all codeset designs.
2
Codeword estimation is a scheduling algorithms where the codewords multiplexed on the line are esti-
mated [26] and transmissions are scheduled. Estimation gives a probabilistic estimate of the codewords and
therefore it cannot guarantee that other codewords are not destroyed. Therefore, it cannot be regarded as truly
cooperative.
72
Preserves self,
Preserves others
Preserves self
Destroys others
Destroys self
Preserves others
Selfish
strategies
Destroys self
Destroys others
Cooperative
strategies
Figure 5.1: The transmission scheduling strategies and the events that they attempt to achieve.
not guaranteed to maximize the network throughput. However, intuitively, this policy should
improve the network throughput when compared to systems that are not scheduled. Perfor-
mance analysis confirms this.
5.3 Transmission scheduling algorithms
The following sections define three transmission scheduling algorithms based on the selfish
and pseudo-cooperative transmission scheduling strategies. The algorithms are Pure self-
ish scheduling, Threshold scheduling and Overlap section scheduling. The algorithms are
compared to Aloha CDMA, which is optical CDMA without any media access control.
73
c
tx
Codeword to be transmitted
state State estimate
hstate hardlimit(state)
t
d
0
for delay = 0 to N
if (hstate & c
tx
6= c
tx
) then
mark delay as a feasible delay
rotate c
tx
to the right by one chip
t
d
any feasible delay
Table 5.1: The Pure selfish transmission scheduling algorithm.
5.3.1 Pure selfish scheduling
The Pure Selfish scheduling algorithm is based on the selfish strategy. The algorithm sched-
ules a packet transmission (chooses a transmission delay) only if the state of the line permits
transmission without loss of its own packet. It uses the condition for packet error as described
in Chapter 3. It schedules the codeword such that a least one ‘1 chip’ does not overlap with
any other ‘1 chip’ in the line state thus ‘selfishly’ attempting to preserve the codeword. No
effort is made to control the impact on (preservation or destruction of) other packets. Note
that the selfish algorithm does not guarantee that the packet transmitted selfishly is received
correctly because subsequent packet arrivals could destroy the codeword.
The algorithm is shown in Table 5.1. The hardlimit() function is a function which takes a
state vector and reduces any element of the vector which is greater than 1 to 1. The algorithm
searches for transmission delays that satisfy the condition. It chooses one of these delays at
random. The computational complexity of the algorithm is O(N).
74
5.3.2 Threshold scheduling
Threshold scheduling is an algorithm based on both the selfish and the pseudo-cooperative
strategies. The algorithm schedules a packet transmission (chooses a transmission delay) only
if the state of the line permits transmission without loss of its own packet and the number
of chip overlaps in the resulting state is below a threshold. The threshold is expressed as
a fraction of the codeword length N, called the threshold parameter α. It schedules the
codeword such that a least one of its ‘1 chip’ does not overlap with any other ‘1 chip’ in the
line state and the number of chip overlaps is below a threshold. This reduces the probability
of destroying other codewords. The algorithm does not guarantee that other packets are not
destroyed, but it reduces the probability of it happening. In addition, this algorithm does not
guarantee that the transmitted packet is received correctly because subsequent packet arrivals
could destroy the codeword.
The algorithm is shown in Table 5.2. The function overlaps() takes a state vector as input
and returns the number of elements that have chip overlaps. The algorithm selects delays as
described above. It chooses one of the delays at random. The computational complexity of
the algorithm is O(N).
Note that if the threshold is chosen such that αN < w, then the threshold algorithm is
both selfish and cooperative because no codewords can be destroyed. The sensitivity analysis
(Section 5.6) of the threshold parameter on throughput shows that such a low value of the
threshold results in low throughput.
75
c
tx
Codeword to be transmitted
state State estimate
hstate hardlimit(state)
t
d
0
for delay = 0 to N
if (hstate & c
tx
6= c
tx
) then
newstate = state+ c
tx
numoverlaps = overlaps(newstate)
if (numoverlaps < threshold)
mark delay as a feasible delay
rotate c
tx
to the right by one chip
t
d
any feasible delay
Table 5.2: The Threshold transmission scheduling algorithm.
5.3.3 Overlap section scheduling
The overlap section scheduling algorithm is based on the selfish and pseudo-cooperative
strategies. The algorithm schedules a packet transmission (chooses a transmission delay)
only if the state of the line permits transmission without loss of its own packet and the num-
ber of chip overlaps in the resulting state is below the number of ones in the state. It reduces
the probability of destroying other packets by constraining the number of overlapping chips
below the number of non-overlapping chips. The algorithm does not guarantee that other
packets are not destroyed, but it reduces the probability of it happening. In addition, this
algorithm does not guarantee that the transmitted packet is received correctly because subse-
quent packet arrivals could destroy the codeword.
The algorithm is shown in Table 5.3. The function ones() takes a state vector as input and
returns the number of elements that have 1 chips. The algorithm selects delays as described
76
c
tx
Codeword to be transmitted
state State estimate
hstate hardlimit(state)
t
d
0
for delay = 0 to N
if (hstate & c
tx
6= c
tx
) then
newstate = state+ c
tx
numoverlaps = overlaps(newstate)
numones = ones(newstate)
if (numoverlaps < numones)
mark delay as a feasible delay
rotate c
tx
to the right by one chip
t
d
any feasible delay
Table 5.3: The Overlap section transmission scheduling algorithm.
above. It chooses one of these delays at random. The computational complexity of the
algorithm is O(N).
5.4 Performance study
This section analyzes the transmission scheduling algorithms. First, the metrics used for eval-
uation are defined. Then, an analysis is described which shows that the algorithms prevent
throughput degradation. It also shows that the threshold and overlap section algorithms have
lower packet errors compared to the pure selfish algorithm. The analysis is validated through
simulation.
5.4.1 Assumptions
The transmission scheduling algorithm requires an estimate of the state as input. This chapter
assumes Perfect state estimation as defined in Chapter 3. The network is homogeneous, i.e.,
77
all nodes use the same transmission scheduling algorithm. In addition it is assumed that the
network has a propagation delay equal to zero. These assumptions are unrealistic but serve
as an aid to understanding and allow easy analysis. Chapter 6 removes these assumptions.
5.4.2 Performance metrics
The main performance metric used in this work is the normalized network throughput. It is
measured at different values of the normalized offered load.
5.4.2.1 Normalized offered load
The normalized offered load is the average arrival rate (in packets/s) expressed as a fraction
of the maximum possible arrival rate (in packets/s) of the network when it is used as a single
channel network
1
. The arrival rate is defined as the aggregate rate at which packets arrive
to all the nodes for transmission on the network. Let the arrival rate be λ packets/s. If the
average packet size is L bytes, the chipping rate is B c/s, then the maximum possible packet
arrival rate on a single channel network is B=8L packets/s. Therefore, the normalized offered
load ρ is,
ρ = 8Lλ=B
Consider an optical CDMA network where the average arrival rate of packets is λ pack-
ets/s. The service time of a packet is the average time needed to transmit the packet. Its
1
For an optical CDMA network of chipping rate B c/s, the maximum possible data rate of the network when
used as a single channel network is B c/s (the chipping rate becomes the bit rate). The maximum possible arrival
rate in packets/s is B divided by the average packet size in bits 8L.
78
inverse, the service rate is μ (in packets/s). For an optical CDMA network using a codeset
(N, w, κ), an average packet size of L bytes, and a chipping rate B c/s the service rate is
μ = B=(8LN) packets/s. Substituting for B in the expression above, the normalized offered
load may be expressed as:
ρ = 8Lλ=(8LNμ)) = λ=μN
5.4.2.2 Normalized network throughput
The normalized network throughput is the ratio of the number of packets that are transmitted
over the network without error to the total number of packets offered for transmission multi-
plied by the normalized offered load. It is a measure of the throughput of packets transmitted
without error at a particular offered load.
For example, a normalized offered load of 0.1 means that the packet arrival rate is 10%
of the maximum arrival rate of a corresponding single channel network. If the normalized
network throughput is 0:09, it means that transmission rate of packets without error is 9% of
the maximum arrival rate. So, at an offered load of 0.1, the fraction of packets transmitted
without error is 0:09=0:1 = 90%. The remaining packets (10%) are either not transmitted or
are transmitted with errors.
Consider an Aloha-CDMA system where packets are transmitted on arrival. Consider a
point on the line at the output of the coupler (d = 0). A packet that is passing by that point
takes 1=μ seconds to cross that point. Packets are arriving at that point at a rate of λ pack-
ets/sec. They arrive in parallel with no waiting time at that point. The number of codewords
79
(packets) multiplexed on the line is defined as the number of codewords transmitted in par-
allel at the output of the coupler (at d = 0). By Little’s law, the average number of packets
multiplexed on the line at that point at any time is λ=μ.
Consider any other system based on a transmission scheduling algorithm where the same
average number of packets is offered for transmission. The transmission scheduling algo-
rithm does not allow all of these packets to be transmitted. Let the average number of packets
admitted by the transmission scheduling algorithm and multiplexed on the line at the output
of the coupler at any time be N
online
, of which a fraction P
e
are lost due to error.
The fraction of packets transmitted without error is N
online
(1P
e
)=(λ=μ) The normalized
offered load is ρ = λ=(μN). Therefore, the normalized throughput of the network is
Th
norm
= (N
online
(1 P
e
)=(λ=μ))(λ=(μN))
= N
online
(1 P
e
)=N
5.4.3 Analysis
This section describes a mathematical analysis of the transmission scheduling algorithms.
The analysis models the system as a Markov chain. The state of the line at the output of
the coupler is used as the system state. Packet arrivals and departures cause state transitions.
The network throughput may be found by obtaining expressions for the average number of
codewords multiplexed on the line at a point in each state, the packet error rate in each state
and the equilibrium state probabilities. A broad outline of the analysis follows. Details may
be found in the appendices. The analysis follows the steps below:
80
First, a concise representation of line state that allows easy mathematical manipulation
is defined (Appendix A).
Using this state representation, expressions are derived for the number of codewords
on the line and the probability of packet error when the system is in any state (Ap-
pendix B).
Based on the transmission scheduling algorithm (Aloha-CDMA, Pure Selfish, Thresh-
old, Overlap section) the state transition probabilities are calculated and a state transi-
tion diagram is constructed. Under the assumptions of Poisson arrivals and exponen-
tially distributed packet sizes, the state transition diagram can be viewed as a Markov
chain. The Markov chain is solved for equilibrium state probabilities at a particular
offered load (Appendix C).
The analysis is used to determine the normalized throughput at any normalized offered
load. A graph of the normalized throughput vs. normalized offered load for different schedul-
ing algorithms is shown in Figure 5.2. The traffic model is Poisson arrivals and exponentially
distributed packet sizes. The destination of a packet is chosen uniform randomly from all the
nodes and codewords are allocated to nodes by choosing them randomly from the codeset.
The graph indicates that a system with no transmission scheduling (Aloha-CDMA) suffers
throughput degradation. Beyond an offered load of around 0.5, the network throughput de-
creases and tends to zero at high offered loads. In contrast, all the transmission scheduling
algorithms prevent throughput degradation. Throughput is stabilized at around 30% of the
maximum throughput and remains stable as offered load increases.
81
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Normalized network throughput
Normalized offered load
Threshold scheduling
Overlap section scheduling
Pure selfish scheduling
Aloha-CDMA
Figure 5.2: Normalized network throughput vs. normalized offered load for different trans-
mission scheduling algorithms based on analysis. The traffic model is Poisson arrivals with
exponentially distributed packet lengths. The codeset is (10;3;3). For the threshold schedul-
ing algorithm, the threshold parameter was set to 0.5. The destination of a packet is chosen
uniform randomly from all the nodes and codewords are allocated to nodes by choosing them
randomly from the codeset.
5.4.4 Simulation
A discrete event based packet simulator is used validate the mathematical analysis. The ob-
jective of the simulator is to validate the analysis and perform a deeper study of transmission
scheduling. The simulator models multiple nodes on a broadcast shared medium optical
CDMA LAN. It supports different state estimation algorithms, transmission scheduling al-
gorithms and a hard-limiting correlation receiver. Unless specified otherwise, the default
parameters for the simulations are specified in Table 5.6. The optical orthogonal codeset
construction method is the greedy construction method [10]. It is used to generate several
codesets for a given set of codeset parameters. The results in this work did not change sub-
stantially with the particular codeset or the algorithm used to generate the specific optical
82
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Normalized network throughput
Normalized offered load
Threshold scheduling
Overlap section scheduling
Pure selfish scheduling
Aloha-CDMA
Figure 5.3: This graph shows the normalized network throughput vs. normalized offered load
for different transmission scheduling algorithms. The results are based on simulation. The
traffic model is Poisson arrivals with exponentially distributed packet lengths. The codeset
is (10;3;3). For the threshold scheduling algorithm, the threshold parameter was set to 0.5.
The destination of a packet is chosen uniform randomly from all the nodes and codewords
are allocated to nodes by choosing them randomly from the codeset.
orthogonal codeset. The results from the simulations are the mean of around 10 runs of
anywhere from 10,000 to 100,000 packets each and standard deviations are shown on the
graphs.
Figure 5.3 shows the results of simulation for the same codeset as described in the analyt-
ical results. The results are quite similar to the analytical results. All transmission scheduling
algorithms prevent throughput degradation. In addition, the overlap section and threshold
scheduling show marginally higher throughput than pure selfish scheduling. The analytical
model over predicts the throughput for Aloha-CDMA. This is because the analysis is based
on a finite state model. A finite state model is suitable for transmission scheduling algorithms,
83
0
1
2
3
4
5
6
7
8
9
10
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Average number of codewords
multiplexed at a point on the line
Normalized offered load
Threshold scheduling
Overlap section scheduling
Pure selfish scheduling
Aloha-CDMA
Figure 5.4: The average number of codewords multiplexed at a point on a receiver fiber
vs. normalized offered load for different transmission scheduling algorithms. The results
are based on simulation. The traffic model is Poisson arrivals with exponentially distributed
packet lengths. The codeset is (10;3;3). For the threshold scheduling algorithm, the threshold
parameter was set to 0.5. The destination of a packet is chosen uniform randomly from all the
nodes and codewords are allocated to nodes by choosing them randomly from the codeset.
which limit the traffic on the line. However for Aloha-CDMA, the finite state model over pre-
dicts the equilibrium state probabilities. As a result, the analytical results differ slightly from
simulation.
5.4.5 Discussion
Though Figures 5.2 and 5.3 indicate that all three scheduling algorithms have approximately
the same throughput, the algorithms differ when the number of codewords multiplexed on the
line at a point and the packet error rate is considered. Figures 5.4 and 5.5 show the average
number of codewords multiplexed on the line at a point on a receive fiber and the average
packet error rate for the transmission scheduling algorithms.
84
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Packet error rate
Normalized offered load
Threshold scheduling
Overlap section scheduling
Pure selfish scheduling
Aloha-CDMA
Figure 5.5: Packet error rate vs. normalized offered load for different transmission schedul-
ing algorithms. The results are based on simulation. The traffic model is Poisson arrivals with
exponentially distributed packet lengths. The codeset is (10;3;3). For the threshold schedul-
ing algorithm, the threshold parameter was set to 0.5. The destination of a packet is chosen
uniform randomly from all the nodes and codewords are allocated to nodes by choosing them
randomly from the codeset.
There is a trade-off between the number of codewords multiplexed on the line at a point
and the packet error rate. The transmission scheduling algorithm tells a node if it can transmit.
It also tells the node when to transmit. By doing this, the transmission scheduling algorithm
controls two quantities:
The number of codewords multiplexed on the line at a point.
The transmission delays of the codewords multiplexed on the line, which affects the
packet error rate.
The trade-off can be understood by considering the performance of Aloha-CDMA. As the
offered load increases, the number of codewords on the line for Aloha-CDMA shows a linear
increase with offered load. Initially as the number of codewords on the line increases and the
85
network throughput increases. However, as the number of codewords on the line increases
further, interference errors increase and as a result the packet error rate increases. As a result
the network throughput falls. Therefore, as the offered load increases, the network throughput
attains a maximum and then decreases. To the left of the maximum, the throughput is low due
to the low number of codewords on the line. To the right of the maximum, the throughput
is low due to the higher packet error rate. The objective of the transmission scheduling
algorithm is to keep the system operating point close to the maximum irrespective of the
offered load. Therefore, if the transmission scheduling algorithm is aggressive and allows
more codewords on the line, the packet error rate increases, lowering throughput. On the
other hand, if the algorithm is conservative and does not allow enough codewords on the line,
the throughput is low. So the transmission scheduling algorithm must carefully balance the
number of codewords on the line and the transmission delays to maximize throughput.
The difference between the three scheduling algorithms is evident in Figure 5.5. There are
significant differences in the packet error rate. The threshold and overlap section scheduling
algorithms are conservative and constrain the number of overlapping chips. This results in a
low number of errors due to interference. However, the selfish algorithm is aggressive and
admits a larger number of codewords with a higher probability of packet error. When packets
are lost due to interference errors, the higher layers of the protocol stack must recover through
some form of Automatic Repeat Request (ARQ) or Forward Error Correction (FEC).
This leads to the first main conclusion of this study: All three transmission scheduling
algorithms prevent throughput degradation at high offered load. All have approximately the
86
same network throughput (which is greater than that of Aloha-CDMA). However, the thresh-
old scheduling and overlap section scheduling algorithms lose a lower number of packets
due to interference errors than the pure selfish algorithm.
5.5 Performance limits of transmission scheduling algorithms
This section evaluates whether there is a limit to the performance of transmission schedul-
ing. The previous section showed that transmission scheduling improves the performance of
an optical CDMA system when compared to an Aloha-CDMA system. As the offered load
increases, the throughput of transmission scheduling increases and then levels off. However,
the analysis gives no intuition as to why the throughput levels off and why it is less than the
maximum throughput. It also does not establish whether the throughput at which it levels
off can be increased or whether there is a limit to the network throughput of optical CDMA
when used with a media access control protocol. The existence of a limit would be useful as
a performance metric with which to compare the performance of the transmission scheduling
algorithms. To establish whether there is a limit, the performance of transmission schedul-
ing is compared to the performance of two optimal codeword scheduling algorithms. The
algorithms are called Centralized perfect scheduling and Distributed perfect scheduling and
are described in the next two sections. These algorithms are codeword scheduling algorithms
for optical CDMA that guarantee that the event is always Preserves self/Preserves others.
Each algorithm requires a capability that transmission scheduling does not have. The algo-
rithms are unrealistic and cannot be implemented in a real network. However, they are ideally
87
state State estimate
c
tx
0
if (numonline == 0)
c
tx
any codeword
else
c
tx
any codeword where (exactly 1 ‘1 chip’ does not have a chip overlap)
AND (all w 1 other chips have chip overlaps)
t
d
0
Table 5.4: The Centralized Perfect Scheduling algorithm.
suited to evaluate the throughput performance of the transmission scheduling algorithms and
to understand the causes for its low throughput.
5.5.1 Centralized perfect scheduling
Centralized Perfect Scheduling (CPS) is an online codeword scheduling algorithm. It takes
as input the state of the line and returns as output a codeword and a transmission delay. The
codeword and the delay are chosen such that zero interference errors occur and the network
throughput is maximized. CPS assumes
Perfect state estimation with a = 0.
Tunable transmitters, tunable receivers with instantaneous tuning and pre-transmission
coordination.
A network based on CPS operates as follows: When a node has a packet to transmit, it
estimates the state of the line (perfect state estimation). It uses the CPS algorithm to calcu-
late the codeword to use for encoding and its transmission delay. Note that the codeword
for encoding is chosen, unlike transmission scheduling where the codeword for encoding
88
c
tx
Codeword to be transmitted
state State estimate
fc
n
;t
n
g decompose(state)
for delay = 0 to N
event calceventtype(fc
n
;t
n
g;c
tx
;delay)
if (event == Preserves self/Preserves others)
mark delay as a feasible delay
rotate c
tx
to the right by one chip
t
d
any feasible delay
Table 5.5: The Distributed Perfect Scheduling algorithm.
depends on the node to which the packet is to be sent. The transmitter and the receiver to
tune instantaneously to the codeword (the pre-transmission coordination may be through a
common coordination channel or through a centralized server). The codeword and delay are
chosen such that the event is always Preserves self/Preserves others, i.e., no codeword has an
interference error. The codeword is chosen such that the number of codewords multiplexed
on the line at a point is maximized. The scheduling algorithm is defined in the Table 5.4.
Appendix E describes CPS in detail. It shows that centralized perfect scheduling is an up-
per bound on the throughput of any transmission scheduling algorithm that follows a selfish
strategy.
5.5.2 Distributed perfect scheduling
Distributed Perfect Scheduling (DPS) is an online codeword scheduling algorithm. It takes as
input an estimate of the state and the codeword to be used for encoding and returns as output
the transmission delay. The delay is chosen such that zero interference errors occur and the
network throughput is maximized. DPS assumes
89
Perfect state estimation with a = 0: As defined previously.
Perfect line state decomposition: There exists an algorithm that allows the line state to
be decomposed uniquely into the codewords on the line.
Tunable transmitter/Fixed receiver: The receiver it is allocated a fixed codeword and
the transmitter has to tune to it. The codeword allocation to the receiver is assumed to
be uniform random over the codeset.
A network based on DPS operates as follows: When a node has a packet to transmit, it
estimates the state of the line. It uses the DPS algorithm to calculate the delay to transmit. The
DPS node is capable of perfect state decomposition, i.e., it can decompose the state vector into
a set of codewords and delays. Perfect state decomposition is a capability that transmission
scheduling does not possess. The transmission delay is chosen such that the node Preserves
self/Preserves others, i.e., no interference error occurs. The scheduling algorithm is defined
in the Table 5.5.
The function calceventtype() takes as input the codeword for encoding, its transmission
delay, the set of codewords multiplexed on the line and their delays, and returns the resulting
event type (PS/PO, PS/DO, DS/PO or DS/DO).
5.5.3 Discussion
Figure 5.6 shows a graph of normalized network throughput vs. normalized offered load for
CPS, DPS and the threshold scheduling algorithm. The threshold algorithm used a threshold
of 0.5 and perfect state estimation. The codeset is (10;3;3). The traffic model is Poisson
90
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Normalized network throughput
Normalized offered load
Centralized perfect scheduling
Distributed perfect scheduling
IA: Threshold scheduling
Figure 5.6: The normalized throughput vs. normalized offered load for the Centralized and
Distributed Perfect Scheduling algorithms and threshold scheduling. The results are based
on both simulation and analysis. The parameters are detailed in the text. The codeset is
(10;3;3). The threshold algorithm used a threshold of 0.5.
arrivals and exponentially distributed packet lengths. The results shown are the average of 10
runs.
The results show that the thresholding algorithm performs reasonably well. The differ-
ence between the throughput of Distributed Perfect Scheduling and Interference Avoidance
is about 10% of the maximum throughput. CPS performs the best because the optimal code-
word and transmission delay are chosen. The reason that it does not reach 100% throughput is
because of the pseudo-orthogonal property of the optical CDMA codewords. There is a limit
to the number of codewords that can be multiplexed without any interference errors. DPS dif-
fers from CPS in that it chooses only the optimal delay and not the codeword. The difference
between CPS and DPS represents the penalty paid for choosing a distributed architecture with
pre-allocated codewords and non-tunable receivers. The threshold scheduling algorithm has
91
a lower throughput than DPS. The difference between DPS and threshold scheduling repre-
sents the penalty paid because perfect line state decomposition is not possible. However, the
difference between the two is not large. This leads to the following conclusion:
Transmission scheduling algorithms can perform reasonably close (within 10% of the
maximum throughput) to optimal distributed codeword scheduling algorithms.
This means that given limited information, threshold scheduling algorithms performs
quite well. An open area of research is to determine whether there exist other transmission
scheduling algorithms whose performance approaches the bound of DPS.
5.6 Sensitivity analysis
This section describes a deeper sensitivity analysis of the transmission scheduling algorithms.
The motivation is to understand the effect of varying parameters at the physical layer (codeset
parameters), the media access control layer (the scheduling algorithm parameters) and the
traffic model (packet arrival and size distributions). The objective of this study is to quantify
