Techniques for increasing number of users in dynamically reconfigurable optical code division multiple access systems and networks

PDF

Download

Open document

Flip pages

Download a page range

Download transcript

Copy asset link

Request this asset

Request accessible transcript

Transcript (if available)

Content
TECHNIQUES FOR INCREASING NUMBER OF
USERS IN DYNAMICALLY RECONFIGURABLE
OPTICAL CODE DIVISION MULTIPLE ACCESS
SYSTEMS AND NETWORKS

by
Poorya Saghari
____________________________________________________

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
(ELECTRICAL ENGINEERING)

December 2006

Copyright 2006 Poorya Saghari

ii

Dedication

To my parents, and dearest friend Sara
for their everlasting love and support.

iii

Acknowledgements

I would like to thank my academic advisor and dissertation committee chairman, Dr.
Alan E. Willner, for his support, guidance, and mentorship throughout my graduate
studies. I was given the opportunity to work on various projects freely, as Dr.
Willner provided complete academia and financial support needed to accomplish
each project. I would also like to share my gratitude with our collaborators in
OCDMA projects, Professor Kumar who helped me understand code and system
design of OCDMA systems; Professors J. Touch and J. Banister who collaborated in
design of the optical CDMA networks; and Professors P. Dapkus and J. O’Brian for
their collaboration with designing OCDMA encoder and decoders. I would also like
to extend my great appreciation to Professor J. O’Brian for his support as my
dissertation and qualifying examination committee member. I would like to thank
Professor. Ming-Deh Huang who joined my dissertation committee as n outside
member; I would also like to thank Professor. J. Touch, Professor. R. Gagliardi, and
Professor. Z. Zhang for their support and guidance during qualification examination.
I would also like to express my deepest gratitude to Professor H. Moradi who gave
me the opportunity to work as his lab assistant throughout my graduate years at
USC.
I would like to pay my heartiest thanks to my colleague, Dr. Reza Omrani,
for his greatest support and invaluable help throughout my graduate career. We

iv
developed most of the analytical results presented in this thesis together. I would like
to thank my several collaborators, in particular, Dr. Purushotham Kamath from ISI
who helped me significantly in the network projects, and Dr. Andrew Stapleton from
MPDG group for his help in the phase encoding projects.
I would also like to express my gratitude to my collaborators from Optical
Communication Laboratory (OCLAB), in particular, Dr. Reza M. Motaghian who
inspired and encouraged me to join OCLAB when I first came to USC; Dr. John
McGeehan who helped me with my first experimental project; Dr. Paniz Ebrahimi
who always inspired me with her insightful discussions; and Dr. Saurabh Kumar for
his great support, comradeship and invaluable discussions throughout my graduate
career. I am grateful to all my colleagues in the OCLAB for their contributions to
each and all the projects, which made it possible for me to achieve desired results.
Last but not least, I would like to thank those who have in many ways
contributed to the success of my academic endeavors. They are Milly Montenegro,
Mayumi Thrasher, Gerrielyn Ramos, Tim Boston , and Diane Demetras.

v
Table of Contents

Dedication ...................................................................................................................ii
Acknowledgements................................................................................................... iii
List of Tables ............................................................................................................vii
List of Figures......................................................................................................... viii
Abstract....................................................................................................................xvi
Chapter 1: Introduction ...........................................................................................1
Chapter 2: Optical CDMA .......................................................................................4
2.1 History..............................................................................................................4
2.2 Optical Code Division Multiple Access (O-CDMA) Systems ........................6
2.3 Optical orthogonal codes ...............................................................................11
2.4 Two-dimensional optical Orthogonal Codes .................................................14
2.5 Error in O-CDMA system..............................................................................17
Chapter 3: Analytical Interference Model for 2-Dimensional (Time-
Wavelength) Asynchronous O-CDMA Systems using Various Receiver
Structures..................................................................................................................20
3.1 Analytical Interference Model for 2-Dimmensional O-CDMA Systems ......20
3.2 O-CDMA System Structure ...........................................................................24
3.3 Interference Model.........................................................................................27
3.4 Probability Distribution of the interference ...................................................35
3.5 System Performance.......................................................................................38
3.6 Spectral Efficiency.........................................................................................45
Chapter 4: Experimental and Theoretical Analysis of the Optimum
Decision Threshold for Varying Numbers of Active Users in a 2D Time-
Wavelength Asynchronous O-CDMA System.......................................................49
4.1 O-CDMA Plug and Play Networks................................................................49
4.2 Effect of varying threshold in an O-CDMA system ......................................53
4.3 Monitoring the number of active users in an O-CDMA system....................67