the impact of these factors on the transmission scheduling algorithms. The sensitivity analysis
consists of quantifying the:
Effect of varying the codeset length.
Effect of varying the codeset weight.
Effect of varying the cross correlation parameter.
Effect of varying the number of wavelengths.
92
Parameter Default value
Codeset parameters:
Codeset length N 100
Number of wavelengths Λ 1
Codeset weight w 3
Maximum cross-correlation parameter κ 3
Number of codewords in codeset 100
Chipping rate: 10 Gc=s
Codeword allocation: Uniform random
Interference Avoidance parameters:
Transmission scheduling algorithm: Threshold scheduling
Threshold: 0.5
State estimation algorithm: Perfect state estimation
Traffic parameters:
Inter-arrival time distribution Exponential
Normalized offered load 1
Packet size distribution Exponential
Average packet size 1000 bytes
Destination address distribution: Uniform random
Topology parameters:
Node to coupler distance distribution Deterministic
Average node to coupler distance 0 m
Number of nodes 100
Table 5.6: Parameter list and default values for the transmission scheduling sensitivity study.
Effect of varying the threshold transmission scheduling parameter.
Effect of different packet size distributions.
Performance under realistic network traffic.
5.6.1 Effect of varying the length of the codeset
Increasing the length of the codeset has two effects. As N increases, the number of codewords
multiplexed on the line increases because the scheduling algorithm can multiplex a larger
93
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 10 20 30 40 50 60 70 80 90 100
Normalized network throughput at
normalized offered load of 1
Codeset length N
Threshold scheduling
Overlap section scheduling
Pure selfish scheduling
Aloha-CDMA
Figure 5.7: The normalized network throughput at normalized offered load of 1 vs. the
codeset length N for different transmission scheduling algorithms. The results are based
on simulation. The traffic model is Poisson arrivals with exponentially distributed packet
lengths. The codeset weight is 3 and κ = 3. For the threshold scheduling algorithm, the
threshold parameter was set to 0.5. The destination of a packet is chosen uniform randomly
from all the nodes and codewords are allocated to nodes by choosing them randomly from
the codeset.
number of codewords simultaneously on the line. Therefore, more nodes can transmit in
parallel without error. However, as N increases the data rate reduces. The results show that
the two effects balance each other and the network throughput is constant when N is varied.
Figure 5.7 shows a graph of network throughput at an offered load of 1 vs. the codeset length.
Therefore, network throughput is independent of codeset length and transmission scheduling
scales with increase in codeset length.
5.6.2 Effect of varying the weight of the codeset
Increasing the codeset weight w has two effects: As w increases, the threshold on the correla-
tion receiver can be increased. Increasing the threshold makes the codewords more resistant
94
to interference, because it takes a larger number of chip overlaps to cause a false positive
error. However, with the increase in weight, each codeword causes more interference with
other codewords. An increase in w reduces the number of potential transmission delays that
the transmission scheduling algorithm can use to schedule codewords on the line without
causing interference errors. This reduces the number of codewords that can be multiplexed
on the line. The results show that as the weight increases the throughput decreases rapidly.
The reduction in the multiplexing of codewords on the line and the increased interference
offset any gains in the resistance to interference. It has been shown [58] that codesets with
higher weight have better bit error rate characteristics at low loads. At low loads, the in-
crease in resistance to interference dominates resulting in higher throughput for high weight
codesets. However as the load is increased, the effect of interference tends to dominate, re-
sulting in lower throughput for high weight codesets. Figure 5.8 shows a graph of the network
throughput at offered load of 1 vs. the weight. The length of the codeset was 100. The weight
is increased from 2 to 10. The graph indicates that lower codeset weights improve the per-
formance of transmission scheduling. The graph also shows that the effect of increasing the
weight is more detrimental to the selfish algorithm than the threshold and overlap scheduling
algorithms. This is because the threshold and overlap scheduling algorithms limit the number
of overlaps while the selfish does not. As the codeset weight increases, for the same number
of codewords multiplexed on the line, the probability that the selfish algorithm will result in
much more overlaps than the threshold scheduling algorithm is high. This results in lower
throughput for the selfish algorithm.
95
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 1 2 3 4 5 6 7 8 9 10
Normalized network throughput at
normalized offered load of 1
Codeset weight w
Threshold scheduling
Overlap section scheduling
Pure selfish scheduling
Aloha-CDMA
Figure 5.8: Normalized network throughput at normalized offered load of 1 for different
transmission scheduling algorithms. The results are based on simulation. The traffic model
is Poisson arrivals with exponentially distributed packet lengths. The codeset length is 100
and κ = 3. For the threshold scheduling algorithm, the threshold parameter was set to 0.5.
The destination of a packet is chosen uniform randomly from all the nodes and codewords
are allocated to nodes by choosing them randomly from the codeset.
5.6.3 Effect of varying the cross correlation parameter
The cross correlation parameter κ controls the interference between pairs of codewords. It
has traditionally been used as a parameter in codeset design.
Although κ controls the interference between pairs of codewords, packet loss is usually
caused by interference between several codewords. Therefore, a low cross correlation param-
eter does not necessarily result in low interference loss at high offered load. κ also controls
the number of codewords in the codeset. Johnson [23] showed a bound on the number of
codewords in a codeset for a given (N;w;κ) codeset. If κ is low (= 1), the interference be-
tween pairs of codewords is minimized, but the number of codewords in the codeset is low
1
.
1
In networks where the number of nodes is greater than the number of codewords, codewords are shared
among the nodes, with packets demultiplexed using a higher layer unique address
96
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 1 2 3 4 5 6 7 8
Normalized network throughput at
normalized offered load of 1
Maximum cross correlation parameter K
Threshold scheduling
Overlap section scheduling
Pure selfish scheduling
Aloha-CDMA
Figure 5.9: Normalized network throughput at normalized offered load of 1 for different
transmission scheduling algorithms. The results are based on simulation. The traffic model
is Poisson arrivals with exponentially distributed packet lengths. The codeset length N = 42
and weight w = 6. The cross correlation parameter κ is varied from 1 to 6. For the threshold
scheduling algorithm, the threshold parameter was set to 0.5. The destination of a packet
is chosen uniform randomly from all the nodes and codewords are allocated to nodes by
choosing them randomly from the codeset.
If κ is high (= w), the interference between pairs of codewords may be high, but the number
of codewords in the codeset is also high.
Figure 5.9 shows the performance of the transmission scheduling algorithms for a codeset
of length 42, weight 6 as κ is varied from 1 to 6. The throughput does not vary significantly
with κ. At high offered load, the number of codewords multiplexed on the line is so large
that interference loss is primarily due to interference among all codewords on the line. A
low value for κ does not help prevent interference loss at high offered load. Note that the
throughput in the figure is lower than the throughput shown in previous performance results.
This is because of the high weight codeset (N = 42;w = 6).
97
5.6.4 Effect of varying the number of wavelengths
The use of other orthogonal dimensions such as wavelengths for codeset design has been
proposed [67]. These are called multidimensional codesets. As the number of wavelengths
is increased, a larger fraction of the optical fiber capacity is used for transmission. As the
wavelengths increase, the scheduling algorithm should be able to schedule a larger number
of codewords simultaneously onto the line. So, the increase in wavelengths increases overall
system transmission capacity and increases the capacity utilized by each user. The results
show that both effects balance each other: though more users can transmit simultaneously,
each user uses more capacity to transmit. The extra capacity that is available through multi-
ple wavelengths is utilized in the same proportion as the utilization of the capacity of a single
wavelength. As a result, the overall network throughput, i.e., the fraction of packets trans-
mitted without error remains the same. Figure 5.10 shows a graph of network throughput at
an offered load of 1 vs. the number of wavelengths. The results show the throughput curves
different (10, 3, 3) codesets with variable number of wavelengths. The graph indicates that
the network throughput is independent of the number of wavelengths. As the capacity of the
fiber increases, the performance of transmission scheduling scales.
5.6.5 Effect of varying the threshold scheduling algorithm parameter
The threshold scheduling algorithm was described in Section 5.3. The performance of this
algorithm is sensitive to the threshold parameter α. The threshold scheduling algorithm con-
strains the number of overlaps in the state to be less than αN. At low values of the threshold,
98
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 1 2 3 4 5 6 7 8 9 10
Normalized network throughput at
normalized offered load of 1
Number of wavelengths
Threshold scheduling
Overlap section scheduling
Pure selfish scheduling
Aloha-CDMA
Figure 5.10: Normalized network throughput at normalized offered load of 1 vs. the num-
ber of wavelengths for different transmission scheduling algorithms. The results are based
on simulation. The traffic model is Poisson arrivals with exponentially distributed packet
lengths. The codeset length is 10, weight is 3 and κ = 3. For the threshold scheduling
algorithm, the threshold parameter was set to 0.5. The destination of a packet is chosen uni-
form randomly from all the nodes and codewords are allocated to nodes by choosing them
randomly from the codeset.
the algorithm constrains the number of codewords on the line and maintains a low probabil-
ity of packet error. As the threshold increases, the algorithm allows more codewords on the
line but with increased probability of error. When the threshold is equal to 1, the threshold
scheduling algorithm reduces to the pure selfish scheduling algorithm. Figure 5.11 shows a
graph of the network throughput at offered load of 1 vs. the threshold. The throughput is low
for low values of the threshold. As the threshold increases, there is an increase in through-
put. Beyond a certain value, the throughput degrades due to increased number of codewords
interfering on the line. Above the value of 0.6, the degradation stops and throughput levels
off. This is because beyond this value the threshold is longer the limiting factor that prevents
degradation: the selfishness of the algorithm prevents further degradation. At low thresholds,
99
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Normalized network throughput at
normalized offered load of 1
Threshold (expressed as a fraction of the codeword length N)
N = 10
N = 50
N = 100
Figure 5.11: Normalized network throughput at normalized offered load of 1 vs. threshold
parameter α for different transmission scheduling algorithms. The results are based on sim-
ulation. The traffic model is Poisson arrivals with exponentially distributed packet lengths.
The codeset is (100;3;3). The destination of a packet is chosen uniform randomly from all
the nodes and codewords are allocated to nodes by choosing them randomly from the codeset.
codesets with large lengths perform better because the transmission scheduling algorithm is
able to schedule more codewords on the line. The graph indicates that cooperative algorithms
for which the threshold parameter is below the weight have low throughput.
5.6.6 Effect of packet size distribution
Figure 5.12 shows the packet throughput as the average packet size is varied. The traffic
model is Poisson arrivals and exponentially distributed packet sizes. The figure shows that
the packet size has no effect on packet throughput. However, studies indicate that real net-
work traffic packet size distributions may not be exponential [53]. Recent packet statistics
obtained from a backbone network [66] exhibit a trimodal distribution. In one trace, about
70% of the packet sizes were 40 bytes, about 20% were 1500 bytes and the remaining were
100
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 100 200 300 400 500 600 700 800 900 1000
Normalized network throughput at
normalized offered load of 1
Mean packet size in bytes
Threshold scheduling
Overlap section scheduling
Pure selfish scheduling
Aloha-CDMA
Figure 5.12: Normalized network throughput vs. average packet size at a normalized offered
load of 1. The results are based on simulation. The traffic model is Poisson arrivals and
exponentially distributed packet sizes. The codeset is (100;3;3). The algorithm was threshold
scheduling; the threshold parameter was set to 0.5. The destination of a packet is chosen
uniform randomly from all the nodes and codewords are allocated to nodes by choosing them
randomly from the codeset.
around 500 bytes long. A traffic model with such a trimodal packet size distribution was used
to drive a simulation that used Poisson arrivals, uniform random allocation of codewords and
a (100, 3, 3) codeset. The results are shown in Figure 5.13. The graph shows interesting be-
havior. Aloha-CDMA does not degrade as much as in the case of Poisson traffic/exponential
packet sizes. The other transmission scheduling algorithms have almost 25% higher through-
put when compared to performance with exponentially distributed packet sizes. A majority
of the packets are small size packets (40 bytes). Most of them get through without error.
Therefore, the aggregate network packet throughput is higher. There are fewer longer pack-
ets transmitted on the line and a larger fraction is lost due to errors. This behavior occurs
when the fraction of shorter packets is fairly high (60-70%). This is similar to behavior on
101
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Normalized network throughput
Normalized offered load
Threshold scheduling
Overlap section scheduling
Pure selfish scheduling
Aloha-CDMA
Figure 5.13: Normalized network throughput vs. normalized offered load for different trans-
mission scheduling algorithms. The results are based on simulation. The traffic model is
Poisson arrivals with a trimodal packet size distribution (70% 40 bytes, 20% 1500 bytes
and 10% 500 bytes). The codeset is (100;3;3). For the threshold scheduling algorithm, the
threshold parameter was set to 0.5. The destination of a packet is chosen uniform randomly
from all the nodes and codewords are allocated to nodes by choosing them randomly from
the codeset.
wireless links where short packets tend to experience lower error rates than long packets [4].
The improvement in throughput is caused by a squeeze through effect where shorter packets
experience lower packet error rates than longer packets.
The squeeze through effect can be demonstrated analytically and through simulation for
a network with a bimodal distribution of packet sizes which uses a pure selfish transmission
scheduling algorithm and a codeset with κ = w. Consider a network where the traffic has two
packet types of sizes l
1
and l
2
where l
1
< l
2
. Let the fraction of packets of size l
1
be γ. Then
the average packet size on the network is l
avg
= (γ)l
1
+(1 γ)l
2
. The throughput of such a
network can be calculated by finding the probability of packet error P
error
and the number of
codewords multiplexed at a point on the line N
l
.
102
The average number of codewords on the line at any point on the receive fiber N
l
depends
on the transmission scheduling algorithm. If there are N
l
codewords on the line, then N
l
w ‘1
chips’ were added to the state. Of these, N
l
+(w1) ‘1 chips’ were aligned with ‘0 chips’ of
the state (because of selfish scheduling) and (N
l
1)(w 1) ‘1 chips’ were added randomly
to any position (κ = w).
The probability that the state vector has no ‘0 chips’ is
P
f ull
= 1(1
1
(N(N
l
+(w 1)))
)
(N
l
1)(w1)
At an offered load of 1, packets arrive for transmission at a rate much higher than the rate
at which packets are transmitted (the transmission scheduling does not allow all packets to
be transmitted). When a packet departs from the line, a few chips of the state may change
from 1 to 0. The next packet arrival results in a transmission of a packet such that the ‘0
chips’ are filled. Therefore, under equilibrium conditions, for the pure selfish scheduling
algorithm, P
f ull
is close to 1. Through simulation P
f ull
is determined to be around 0.85 for
the pure selfish algorithm under Poisson arrivals and exponentially distributed packet sizes.
This analysis assumes that this is true for bimodal packet distributions too. Therefore, the
number of codewords on the line can be calculated by finding N
l
such that P
f ull
is close to 1.
Interference errors in a packet on the line are caused by packets that arrive during the
packet’s transmission. The transmission scheduling algorithm allows only a fraction of the
arriving packets (called colliding packets) to be transmitted. The probability of packet error
in a codeword on the line is the probability that at least one of its colliding packets causes
103
an interference error. If the number of colliding packets is n
c
, then n
c
‘1 chips’ are added
to the state selfishly (align with ‘0 chips’) and n
c
(w 1) ‘1 chips’ are added to the state in
random positions. These random positions are chosen from N 1 possible choices (1 chip is
chosen selfishly). The probability that one of the added ‘1 chips’ overlaps with the one of the
‘1 chips’ of the codeword on the line is p = w=(N 1). The probability of packet error is the
probability that more than w 1 overlaps occur. Therefore,
P
error
= 1
w1
∑
k=0
0
B
B
@
n
c
(w 1)
k
1
C
C
A
p
k
(1 p)
n
c
(w1)k
At a normalized offered load of 1, the average packet inter-arrival time is t
arrival
= l
avg
=B
where B is the chipping rate of the network. The transmission time for packets of type 1 is
t
1
= l
1
=(B=N) where N is the codeset length. The average number of colliding packets for
packet type 1 is,
n
c1
= (t
1
=t
arrival
)(N
l
=N)
A similar expression can be derived for n
c2
. This can be used to calculate the probability of
packet error for each type of packet P
error1
and P
error2
.
The normalized network throughput is given by:
Th = (N
l
=N)(γ(1 P
error1
)+(1 γ)(1 P
error2
))
104
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Normalized network throughput
at an offered load of 1
Fraction of short packets
Simulation
Analysis
Figure 5.14: The squeeze through effect. The throughput is maximized when the fraction of
short packets is 0.9. The graph shows both analytical and simulation results. The transmission
scheduling algorithm is pure selfish. The packet sizes are 50 bytes and 1000 bytes. The
codeset is (100,3,3).
A graph of normalized network throughput vs. the fraction of short packets is shown in
Figure 5.14. The packet sizes were set to 50 bytes and 1000 bytes. The results (both analysis
and simulation) show that the normalized network throughput peaks at a particular value
of the fraction of small packets confirming the squeeze through effect. The long packets
experience high packet error rates and the short packets experience low error rates. The
throughput attains a maximum when the fraction of short packets reaches a particular value
(around 0.9).
The higher throughput of shorter packets may not be a desirable characteristic, because it
is unfair to longer packets. Future work will address the issue of providing a uniform packet
error rate to all traffic. Possible alternatives include using constant packet sizes or using
different codeset lengths for different size packets.
105
5.6.7 Performance with real network traffic
This section discusses the performance of transmission scheduling with realistic network
traffic. The assumption of Poisson arrival and exponential distributed packets lengths is con-
venient for analysis. However, the inter-arrival and packet size distribution of real network
traffic could be different depending on when and where it is observed.
Simulations were performed with traffic traces obtained from a real network link to un-
derstand the impact of real packet arrival times. Traffic traces from a single OC48 [51] link
were used. Several of these traces were merged to generate traffic of different offered loads.
The packet sizes, source addresses, and destination addresses were preserved during merg-
ing. The packet size distribution was trimodal (35% of the packets were 40 bytes, 30% were
500 bytes and 35% were 1500 bytes). The traffic file had approximately 6000 unique source
addresses and 40000 unique destination addresses. In contrast to all the previously described
results, in this case the destination addresses were mapped to codewords. Codeword reuse
was used where codewords were insufficient.
The results of the simulation are shown in Figure 5.15. The results indicate that the per-
formance is similar to that of the Poisson arrivals/exponentially distributed model, indicating
that it was a reasonable choice for analysis. Note that the performance improvements of the
previous section due to the squeeze through effect are not visible here. The proportion of
short packets (40 bytes) in the traffic was insufficient to cause the squeeze through effect.
106
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Normalized network throughput
Normalized offered load
Threshold scheduling
Overlap section scheduling
Pure selfish scheduling
Aloha-CDMA
Figure 5.15: Normalized network throughput vs. normalized offered load for different trans-
mission scheduling algorithms. The results are based on simulation. The traffic model was
based on real network traffic traces (see description). The codeset is (100;3;3) and codewords
are allocated to addresses. For the threshold scheduling algorithm, the threshold parameter
was set to 0.5
5.7 Conclusions and future work
This work has presented an analysis of transmission scheduling algorithms. The transmission
scheduling algorithms trade-off the number of codewords on the line with the packet error
rate to keep the network throughput high. It was shown that several transmission schedul-
ing algorithms perform comparably well (with 15% of max) compared to optimal codeword
scheduling algorithms. Simulations also showed that transmission scheduling performs well
when used with a realistic traffic model based on traffic obtained from a real network.
Open problems in this area include the design of transmission scheduling algorithms that
approach the bound of optimal codeword scheduling algorithms such as CPS.
107
Chapter 6
State estimation
State estimation is the process by which a node calculates an estimate of the state at a point
on the line at some time using state observations obtained at some (possibly different) point
on the line at some (possibly different) time. The estimated state is used as input to a trans-
mission scheduling algorithm. Chapter 5 analyzed the throughput of transmission scheduling
under perfect state estimation with a propagation delay of zero. This chapter studies the
performance of Interference Avoidance with realistic state estimation, i.e., using a state esti-
mation algorithm in a network with normalized propagation delay greater than zero. It shows
that as the diameter of the network increases, errors occur in state estimation. Errors in state
estimation result in inaccurate transmission scheduling and a degradation of throughput. The
degradation can be mitigated by using the threshold scheduling algorithm with a low thresh-
old and a long codeset length.
108
A
B
Estimation point:
Estimation
occurs here
State = S(d
e
, t
e
)
Transmission point:
Transmission
occurs here
Merging point:
Merging occurs
here
State = S(d
m
, t
m
)
Figure 6.1: The points on the optical fiber where state is estimated and transmissions merge.
The state is estimated by a node at its estimation point at the estimation time. The node
transmits a packet at the transmission time and it merges with other packets at the merging
point (coupler) at the merging time.
Section 6.1 formulates the state estimation problem and discusses its relationship to trans-
mission scheduling. Section 6.2 discusses the state estimation algorithms. Section 6.3 dis-
cusses the causes for packet loss in a network with realistic state estimation and a> 0. Sec-
tion 6.4 studies the performance of realistic state estimation. Section 6.5 presents results for
the sensitivity analysis of state estimation algorithms.
6.1 The state estimation problem
The state estimation problem can be stated as follows: Given a series of observations of
the state S
0
;S
1
;S
2
;::::S
K1
at times t;t + t
b
;t + 2t
b
;::::t +(K 1)t
b
, (where t
b
is a bit time)
109
calculate an estimate of the state such that the throughput of the transmission scheduling
algorithm is maximized.
Figure 6.1 illustrates the process of state estimation. Node B is the node estimating the
state. It collects K observations of the state from the signal at the estimation point. Chapter 7
describes hardware design using optical devices and electronic hardware that is capable of
performing the observation function. The state estimation algorithm takes the K observations
of the state as input. It calculates an estimate of the state called the estimated state. It uses
this value as the input to the transmission scheduling
1
.
When the node transmits its packet, it merges with other transmitted packets at the cou-
pler. The state of the line at the coupler at the merging time may differ from the estimated
state. The reason for the difference is because of state transitions. A state transition could
occur during the collection of observations or between the estimation and the merging. A
state transmission could result in an inaccurate state estimate.
Note that the metric to measure state estimation is the aggregate network throughput
when it is used with a particular transmission scheduling algorithm. Other metrics such as
correlation or distance metrics (L
1
;L
2
;L
p
norms) could have been chosen to measure the
accuracy of state estimation. However, it is difficult to relate these metrics to potential im-
provements in the throughput of the network. Therefore, because state estimation is always
used with transmission scheduling, the throughput of transmission scheduling is the most
suitable metric.
1
This work assumes that the estimation point and transmission point are separated by an integral number of
state spans. If this is not true, a ranging procedure as described in Chapter 7 can determine the difference in chip
times and rotate the estimated state by the appropriate offset.
110
1 0 0 3 1 1 1 1
0 1 0 1 0 0 1 0
1 1 0 0 0 1 0
0 0 0 0 0 0 0 0
0
0 0 1 0 0 1 1 0
0 1 0 1 0 0 1 0
0 0 0 0 0 0 0
0 0 0 0 0 1 1 1
0
0 0 1 0 0 1 1 0
0 1 0 1 0 0 1 0
1 1 0 0 0 1 0
0 0 0 0 0 0 0 0
0
0 0 0 0 0 0 0 0
0 0 0 2 1 1 0 0 1 1 0 2 0 2 2 2
C3
C2
C1
C0
Line
t=0
State samples: [11113011], [22202011],[00112000]
True state: [2 2 2 1 3 0 1 1]
Chip samples (chip at t =0) : 1, 2, 0
Mean (chip at t=0): (1+2)/3 = 1
Estimated value of sample (chip at t=0) : 2*1 = 2
Estimated state: [2 2 3 1 5 0 1 1]
Figure 6.2: Observations of the state at a point. The state estimation algorithm calculates a
state estimate from the state observations.
6.2 State estimation algorithms
The state estimation problem can be reduced to a standard problem in estimation theory. Es-
timation theory deals with algorithms to estimate the parameters of a distribution given ob-
servations drawn from the distribution. Parameter estimation algorithms have been classified
into sample means estimators, linear model estimators, random walk models and smoothed
average estimators. The first step in identifying a suitable parameter estimation algorithm is
to identify the distribution from which the observation is drawn. This section discusses the
distribution of the state and suitable estimation algorithms.
111
6.2.1 Distribution of the state
This section shows that the probability distribution of the chip magnitude of the components
of the state observation is a binomial distribution. Therefore, the sample means estimator is
the optimal estimator for the state.
Consider K state observations collected at a point on the receive fiber between two state
transitions, i.e., between consecutive packet arrivals or departure. The state at the point at
every state measurement instant is the same, say S. The state observations may be different
from each other because of ON-OFF keying.
Consider the K observations of the first chip of each state observation. These chip obser-
vations form a time series of K samples. Consider the first chip of the corresponding state S.
Assume that first chip of the state S has chip magnitude m. The chip observation is the sum
of the m chips, each of which is turned ON or OFF with probability p = 0:5
1
. Therefore, the
chip observations may be considered to be the number of successes in a series of m Bernoulli
trials. Therefore, the distribution of the chip magnitude of the chip observations is a Binomial
distribution. The mean number of successes of a binomial distribution of m trials where p
is probability of success is μ = mp. The distribution is stationary between state transitions.
The mean of a stationary binomial distribution can be estimated by using a sample means
estimator. The sample means estimator is the estimator for the mean that minimizes the es-
timation error for the binomial distribution. It is a minimum variance, unbiased maximum
likelihood estimator. It can be shown to converge to the mean as the number of observations
1
This argument assumes that the packet data has 0 and 1 bits with equal probability (p= 0:5). If the probability
is different (say, due to the use of a higher layer encoding such as 4B/5B), then the value of p must be changed
accordingly. The higher layer encoding may be chosen to ensure a particular value of p.
112
0
50
100
150
200
250
300
350
400
450
500
0 10 20 30 40 50 60 70 80 90 100
Change interval (bits)
Codeset length
Figure 6.3: The mean number of bits between a state change for different codeset lengths
at an offered load of 1. The network is an Aloha-CDMA network with Poisson arrivals and
exponentially distributed packet lengths. The average packet length is 1000 bytes.
increases. If the estimated mean is μ
e
, then μ
e
= mp, where p = 0:5, i.e., m = 2μ
e
. The
procedure can be applied to the observations of each element and the estimated state vector
can be calculated.
Figure 6.2 shows three state observations [11113001], [22202011] and [00112000]. The
chip observations from the first chip of each of the state observations are 1, 2, 0. In Figure 6.2,
the state is [22213011]. The value of the element in the first chip is 2. So in Figure 6.2, (1,
2, 0) are observations of the number of successes in a Bernoulli trials with m = 2. The mean
value of the observations is (1+2+0)=3 = 1. Therefore, the estimated value is 2μ
e
= 21 =
2. The same can be repeated for every element of the state vector. The estimated state vector
in Figure 6.2 is [22315011].
The sample means estimator is the optimal estimator if the distribution is stationary, i.e.,
the state does not transition during the collection of observations. A state transition (an arrival
113
or a departure of a packet) may change the mean of the distribution of the chip observations
of the state observations. The sample means estimator needs enough observations before
the estimates approaches the mean value. If the time needed to collect observations is com-
parable to the interval between state transitions then the estimation error increases because
the distribution is no longer stationary
1
. Therefore, to justify the sample means estimator,
it must be shown that the interval between state changes is larger than the time needed to
collect sufficient observations.
The sample means estimator may be justified by a simple experiment that determines the
interval between state changes. Consider an optical CDMA LAN using Aloha CDMA with
Poisson arrivals and exponentially distributed packet lengths. The average packet length is
1000 bytes. The normalized offered load is 1. Figure 6.3 shows the average interval (in bits)
between changes of the state of the line at a point. The interval between state changes is
shown for different codeset lengths. Note that the graph shows the interval between state
changes in terms of bit transmission times, and not in absolute time. This is intentional: the
time to collect a single observation of the state depends on the codeset length (bit length).
In one bit time, 1 observation of the state can be collected. Therefore, the time between
state changes in bit times gives a measure of how slow the state is changing in comparison
to the observation collection time. Even for codeset lengths of 100, state changes happen at
most every 50 bits. For transmission scheduling algorithms, which allow around 1/3 as many
1
A nonstationary distribution where the mean changes at a rate comparable to the rate at which observations
are collected or which has a high variance is best estimated using a smoothed average rather than a sample
means. For example, the Round Trip Time (RTT) estimator for the Transmission Control Protocol (TCP) uses an
exponentially smoothed estimator because the rate at the which the RTT varies is comparable to the rate at which
observations are collected.
114
packets on the line (for a codeset of weight 3) at 100% offered load, the interval between state
changes is 2-3 times larger. The following sections shows that a sample means estimator
needs around 10-20 observations to obtain a reasonable estimate of the state. Therefore,
there are very few state changes during collection of the set of observations. Under these
conditions, the sample means is a reasonable estimator
2
.
6.2.2 Implementation
The state estimation hardware consists of an observation module and an estimation module.
The observation module collects observations and the estimation module uses the observa-
tions to estimate the state. Chapter 7 describes the implementation. This section describes
the observation and estimation parameters.
6.2.2.1 Observation parameters
The three parameters that control observations are
Observation start time t
s
: The time when the observation starts.
Observation count n
s
: The number of state observations collected.
Buffer size b
s
: The number of state observations that can be stored. The buffer is
assumed to be a FIFO queue.
For example, if t
s
= 0 and n
s
= ∞, collecting observations begins when the node is
switched on and the node samples the state continuously. If t
s
= t
a
and n
s
= b
s
, sampling
2
Note that these conditions may change depending on the traffic model. A different traffic model may change
the interval between state transitions and may require a different estimator. Section 6.5 studies the performance
of state estimation under realistic traffic and finds that the performance does not degrade noticeably.
115
begins when a packet arrives and ends when b
s
samples have been collected. State samples
are stored in a circular buffer of size b
s
state samples. When the buffer is full, the oldest
values are overwritten. It follows that the following relationship must hold: b
s
n
s
.
6.2.2.2 Estimation parameters
The three parameters that control sampling are
Estimation start time t
e
: The time when the estimation algorithm is run.
Estimation count n
e
: The number of state samples used by the estimation algorithm.
Inter-estimation time δ
e
: The time between successive runs of the state estimation
algorithm.
Estimation can be started at any time when there are at least n
e
state samples available.
The estimation algorithm takes as input the instantaneous samples in the buffer ( at least n
s
samples). Its follows that the following relationship must hold: b
s
n
s
n
e
. The estimation
algorithm is shown in Table 6.1. The computation complexity of the estimation algorithm is
O(n
e
). Therefore, the latency of the estimation algorithm is controlled by n
e
.
6.2.3 State estimation algorithms
The sampling and estimation parameters control when the state estimate becomes available
for use by the transmission scheduling algorithm. Transmission scheduling begins any time
after a packet arrives and the state estimate is available
116
estimate()
f
p 0.5
eststate 0
totalstate 0
for count = 0 to n
e
totalstate+ =buffer[count]
eststate totalstate=(pn
e
)
g
Table 6.1: The Sample means state estimation algorithm.
S
0
S
1
S
4
S
3
S
2
S
5
S
6
S
8
S
7
S
9
t
s
t
e2
= t
e
+ n
e
t
b
t
e
= t
s
+ n
e
t
b
į e
= n
e
t
b
n
e
= 5
Figure 6.4: The state estimation parameters. The figure shows 10 state observations. The
collection of state observations begins at t
s
. Estimation is run after n
e
= 5 observations are
collected at time t
e
.
The parameters control a trade off between the access latency and the state estimation
accuracy. The access latency can be minimized if, on packet arrival, transmission scheduling
is started immediately using the last calculated state estimate. This may result in an inaccurate
state estimate because of possible state transitions in the time between the last state estimation
and transmission scheduling.
117
The estimation accuracy can be maximized by using the state estimate as soon as it is
available. A way to do this is to defer transmission scheduling until a new state estimate is
available. However, this results in an increase in access latency.
To evaluate this trade off this work considers two algorithms:
Continuous estimation: t
s
= 0; n
s
= ∞; t
e
> n
e
t
b
; t
e
< t
arr
; δ
e
= t
b
; n
e
= 10 to 100:
The collection of observations begins when the node starts up and are collected every
bit time. Estimation begins anytime before the first packet arrives. It is repeated after
n
e
new observations are collected (it is assumed that the state estimation hardware can
be designed to complete the state estimation function before the next n
e
observations
are collected). When a packet arrives for transmission, transmission scheduling uses
the last estimated state. Continuous estimation minimizes access latency but uses a
potentially less accurate state estimate.
On demand estimation: t
s
= t
arr
; n
s
= n
e
; t
e
= t
a
+ n
e
t
b
; δ
e
= δ
a
; n
e
= 10 to 100: Ob-
servations are collected on packet arrival and n
e
observations are collected. Estimation
begins after observations are collected. When a packet arrives for transmission, ob-
servations are collected, state is estimated, and transmission scheduling uses the latest
estimated state. On demand estimation uses the most accurate state estimate but has
the maximum access latency.
Other values of the sampling and estimation parameters are possible. Section 6.4 shows
that the parameters of the state estimation algorithm do not significantly affect the perfor-
mance as long as n
e
is sufficiently large and t
e
is within a few bit times of the start of the
118
transmission scheduling. This is because the correlation of the system is high (high correla-
tion of state over distances of around 1000m), and the state remains constant for periods on
the order of 100s of bit transmission times. Therefore, a using a state estimate that is 10s of
bit transmission times old does not result in noticeable degradation.
6.3 Causes for packet loss
This section discusses the causes for packet errors when realistic state estimation is used.
Under the assumption of perfect state estimation and normalized propagation delay a = 0
the sole cause of interference is erroneous transmission scheduling. When realistic state
estimation is used with transmission scheduling there are three sources of interference. The
three causes are listed below
1
.
Erroneous transmission scheduling.
Collisions.
Erroneous state estimation.
6.3.1 Interference because of erroneous transmission scheduling
When a transmission scheduling algorithm (threshold, selfish, overlap scheduling) is used,
a small fraction of the packets are lost due to interference. This is because the algorithms
1
It is important to note that all these factors increase interference, i.e., chip overlaps. However, the condition
for a bit error is w chip overlaps. The w chip overlaps may be due to any combination of the causes mentioned
above. Therefore, while interference may be attributed to the causes above, a particular packet loss cannot be
attributed to any one particular cause.
119
d
A
A has scheduled and
transmitted based on
S(d
A
, t
A
)
A
B
d
B
B has scheduled and
transmitted based on
state S(d
B
, t
B
)
Figure 6.5: Collisions on an optical CDMA network. Transmissions from nodes A and B
collide because neither can see the others’ transmission.
are either pseudo-cooperative or selfish. These strategies do not guarantee that a node’s
transmission Preserves self/Preserves others. Chapter 5 showed a graph (Figure 5.5) of the
probability of packet error. The graph shows how all the scheduling algorithms lose a fraction
of their packets due to interference.
6.3.2 Interference because of collisions
A collision is an event where two or more nodes schedule their transmissions using state
estimates that do not contain the codewords transmitted by each other. As a result, the trans-
missions of the nodes may interfere with each other. Another way of describing a collision is
a state transition that occurs at the coupler in the interval between estimation of the state and
120
the merging of the transmitted packet at the coupler. A collision may or may not result in an
interference error.
Consider two nodes located at different distances from the coupler, each estimating the
state of the line. Consider two nodes A and B at distances d
A
and d
B
from the coupler
where d
A
> d
B
. This is shown in Figure 6.5 Assume that node A estimates, schedules and
transmits at time t
A
and node B at t
B
such that t
A
< t
B
. and t
B
t
A
< d
A
=c. Then both A
and B have estimated and scheduled their transmissions without being aware of each other’s
transmissions.
As the average distance from the coupler increases the probability of collisions occurring
increases. This is analogous to collisions on a single channel network and happens because
of the separation of the nodes in space on the network.
6.3.3 Interference because of erroneous state estimation
An error in state estimation can occur for two reasons:
State transitions: A state transition during the collection of observations
Low number of samples: The number of samples is not large enough. As a result, the
estimate does not approach the mean.
Inaccurate state estimates can cause erroneous transmission scheduling.
121
6.4 Performance study
This section describes three experiments to quantify the effect of the three causes of error (er-
roneous transmission scheduling, collisions, and erroneous state estimation). Two parameters
can be varied: the normalized propagation delay a (a = 0 or a> 0) and the state estimation
algorithm (perfect or realistic). By varying them, the causes for interference can be isolated
and the reduction in throughput due to the causes can be quantified.
The experiments and the causes that they isolate are:
Perfect state estimation, normalized propagation delay a = 0: The nodes are at zero
distance from the coupler and every node does perfect state estimation. Collisions
or errors in state estimation are not possible. Therefore, interference is only due to
erroneous transmission scheduling. This set of experiments is identical to the analysis
in Chapter 5.
Perfect state estimation, a > 0: Nodes do perfect state estimation at the estimation
point. Therefore, there are no errors in state estimation due to a low number of samples.
However, nodes are at different distances from the coupler. Therefore, collisions can
occur. Therefore, interference is due to erroneous scheduling and collisions.
Realistic state estimation, a> 0: Interference is due to erroneous scheduling, collisions
and erroneous state estimation (both state transitions and low number of samples).
The results described in this section are simulation results. Unless explicitly stated the
value of the parameters used in the simulation are the default values provided in Table 6.2
122
Parameter Default value
Codeset parameters:
Codeset length N 100
Number of wavelengths A 1
Codeset weight w 3
Maximum cross-correlation parameter κ 3
Number of codewords in codeset 100
Chipping rate: 10Gb/s
Codeword allocation: Codewords are chosen
uniform randomly from
the codeset
Interference Avoidance parameters:
Transmission scheduling algorithm: Threshold scheduling
Threshold: 0.3
State estimation algorithm: On demand state estimation
Window: 10 bits
Traffic parameters:
Inter-arrival time distribution Exponential
Normalized offered load 1
Packet size distribution Exponential
Average packet size 1000 bytes
Destination address distribution: Destinations are chosen
uniform randomly from
all the nodes
Topology parameters:
Node to coupler distance distribution Uniform
Average node to coupler distance 1000 m
Number of nodes 100
Table 6.2: Parameter list and default values for the state estimation performance and sensi-
tivity study.
6.4.1 Perfect state estimation, a = 0
Figures 6.6, 6.7 and 6.8 show the results for perfect state estimation, equidistant nodes for
different codeset lengths (N = 10;100;200). These results are identical to those in the pre-
vious chapter. The throughput of the threshold algorithm is slightly lower than indicated in
123
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Normalized network throughput
Normalized offered load
Threshold scheduling
Overlap section scheduling
Pure selfish scheduling
Aloha-CDMA
Figure 6.6: Normalized network throughput
vs. normalized offered load for perfect state
estimation, normalized propagation delay a =
0. The results are based on simulation. The
codeset length is 10. All other parameters are
as specified in Table 6.2
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Normalized network throughput
Normalized offered load
Threshold scheduling
Overlap section scheduling
Pure selfish scheduling
Aloha-CDMA
Figure 6.7: Normalized network throughput
vs. normalized offered load for perfect state
estimation, normalized propagation delay a =
0. The results are based on simulation. The
codeset length is 100. All other parameters
are as specified in Table 6.2
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Normalized network throughput
Normalized offered load
Threshold scheduling
Overlap section scheduling
Pure selfish scheduling
Aloha-CDMA
Figure 6.8: Normalized network throughput vs. normalized offered load for perfect state
estimation, normalized propagation delay a = 0. The results are based on simulation. The
codeset length is 200. All other parameters are as specified in Table 6.2
the previous chapter because the threshold parameter is slightly lower (0.3). The important
conclusion is that under perfect state estimation and equidistant nodes, all algorithms perform
approximately the same and all prevent throughput degradation.
124
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Normalized network throughput
Normalized offered load
Threshold scheduling
Overlap section scheduling
Pure selfish scheduling
Aloha-CDMA
Figure 6.9: Normalized network through-
put vs. normalized offered load for perfect
state estimation, normalized propagation de-
lay a > 0 (average distance from the coupler
is 1000m). The results are based on simula-
tion. The codeset length is 10. All other pa-
rameters are as specified in Table 6.2
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Normalized network throughput
Normalized offered load
Threshold scheduling
Overlap section scheduling
Pure selfish scheduling
Aloha-CDMA
Figure 6.10: Normalized network through-
put vs. normalized offered load for perfect
state estimation, normalized propagation de-
lay a > 0 (average distance from the coupler
is 1000m). The results are based on simula-
tion. The codeset length is 100. All other pa-
rameters are as specified in Table 6.2
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Normalized network throughput
Normalized offered load
Threshold scheduling
Overlap section scheduling
Pure selfish scheduling
Aloha-CDMA
Figure 6.11: Normalized network throughput vs. normalized offered load for perfect state
estimation, normalized propagation delay a> 0 (average distance from the coupler is 1000m).
The results are based on simulation. The codeset length is 200. All other parameters are as
specified in Table 6.2
6.4.2 Perfect state estimation, a> 0
Figures 6.9, 6.10 and 6.11 show the throughput curves for perfect state estimation with code-
sets of length N = 10;100 and 200. The nodes are located at an average distance of 1000m
125
from the coupler. The distances are uniformly distributed. The graphs show two clear differ-
ences from the results in the previous section: Firstly, selfish and overlap section scheduling
have lower throughput at high offered load than threshold scheduling. Throughput degrades
more rapidly for pure selfish and overlap length scheduling than for threshold scheduling.
The threshold setting for these experiments is 0.3. Because of this, the number of code-
words on the line for threshold scheduling is low compared to the other algorithms. Both
the selfish and overlap scheduling aggressively transmit packets. When nodes are located at
different distances from the coupler, collisions can occur. When collisions are possible, it
is better to send less aggressively and lower the probability of collisions. This is the reason
why threshold scheduling with a low threshold value performs better. The second difference
is that the throughput at high offered load of threshold scheduling is best for long codeset
lengths (N=200). As mentioned in Chapter 3, this improves correlation between the esti-
mated state and the state. In addition, as the codeset length increases, the probability that
colliding packets affect the same chip reduces. This leads to the first three conclusions of this
study:
The throughput of the threshold transmission scheduling is greater than overlap and self-
ish scheduling. The throughput of all three transmission scheduling algorithms exceeds that
of Aloha-CDMA.
When nodes are different distances from the coupler, collisions can occur. Collisions
increase interference. To compensate, nodes must transmit conservatively. In particular,
threshold transmission scheduling with a low threshold value is suitable.
126
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Normalized network throughput
Normalized offered load
Threshold scheduling
Overlap section scheduling
Pure selfish scheduling
Aloha-CDMA
Figure 6.12: Normalized network throughput
vs. normalized offered load for continuous
state estimation, normalized propagation de-
lay a > 0 (average distance from the coupler
is 1000m). The results are based on simula-
tion. The codeset length is 10. All other pa-
rameters are as specified in Table 6.2
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Normalized network throughput
Normalized offered load
Threshold scheduling with perfect state estimation
Threshold scheduling with continuous state estimation
Overlap section scheduling with continuous state estimation
Pure selfish scheduling with continuous state estimation
Aloha-CDMA
Figure 6.13: Normalized network throughput
vs. normalized offered load for continuous
state estimation, normalized propagation de-
lay a > 0 (average distance from the coupler
is 1000m). The results are based on simula-
tion. The codeset length is 100. All other pa-
rameters are as specified in Table 6.2
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Normalized network throughput
Normalized offered load
Threshold scheduling
Overlap section scheduling
Pure selfish scheduling
Aloha-CDMA
Figure 6.14: Normalized network throughput vs. normalized offered load for continuous
state estimation, normalized propagation delay a > 0 (average distance from the coupler is
1000m). The results are based on simulation. The codeset length is 200. All other parameters
are as specified in Table 6.2
Longer codeset lengths increase correlation and reduce the number of packets lost be-
cause of collisions, and therefore improve throughput.
127
6.4.3 Realistic state estimation, a> 0
Figures 6.12, 6.13 and 6.14 show the throughput curves for continuous state estimation with
nodes located at different distances from the coupler (uniformly distributed with an average
distance of 1000m). The graphs show two differences from the results in the previous sec-
tions. Firstly, the normalized throughput at high offered load of all algorithms has decreased
from the results in the previous section. The reason for this is the error in state estimation.
Increasing the codeset length increases the correlation thereby reduces the error in state esti-
mation. This is shown in Figure 6.15 where the throughput at normalized offered load of 1
increases with increase in N. This leads to the next two conclusions of this study:
Errors in state estimation result in a degradation in throughput. Longer codeset lengths
can help compensate for this effect.
6.5 Sensitivity analysis
This section studies the performance of Interference Avoidance under realistic state estima-
tion when codeset, MAC and traffic parameters are varied. All results are based on simula-
tion. Unless explicitly specified the default parameters are as specified in Table 6.2. Each
point is the average of 10 simulation runs. Standard deviations are indicated on the graphs.
The sensitivity analysis consisted of quantifying the:
Effect of varying the codeset length.
Effect of varying the codeset weight.
Effect of varying the cross correlation parameter.
128
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 50 100 150 200 250
Normalized network throughput at
normalized offered load of 1
Codeset length N
Threshold scheduling
Overlap section scheduling
Pure selfish scheduling
Aloha-CDMA
Figure 6.15: Normalized network throughput vs. codeset length N for different transmission
scheduling algorithms and on-demand state estimation. The results are based on simulation.
The traffic model is Poisson arrivals with exponentially distributed packet lengths. The code-
set is (N;3;3). For the threshold scheduling algorithm, the threshold parameter was set to
0.3. All other parameters are specified in Table 6.2
Effect of varying the number of wavelengths.
Effect of varying the threshold transmission scheduling parameter.
Effect of varying the number of state observations collected.
Effect of different state estimation parameters
Effect of different packet size distributions.
Performance under realistic network traffic.
Performance under very high loads.
129
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 1 2 3 4 5 6 7 8 9 10
Normalized network throughput at
normalized offered load of 1
Codeset weight w
Threshold scheduling
Overlap section scheduling
Pure selfish scheduling
Aloha-CDMA
Figure 6.16: Normalized network throughput vs. codeset weight w for different transmission
scheduling algorithms and on-demand state estimation. The results are based on simulation.
The traffic model is Poisson arrivals with exponentially distributed packet lengths. The code-
set is (100;w;w). For the threshold scheduling algorithm, the threshold parameter was set to
0.3. All other parameters are specified in Table 6.2
6.5.1 Effect of varying the codeset length
Figure 6.15 shows the effect of varying the codeset length N. Chapter 5 showed that with
perfect state estimation and a = 0, the codeset length had no effect on transmission schedul-
ing. An increase in codeset length allowed more codewords to be multiplexed on the line.
However, it also reduced the data rate. The two effects balanced each other resulting in no
change in throughput. When a> 0, the throughput falls due to collisions and erroneous state
estimation. When N increases, throughput improves. As discussed in the previous section
this effect is because of the improved correlation. The magnitude of this improvement can be
seen in the graph.
130
6.5.2 Effect of varying the codeset weight
Figure 6.16 shows the effect of varying the codeset length weight w. Chapter 5 discussed the
effect of varying w under perfect state estimation. As the weight of the codeset increased, the
throughput degraded. This was due to the increase in interference between codewords and the
difficulty in packing more codewords on the line. When a> 0 and realistic state estimation
is used, throughput degrades further due to the collisions and erroneous state estimation.
6.5.3 Effect of varying the cross correlation parameter
The cross correlation parameter κ controls the interference between pairs of codewords.
Chapter 5 discussed the effect of κ on codeset design. Figure 6.17 shows the performance
of the transmission scheduling algorithms under continuous state estimation for a codeset of
length 42, weight 6 as κ is varied from 1 to 6. As may be seen the throughput does not