vi
Chapter 5: M-ary Modulation in O-CDMA Systems to Increase the
Spectral Efficiency ...................................................................................................72
5.1 Experimental Demonstration of Code Position Modulation in 2-D O-
CDMA Systems .........................................................................................................72
5.1.1 Code-Position Modulation.....................................................................74
5.1.2 Experimental Results.............................................................................76
5.2 Analytical Model for PPM O-CDMA Systems .............................................81
5.2.1 Mathematical Model..............................................................................82
5.2.2 Performance Analysis............................................................................88
5. 3 Demonstration of Double Pulse Position Modulation (2-PPM) in Time-
Wavelength Optical CDMA Systems ........................................................................92
5.3.1. 2-PPM Concept......................................................................................92
5.3.2 2- PPM Experimental Result..................................................................95
5.3.3 10GB/S 2-PPM......................................................................................97
5.4 Differential-Pulse-Position-Modulation (DPPM) in OCDMA Networks
to Achieve Higher Data-Rate/User ..........................................................................101
5.4.1 Differential-Pulse Position modulation (DPPM) .......................................102
5.4.2 Experimental Setup and Results ..........................................................104
Chapter 6: O-CDMA Networks...........................................................................108
6.1 Optical CDMA Networks ............................................................................108
6.2 Variable Quality of Service to Increase the Number of Users in an O-
CDMA Network.......................................................................................................110
6.2.1 Concept of variable Quality of Service................................................112
6.2.2 Analytical Interference Model For Variable QoS................................113
6.2.3 Analysis of the network performance ..................................................118
6.2.4 Experimental Results...........................................................................119
6.3 Variable Bit Rate Optical CDMA Networks Using Multiple Pulse
Position Modulation.................................................................................................122
6.3.1 Concept and Experimental Setup.........................................................125
6.3.2 Results and Discussion.........................................................................128
6.4 Experimental Demonstration of an Interference-Avoidance-Based
Protocol for O-CDMA Networks.............................................................................130
6.4.1 Interference Avoidance........................................................................132
6.4.2 Experimental Result.............................................................................136
Chapter 7: Conclusion ..........................................................................................141
References ...............................................................................................................144

vii
List of Tables

Table 2.1. Code size for various 1 dimensional code sets using Johnson bounds.....13
Table 2.2. Code size for various 2 dimensional code sets using Johnson bounds.....16
Table 2.3. Code size for various 2 dimensional code sets using Johnson bounds.....17

viii
List of Figures
Fig 2.1. Using fiber Bragg grating as an O-CDMA encoder. Stack of pulses in
different wavelength is fed to the FBG array. Each wavelength is then
reflected at by its respective grating. The spacing between different FBG’s in
the array are designed to provides the appropriate delay between chips.............9
Fig 2.2. Schematic of two dimensional O-CDMA system using Mux/Demux and
tunable delay lines as an encoder/decoder system. Stacks of pulses are split
using the Demux. Each pulse is delayed appropriately using the optical delay
line......................................................................................................................10
Fig 2.3. Schematic of an optical CDMA system. The input bit is fed through the
2D O-CDMA encoder. The output of the encoder is the 2D O-CDMA
matrix. All users are multiplexed through a star coupler and transmitted
through output fibers. The user with the matched decoder can line up the
autocorrelation peak and recover the data by thresholidng. An unmatched
decoder only sees MAI.......................................................................................11
Fig. 2.4. Example of sub-optimal two-dimensional codes. This code is using 3
wavelength and 8 chip times and can support 7 codes.......................................15
Fig. 2.5 Example of MAI, user “1” is the user of interest and user 2-4 are acting
as interferes ........................................................................................................19
Fig. 3.1. Schematic of the conventional O-CDMA system: Encoded signal of
desired user along with interference is fed to the decoder and photo-receiver
resulting in autocorrelation peak along with MAI. Threshold detector detects
“1” autocorrelation is more than weight of the signal otherwise it detects “0”. 25
Fig. 3.2. Hard-limiting concept.: Limiting each time-wavelength bin to a single
pulse decrease the MAI tremendously (grey squares are the bins that receiver
look at); (a) user of interest transmitting “1” in the absence of MAI (b) user
of interest transmitting “0” but MAI is present; conventional receiver detects
“1” and hard-limiter detects “0”.........................................................................26
Fig. 3.3. Pmf of the interference (number of collision induced from other users)
for code of size (Λ⋅Τ,ω)= (a) (20,8,15) (b) (64,40,31) for different number of
active users. When the code size and number of users increase the pdfs starts
too look like Gaussian........................................................................................36