vary significantly with κ. Note that the throughput in the figure is significantly lower than
the throughput shown in previous performance results. This is due to the use of a codeset of
N = 42;w = 6.
6.5.4 Effect of varying the number of wavelengths
Figure 6.18 shows the effect of varying the number of wavelengths on the network through-
put. As the number of wavelengths is increased, the overall network throughput remains
around the same. Under perfect state estimation and a = 0, increasing the number of wave-
lengths has no effect on throughput. The capacity of the system was increased, but the users
131
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 1 2 3 4 5 6 7 8
Normalized network throughput at
normalized offered load of 1
Maximum cross correlation parameter K
Threshold scheduling
Overlap section scheduling
Pure selfish scheduling
Aloha-CDMA
Figure 6.17: Normalized network throughput at normalized offered load of 1 for different
transmission scheduling algorithms. The results are based on simulation. The traffic model
is Poisson arrivals with exponentially distributed packet lengths. The codeset length N = 42
and weight w = 6. The cross correlation parameter κ is varied from 1 to 6. For the threshold
scheduling algorithm, the threshold parameter was set to 0.5
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 1 2 3 4 5 6 7 8 9 10
Normalized network throughput at
normalized offered load of 1
Number of wavelengths
Threshold scheduling
Overlap section scheduling
Pure selfish scheduling
Aloha-CDMA
Figure 6.18: Normalized network throughput vs. number of wavelength for different trans-
mission scheduling algorithms and on-demand state estimation. The results are based on sim-
ulation. The traffic model is Poisson arrivals with exponentially distributed packet lengths.
The codeset is (10;3;3). For the threshold scheduling algorithm, the threshold parameter was
set to 0.3. All other parameters are specified in Table 6.2
132
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Normalized network throughput at
normalized offered load of 1
Threshold (expressed as a fraction of the codeword length N)
N = 10
N = 50
N = 100
Figure 6.19: Normalized network throughput vs. threshold for the threshold scheduling al-
gorithms and on-demand state estimation. The results are based on simulation. The traffic
model is Poisson arrivals with exponentially distributed packet lengths. The codeset lengths
are 10;100 and 200. All other parameters are specified in Table 6.2
could use only the same fraction of the capacity, so overall network throughput was around
the same. There is no change when a> 0 and realistic state estimation is used.
6.5.5 Effect of varying threshold
Figure 6.19 shows the effect of varying the threshold on network throughput. The results
in the previous chapter (for perfect state estimation, a = 0) showed that there is an optimal
threshold, although network throughput at the optimal threshold was not significantly higher
than at other values. Two interesting differences can be seen in these results:
The peak network throughput occurs at a lower threshold, i.e., the optimal threshold is
lower.
At higher thresholds there is a degradation in throughput.
133
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1 Normalized
offered load
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Threshold
parameter
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Normalized network
throughput
Figure 6.20: Normalized network throughput vs. threshold vs. offered load for the threshold
scheduling algorithms and on-demand state estimation. The results are based on simulation.
The traffic model is Poisson arrivals with exponentially distributed packet lengths. The code-
set length is 100. All other parameters are specified in Table 6.2
The reason for both these effects is the new sources of interference that are introduced:
collisions and erroneous state estimation. In the presence of both these effects, it is better for
a node to transmit conservatively, resulting in a lower number of codewords multiplexed on
the line. This reduces the packets lost due to interference from collisions and erroneous state
estimation and this improves the throughput. Figure 6.19 shows the normalized throughput
for different threshold parameter values.
6.5.6 Effect of different estimation algorithms
Figure 6.21 shows the throughput curves for on-demand state estimation for N = 200. Com-
paring with Figure 6.13 indicates that there is no difference between the performance of
on-demand and continuous state estimation. This is because small windows (10 bits) are
134
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Normalized network throughput
Normalized offered load
Threshold scheduling with perfect state estimation
Threshold scheduling with on-demand state estimation
Overlap section scheduling with on-demand state estimation
Pure selfish scheduling with on-demand state estimation
Aloha-CDMA
Figure 6.21: Normalized network throughput vs. normalized offered load for on demand
state estimation, normalized propagation delay a > 0 (average distance from the coupler is
1000m). The codeset length is N = 200. The results are based on simulation. All other
parameters are specified in Table 6.2
sufficient for state estimation. Therefore the delay is negligible when compared to the state
estimation time. Continuous state estimation performs the same as on demand state estima-
tion.
6.5.7 Effect of varying the number of state observations collected
Figure 6.22 shows the effect of varying the number of state observations collected (window)
on the throughput. When the window is above 10 bits, it does not have an appreciable dif-
ference in improving the throughput. However, the correct window size is dependent on the
codeset length. As N increases, the transmission scheduling algorithm multiplexes a larger
135
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 5 10 15 20 25 30
Normalized network throughput at
normalized offered load of 1
Number of observations
Threshold scheduling (on demand)
Threshold scheduling (continous)
Overlap section scheduling
Pure selfish scheduling
Figure 6.22: Normalized network throughput vs. state estimation window (in bits) for the
transmission scheduling algorithms and continuous and on-demand state estimation. The
results are based on simulation. All other parameters are specified in Table 6.2
number of codewords on the fiber. For larger N, there is a larger difference in the state ob-
servations because of ON-OFF keying. Therefore, the window needs to be chosen depending
on the codeset length. For codeset lengths of up to 100, a window of 10 is sufficient.
6.5.8 Effect of varying the average distance from the coupler
Figures 6.23, 6.24 and 6.25 show the effect of increasing distance on the throughput. As
explained earlier, the effect of increasing distance is to increase the probability of collisions.
The results show that this effect reduces for larger values of N. The graph also shows that
at zero distance, the throughput of selfish and overlap scheduling is better for N = 10. The
reason for this is that as N increases, the differences between state observations increases and
more observations are needed for accurate state estimation. The selfish and overlap section
allow a large number of codewords on the line. Therefore, the error in state estimation is
136
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 100 200 300 400 500 600 700 800 900 1000
Normalized network throughput at
normalized offered load of 1
Average distance from coupler (m)
Threshold scheduling
Overlap section scheduling
Pure selfish scheduling
Aloha-CDMA
Figure 6.23: Normalized network throughput
vs. average distance from coupler (uniform
distribution) for the transmission scheduling
algorithms and continuous state estimation.
The results are based on simulation. The
codeset length is 10. All other parameters are
specified in Table 6.2
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 100 200 300 400 500 600 700 800 900 1000
Normalized network throughput at
normalized offered load of 1
Average distance from coupler (m)
Threshold scheduling
Overlap section scheduling
Pure selfish scheduling
Aloha-CDMA
Figure 6.24: Normalized throughput vs. av-
erage distance from coupler (uniform distri-
bution) for the transmission scheduling algo-
rithms and continuous state estimation. The
results are based on simulation. The codeset
length is 100. All other parameters are speci-
fied in Table 6.2
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 100 200 300 400 500 600 700 800 900 1000
Normalized network throughput at
normalized offered load of 1
Average distance from coupler (m)
Threshold scheduling
Overlap section scheduling
Pure selfish scheduling
Aloha-CDMA
Figure 6.25: Normalized throughput vs. average distance from coupler (uniform distribu-
tion) for the transmission scheduling algorithms and continuous state estimation. The results
are based on simulation. The codeset length is 200. All other parameters are specified in
Table 6.2
large for these algorithms. The threshold scheduling algorithm allows a lower number of
codewords on the line (due to the low threshold of 0.3). Hence this effect is less pronounced.
137
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 100 200 300 400 500 600 700 800 900 1000
Normalized network throughput at
normalized offered load of 1
Mean packet size in bytes
Threshold scheduling
Overlap section scheduling
Pure selfish scheduling
Aloha-CDMA
Figure 6.26: Normalized network throughput vs. average packet length (in bytes) for the
transmission scheduling algorithms and on-demand state estimation. The results are based
on simulation. The traffic model is Poisson arrivals with exponentially distributed packet
lengths. The codeset is (100;3;3). For the threshold scheduling algorithm, the threshold
parameter was set to 0.3. All other parameters are specified in Table 6.2
6.5.9 Effect of varying the packet length
Figure 6.26 shows the effect of different packet sizes on network throughput. When nodes
are distributed on the line and they use realistic state estimation, the effect of varying packet
length is similar to the effect of increasing N. With large packets sizes, the packets remain on
the line much longer. This improves correlation, resulting in an improvement in throughput.
6.5.10 Performance with real network traffic
Figure 6.27 shows the performance with realistic network traffic. As before, a traffic trace
from an OC48 link was used. To generate the required load several traces were merged.
The packet sizes, source address, destination address were preserved during merging. The
average packet size of the resulting traffic file was 500 bytes. The trace file had around
138
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Normalized network throughput
Normalized offered load
Threshold scheduling
Overlap section scheduling
Pure selfish scheduling
Aloha-CDMA
Figure 6.27: Normalized network throughput vs. normalized offered load for the transmis-
sion scheduling algorithms and continuous state estimation with realistic network traffic. The
results are based on simulation. All other parameters are specified in Table 6.2
6000 unique source addresses and 6000 unique destination addresses. Care was taken during
merging to ensure that the traffic of the appropriate load was generated. In contrast to all the
previously described results, in this case destination addresses were mapped to codewords.
Where codewords were insufficient, codeword sharing was used. The results show a slight
improvement in network throughput. The packet squeeze through effect described in the
previous chapter increases throughput.
6.5.11 Performance under very high load
Figures 6.28 and 6.29 show the performance of Interference Avoidance under very high load.
The results show that eventually, at load between ten and a hundred times the transmission
capacity, the throughput of Interference Avoidance will collapse. The collapse occurs because
collisions increase as the load increases. However, the load at which Interference Avoidance
139
0.01
0.1
1
10
100
0.01 0.1 1 10 100
Normalized network throughput
Normalized offered load
Threshold scheduling, N=10
Aloha-CDMA, N=10
Figure 6.28: Normalized network throughput vs. normalized offered load for the threshold
scheduling transmission scheduling algorithms and continuous state estimation with Poisson
arrivals, exponentially distributed packet sizes. The codeset length is 10. The results are
based on simulation. All other parameters are specified in Table 6.2
0.01
0.1
1
10
100
0.01 0.1 1 10 100
Normalized network throughput
Normalized offered load
Threshold scheduling, N=100
Aloha-CDMA, N=100
Figure 6.29: Normalized network throughput vs. normalized offered load for the threshold
scheduling transmission scheduling algorithms and continuous state estimation with Poisson
arrivals, exponentially distributed packet sizes. The codeset length is 100. The results are
based on simulation. All other parameters are specified in Table 6.2
140
0.01
0.1
1
10
100
0.01 0.1 1 10 100
Normalized network throughput
Normalized offered load
Threshold scheduling, N=100
Aloha-CDMA, N=100
Figure 6.30: Normalized network throughput vs. normalized offered load for the threshold
scheduling transmission scheduling algorithms and continuous state estimation with real traf-
fic. The codeset length is 100. The results are based on simulation. All other parameters are
specified in Table 6.2
collapses depends on the codeset length. As described in the previous sections, the effect of
collisions reduces as the codeset length increases. The graphs in the figures indicate that for
codeset lengths of around 100, collapse can be prevented upto loads of around 100.
Finally, Figure 6.30 shows the performance of Interference Avoidance under heavy loads
with realistic traffic. It shows the normalized throughput vs. normalized offered load curve
for threshold scheduling with continuous state estimation. The average distance between
the nodes and the coupler is 1000m and the codeset length is 100. All other parameters are
specified in Table 6.2. The graph indicates that Interference Avoidance, with suitable codeset
parameters, can be used in a real network, even at very high offered load.
141
6.6 Conclusions and future work
This study has indicated that the performance of state estimation depends on several param-
eters. In particular, as the distance of the nodes from the coupler increases, the throughput
falls due to collisions and inaccurate state estimation. By increasing the codeset length and
decreasing the codeset weight, the performance of realistic state estimation tends to perfect
state estimation.
An open area of research is the tuning of the state estimation algorithms to specific net-
work traffic distributions by using more complex estimators. The objective is to design es-
timators that approach the bound of perfect state estimation for low values of the codeset
length.
142
Chapter 7
Implementation
This chapter describes an experimental evaluation of Interference Avoidance and how it may
be implemented. Section 7.1 describes a laboratory testbed for optical CDMA experimen-
tation. The testbed was used to measure the performance of transmission scheduling. The
testbed was set up at the USC Optical Communication Laboratory by members of the Opti-
cal Communications Laboratory. The transmission scheduling experiments were carried out
by the author. Results from the measurements show that in the presence of physical layer
noise, transmission scheduling can provide up to 2 orders of magnitude improvement in Bit
Error Rate (BER). Section 7.2 describes the design and operation of a Network Interface Card
(NIC) that implements Interference Avoidance over optical CDMA.
7.1 Experimental demonstration and measurement of transmission
scheduling
The optical CDMA testbed is a network with 4 nodes (also called users). A simplified dia-
gram of the network is shown in Figure 7.1. The testbed has a transmitter component and a
143
Modulator
Encoder
Encoder
Encoder
Encoder
Coupler
Receiver
Pattern
generator
BERT
Transmitters
Figure 7.1: A block diagram of the optical CDMA experimental testbed constructed at the
USC Electrical Engineering department’s Optical Communications Laboratory.
receiver component. The transmitter has one modulator and 4 encoders, one for each user.
The 4 encoders transmit 4 different codewords (C1C4). The testbed has only one receiver.
The receiver receives the codeword C4, i.e., the codeword for user 4. The transmitter and the
receiver components are discussed in detail in the next two sections.
The optical CDMA codeset is a (11, 6, 6, 1) codeset, i.e., the codeword length N is 11
chips, the number of wavelengths Λ is 6, the weight w is 6 and maximum cross-correlation
parameter κ is 1. The chipping rate used is 11Gc/s. The data rate is 1Gb/s. The codewords
are shown in Table 7.1.
144
Ȝ 6
Laser
Array
Coupler
(C)
Modulator EDFA (D)
Polarization
Controllers
(B)
Ȝ 1
Pattern
generator
To BERT
(A)
Figure 7.2: A block diagram of the modulator part of the Optical CDMA testbed.
Couplers
(H)
TDLs
(G)
TDLs
(I )
EDFAs
(J)
Polarization
Controllers
(K)
AWG
(E)
TDL
TDL
TDL EDFA
EDFA
EDFA
EDFA
Polarization
controller
Splitters
(F)
TDL 1
TDL 4
TDL 3
TDL 2
Polarization
controller
Polarization
controller
Polarization
controller
Ȝ 1
Ȝ 6
Ȝ 1
Ȝ 6
User 1
From
modulator
User 4
Coupler
(L)
Figure 7.3: A block diagram of the four encoders of the Optical CDMA testbed.
145
User 1 λ
1
1 0 0 0 0 0 0 0 0 0 0
λ
2
0 0 0 0 0 1 0 0 0 0 0
λ
3
0 0 0 0 0 0 0 0 0 0 1
λ
4
0 0 0 0 0 1 0 0 0 0 0
λ
5
0 0 1 0 0 0 0 0 0 0 0
λ
6
0 0 0 0 0 0 0 1 0 0 0
User 2 λ
1
0 0 0 0 0 1 0 0 0 0 0
λ
2
0 0 0 0 0 0 0 0 1 0 0
λ
3
0 0 0 0 0 0 0 0 0 0 1
λ
4
0 0 1 0 0 0 0 0 0 0 0
λ
5
0 0 0 0 0 1 0 0 0 0 0
λ
6
0 0 0 1 0 0 0 0 0 0 0
User 3 λ
1
0 0 0 0 0 0 1 0 0 0 0
λ
2
0 0 0 0 1 0 0 0 0 0 0
λ
3
0 0 0 0 0 0 0 0 0 0 1
λ
4
0 0 0 0 0 0 0 0 1 0 0
λ
5
0 0 0 0 0 0 0 0 0 1 0
λ
6
1 0 0 0 0 0 0 0 0 0 0
User 4 λ
1
0 0 0 0 0 0 0 1 0 0 0
λ
2
1 0 0 0 0 0 0 0 0 0 0
λ
3
0 0 0 0 0 0 0 0 0 0 1
λ
4
0 0 0 1 0 0 0 0 0 0 0
λ
5
0 1 0 0 0 0 0 0 0 0 0
λ
6
0 0 0 0 0 0 0 0 1 0 0
Table 7.1: Codewords for the 4 nodes in the experimental testbed. The codewords are from a
2 D codeset (more than one wavelengths is used) with parameters (11, 6, 6, 1).
7.1.1 Optical CDMA transmitter component
The transmitter component consists of one modulator and 4 encoders. A diagram of the
modulator is shown in Figure 7.2. The function of the modulator is to generate the six wave-
lengths and modulate them with the data. Ideally, there should be one modulator for each
user (encoder). However, four modulators could not be built for the four users because the
146
necessary equipment was not available. Therefore, a single modulator was used. The modu-
lated data from the modulator is sent to the 4 encoders. The encoders encode the modulated
wavelengths with the optical CDMA codewords. A diagram of the encoders is shown in Fig-
ure 7.3. The limitation of using one modulator for 4 encoders is that data generated for the
four users is identical and bit synchronized. To eliminate the bit synchronization, fibers of
different lengths and tunable delay lines give each user a random delay.
7.1.1.1 Modulator
The modulator consists of a laser array, polarization controllers, a coupler, the data modulator,
and an Erbium Doped Fiber Amplifier (EDFA). Figure 7.2 shows a block diagram of the
modulator.
Laser array (A): The array of lasers generates the wavelengths for transmission. The
six wavelengths are denoted by (λ
1
::::λ
6
).
Polarization controllers (B): The polarization controllers are used to adjust the polar-
izations of the wavelengths for maximum output power. The data modulator (described
below) modulates with the maximum power gain when the wavelengths are at a partic-
ular polarization. By tuning the polarization controllers, the modulated signal can be
adjusted to obtain maximum output power.
Coupler (C): The coupler couples the wavelengths on to a single fiber. The coupler is
used so that all the wavelengths can be modulated together.
147
Data modulator: The data modulator modulates the incoming wavelengths. It is driven
by a pattern generator. The pattern generator generates a sequence of bits. It operates
at 11 Gb/s (the chipping rate). The pattern generator is configured to send a pattern of
0000000001 to represent a 1 bit. It sends a pattern of 0000000000 to represent a 0 bit.
These two patterns are 11 chips long. Note that the pattern for a 1 bit has a single ‘1
chip’ and the pattern for a 0 bit has no ‘1 chips’. These patterns are used to generate
the codeword. The reason for this pattern is explained in the next section.
Erbium Doped Fiber Amplifier EDFA (D): The EDFA is used to amplify the signal
before the encoders.
7.1.1.2 Encoders
The encoders encode the modulated data. The encoder consists of an Arrayed Waveguide
(AWG), a splitter, tunable delay lines, couplers, tunable delay lines, EDFAs and polarization
controllers. Figure 7.3 shows a block diagram of the encoders.
Arrayed Waveguide (AWG) (E): The AWG splits the incoming signal into its compos-
ite wavelengths.
Splitters (F): The six splitters split each wavelength into 4 signals. A group of six
wavelengths is used to encode each user’s codeword.
Tunable delay lines (G): The delay lines are used to encode the data. Each user has
its own set of tunable delay lines. Figure 7.4 shows how it works. Assume the data
modulator has sent a 1 bit. Then on each wavelength, the pattern 00000000001 enters
148
TDL
TDL
TDL
TDL
TDL
Coupl er
TDL
AWG
Ȝ 1
Ȝ 1
Ȝ 2
Ȝ 2
Ȝ 3
Ȝ 3
Ȝ 4
Ȝ 4
Ȝ 5
Ȝ 5
Ȝ 6
Ȝ 6
Figure 7.4: The optical CDMA encoders. The tunable delay lines (TDLs) of the encoder
encode an optical CDMA codeword.
the delay lines. Each delay line delays the pulse (the ’1 chip’ in the pattern) by a
different amount of time. The codeword for user 1 is shown in Table 7.1. For codeword
1 the delays for the wavelengths 1 to 6 are respectively 1, 7, 11, 6, 3 and 8. By carefully
tuning the delay lines, the total delay of a path from the splitter F to the coupler H can
be controlled to generate the appropriate delays. In the testbed, some delay lines are
free space, some are fiber based and some are tunable. Note that the output of a single
modulator enters all four encoders. This creates a problem: the data of all four users
are identical and bit synchronized. Random delays are introduced after the encoders
by using optical fibers of different lengths to eliminate the synchronization.
Couplers (H): Each encoder has a coupler that couples the six wavelengths. The output
of the coupler is the encoded data.
149
Tunable delay lines (I): Tunable delay lines are used after the coupler to give random
delays to each of the users. The tunable delay lines along with the different fiber
lengths between the couplers (H) and the coupler L eliminate the bit synchronization
of the codewords of the users.
EDFA (J): The EDFAs are used to amplify the signals. The wavelengths undergo power
attenuation due to loss at the free space delay lines. The EDFAs compensate for this.
Polarization controllers (K): The polarization controllers are used to protect against
beat noise [71]. ‘1 chip’ overlaps at the same time and wavelength causes beat noise.
The beat noise can be avoided if the users’ wavelengths are on different polarizations.
This eliminates the beat noise but does not affect the interference.
Coupler (L): The coupler couples the encoded data from each user on to a single fiber.
The signal at the output of the coupler is a multilevel optical signal equal to the sum of
the multiplexed codewords.
7.1.2 Optical CDMA receiver
The optical CDMA receiver is a correlation receiver. Note that it is not a hard-limiting re-
ceiver. The receiver decodes the codeword C4. It consists of an arrayed waveguide, tunable
delay lines, a coupler, an optical attenuator, a photodetector, an amplifier, an attenuator, and
a threshold detector.
Arrayed waveguide (N): The AWG splits the signal into its six wavelengths.
Tunable delay lines (O): The tunable delay lines are tuned to the delays corresponding
150
Photo-
detector
AWG
TDL
TDL
TDL
Ȝ 1
Ȝ 6
TDL
TDL
TDL
Optical
attenuator
Electrical
attenuator
Electrical
amplif ier
Threshold
detector
BERT
Pattern
generator
To
modulator
Coupler
(P)
EDFA
(M)
TDLs
(O)
AWG
(N)
EDFA
Figure 7.5: The receiver of the optical CDMA testbed.
TDL
TDL
TDL
TDL
TDL
Coupl er
TDL
AWG
Ȝ 1 Ȝ 1
Ȝ 2 Ȝ 2
Ȝ 3 Ȝ 3
Ȝ 4 Ȝ 4
Ȝ 5 Ȝ 5
Ȝ 6 Ȝ 6
Figure 7.6: The decoder of the optical CDMA receiver. The figure shows how the Tunable
Delay Lines (TDLs) of the receiver decode the optical CDMA codeword.
151
to a receiver for user 4. Figure 7.6 shows how the decoder works. The decoder reverses
the operation of the encoder. For codeword C4 the delays are 4, 11, 1, 8, 10, 3 chip
times. The codeword enters the delay lines and at the output, the pulses are stacked up
in time.
Coupler (P): The signal from each of the wavelengths is coupled. At the output of the
coupler, the ‘1 chips’ of the codeword should be aligned in time.
Optical attenuator: The optical attenuator attenuates the optical signal to a value within
the photodetector’s range.
Photo detector: The photodetector converts the incident light energy to electrical power.
The photodetector is a PIN diode.
Attenuator: An attenuator is used to bring the electrical power down to within the
threshold detector’s range.
Threshold detector: The threshold detector generates a pulse if the input is higher than
the threshold.
7.1.3 Measurement instruments
The measurement instruments are the pattern generator and the Bit Error Rate Tester (BERT).
Pattern generator: The pattern generator generates a sequence of bits. As described
earlier, to send a 1 data bit, the pattern 00000000001 is sent. To send a 0 data bit, the
pattern 00000000000 is sent. The sequence is 1024 bits longs.
152
BERT: The Bit Error rate Tester (BERT) compares the input from the pattern generator
to the detected signal and reports the bit error rate.
7.1.4 Limitations of the testbed
The experimental testbed has several limitations that makes it difficult to compare results to
the theoretical work described in Chapters 5 and 6. Firstly, the limited number of components
in the testbed meant that only a four user system could be tested. For the codeset (11, 6, 6,
1), a four user system is a very lightly loaded system. The normalized offered load is 0.06 (=
(Number of codewords multiplexed on the line )/ (ΛN) = 4/(6*11). According to the theory
of the previous chapters, transmission scheduling improves throughput only at high offered
load.
Secondly, the system was noisy. Noise was introduced through several sources: the free
space delay lines, the amplifiers, mode hopping of the lasers. Due to the noise, the receiver
threshold for the receiving user had to be set to half the weight of the code. This is the optimal
setting for detecting a codeword when only one user is transmitting under noisy conditions.
Thirdly, the specification of the power input to the receiver was low and therefore the
power input had to be kept below a limit. This was done by a target amplifier that limited the
input power to the receiver. Therefore, the input power to the receiver was the same whether
there were 1 , 2, 3 or 4 users on the system. Therefore, when four users are transmitting, the
power of each user’s individual codeword is reduced. To compensate for this, the threshold
had to be lowered each time a new user was added. The consequence of this is that the noise
had a greater impact when the number of users was increased.
153
Lastly, the receiver was not a hard-limiting receiver. Therefore, noise and interference
effects were greater than with a hard-limiting receiver.
The experiment shows that the last three limitations introduce enough noise that trans-
mission scheduling resulted in a performance benefit (a reduction in BER) even at the low
loads used in the experiment.
7.1.5 Objective of the experiment
The objective of the experiment was to determine whether transmission scheduling provides
any benefit under realistic conditions.
To do this the bit error rate was measured as the number of simultaneous users was in-
creased. The transmission delays of the users were varied and the bit error rates were noted.
The number of chip overlaps in each case was determined from knowledge of the codesets.
The chip overlaps were also viewed on an oscilloscope connected to the output of coupler
L. To evaluate the performance of transmission scheduling, the performance of a threshold
scheduling algorithm with a low threshold of 1 overlap (threshold parameter = 0.015) was
used. This threshold allows codewords to be transmitted only if there are no overlaps. The
readings from the experiment and the number of chip overlaps for each case were used to
determine the BER of threshold scheduling. Any reading with zero overlaps was considered
to be a case of threshold scheduling with threshold of 0.015. This was compared against the