ix
Fig. 3.4. Distribution of interference for the system with and without hard limiter
for 175 active users  (Λ,Τ,ω,κ)=(64,40,31,1)......................................................37
Fig. 3.5. Minimum number of wavelengths and chip times required for error free
signaling for various number of active users .....................................................39
Fig. 3.6. OOC code of size (64,100,w, 1) (a) Number of potential users (b)
Number of active users to support BER<1E-9 and 1E-6 ...................................41
Fig. 3.7. Probability of error versus weight for different number of active users for
a fixed number of wavelength and chip time Vs. weight. as the weight
increases, the probability of error for a given number of active users
decreases ............................................................................................................42
Fig. 3.8. Maximum number of active users for a code with 64 wavelength, and 40
chip time for varying weight for different preset BER. Number of is limited
by MAI so the maximum number of users as code weight increases till it
reaches the code cardinality and from that point the number of users is
limited by the number of potential users in which increasing the code weight
has the reverse effect..........................................................................................43
Fig. 3.9. Hard-limiting based improvement ratio in number of active users for
codes with different (Λ,Τ) = (# of wavelengths, # of chip times) at the BER
of 1e-9. Increasing the number of wavelength in hard limiting gain is more
important than increasing the number of chip times..........................................44
Fig. 3.10. Probability of error vs. # of active users for code weights 15, and 31
(Λ=64, Τ=40). We can observe a significant improvement in system
performance using Hard limiting receiver .........................................................45
Fig. 3.11. Maximum spectral efficiency achievable for the wavelengths and chip-
times in the range of 4 to 40 using conventional receivers (a)BER<1E-9
(b)BER<1E-3; all point are derived for optimum weight and MCP..................47
Fig. 3.12. Maximum spectral efficiency achievable for the wavelengths and chip-
times in the range of 4 to 40 using hard limiting receivers (a)BER<1E-9
(b)BER<1E-3; all point are derived for optimum weight ..................................48

x
Fig. 4.1. Concept: Effect of multiple access interference (MAI) on the error
margin for varying threshold (a) detected autocorrelation peak along with
MAI from interferers (b) detected autocorrelation peak of a single user...........53
Fig. 4.2. Simulation results for the probability of MAI for transmitted “0” bit and
“1” bit for a code with 16 wavelengths, 40 chip times, code weight 16, and
(a) number of active users 12, (b) number of active users 20............................56
Fig. 4.3. Simulation results for threshold level vs. BER as the number of active
users is varied for (a) a code with 16 wavelengths, 40 chip times, code
weight 16 (threshold is normalized to code weight) (b) a code with 6
wavelengths, 11 chip times, code weight 6 (threshold is normalized for an
electrical signal within –1 and 0 ; A is the number of active users....................59
Fig. 4.4. Experimental setup for the O-CDMA system (EDFA: Erbium doped
fiber amplifier , RX: photo receiver, BPF: Band-pass filter, MOD:
modulator) ..........................................................................................................61
Fig. 4.5. (a) Experimental results for BER vs. threshold level as the number of
active users is varied. (b) BER vs. Threshold level for 2 active users as the
amount of collision between the two users is varied. ........................................64
Fig. 4.6. (a) Encoded O-CDMA data of user 1 when the pattern 11010 is sent. (b)
Decoded O-CDMA data of the first user (c) Decoded O-CDMA data of the
first user with one interferer (d) Decoded O-CDMA data of the first user
with two interfere. (e) 1 Gbit/s decoded data after threshold detection............65
Fig. 4.7. Bit-error-rate curves for the case of (a) threshold fixed for 2 active
users, then re-optimized for a single user and (b) threshold fixed for 3 active
users-two users and single user are taken, and then re-optimized for one or
two active users. Adaptive threshold results in significant sensitivity
enhancement.......................................................................................................67
Fig. 4.8. Conceptual diagram of our RF tone monitoring scheme: Increasing the
number of active users will cause the harmonics of RF component to drop .....68
Fig. 4.9. 5 GHz RF tone power vs. number of active users. .....................................70
Fig. 4.10. RF spectra for the case of (a) single user and (b) 4 users present ............71

xi
Fig. 5.1. Autocorrelation peak of the OCDMA appears in different chip times to
represent different symbol..................................................................................74
Fig. 5.2. CPM O-CDMA: Each symbol is represented by a time shift of the
spreading sequence, the time shift will be translated as the position of
autocorrelation peak within the symbol time after the receiver.........................76
Fig. 5.3. CPM system: input bit stream is converted to symbols, each symbol is
represented by various time shifts of the peak...................................................77
Fig. 5.4. (a) modulated CPM data, various shifts of the autocorrelation peak
represents the symbols (b) CPM-OCDMA encoded data (c) decoded CPM-
OCDMA data ; the scale is 1 ns/div...................................................................78
Fig. 5.5. (left) shows the encoded data of the user of interest for 1 thought 6
users. (right) the decoded version of the same signal along with the
interference: as the number of users increase the traffic on the link becomes
more regulated....................................................................................................79
Fig. 5.6. BER vs. received optical power...................................................................81
Fig. 5.7. The upper window shows the correlation window and the lower shows
various possible positions of 3 possible symbols that can collide with the
correlation window.............................................................................................84
Fig. 5.8. Probability distribution of interference in PPM O-CDMA as the number
of users increase .................................................................................................86
Fig. 5.9. Comparison of probability distribution of interference in OOK OCDMA
for number of active users (10,20,30,40) and PPM (10,20). Rule of Thumb:
pmf of PPM is close to pmf of OOK with twice the number of users ...............87
Fig. 5.10. BER vs. number of active users.................................................................88
Fig. 5.11. BER vs. number of active users: Increasing code size improves the
performance........................................................................................................89
Fig. 5.12. BER vs. code weight: Increasing code weight improves the system
performance........................................................................................................89

xii
Fig. 5.13. % increase of PPM and CCM vs OOK. Both PPM and CCM achieve
higher spectral efficiency with respect to OOK.................................................90
Fig. 5.14. % increase of PPM vs OOK and the ideal curve. (1) ideal case:
log
2
(T)/2, as the bit/symbol is increased by log
2
(T), and the number of active
users is reduced by a factor of 2 (2).Modeling. The increase in spectral
efficiency decreases more as the number of chip times increase because of
the increased tail of the MAI due to CPM, and sampling on every chip times .91
Fig. 5.15. 2-PPM-OCDMA System. Different wavelengths are shown by different
patterns and multiple access interference (MAI) is shown by black pulses.
Error in transmission happens when MAI or noise changes a zero slot to one. 93
Fig. 5.16. Experimental Setup....................................................................................94
Fig. 5.17. (a) 2-PPM symbols (b) Encoded symbols (c) Decoded symbols with 5
active users.........................................................................................................95
Fig. 5.18. (a) 2-PPM symbols (b) Encoded symbols (c) Decoded symbols with 5
active users.........................................................................................................96
Fig. 5.19. (a) 2-PPM symbols (b) Encoded symbols (c) Decoded symbols with 5
active users.........................................................................................................97
Fig. 5.20. (a) 2PPM encoded data of user (chip rate 24 Gchip/sec) (b) decoded
data – single user: boundaries of each symbol is shown with dotted lines.
Two peaks within each symbol time represents the transmitted symbol (c)
eye diagram of the received autocorrelation ......................................................98
Fig. 5.21. (a) 2PPM encoded data of all user (chip rate 24 Gchip/sec) (b)
decoded data of user of interest along with 7 interferers. Boundaries of each
symbol is shown with dotted lines. The autocorrelation peak is higher than
the MAI from other users (c) eye diagram of the received autocorrelation.......99
Fig. 5.22. BER Vs. received optical power..............................................................100
Fig. 5.23. power penalty Vs number of users in the system ....................................101
Fig. 5.24. Comparison of Conventional OCDMA with PPM OCDMA .................103