worst case bit error rate and the average case bit error rate. The average case bit error rate
can be considered to be the bit error rate of Aloha-CDMA.
154
7.1.6 Experimental procedure
This section describes the experimental procedure. First, preliminary checks are performed
to ensure that the system is functioning normally. These checks are made before taking any
reading and during the experiment.
7.1.6.1 Preliminary checks
First, the encoders are checked to determine whether the data is being encoded properly. Only
one of the EDFAs (J) in Figure 7.3 is switched on. An oscilloscope and a spectrum analyzer
are connected to the output of coupler L. The output is visually checked to determine whether
all six wavelengths are present and that their powers are equal. The transmission delay of
the codeword is checked to see if they are correct. These checks are performed for all 4
codewords.
Next, the threshold detector clock (trigger) is synchronized to the output of the photode-
tector. The EDFA (J) corresponding to user 4 is switched on. All other EDFAs are switched
off. An oscilloscope is connected to the output of the photodetector, the threshold detector,
and the clock input. The positive edge of the clock input to the threshold detector is aligned
to the output of the photodetector.
155
7.1.6.2 Measurements
Three experiments were conducted. In each experiment, the receiver was tuned to the code-
word of user 4. The codewords for users 1, 2, 3 were the interfering codewords. The exper-
iments measured the bit error rate (BER) for user 4 in the presence of one, two, and three
interfering users.
The steps were as follows:
User 4 (the receiving user) is switched on using EDFA J.
The receiver threshold is adjusted for the best possible BER.
One user is added to the system by switching on its EDFA (J).
The receiver threshold is adjusted for the best possible BER.
The transmission delay of the user is adjusted using the tunable line delay (I) and
different fiber lengths between the TDL (I) and the EDFA (J) until the best BER is
obtained.
The transmission delay of the user is varied and BER readings are noted. The oscillo-
scope is used to check the transmission delay is used.
Each measurement is repeated 5 times and the mean of the readings is noted.
The experiment is repeated by adding more interfering users.
156
Codeword delay of Codeword delay of Number of overlaps Bit error rate
User 4 User 1
0 0 1 2E-7
0 1 1 4E-7
0 2 0 1E-9
0 3 0 3E-9
0 4 0 1E-9
0 5 0 7E-9
0 6 1 2E-7
0 7 1 6E-7
0 8 0 1E-9
0 9 1 3E-7
0 10 1 4E-7
Table 7.2: Testbed bit error rate in the presence of 1 interfering user.
7.1.7 Results
The results for 1, 2 and 3 interfering users are shown in Tables 7.2, 7.3, and 7.4. The results
show the bit error rates for particular transmission delay of the users. The table also shows
the number of chip overlaps. Only a few results are presented here to illustrate the effect of
transmission scheduling on BER. Several more readings were taken.
The limitation of the setup (four users and a (11, 6, 6, 1) codeset) means that the system
is operating under very low load. Under low loads, according to the analysis in the previous
chapters, transmission scheduling should not provide any benefit. In fact, Aloha-CDMA
should perform just as well as any transmission scheduling. However, there are three reasons
why transmission scheduling improves the performance even under low loads.
Firstly, under normal operating conditions the bit error rate is very high. This is because
of the noise introduced by other sources, e.g., thermal noise, amplifiers, inaccurate delay
157
Codeword Codeword Codeword Number of Bit error
delay of delay of delay of overlaps rate
User 4 User 1 User 2
0 10 0 2 3E-5
0 10 1 2 1E-5
0 10 2 2 4E-5
0 10 3 2 3E-5
0 10 4 1 4E-7
0 10 5 2 2E-5
0 10 6 1 3E-7
0 10 7 1 3E-7
0 10 8 1 2E-7
0 10 9 1 1E-7
0 10 10 1 3E-7
0 8 0 1 4E-7
0 8 1 1 3E-7
0 8 2 1 5E-7
0 8 3 1 4E-7
0 8 4 0 9E-9
0 8 5 1 2E-7
0 8 6 0 3E-9
0 8 7 1 3E-7
0 8 8 0 2E-8
0 8 9 0 1E-8
0 8 10 0 4E-9
Table 7.3: Testbed bit error rate in the presence of 2 interfering users.
lines, free space delay lines, mode hopping lasers, and environmental conditions. The major
reason for these sources of noise is that the testbed is built from discrete components. Sec-
ondly, the power input to the receiver AWG must be kept below a limit. This is done by
using an EDFA (M). This means that as the number of users increases, the power per chip
decreases. To compensate for this the receiver threshold must be lowered when a new user is
added on. Therefore, as the number of users increases, the effect of noise increases. Thirdly,
158
Codeword Codeword Codeword Codeword Number of Bit error
delay of delay of delay of delay of overlaps rate
User 4 User 1 User 2 User 3
0 10 3 0 3 Non recoverable
0 10 3 1 3 Non recoverable
0 10 3 2 2 4E-5
0 10 3 3 2 7E-5
0 10 3 4 2 5E-5
0 10 3 5 2 2E-5
0 10 3 6 2 2E-5
0 10 3 7 3 3E-4
0 10 3 8 2 8E-5
0 10 3 9 2 2E-5
0 10 3 10 2 3E-5
0 10 8 0 2 2E-5
0 10 8 1 2 8E-5
0 10 8 2 1 6E-7
0 10 8 3 1 9E-7
0 10 8 4 1 7E-7
0 10 8 5 1 1E-7
0 10 8 6 2 3E-5
0 10 8 7 2 2E-5
0 10 8 8 2 7E-5
0 10 8 9 1 4E-7
0 10 8 10 1 2E-7
0 8 4 0 1 2E-7
0 8 4 1 1 7E-7
0 8 4 2 0 3E-8
0 8 4 3 1 8E-7
0 8 4 4 0 3E-8
0 8 4 5 0 6E-8
0 8 4 6 1 8E-7
0 8 4 7 1 4E-7
0 8 4 8 1 9E-7
0 8 4 9 0 3E-8
0 8 4 10 0 2E-8
Table 7.4: Testbed bit error rate in the presence of 3 interfering users.
159
1e-09
1e-08
1e-07
1e-06
1e-05
0.0001
0.001
0.01
0 1 2 3 4 5
Bit error rate
Number of interfering users
Worst case BER
Aloha CDMA
Threshold scheduling (threshold = 0.015)
Figure 7.7: Experimental results: The transmission scheduling algorithm results in the best
case BER. It occurred under cases when there were zero overlaps. The worst case BER is
the worst possible bit error rate that was measured. It occurred in cases when the number of
overlaps was the maximum possible. Aloha-CDMA does not control the number of overlaps.
Its BER is the average over all the measured cases.
the receiver does not do hard-limiting which increases the interference errors [57]. Finally,
beat noise also was a source of noise.
The multi-user interference increases the bit error rate further. Therefore, in this system,
even under low loads, transmission scheduling helps improve the throughput. This may be
seen from the difference in bit error rates when the number of overlaps increases. As few as
one chip overlap can cause the bit error rate to increase by 2 orders of magnitude from 10
9
to 10
7
Table 7.2 shows the bit error rates for different transmission delay when there is one inter-
fering user on the line. The number of chip overlaps for each case is also shown. Tables 7.3
and 7.4 show the same results for 2 interfering users and 3 interfering users. Note that only a
few transmission delays are shown because the total number of combinations of transmission
160
delays is too large to present. Entries marked ‘non-recoverable’ indicate that the bit error rate
was above 1E-4. The BERT did not provide any BER readings above 1E-4. Figure 7.7 shows
the bit error rate for threshold scheduling, Aloha-CDMA and the worst case BER. Note that
the measured cases are a small subset of the total number of possible combinations. The
average case is closer to the worst case than to the best case. This is because the worst case
BER is 2 orders of magnitude worse than the best case and the worst case condition happens
fairly frequently as may be seen from the Tables 7.2, 7.3 and 7.4.
Under high load conditions, more and more overlaps are likely to occur and the worst
case conditions are seen more often for an Aloha-CDMA protocol. A transmission scheduling
algorithm however allows only a limited number of codewords on the line and would schedule
the transmissions such that the system would have the best case BER.
The two conclusions of this study are:
In the presence of significant physical layer noise, transmission scheduling can improve
performance even under low offered load.
7.2 Implementation of a network interface card
This section describes the high level hardware design of a Network Interface Card (NIC)
for the Interference Avoidance MAC protocol over optical CDMA. The design goals of this
implementation are:
To design a NIC card that functions correctly.
To minimize the latency of the state estimation and transmission scheduling.
161
As the latency of state estimation and transmission scheduling increases, the state esti-
mate becomes less accurate and therefore the throughput of Interference Avoidance falls. For
a network of maximum diameter 2000m, the delay between the estimation and the merging
of packets is approximately 5μs. The throughput of Interference Avoidance does not degrade
significantly at this latency. Therefore, as long as the latency of the hardware is a small frac-
tion of 5μs, the throughput does not fall significantly. The primary design goal is to ensure
that the latency of the hardware is a small fraction of 5μs. The secondary design goals are to
reduce the required logic and the memory.
The NIC card is designed for a network of maximum diameter 2000m, and uses 1 wave-
length and a chipping rate B of 10Gc/s. It supports codeset lengths of up to N = 100 and
a weight of w = 3 (can be extended). The card design is for a Tunable Transmitter-Fixed
Receiver (TT-FR) architecture (the transmitter may be tuned to any codeword while the re-
ceiver codeword is hardcoded into the NIC). The state estimation algorithm is continuous
state estimation using the sample means algorithm (Chapter 6). The transmission scheduling
algorithm is the threshold scheduling algorithm (Chapter 5).
Figure 7.8 shows a block diagram of the hardware of the NIC. The NIC hardware con-
sists of the Controller module, State observation collection module, State estimation module,
Transmission scheduling module, Ranging module, Synchronization module, optical CDMA
transmitter and optical CDMA receiver
1
. When a packet arrives on the receive fiber, it is de-
coded by the optical CDMA receiver and written to the receive buffer. When a packet arrives
1
The block diagram does not show any amplifiers that may be needed to amplify signals.
162
Optical CDMA
Receiver
Transmit
buffer
State
estimation
module
Transmission
scheduling
module
Sampling
module
Bus
Codeword
buffer
Optical CDMA
Transmitter
Synchronization
module
Receive
buffer
Ranging
module
Bus
Controller
Transmit
fiber
Receive
fiber
Figure 7.8: A block diagram of an Interference Avoidance Network Interface Card.
on the bus, it is written to the transmit buffer. The transmission scheduling algorithm calcu-
lates the appropriate transmission delay tunes the tunable delay lines (TDLs) and signals the
transmitter. The optical CDMA transmitter transmits the packet on the transmit fiber. The
state observation collection and state estimation modules run continuously and write the state
estimate to the transmission scheduling module.
The following sections describe the operation of the individual components of the NIC
card.
7.2.1 Bus interface
The function of the bus interface is to transfer data between the node processor and the net-
work interface card. When a packet is available for transmission at the node processor, the
163
packet to be transmitted and the codeword to be used for optical CDMA encoding are sent
by the node processor to the NIC across the data lines of bus
1
. The packet and the code-
word are stored in buffers (called the transmit buffer and the codeword buffer respectively).
The transmit buffer should be large enough to store at least 1 packet, while the codeword
buffer must be large enough to store at least 1 codeword. If packets are arriving faster than
the transmission scheduling module can process them (100 ns) then additional buffering is
needed. The bus could be a commercially available or future version of a bus such as PCI or
USB. The bus could be replaced by a network interface for another LAN such as Ethernet.
7.2.2 State observation collection module
The function of the state observation collection module is to convert a multivalued optical
input signal to an electronic digital signal. The state observation collection module has both
electronic and optical components.
Figure 7.9 shows a diagram of the state observation collection module. The input to the
state observation collection module is the incoming signal on the receive fiber
2
. The module
consists of a splitter, a photodetector, threshold detectors, and collection module. The dia-
gram shows an implementation of the state observation collection module with four threshold
detectors. In any given chip time, the signal is a multivalued input because it is the sum of a
particular number of ‘1 chips’. The photodetector converts the multilevel input signal to an
electrical signal. The threshold detectors and the logic convert the signal to a digital value.
1
As described in Chapter 4, the codeword used for encoding is determined by a higher layer address to
codeword mapping. This mapping is out of the scope of this work
2
For this discussion the ranging module is ignored.
164
Control
Photo
detector
Logic
Chip sample
(to state
estimation
hardware)
Threshold
detector
Threshold
detector
Threshold
detector
Threshold
detector
Incoming
signal
(from receive
fiber)
R bits
Figure 7.9: State observation collection module. The input to the state observation collection
module is a multivalued optical signal that arrives at the chipping rate. The output is an
electronic digital value, a chip observation, which changes at the chipping rate. Each chip
observation represents the magnitude of the multivalued signal in a chip time. The figure
shows 4 threshold detectors, enough to detect up to 4 different chip magnitudes. The number
of detectors can be modified based on the accuracy desired. Section 7.2.6 discusses why a
minimum of 3 is needed.
The thresholds of the threshold detectors are set to values that correspond to increasing values
of the multilevel input signal. For example in Figure 7.9, they are set to correspond to 0.5.
1.5, 2.5 and 3.5 chips that are the values needed to differentiate between chip magnitudes
0, 1, 2, 3, and greater than 3. The number of threshold detectors that are triggered depends
on the value of the signal. The logic is an encoder that converts the output of the threshold
detectors to bits. The output of the state observation collection module is a digital signal that
corresponds to the multivalued input. This output is called the chip observation. The flash
ADC is a good candidate for this function and flash ADC with resolutions of 3 bits have been
165
demonstrated at speeds of up to 10G samples/s [21]
1
. The output of the state observation
collection module is connected to the state estimation hardware.
The state observation collection module operates at the chipping rate (10 Gc/s). It writes
new chip observations to the state estimation module at 10GHz. It can be implemented as a
custom ASIC which interfaces with the photodetector.
The number of bits in the chip observation is called the resolution R of the state observa-
tion collection module. The larger the resolution of the module, the more accurate the state
estimate. The resolution should be logN for accurate representation of the state (at 100%
normalized offered load, N codewords are on the line, and therefore the maximum size of a
chip observation is N). However, the larger the resolution, the greater the number of com-
ponents in the hardware and therefore the higher the cost of implementation. Section 7.2.6
discusses how to reduce the required resolution without substantially affecting the accuracy
of state estimation.
7.2.3 State estimation module
The function of the state estimation module is to calculate the estimated state vector from
the chip observations provided as input from the state observation collection hardware. This
implementation is based on the continuous state estimation algorithm as specified in Chap-
ter 6. It works by collecting a number of state observations (n
e
), adding them, multiplying
the result by 2 and dividing the result by the number of state observations (Refer Chapter 6).
Hardware can use parallelism to operate concurrently on every chip observation of the state.
1
An alternative is to perform optical analog to digital conversion. Optical analog to digital conversion has
been demonstrated at resolutions of 5 bits at optical transmission rates (10 Gb/s) [7].
166
State estimate
(to transmission
scheduling
hardware)
Chip sample
(from
sampling
hardware)
R bits
Shift Adder
State
buffer
State
buffer
State
buffer
NR bits
N(R + logn
e
) bits
n
e
+1
NR bits
Figure 7.10: State estimation module. The input is a stream of chip observations arriving at
the chipping rate. The output is a state estimate that is output at the clock rate of the hardware.
The figure also shows the width of the data lines in the hardware.
Figure 7.10 shows a diagram of the state estimation hardware. The module consists of
latches, an adder and a shifter. The latches are arranged into (n
e
+ 1) groups called state
buffers. Each state buffer stores one state observation. Each state buffer consists of N chip
buffers. Each chip buffer stores one chip observation. The (n
e
+ 1) state buffers are designed
as a circular buffer, i.e., new values of the chip observations overwrite the older values. The
state observation collection module writes chip observations to the input of the state estima-
tion module at the chipping rate (10Gc/s). Therefore, the latches must operate at clock speed
of 10GHz. Every clock cycle, a chip observation is written to a different chip buffer. N clock
cycles after startup, one state buffer has a state observation. n
e
N clock cycles after startup,
all state buffers are filled. Subsequent chip observations overwrite the older ones. The adder
167
adds n
e
state observations (the state buffer that is currently being written not used as input to
the adder). The output of the adder is multiplied by 2 and divided by n
e
. In this implemen-
tation n
e
is set to 16
1
. Therefore, the result can be obtained by dividing by 16=2 = 8, i.e.,
shifting it left by 3 chips. The division can be done by a simple reordering of the output of
the adder. A 1 must be added to the output of the adder before the division to ensure that the
division rounds up. The output of the shifter is the state estimate. The adder is run only when
a new state observation is available, i.e., after N chip observations are collected. Note that the
state buffer is written to at the chipping rate, i.e., 10 GHz. However, the adder and the shifter
need only run at a speed of 10GHz=N = 100 MHz.
FPGA hardware available currently along with a custom ASIC may be used for imple-
mentation. The first stage of the hardware (the state buffers) may need to be a custom ASIC
because of the high rate at which chip observations are written to the latches (10GHz). Subse-
quent stages operate at a lower clock speed (100MHz) and can be implemented in an FPGA.
If the hardware clock is lower than the data rate, the design may need to be modified by
adding sufficient buffering. The clock speed of current FPGA hardware is 400MHz, well
above the requirements of the hardware.
The latency of this implementation is well below the design goal of 5μs. If the adder
completes its operation in 1 clock cycle, i.e., 1/100 MHz = 10 ns, then for n
e
= 16, N =
100, B = 10Gc/s, it takes 160ns for the first state estimate and 10ns for the subsequent state
estimates.
1
Chapter 6 showed than any value of n
e
greater than 10 is sufficient for state estimation in a codeset of length
N = 100.
168
The processing requirements of the state estimation module are within the capability of
current FPGA hardware. Each operation on a component of the vector needs a separate
hardware unit. The adder must perform N parallel additions, each of which has inputs of
n
e
chip observations of R bits each. Therefore, it needs Nn
e
hardware units. For N = 100,
n = 16 this is 1600 hardware units. This is well within the capabilities of current FPGA
chips which can have around 100000 hardware units [73]. Note that the design allows the
latency of the module to be traded against the complexity of implementation by serializing
some operations. A deeper study of this trade-off is an area for future work.
The buffer requirements for the hardware algorithm are very low. The state buffers con-
tain NR(n
e
+ 1) bits. For N = 100, R = 2, n
e
= 16 this is 3400 bits or approximately 0.5kB.
This is a negligible compared to current ASIC chips or even FPGA chips, which have up to
100000 latches and typical on-chip memories of 8MB [73].
7.2.4 Controller module
The controller module provides top level control to the NIC card. On arrival of a packet
for transmission, it signals the transmission scheduling module. On completion of transmis-
sion scheduling, it reads the results and signals the transmitter to begin transmission at the
appropriate time.
7.2.5 Transmission scheduling module
The function of the transmission scheduling module is to take as input the state estimate and
the codeword to be transmitted and calculate the delay at which to transmit the codeword.
169
State estimate
(from state
estimation hardware)
Threshold
Codeword
(from
codeword
buffer)
Num
overlaps
Add Comparator
Selector
Num
overlaps
Add Comparator
Num
overlaps
Add Comparator
Rotate
Rotate
Rotate
Delay
(to tunable
delay lines)
logN bits
Transmit
interrupt
(to transmitter)
NR
bits
logN
bits
N
N bits NR bits logN bits N bits
Figure 7.11: Transmission scheduling hardware. There are two inputs: the codeword that
arrives on packet arrival and the state estimate, which changes every clock cycle. The output
is the delay in terms of number of chips from the start of the hardware clock cycle. This delay
is used to delay the transmission. The width of the data lines is also shown in the figure.
The hardware implements the threshold scheduling algorithm. It checks every possible delay
of the codeword to see if it satisfies two criteria: The number of overlaps in the resulting
state should be below a threshold and the codeword should not be lost due to an error. It
chooses a transmission delay that satisfies these criteria. This algorithm can be implemented
using parallelism to operate concurrently on different rotations of the codeword vector and to
operate concurrently on each component of the vector.
Figure 7.11 shows the transmission scheduling hardware. The module consists of rota-
tors, adders, combinational logic, comparators, and an encoder. The input to each of these is
either one or two vectors. The input to the module is the codeword for encoding and the state
estimate. The rotate logic rewires each codeword such that a different rotation enters the next
170
stage. Each rotation corresponds to transmission of the codeword at a different delay. There
are N possible rotations, so there are N parallel paths. The next stage (the adder) adds the
rotated codeword to the state estimate. The two stages (the number of overlaps combinational
logic, and the comparator) determine if the rotation satisfies the two criteria. The output of
the comparator sets its output bit to 1 if the criteria are satisfied. The next stage (the selector)
selects one of the enabled inputs at random. The output of the selector is used to tune the
tunable delay lines. The delay lines can be tuned in steps of the chip time t
c
, from 0 to Nt
c
.
The transmitter can transmit after the transmission scheduling and tuning of the delay lines.
It is assumed that each stage takes one clock cycle to complete. Therefore, after 4 cycles
the result is available. For a clock speed of 100 MHz, this is 40ns. The tunable delay lines
can be tuned at speeds of up to 1 GHz, i.e., latencies of 1ns. Therefore, the latency of the
module is a very small fraction of 5μs.
The processing requirements of the hardware for transmission scheduling are within the
capability of current FPGA hardware. Each operation on a component of the vector needs
a separate hardware unit. There are 3 stages (adder, combinational logic and comparator)
which operate on the vectors. There are a total of 3 N N = 3N
2
units. For N = 100,
this corresponds to 30,000 hardware units. This is within the capabilities of current FPGAs,
which have up to 100;000 units. The tunable delay lines can be implemented using photonic
VLSI tunable delay lines [40], [20]. For a codeset with N = 100, at a chipping rate of 10 Gc/s,
the tunable delay lines must be tunable from 0 to 10ns in steps of 0.1ns. This corresponds to
delay lines of length 2m that can be tuned in steps of 2cm. These figures are well within the
range of photonic VLSI tunable delay lines.
171
The memory requirements for this algorithm are negligible. It has to store the result,
which is a delay in the range 0 to N. This is logN bits of memory which is 8 for N = 100. The
hardware may also need latches to store intermediate results or to store inputs. The latches
are not indicated in the diagram. The hardware may be integrated with the state estimation
hardware on a single FPGA.
7.2.6 Optimizing the state observation collection and state estimation module
This section discusses how the limitations of the state observation collection module may be
overcome. The required sampling rate of the ADC is equal to the chipping rate (10Gc/s). In
general, for an ADC, the maximum possible resolution reduces as the sampling rate increases.
High resolution, high sampling rate ADCs cost significantly more, occupy large die space,
and dissipate more power. Therefore, a low resolution has several advantages. The number
of components of the other hardware units (state estimation and transmission scheduling) and
their latency are also reduced.
With a resolution of 2 bits, the hardware can differentiate between 0, 1 and an overlap (a
minimum of 3 threshold detectors are needed for this). The output of the state observation
collection module is a 2 bit value (00 for a chip magnitude of 0, 01 for a chip magnitude of 1
and 10 for an overlap (a chip magnitude greater than 1)).
The consequence of this reduction of resolution is that the state observations and the es-
timated state have no information about the magnitude of an overlap. However, the threshold
scheduling algorithm can operate with such a reduced state estimate
1
. The algorithm needs
1
Other transmission scheduling algorithms such as codeword estimation may need a complete state estimate.
172
to know the number and the location of overlaps in the estimated state. It does not need the
magnitude of each overlap. Therefore, the threshold scheduling algorithm can use this re-
duced estimated state as input. The state estimation and transmission scheduling algorithms
and hardware remain unchanged.
This results in savings in the state observation collection hardware. While this does
not result in significant cost reduction in the state estimation and transmission scheduling
hardware, the size and latency of the circuitry reduces. Determining the extent of these gains
is an area for future research.
7.2.7 Ranging and synchronization modules
The function of the ranging module is to compensate for the difference in the bit clock at
the transmission and estimation points. It does this by adding a delay to the signal before it
enters the state observation collection module.
The state is estimated by collecting observations at the estimation point. This state is
used for transmission scheduling at the transmission point. Chapter 6 explained how the state
at the state estimation point can be used for scheduling at the transmission point only if they
are separated by an integral number of state spans. However, the separation may not be an
integral number of state spans because the fiber length may not necessarily be an integral
number of state spans. The ranging module compensates for this by adding a delay to the
signal before it enters the state observation collection module. It consists of a comparator
and tunable delay lines. When the node is booted up, the ranging module modulates the
optical CDMA transmitter to continuously transmit a ranging sequence. The sequence passes
173
through the coupler and returns on the receive fiber and passes through the delay lines. The
ranging module then compares a stored value of the transmitted signal with the signal at the
output of the delay lines. It tunes its delay lines until the sequences are identical, i.e., there
is no phase difference between the two. The signal from the receive fiber passes through
the delay lines before entering the state estimator. Care must be taken during layout of the
chips to ensure that the delay between ranging hardware output and the state estimator is
insignificant compared to a chip time or that it is compensated for. The ranging operation is
done at startup and periodically thereafter at intervals to be determined empirically. It may
be performed on a different wavelength from the data.
The function of the synchronization module is to detect the start of a frame destined for
the node. Several synchronization algorithms have been proposed for optical CDMA [29,
30]. These algorithms may be implemented in hardware as a separate block on the interface
card. Synchronization hardware may be constructed of Phase Locked Loops (PLLs), V oltage
Controlled Oscillators (VCOs) and other electronic components.
Note that the performance (latency) of ranging and synchronization may be affected by
multi-user interference. The interaction between the ranging/synchronization algorithms and
Interference Avoidance is an area for future work.
7.2.8 Optical CDMA transmitter
The function of the transmitter is to encode the packet to be transmitted using the codeword
of the receiver. The transmitter consists of tuning hardware, an encoder, and a modulator.
174
TDL
TDL
Control
TDL
Splitter
Coupler
Laser
Modulator
Data
Figure 7.12: Optical CDMA transmitter hardware implementation. The input is a stream of
bits. It modulates a stream of codewords being transmitted by the laser and encoder.
Figure 7.12 shows a typical transmitter. The encoder consists of a laser followed by a
splitter and w (in the figure w is 3) tunable delay lines. The output power of the laser is
around 10dBm. Every t
b
(10ns) the laser produces a pulse of width equal to the chip time
t
c
(0.1ns) The splitter splits the pulse and three pulses enter the tunable delay lines. Each
tunable delay line can be tuned from 0 to Nt
c
in steps of t
c
. The coupler couples the signals
from the delay lines and the codeword emerges from the coupler. For a codeset with N = 100
and w = 3 at a chipping rate of 10 Gc/s, this means 3 arrays of tunable delay lines each
of which can be tuned from 0 to 10ns in steps of 0.1ns. This corresponds to a length of 2m,
which can be tuned in steps of 2cm. The delay lines are tuned by switching the required delay
lines in or out of the path. Photonic VLSI tunable delay lines can be used for this [40], [20].
175
TDL
TDL
Control
TDL
Splitter Coupler
Threshold
detector
Photo-
detector
Hard-
limiter
Figure 7.13: Optical CDMA receiver hardware. The input is the signal on the optical fiber at
the chipping rate and the output is the received data at the bit rate.
The encoder produces a stream that consists of the repeated codeword. This stream is ex-
ternally modulated by the data. The modulator is based on a laser modulator. It is modulated
at the data rate (100 Mb/s) which is well within the capabilities of current modulators.
The encoder hardware polls the codeword buffer. It reads the codeword from the code-
word buffer and tunes the delay lines of the encoder. The tunable delay lines can be tuned at
speeds of up to 1 GHz. Therefore, the latency of the tuning is around 1ns.
7.2.9 Optical CDMA receiver
The function of the receiver is to decode the received signal and receive packets. The receiver
is a hard-limiting correlation receiver. Chapter 2 discussed the design of such a receiver.
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Figure 7.13 shows a diagram of the receiver. It consists of a hard-limiter, photodetector,
delay lines, and a threshold detector.
The optical hard-limiter [57] limits the power in each chip time to the power of a single
chip. The splitter splits the optical signal. The delay lines are designed such that the specific
chips corresponding to a particular codeword align in time at the coupler. The delay lines
are the same type as those described in the transmitter design. The coupler couples the
signals. The photodetector is a PIN diode. It converts incident light power to electric current.
The receiver sensitivity of the photodetector is around -20dBm. A threshold detector [57]
determines whether the signal exceeded the threshold which is set to w (in the figure, 3)
times the value of a single chips power. If the signal exceeds the threshold, a 1 is detected,
else a 0 is detected. The data is written to the receive buffer.
The network architecture is a Tunable Transmitter Fixed Receiver architecture. The re-
ceiver codeword may be hardwired into the NIC. However, to allow NICs to be used across
nodes, the receiver codeword is made tunable by providing tunable delay lines as shown.
This feature is not used to tune the receiver during network operation. Hardware to perform
link layer functions such as link layer address checking and error checking is placed after the
receive buffer.
7.2.10 Timing
A timing diagram based on the timing constraints discussed in the previous sections is shown
in Figure 7.14. The diagram shows a single cycle from arrival of the packet to transmission
scheduling to eventual transmission and merging. The first line shows the state estimation
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State
estimation
hardware
time
10ns
State estimation
hardware latency
50ns
Packet written
to transmit
buffer
Transmission
scheduling
hardware
latency
TDL tuning
latency
1ns
Transmission
scheduling
hardware
time
Residual chip time
(<10ns) + t
d
(<10ns)
Transmitter
time
Transmitter encoder
tuning latency
1ns
>5μs
Transmission Merge
Figure 7.14: Timing diagram (not to scale). The diagram shows the timing of events on a
NIC for a 10Gc/s network using a codeset of length N = 100, weight w = 3. The hardware
clock speed is 100MHz. The hardware design is as described in this section. A new state
estimate is generated every 10ns. On packet arrival, the transmission scheduling hardware
operates on its input and produces its result in 50ns. After tuning delays and the calculated
delay (t
d
), the packet is transmitted. The residual chip time (the time between the delay line
tuning and the start of the next hardware clock cycle) is also shown.
hardware. Every 10ns a new state estimate is written to the output. The second line shows the
operation of the transmission scheduling algorithm. When a packet arrives, the codeword and
state estimate are read and the algorithm takes 50ns to execute. After 50ns the tunable delay
lines are tuned (1ns) and the transmitter is interrupted. The third line shows the transmitter
operation. The transmitter is tuned on packet arrival (1ns) and the transmission is started
when the transmission scheduling hardware raises an interrupt.
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7.3 Conclusions
This chapter studied the performance of transmission scheduling under real world conditions.
The testbed operated under conditions of severe physical layer noise and had a limitation on
the offered load. The main sources of noise were the discrete components. The non-hard-
limiting receiver and the reduction of the receiver threshold further increased the impact of
noise. Under these conditions, threshold transmission scheduling with a very low threshold
improved the BER by two orders of magnitude. The laboratory testbed provided insight into
how a NIC for Interference Avoidance can be designed. This work indicates that a NIC based
on present day hardware and optical devices can implement Interference Avoidance.
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Chapter 8
Related work
Prior work related to Interference Avoidance may be classified based on the type of physical
layer:
Wired networks with a single channel.
Wired networks with multiple orthogonal channels.
Wired networks with multiple pseudo-orthogonal channels (Optical CDMA networks).
Wireless networks.
Chapter 3 discussed the differences in state and its properties in optical CDMA and single
channel, shared medium, wired, and wireless networks. This chapter extends that discussion
with descriptions of the media access control protocols and features that distinguish them
from Interference Avoidance.
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8.1 Wired networks with a single channel
A single channel network is a network where the transmission medium has only a single
channel, e.g., a frequency that is shared by all nodes on the network for transmission and
reception. Media access control for shared medium single channel networks has been classi-
fied [5] into the following types
Contention, e.g., Aloha [5], CSMA/CD [68], 802.11 [55]
Reservation, e.g., Token ring, token bus, DQDB [5], IEEE 802.14 [19], FDDI [5]
8.1.1 Contention protocols
In contention protocols (also called random access protocols) nodes contend for access to
the channel. Chapter 3 discussed the differences between optical CDMA and single channel
shared medium networks in the areas of state, interference, and correlation of state. To sum-
marize that chapter, state is a scalar value (Idle, Busy, or Collision). Collisions are mutually
destructive and the network exhibits state correlation at low speeds and low diameter.
Several media access control techniques have been devised to reduce the probability of
collisions. Among the well studied random access protocols are the Aloha mechanisms and
the Carrier Sense Multiple Access (CSMA) mechanisms. With the Aloha [5] protocol, the
maximum throughput is limited to around 18% because of collisions. Time slotted Aloha
reduces collisions and increases the throughput to 36%. Carrier sensing [68] is a mechanism
by which nodes first sense the medium to ensure that the medium is free before transmitting.
Collision detection [68] is a mechanism by which nodes continue to monitor the medium
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during transmission and abort if they detect a collision. Both mechanisms further reduce
collisions, raising the maximum throughput to around 80% [34]. Carrier Sensing and colli-
sion detection are effective for networks where the normalized propagation delay is low. As
the diameter of the network increases, or the transmission speed increases or packet size de-
creases, CSMA/CD becomes ineffective. To compensate for this effect Gigabit Ethernet [18]
has defined two mechanisms: Carrier Extension and Packet Bursting. In Carrier Extension,
the packet transmission is followed by transmission of a carrier signal that prevents other
nodes from transmission. In Packet Bursting, packets are buffered until a larger size packet
may be created. The larger size of the packet means that the normalized propagation de-
lay is reduced. Both mechanisms improve the throughput of Gigabit Ethernet. Interference
Avoidance may be regarded as another method of extending Carrier Sensing. It improves
performance by increasing the normalized propagation delay by a factor equal to the codeset
length N because of encoding (Appendix F).
In the case of a collision in a single channel network, several conflict resolution al-
gorithms [44] and splitting algorithms [5] have been proposed to resolve collisions. Each
mechanism results in some improvement in throughput and reduction of delay. Mechanisms
to reduce collisions by controlling when a node transmits (1-persistent, non-persistent, p-
persistent) [68] and algorithms to defer retransmissions (Binary Exponential Backoff (BEB),
Binary Logarithmic Arbitration Method (BLAM)) have also been proposed. The perfor-
mance analysis of Interference Avoidance in this work assumes 1 persistent sensing and that
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packets are dropped if they cannot be transmitted. The throughput, delay and stability per-
formance of Interference Avoidance with the other defer mechanisms is an area for further
research.
8.1.2 Reservation protocols
In reservation protocols, nodes are selected to transmit by a controller, either centralized or
distributed. The controller may be a central server, a broadcast channel, or a token. Ex-
amples of this type of access mechanism are Token ring/bus and polling protocols such as
DOCSIS/IEEE 802.14. Reservation MAC protocols [5] do not have a limitation on diameter
or speed of the network. However, reservation MAC protocols need a centralized scheduler
and a channel for reservation. The chief drawbacks of these networks are the management
of the scheduling mechanism and the access delay. Reservation protocols represent the other
end of the spectrum of media access control protocols where collisions are eliminated by
centralized control.
The DOCSIS 2.0 [19] specifications define a standard called Synchronous-CDMA for
the physical layer of a cable TV based network. It is based on a combination of TDM and
synchronous CDMA. Time is divided into minislots. The MAC protocol is a reservation type
protocol. Nodes reserve codewords to use in a time slot. In any given minislot, several nodes
on the network may transmit simultaneously using different CDMA codes. The codeset
specifies a set of 128 orthogonal codes. The specification limits the number of simultaneous
codewords. The disadvantages of this mechanism include the necessity for slot synchroniza-
tion, the use of fixed length codesets and a media access control based on limiting the number
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of codewords. This mechanism is similar to the Interference Avoidance techniques in that it
performs admission control and restricts the number of simultaneous users on the network
in a wired CDMA network. However, it is centralized and admission control is static (by
codeword assignment) and does not depend on the current state of the line. The application
of reservation protocol principles to optical CDMA is an area of open research.
8.2 Wired networks with multiple orthogonal channels
The bandwidth of a large bandwidth (high speed) physical medium may be divided into
slower channels. One way to do this is through Frequency Division Multiplexing (on high
speed optical LANs wavelengths can be used as channels). The data rate on each channel is
lower than the data rate of the single high speed channel. If the frequencies are sufficiently
far apart, the channels are orthogonal, i.e., they do not interference with each other. Carrier
sensing techniques can be used on the slower channels. [41] studied the use of Carrier
Sensing in multi-channel networks (MC-CSMA). State in a multichannel network is a vector.
Each component of the vector represents the state of a particular channel and can take on a
value of Idle, Busy, or Collision. Collisions on a channel are mutually destructive and the
network exhibits correlation of state if the channel has low normalized propagation delay.
MC-CSMA also extends the carrier sensing principle to high speed networks. The difference
is that Interference Avoidance operates on pseudo-orthogonal channels. In networks where
the cost of creating orthogonal channels is high (tunable lasers for WDM may be expensive),
Interference Avoidance may be preferred.
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8.3 Wired networks with pseudo-orthogonal channels
Optical CDMA is a physical layer with pseudo-orthogonal channels. Transmissions on dif-
ferent channels (codewords) interfere with each other. Interference Avoidance is a contention
based media access control for pseudo-orthogonal channel. It is carrier sensing applied to
a network with multiple interfering channels. Both mechanisms attempt to determine the
state of the medium and schedule packet transmissions to improve throughput. As discussed,
Interference Avoidance techniques can be reduced to the simpler Carrier Sensing and Aloha
protocols (Appendix F).
Other work in the area of MAC protocols for optical CDMA networks has focused on
codeword choice [63] and eliminating receiver collisions [74]. Shalaby [63] studied a ran-
dom access MAC protocol for optical CDMA. The protocol is based on pre-transmission
coordination between the sender and receiver before transmission. Codewords are selected
from a codeword pool with or without replacement. Codewords are randomly shifted before
use. A control packet is sent on a common control channel before the transmission. These
protocols control the use of codewords of a codeset, in contrast to the Interference Avoid-
ance techniques studied in this work that focus on throughput maximization by scheduling
transmissions.
8.4 Wireless networks
Chapter 3 discussed the differences between optical CDMA and single channel shared medium
wireless networks in the areas of state, interference, and correlation of state. To summarize
185
that chapter, state is a scalar value (depends on the channel conditions), collisions are non-
mutually destructive (transmissions may be captured) and the network exhibits very low cor-
relation. Depending on the receiver design, modulation and channel condition, the receiver
can capture [72] transmissions. Capture is the ability of a receiver to receive a packet even
if it overlaps with other packets. In a network that exhibits capture, a node can preserve it-
self by raising its transmission power, while possibly destroying other transmissions. While
capture is similar to the non-mutually destructive optical CDMA interference, the difference
is that it is controlled by power rather than delay. The subset of packets being destroyed
cannot be controlled. As mentioned in Chapter 3, a multi-packet reception model [69] has
been proposed for modeling the reception of a subset of packets.
This section looks at other techniques that exploit the non-destructive property or capture
through means such as centralized admission control.
8.4.1 Channel load sensing
Channel load sensing [1, 24, 70] is a packet radio system where nodes sense the channel
load and refrain from transmitting if the load exceeds a threshold. The load is measured by
estimating the number of simultaneous transmissions. One method of estimating the load
is to measure the received pseudo noise power. Abdelmonen et al. [1] analyzed this type
of protocol and developed throughput-delay curves and showed the effects of threshold on
channel backlog. Judge et al. [24] considered a similar scheme where the multiple access
interference threshold (number of simultaneous users) is tuned dynamically. They have ana-
lyzed such a scheme and found it can increase throughput. Toshimitsu et al. [70] examined a
186
channel load sensing protocol based on a slotted system where slot size was less than packet
size, thereby enabling the system to handle access timing delays (in the absence of such a
scheme, access timing delays normally cause a degradation of throughput). Note that in all
these schemes the media access is through admission control, i.e., the number of simultane-
ous users is controlled. Interference Avoidance differs from these by performing scheduling
rather than admission control. It may be noted that scheduling can be reduced to admission
control, e.g., by using a threshold scheduling algorithm with a low value of threshold.
8.4.2 Multi-user interference estimation
Multi-user interference estimation is used to estimate interference levels in wireless networks.
[75] uses a multi-timescale interference predictor to predict the occurrence of interference.
Depending on the level of interference, rate and admission control are used to control trans-
missions on the network. The time scales at which these algorithms work are usually on the
order of seconds (1 s). The algorithms depend on the self similar nature of traffic. In contrast,
state estimation makes no assumption on traffic characteristics and operates on smaller time
scales.
8.4.3 MIMO and CSIT
Multiple Input-Multiple Output (MIMO) is a technique in wireless communication. It ex-
ploits spatial diversity by using multiple transmit and multiple receive antennas. The receiver
receives signals on multiple channels. The signals can be processed to obtain the transmitted
data. If channel information is known (Channel State Information at the Transmitter (CSIT))
187
the diversity obtained by using multiple antennas can be exploited to improve performance.
State is conveyed to the sender by the receiver.
MIMO/CSIT attempts to replicate signal transmissions based on channel state informa-
tion to improve detection probability. This technique is similar in principle to state estimation
and transmission scheduling mechanisms described in this work. The difference is that Inter-
ference Avoidance attempts to schedule packet transmissions based on line state estimates to
minimize interference with other packets.
Adireddy [56] proposed a decentralized access protocol called transmission control that
uses channel state information to schedule packet transmissions. The channel state calculated
by a node in a slot interval is used to calculate the probability with which a node should trans-
mit a packet in the next interval. Results for this mechanism show that it stabilizes throughput
when compared to simple Aloha mechanisms. The differences between this mechanism and
Interference Avoidance are the state description. In transmission control, state is a single
valued variable which is used to decide a probability of transmission in a slotted system. In
Interference Avoidance, state is a vector used to calculate the transmission times.
8.4.4 Other related work in transmission scheduling
Shepard [64] proposed scheduling algorithms for wireless CDMA networks. A node de-
cides its transmission schedule and broadcasts it to surrounding nodes. Surrounding nodes
choose their schedules based on schedules they receive. Nodes synchronize their clock and
choose schedules to minimize interference. It was shown that this mechanism can reduce
loss of packet errors when compared to random access. Similar to Interference Avoidance,
188
this mechanism also schedules based on state of the medium. However, the difference is that
Interference Avoidance calculates state in a distributed manner whereas this mechanism uses
broadcasts of future schedules to propagate state information. Similar to this mechanism,
Chockler [8] considered adaptive algorithms to eliminate collisions in a wireless network.
The algorithms allowed nodes on the network to reach consensus about transmission sched-
ules.
8.5 Other relevant work in optical CDMA networks
Work in the area of optical CDMA can be classified into the following categories: Bit error
rate analysis, codeset design, effect of FEC and media access control. The work described
below is relevant to this work because it describes the behavior of optical CDMA under
different conditions or parameters. However, none of these focuses on the behavior of the
system in the high load regime.
8.5.1 Codeset design
The objective of most of the work in codeset design is to generate codesets with as large a
number of codewords as possible. The work has focused on construction of codesets whose
size approaches the Johnson bound. Chung et al. [10] described several algorithms to con-
struct OOCs. These constructions are for codes with maximum cross-correlation parameter
κ = 1. Chung and Kumar [9] described a method for construction of codes with κ = 2.
Several construction methods for OOCs are described in [45] and [11] among others. The
construction methods focus on codes with low cross-correlation parameter. This work has
189
shown that irrespective of the codeset parameters, at high offered load, throughput will col-
lapse without media access control (or other form of error handling).
8.5.2 Bit error rate performance analysis
In the area of optical CDMA network design, Salehi [57, 58] analyzed an optical CDMA
based network and developed expressions for the bit error rate of a network that uses codesets
with κ = 1. Azizoglu et al. [3] determined the error rate for codesets with κ = 2. They
showed that the bit error rate does not degrade significantly when κ is increased from 1 to
2. Shalaby [61, 62] examined the effect of two different cross-correlation parameters on the
throughput of an OOK-CDMA network. The result of the analysis was that under low load
conditions, throughput could be increased by increasing the κ from 1 to 2. All of the above
work considers the performance under low load conditions unlike Interference Avoidance,
which focuses on the high load regime.
8.5.3 Forward error correction
Hsu et al. [16, 17] analyzed the performance of slotted and unslotted optical CDMA packet
networks. They developed expressions for the throughput of the network and showed perfor-
mance can be improved using Forward Error Correction (FEC) codes and hard limiters. Lee
et al. [39] analyzed the performance of OOCs by assuming cross-correlation distributions to
be Gaussian. They used their analysis to compare the performance of different code con-
structions. They showed that under low load conditions the performance of optical CDMA
networks depends on the mean and variance of cross-correlation values. Muckenheim et
190
al. [46, 47] studied the effect of bit error probability on the packet error probability and sug-
gested the use of block codes to reduce packet errors. They also described a random delay
protocol to reduce the errors incurred during periods of high activity. Forward Error Cor-
rection may be added to Interference Avoidance to further reduce interference losses. The
impact of FEC on Interference Avoidance is an area for future work.
191
Chapter 9
Conclusions and future directions
This chapter discusses the contributions and conclusions of this work and future directions
that the research opens up.
9.1 Conclusions
Optical CDMA has been studied for years as an experimental technology for optical LANs.
Several researchers have proposed its use for different types of networks. The current effort
to deploy Fiber to the Home networks has provided motivation for studying those properties
of optical CDMA that may prove useful in an all optical access network.
However, optical CDMA has not yet reached the stage where it can be deployed at a
viable, high performance, scalable system. Several concerns have been expressed about the
use of spread spectrum on an optical link. The main concern is that the use of optical CDMA
results in low network throughput [38].
The contribution of this dissertation is the concept of Interference Avoidance. Interfer-
ence Avoidance mitigates the problem of throughput collapse through media access control.
192
Prior to this work, little work had been done in the area of media access control for opti-
cal CDMA. This work identified two properties exhibited by optical CDMA LANs: non-
mutually destructive interference and state correlation. These properties are exploited by
Interference Avoidance, which is a generalization of Carrier Sensing (Appendix F). This
led to the proposal of two mechanisms: State estimation and Transmission scheduling. This
study demonstrates that when all the configurable parameters (codeset, transmission schedul-
ing, and state estimation) are chosen correctly, throughput collapse under high offered load
can be prevented. Pure selfish, overlap section and threshold scheduling algorithms can ef-
fectively prevent throughput degradation at high loads when used with low codeset weights.
The algorithms performed within 15% of an optimal codeword scheduling algorithm. Optical
CDMA networks have a wide range of parameters at the physical and media access control
layers. The techniques presented in this work are effective tools that may be used to deter-
mine the optimal network configuration for a given condition. Based on the performance
analysis, the ideal parameter settings are determined to be the threshold scheduling algorithm
with a low threshold (< 0:3), continuous state estimation with a low number of observations
(< 10) and a long codeset length (> 100) and low weight (< 5).
While this work solves the throughput collapse problem, it represents a small piece in
a larger, complex, optical CDMA network architecture. In the wireless domain, CDMA
networks have been built by integrating several complex pieces which address many differ-
ent problems such as code acquisition, the near far problem, equalization etc. Similarly, an
optical CDMA network will need several other pieces before it can be considered a viable
technology. Firstly, the physical layer and link layer need extensive research. There are three
193
main areas where significant analytical and experimental work needs to be done. They are:
power control, ranging algorithms and synchronization algorithms. These three functions
represent the bare minimum needed, along with Interference Avoidance, to provide low la-
tency, low packet error rate access to a shared medium. Secondly, once these areas are well
understood, the interactions between the mechanisms need to be studied. For example, the In-
terference Avoidance mechanism may improve the serial search algorithm, leading to shorter
synchronization times. Cross layer or cross mechanism design can be used to optimize the
performance of the four mechanisms. Such a study represents a challenge in understanding
how the independently designed pieces will interact to impact overall throughput, latency
and other quality of service metrics. Finally, an integrated systems implementation of all
four mechanisms will be needed to study real world performance.
Once these three steps are complete, these four mechanisms will provide physical, link
and media access control layers that are scalable and fault tolerant. Network designers will
then be able to be integrate optical CDMA easily with higher layer protocols such as TCP/IP.
This design of optical CDMA does not constrain a designer to any particular technology, e.g.,
a higher layer could be circuit or packet switched. However, the network protocol most likely
to be used with this system is IP, with the any other needed functionality being provided
by higher layer transport and application layers. The resulting architecture will allow the
creation of low latency, low packet error rate access networks capable of providing variable
quality of service at a low cost.
194
9.2 Future directions
Three areas of future work have been identified: enhancements to Interference Avoidance
and application of Interference Avoidance mechanisms to two other domains: power control
and switch design.
9.2.1 Analysis of Interference Avoidance
This section discusses further improvements that may be made to Interference Avoidance.
9.2.1.1 Optimal transmission scheduling algorithms
An open area of research is whether new transmission scheduling algorithms may be defined
which close the gap between the proposed algorithms and the upper bounds shown. An opti-
mal transmission scheduling algorithm is an algorithm that maximizes the network through-
put. A transmission scheduling algorithm based on a cooperative strategy can improve the
throughput above that of pseudo-cooperative algorithms. One way of implementing a coop-
erative strategy is to use a decomposition algorithm that decomposes the state vector into its
constituent codewords. It may be possible to construct codesets that guarantee decomposition
of the state vector into unique codewords. To do this the codeset must consist of codewords
that are linearly independent. The design of such codesets is an open area of research. To be
useful, the algorithm must be able to perform decomposition in polynomial time (in terms of
codeset length).
195
9.2.1.2 Delay
Another area of research is study of delay and the effect of defer algorithms. When a node
cannot transmit a packet, it needs to defer transmission. Algorithms to defer transmissions
in single channel, shared medium networks have been studied extensively. Several backoff
algorithms [5] such as binary exponential backoff and binary logarithm arbitration method
have been proposed. Algorithms to control when a packet is transmitted have been classified
into 1, non- or p-persistent algorithms [68]. The effect of these algorithms on the access
latency of optical CDMA is an area for further study.
9.2.1.3 Fairness and quality of service
An issue not addressed in this work is fairness. As the distance from the coupler increases
the probability of errors in state estimation increases. Interference Avoidance could be unfair
to nodes that are at greater distances from the coupler. A quantitative study of fairness and
the tuning of parameters to ensure fairness are needed. Another issue that is not addressed
in this work is quality of service. Optical CDMA with variable codeset parameters is ideally
suited for providing differentiated service. State in such a system must be redefined to take
into account variable codeset parameters. A quantitative study of variable codeset parameters
and Interference Avoidance algorithms is an open area.
9.2.1.4 Error control
Some improvements that may be added to Interference Avoidance include Interference De-
tection [27]. In Interference Detection, nodes have a receiver to receive packets that they have
196
transmitted. If an error is detected during transmission due to interference, the transmission
is aborted. This is similar in principle to collision detection and could provide some perfor-
mance improvement. Another area is the design of Forward Error Correction optimized for
Interference Avoidance.
9.2.2 Architectural issues
The architecture of the network will need to address issues such as automated network con-
figuration, network management, and security. These issues have been studied in the context
of existing networks. However, optical CDMA may require that these issues be re-evaluated.
For example, this work assumed pre-existing configuration. Codewords were allocated to
nodes and the assigned codewords were static. In reality, a automated bootstrapping mecha-
nism for optical CDMA which handles codeword allocation may be needed. Such a mecha-
nism may need a central server or a broadcast mechanism or both. The architecture will need
to address such problems.
9.2.2.1 Other areas
The analysis discussed in this work made several assumptions for ease of analysis. One
assumption made was that synchronization phase losses were zero. An open area of research
is to understand the impact of Interference Avoidance on synchronization loss. Does the
line state created by this protocol improve or degrade the performance of synchronization
algorithms? Another area of research is a quantification of the maximum tolerable error
197
in scheduling. Another interesting area is the behavior of a heterogeneous network, i.e., a
network where nodes use a mixture of transmission scheduling algorithms or thresholds.
9.2.3 Power control in optical CDMA LANs
Power control is the mechanism used by nodes to tune the output power of their transmit-
ters. This work assumed that the power transmitted by each node on the network is the same.
Also, the power at the output of the coupler is the same for all users. In reality, this may not
be true. Transmitter power constantly fluctuates, the fiber attenuates the signal at 0.2dB/km
and there is loss in the coupler. Therefore, an optical CDMA network needs a power control
mechanism. State estimation could be used as part of a distributed power control estimation
algorithm where the nodes on the network use the state estimate to determine how many
nodes are transmitting and whether the transmitter power needs to be adjusted before trans-
mission. Further experiments and analysis are needed before it can be determined whether
this is feasible.
9.2.4 Optical CDMA switch design
Optical CDMA has been proposed as a technology for switch design [15], [25]. The primary
use is to avoid output port contention in an all optical switch. Note that although optical
CDMA multiplexing eliminates contention, it reduces the data rate. Though it eliminates
output port contention, interference still causes packet errors at the output port. Transmission
scheduling may be used at the output port to schedule packet transmission at the output port,
thus reducing error losses. Delay lines are needed to buffer packets that cannot be scheduled.
198
Interesting areas to study include the comparison of the performance of this type of switch
to a unbuffered switch, a study of the trade-offs between the number and length of the delay
lines and the trade-off between output port contention and data rate.
199
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Appendix A
State representation
This appendix defines a representation for the state of the line. The representation allows
analysis of the transmission scheduling algorithms.
Consider a shared medium optical CDMA network where multiple nodes are transmitting
packets simultaneously. Figure A.1 shows a snapshot of the codewords on the line for a
network using a codeset (N, w, κ) = (8, 3, 3). The state of the line is shown below the
codewords. Below the state, the chips of the state have been rearranged for convenience.
Chip positions with overlapping ‘1 chips’ have been moved to the right, chip positions with
‘0 chips’ have been moved to the left. The state of the line can be divided into three sections:
the overlap section, i.e., the chip positions with overlapping chips, the ones section, i.e., the
section with ‘1 chips’ and the zeroes section, i.e., the section with ‘0 chips’.
The state of the line can be represented by a pair (n
0
, n
1
) where n
0
< N and n
1
< N. n
0
is the length of the zeroes section and n
1
is the length of the ones section. The size of the
overlap section is n
ov
= N - (n
1
+ n
0
). The term state refers to this reduced representation of
the state of the line.
206
0 1 0 1 0 0 1 0
1 1 0 0 0 1 0 0
C2
C1
0 0 1 1 0 0 0 1
1 0
0
C0
1 0 3 2 1 0 0 2
State of the line
3 2 2 1 1 0 0 0
State rearranged
One’s
section
(length = 2)
Overlap
section
(length = 3)
Zero’s
section
(length = 3)
Figure A.1: State can be represented mathematically by a pair (n
0
, n
1
) where n
0
is the size of
the zeros section and n
1
is the size of the ones section.
The state of the line could be any value (n
0
, n
1
) where 0 n
0
N and 0 n
1
N. A
valid state is defined as a state where n
0
+ n
1
N. All other states are invalid. The initial
state is defined as the state of the line when no codewords are on the line, i.e., (N;0). A
reachable state is defined as a state that can be reached from the initial state by a series of
state transitions due to packet arrivals. The initial state (N;0) is, by definition, a reachable
state. The set of reachable states depends on the transmission scheduling algorithm.
When there are no codewords on the line, i.e., no node is transmitting packets, the state
at a point on the line is the initial state, (N, 0), i.e., N zeroes and 0 ones and overlaps. The
207
arrival of a single codeword adds w ‘1 chips’ to the state of the line and the state changes.
This is called a state transition.
Let the start state of a state transition be ( f rom
n0
, f rom
n1
) and the destination state be
(to
n0
, to
n1
). A state transition may be caused only by a packet arrival or departure
1
. When
a codeword is added to the line, w ‘1 chips’ are added. A ‘1 chip’ could go to the zeroes
section, ones section or the overlap section. Let the number of ‘1 chips’ going to the zeroes,
ones and overlap sections be c
0
, c
1
and c
overlap
respectively.
Then:
c
0
= f rom
n0
to
n0
c
1
= to
noverlap
f rom
noverlap
c
overlap
= w(c
0
+ c
1
)
A valid transition is defined as a transition where the start state and the destination state
are valid, reachable states and:
c
0
0
c
1
0
c
overlap
0
An admissible transition is defined as a valid transition which is permitted by the trans-
mission scheduling algorithm. A same state transition is defined as a transition from a state
to itself.
1
ON-OFF keyed modulation does not affect the state. The state is defined as the sum of codewords when all
codewords are transmitting 1 data bits.
208
N, 0
N-w, w
N-w-1, w-1
N-w-2,w-2
N-w-1, w
N-w-1, w-1
Figure A.2: The initial few states of a state transition diagram.
For example, Aloha-CDMA allows a transition from any state to any state, with the con-
straint that w chips must be added to the line during an arrival. A selfish algorithm allows
only those transitions where at least one ‘1 chip’ goes to the zeroes section, i.e., c
1
> 0.
A state transition diagram can be drawn based on the admissible transitions. Figure A.2
shows a portion of a state transition diagram. Because of the large size of the diagram, only a
few states are shown. Invalid states are not indicated in the diagram. The diagram shows the
initial state (N;0) and state transitions to a few states.
209
Appendix B
Packet error rate and number of codewords multiplexed on the
line
This appendix explains how to calculate the probability of error and the number of codewords
on the line when the system is in state (n
0
, n
1
).
B.1 Packet error rate
The probability of error depends on the state. For a state (n
0
, n
1
), the probability of error is the
probability that for any codeword, all its ‘1 chips’ overlap with other ‘1 chips’ or overlaps. To
calculate the probability of error, the locations of the ‘1 chips’ in the codeword are assumed
to be chosen uniform randomly, i.e., the codeset construction uses κ = w. For any selfish
algorithm, in state (n
0
, n
1
), if N
online
(n
0
;n
1
) codewords are multiplexed at a point on the line,
then at most n
1
codewords are transmitted without error. Therefore, the probability of packet
error can be approximated by the expression below:
210
For valid states:
P
e
(n
0
;n
1
) = 0 when N
online
(n
0
;n
1
) n
1
=
(N
online
(n
0
;n
1
) n
1
)
N
online
(n
0
;n
1
)
otherwise
For invalid states:
P
e
(n
0
;n
1
) = 0
Note that a packet is considered lost if there are other codewords on the line whose chips
overlap with all w chips of the packet’s codeword. The other codewords on the line are as-
sumed to be ON, i.e., transmitting 1 bits although that may not necessarily be true. Therefore
the calculated packet error rate is the worst case packet error rate.
B.2 Number of codewords multiplexed on the line
The state transition diagram is used to calculate the number of codewords multiplexed at a
point on the line.
Consider a graph where the nodes of the graph are the states and each state transition due
to an arrival forms a directed edge (neglect same state transitions). Appendix D shows that
for any selfish transmission scheduling algorithm, this graph is a directed acyclic graph. In
the graph, each edge represents the arrival of exactly one packet. Therefore the number of
codewords on the line for a state (n
0
, n
1
) depends on the number of edges from the initial
state (N;0) to (n
0
, n
1
). Note that there may be several paths (possibly of different lengths)
211
between the initial state and the desired state. Because the graph is a DAG, the length of the
longest path from the initial state to that state is an upper bound on the number of codewords
on the line when the line is in that state. The length of the shortest path from the initial state
(N, 0) to that state is a lower bound on that number. The length of the longest path is an upper
bound on that number.
1
Because the graph is a DAG, both the shortest and the longest path
may be calculated in polynomial time [13].
Therefore, for valid states:
N
online
(n
0
;n
1
) ShortestPath((N;0);(n
0
;n
1
))
N
online
(n
0
;n
1
) LongestPath((N;0);(n
0
;n
1
))
For invalid states:
N
online
(n
0
;n
1
) = 0
1
In a real system the actual number of codewords on the line is between these two values and its distribution
depends on the transmission scheduling algorithm. This work assumes the number of codewords multiplexed on
the line is equal to the lower bound. Therefore, it is a worst case assumption and the calculated throughput is a
lower bound on the achievable throughput.
212
Appendix C
Equilibrium state probabilities
The performance of the transmission scheduling algorithms depends on the equilibrium state
probabilities. This section calculates the equilibrium state probabilities.
C.1 Assumptions
As mentioned earlier it is assumed that perfect state estimation is possible by all nodes and
the only reason for a state transition is an arrival or a departure of a packet.
Packet arrivals are assumed to be Poisson arrivals and packet lengths are exponentially
distributed. Assume that codeword selection is random, i.e., the particular codeword that
arrives is uniformly chosen from the codeset. Under this assumption, the probability of tran-
sitioning to a particular state on an arrival is dependent only on the current state and not on
the path taken to reach that state. However, the probability of transitioning to a particular
state on a departure does not have this property. On a departure the system returns to a state
that depends on the remaining packets multiplexed on the line. However, if it is assumed that
the probability of departure to a state is proportional to the rate of arrival from that particular
213
state then the next state is dependent only on the current state and not on the path taken to
reach that state. If the probability of departure to a state is proportional to the probability of
arrival then on an average the trajectory followed by a departure follows that of an arrival.
Under these circumstances, the state diagram for arrivals and departures is a Markov chain.
Equilibrium probabilities may be found by solving the balance equations for the system.
The following are the steps needed to determine the rates of transition between two states
( f rom
n0
; f rom
n1
) and (to
n0
;to
n1
): First, it must first be determined whether the transition is
admissible or not. Then the probability of an arrival or departure transition between the two
state must be calculated. This probability can be used to determine the transition rates. The
next few sections describe how to determine whether a transition is admissible and if it is,
how to calculate the transition probabilities and write the balance equations.
C.2 Admissible transmissions
This section describes how to identify admissible state transitions given a codeset and a trans-
mission scheduling algorithm.
1
C.2.1 Aloha-CDMA
For Aloha-CDMA, all transitions are admissible.
1
It is assumed that if a packet cannot be transmitted upon arrival, the system undergoes a same state transition
and the packet is dropped. Note that during a same state transition the number of packets on the line does not
change. Only packet arrivals which arrive at times instants that allow admissible transitions are allowed on the
line.
214
C.2.2 Pure selfish scheduling
A pure selfish algorithm schedules transmission such that at least 1 ‘1’ chip goes to the zeroes
section.
Therefore a transmission is admissible if,
c
0
1
C.2.3 Threshold scheduling
The threshold scheduling algorithm schedules transmission such that at least 1 ‘1’ chip goes
to the zeroes section and the number of overlaps (the size of the overlap section) is below a
threshold. The threshold can be expressed as a fraction of the length of the codeword α.
Therefore, a transmission is admissible if:
c
0
1
to
noverlap
αN
C.2.4 Overlap section scheduling
The overlap section scheduling algorithm schedules transmission such that at least 1 ‘1’ chip
goes to the zeroes section and the number of overlaps (the size of the overlap section) is
below the number of ones (the size of the ones section).
215
Therefore, a transmission is admissible if:
c
0
1
to
noverlap
to
n1
C.3 Arrival state transition probabilities
The arrival and departure probabilities for state transitions can be calculated, based on whether
a transition is admissible or not. Two matrices are generated: an arrival probability ma-
trix and a departure transition matrix whose elements are the state transition probabilities,
P
arrival
(n
0
;n
1
;s
0
;s
1
) and P
departure
(n
0
;n
1
;s
0
;s
1
).
The arrival rates from a state ( f rom
n0
; f rom
n1
) to a state (to
n0
;to
n1
) can be calculated as
below.
For an admissible transition:
P
arrival
( f rom
n0
; f rom
n1
;to
n0
;to
n1
) = N
admitted
=N
total
where:
N
admitted
=
0
B
B
@
f rom
n0
c
0
1
C
C
A
0
B
B
@
f rom
n1
c
1
1
C
C
A
0
B
B
@
f rom
noverlap
c
overlap
1
C
C
A
N
total
=
0
B
B
@
N
w
1
C
C
A
216
For a non-admissible transition:
P
arrival
( f rom
n0
; f rom
n1
;to
n0
;to
n1
) = 0
For a same state non-admissible transition:
P
arrival
(s
0
;s
1
;s
0
;s
1
) = 1 ∑
N
n
0
=0
∑
N
n
1
=0
P
arrival
(s
0
;s
1
;n
0
;n
1
)
((n
0
;n
1
)6= (s
0
;s
1
))
C.4 Departure state transition probabilities
As described in the assumptions, the departure probabilities from one state to another state
are proportional to the arrival rates into the state. Therefore:
P
departure
(s
0
;s
1
;d
0
;d
1
) =
P
arrival
(d
0
;d
1
;s
0
;s
1
)
∑
N
n
0
=0
∑
N
n
1
=0
P
arrival
(n
0
;n
1
;s
0
;s
1
)
C.5 Balance equations
When the system is in equilibrium, the flow into any state must equal the flow out of the state.
Therefore, for a valid, reachable state (s
0
, s
1
):
(λ + N
online
(s
0
;s
1
)μ) P
state
(s
0
;s
1
) = ∑
N
n
0
=0
∑
N
n
1
=0
P
state
(n
0
;n
1
)λP
arrival
(n
0
;n
1
;s
0
;s
1
)
+ ∑
N
n
0
=0
∑
N
n
1
=0
P
state
(n
0
;n
1
)N
online
(n
0
;n
1
)μP
departure
(n
0
;n
1
;s
0
;s
1
)
217
Also,
N
∑
n
0
=0
N
∑
n
1
=0
P
state
(n
0
;n
1
) = 1;
These equations can be solved for the equilibrium state probabilities P
state
(s
0
;s
1
). The
variables n
0
and n
1
can take on values in the range [0;N], subject to n
0
+ n
1
N. Therefore,
there are N(N + 1)=2 states. The analysis above provides a system of N(N + 1)=2 linear
equations. The system of linear equations is sparse because the number of states between
which admissible transitions occur is much less than the total number of pairs of states. The
equations can be solved rapidly using mathematical tool sets.
218
Appendix D
Arrival state transition diagram
Lemma: For any selfish transmission scheduling algorithm, the directed graph constructed
from the arrival state transition diagram is acyclic.
Consider a directed graph where the vertices of the graph are the states and each state
transition due to an arrival forms a directed edge.
1
. Assume there exists a cycle in the graph.
Let the sequence of states in the cycle be
(N
0
0
;N
0
1
);(N
1
0
;N
1
1
)::::::::::::(N
i
0
;N
i
1
);(N
0
0
;N
0
1
)
By the definition of a selfish scheduling algorithm, for any admissible transition:
c
0
1
Consider any edge of the graph. The edge represents an admissible transition. Let the vertices
be the states (N
i
0
;N
i
1
)) and (N
i+1
0
;N
i+1
1
).
1
Neglect same state transitions (for selfish scheduling, same state transitions do not represent arrivals to the
line)
219
Therefore,
N
i
0
N
i+1
0
= c
0
Therefore,
N
i
0
> N
i+1
0
Therefore, N
0
0
> N
1
0
>:::::::> N
n
0
> N
0
0
which is a contradiction. Therefore the graph cannot
contain a cycle. Therefore it is a directed acyclic graph.
220
Appendix E
Throughput of Centralized Perfect Scheduling
This section determines the throughput of Centralized Perfect Scheduling (CPS). It is shown
that its throughput is an upper bound to the performance of any selfish transmission schedul-
ing algorithm. The proof is organized into three parts. First, Centralized Perfect Scheduling
is defined. Next, it is shown that the throughput of this algorithm is greater than or equal to
that of than any selfish transmission scheduling algorithm. Finally, it is shown that the state
model of this algorithm corresponds to a birth death process easily modeled by an M=M=1=K
queuing system where K = N(w1). An expression for the average throughput of the cen-
tralized perfect scheduling is derived.
Consider a scheduling algorithm that operates as follows. Nodes can do perfect state es-
timation and perfect line state decomposition, i.e., the line state can be decomposed uniquely
into codewords on the line. Transmitters and receivers can both be tuned instantaneously to
any codeword. When a packet is to be transmitted, there is a centralized mechanism (such as
a centralized scheduler or control channel) which coordinates the allocation of a codeword
221
and a transmission delay to be used for transmission. The allocation is such that the codeword
and delay ensure that
The codeword does not destroy itself or any other codeword on the line, i.e., the event
is always a Preserve self/Preserve others event.
It maximizes the number of codewords that can be added to the line after this transmis-
sion.
On arrival of the first codeword, any codeword may be allocated. The state of the line is
now (N w, w) When the second packet arrives, it is allocated a codeword such that exactly
one ‘1 chip’ goes to the zeroes section and the remaining w 1 chips overlap with the other
chips on the line. Thereafter, any codeword that is added has exactly one chip that goes to
the zeroes section and the remaining w 1 go to the overlap section. This continues until no
more codewords can be added. When this happens there are N(w 1) codewords on the
line and the state is (0;N(w 1)). No further codewords are allowed on the line until a
codeword departs. The next packet that arrives is allocated the codeword that departed and
so on.
Consider a time instant case when the system (all nodes in the network) has N
offered
packets to transmit. Under these condition, the transmission scheduling algorithm allows
N
online
packets on the line and the system enters a particular state (N
0
;N
1
). The throughput
of the system depends on the number of codewords on the line N
online
and the probability
of error P
e
in that state. Two cases are considered: when N
offered
> N(w 1) and when
N
offered
N(w 1).
222
E.1 N
offered
N(w 1)
In this case for CPS:
N
online
= N(w 1)
P
e
= 0
Therefore:
Th = (N(w 1))=N (E.1)
For any selfish transmission scheduling algorithm, when a codeword is added to the line
the size of the zeroes section is reduced by at least one. The first codeword reduces it by w.
Therefore:
N
online
N N
0
(w 1)
P
e
0
T h ((N N
0
(w 1))=N)(1 P
e
) (E.2)
223
From inspection of results E.1 and E.2, it can be seen that the throughput of the Central-
ized Perfect Scheduling is greater than or equal to the throughput of any other selfish trans-
mission scheduling algorithm. The maximum throughput occurs in state (0;N (w 1)).
The value of the maximum throughput is (N(w 1))=N.
E.2 N
offered
< N(w 1)
In this case for CPS:
N
online
= N
offered
P
e
= 0
Therefore:
Th = (N
offered
)=N (E.3)
For any other selfish transmission scheduling algorithm, the number of codewords on the line
can be at most N
offered
and the probability of error is greater than or equal to zero.
N
online
N
offered
P
e
0
224
Therefore:
Th ((N
offered
)=N)(1 P
e
) (E.4)
From inspection of results E.3 and E.4, it can be seen that the throughput of the Centralized
Perfect Scheduling is greater than or equal to the throughput of any other selfish transmission
scheduling algorithms.
For any number of packets N
offered
that the system has to transmit, the Centralized Perfect
Scheduling results in the transmission of the maximum number of error free packets, i.e., its
throughput is greater than any other selfish algorithm.
The centralized perfect scheduling goes through a sequence of states (N;0), (N w;w),
(N(w 1);2), (N(w 2);3).....(0, N(w 1)). The state transition diagram reduces
to a simple birth death Markov chain. It forms an M=M=1=K queuing system where K =
N(w 1). The state probabilities may be found easily using well known results [33]. The
throughput is given by:
Th =
n=K
∑
n=0
p(n) n=N
where p(n) is the probability that n packets are on the line,
p(n) =
(1(λ=μ))(λ=μ)
n
1(λ=μ)
(K+1)
225
Th =
n=K
∑
n=0
(1(λ=μ))(λ=μ)
n
1(λ=μ)
(K+1)
n=N
=
K(λ=μ)
K+2
(K + 1)(λ=μ)
K+1
+(λ=μ)
N(1(λ=μ))(1(λ=μ)
K+1
)
226
Appendix F
Interference Avoidance is a generalization of Carrier Sensing and
CDMA
Interference Avoidance is a generalization of Carrier Sensing. Carrier Sensing has been stud-
ied in single channel shared medium wired networks and wireless networks. A node senses
the state of the network (idle, busy or collision) and schedules its transmission if the state is
idle. Carrier Sensing is effective if the normalized propagation delay is low. The normal-
ized propagation delay of a network a is the ratio of the propagation delay of the network
to the packet transmission time. Carrier sensing can significantly reduce collision losses, for
Protocol Length of Weight of State estimation Transmission scheduling
codeset N codeset w algorithm algorithm
Aloha-CDMA Any Any None Pure threshold
scheduling th = ∞
Aloha 1 1 None Pure threshold
scheduling th = ∞
CSMA 1 1 On demand, Pure selfish
n
e
= 1 scheduling
Table F.1: Reduction of Interference Avoidance to the Aloha, Aloha-CDMA, and CSMA
protocols.
227
1
2
3
4
5
6
7
8
9
10
Codeset weight
10
20
30
40
50
Codeset length
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Normalized network
throughput
Figure F.1: The performance of Interference Avoidance vs. codeset length and codeset
weight. The results are based on simulation. The graph shows the normalized network
throughput at a normalized offered load of 1 and normalized propagation delay of a = 0.
The traffic model is Poisson arrivals, exponentially distributed packet sizes.
certain values of a (0:01 < a < 0:2) [68]. For a network of speed 100Mb=s, packet length
1000 bytes, diameter 4000m a = 0:1. As normalized propagation delay increases (the speed
of the network or the diameter of the network increases, or packet size decreases), the corre-
lation of state reduces and the efficiency of carrier sensing decreases. For an optical CDMA
network the normalized propagation delay is reduced by a factor of N. For a network of
diameter 4000m, chipping rate 10 Gc/s, packet length 1000 bytes, codeset length N = 100,
a = 0:25. This is the reason why Interference Avoidance works. The codeset length increases
the normalized propagation delay of a packet. This in turn increases the correlation of state.
By changing the value of four parameters: the codeset length N, the codeset weight w, the
state estimation algorithm and the transmission scheduling algorithm, Interference Avoidance
can be reduced to Aloha, Aloha-CDMA or to CSMA. As the codeset length N is reduced,
228
Interference Avoidance reduces to Carrier Sensing. Table F.1 shows the values of N and w
for different media access control algorithms.
Figure F.1 shows the throughput of Interference Avoidance with selfish scheduling for
different values of codeset length N and codeset weight w and a normalized propagation
delay of a = 0. As N and w tend to 1, Interference Avoidance reduces to Carrier Sensing.
The throughput at N = 1;w = 1 is equal to 0.5. This is the value predicted for Carrier Sensing
with non persistent sensing [68].
229

Abstract (if available)

Abstract This work proposes Interference Avoidance, a contention media access control protocol for optical Code Division Multiple Access (CDMA) Local Area Networks (LANs). Optical CDMA is a direct sequence spread spectrum technology for multiplexing transmissions on an optical fiber. When used as the physical layer of a LAN, its throughput tends to zero at high offered load because of multiuser interference. Interference Avoidance prevents this throughput collapse of optical CDMA networks at high offered load.

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Asset Metadata

Creator Kamath, Purushotham V. (author)

Core Title Media access control for optical CDMA networks through interference avoidance

School Andrew and Erna Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Computer Engineering

Publication Date 10/07/2006

Defense Date 05/30/2006

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag CDMA,media access control,networks,OAI-PMH Harvest,optical

Language English

Advisor Bannister, Joseph A. (committee chair), Touch, Joseph D. (committee member), Willner, Alan E. (committee member)

Creator Email pkamath@isi.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-m88

Unique identifier UC1167758

Identifier etd-Kamath-20061007 (filename),usctheses-m40 (legacy collection record id),usctheses-c127-20780 (legacy record id),usctheses-m88 (legacy record id)

Legacy Identifier etd-Kamath-20061007.pdf

Dmrecord 20780

Document Type Dissertation

Rights Kamath, Purushotham V.

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Repository Name Libraries, University of Southern California

Repository Location Los Angeles, California

Repository Email cisadmin@lib.usc.edu