xiii
Fig. 5.25. Experimental Set up.................................................................................104
Fig. 5.26. Demonstration of variable symbol length in DPPM..............................105
Fig. 5.27. DPPM, PPM and conventional OCDMA transmission time comparison106
Fig. 5.28. BER measurements and Eye diagrams ....................................................107
Fig. 6.1. A typical Fiber to the Home (FTTH) network topology. ..........................109
Fig. 6.2. Concept of Variable QoS: Codes with higher weight has higher
autocorrelation peak so better MAI resistance.................................................112
Fig. 6.3 (a) number of codes in a 2-D O-CDMA system for varying weight: lower
weights correspond to larger numbers of users as higher weight corresponds
to smaller number of users(b) BER vs. numbers of active users for weights
24, and 48: A higher code weight corresponds to lower BER.........................113
Fig. 6.4. (a) the maximum numbers of users of QoS(1) vs, varying numbers of
users with QoS(2) for the user of interest of both types. (b) the maximum
achievable number of users for different code sets. This curves are drawn for
2 different BER for High QoS and Low QoS users .........................................117
Fig. 6.5. Throughput of the network based on percent of packet loss for (a) high
QoS user (b) low QoS user : The throughput of user type 1 does not degrade
as fast as that of user type 2 .............................................................................118
Fig. 6.7. Experimental Setup....................................................................................120
Fig. 6.8. System performance for 1 high QoS user (code weight 6) and 3 low QoS
user (weight 4) for (a) high QoS user is detected(b) low QoS user is detected
: The high QoS user exhibits a smaller amount of power penalty for
increasing number of users...............................................................................121
Fig. 6.9. Examples of PPM, 2-PPM, and 3-PPM Symbols. Number of possible
symbols is written beside each pattern.............................................................123
Fig. 6.10. Number of bits per symbol for PPM, 2-PPM, and 3-PPM symbols
versus the code length, M.................................................................................124

xiv
Fig. 6.11. A variable bit rate OCDMA network using PPM, 2-PPM and 3-PPM
formats. With a fixed symbol time, but different number of bits/symbol,
variable bit rate is achievable...........................................................................125
Fig. 6.12. Block diagram of an MPPM-OCDMA system with N=3 (3-PPM-
OCDMA). It is assumed that codes have a weight of 4. Different
wavelengths are shown with different patterns in the pulses and black pulses
show MAI due to other users in the network. Ts is the symbol time...............126
Fig. 6.13. Experimental setup for a variable bit rate OCDMA network..................127
Fig. 6.14. (a) PPM symbols, (b) 3-PPM symbols, after the modulators. In each
case three symbols are shown and adjacent symbols are separated by dotted
lines. .................................................................................................................128
Fig. 6.15. (a)Decoded PPM symbols (b) Decoded 3-PPM symbols and their eye
diagram. Small pulses are multiple-access-interference (MAI) due to other
users in the network. ........................................................................................129
Fig. 6.16. Power penalty versus the number of PPM users to achieve various
combinations of users operating at different bit rates ......................................130
Fig. 6.17. O-CDMA network: The nodes are connected by transmit and receive
(upstream, downstream) fibers to a passive star coupler to enable a shared
medium LAN....................................................................................................132
Fig. 6.18. Block diagram of an Interference Avoidance(IA) network interface
card (NIC) ........................................................................................................133
Fig. 6.19. Upper: link after the decoder of user of interest. Lower: the data is
transmitted such that the autocorrelation is in the chip time with least
interference.......................................................................................................134
Fig. 6.20. The normalized network throughput vs. normalized offered load for
Aloha-CDMA and transmission scheduling. The results are based on
simulation. The throughput of the network does not collapse in high loads
The traffic model is Poisson arrivals with exponentially distributed packet
lengths. .............................................................................................................135
Fig. 6.21. Experimental setup ..................................................................................136

xv
Fig. 6.22. Eye diagram of the correlation for (a) single user (b) bit pattern of
10110................................................................................................................137
Fig. 6.23. Eye diagram of the correlation for (a) single user (b) multiple user
using transmission scheduling (c) random case...............................................138
Fig. 6.24. BER vs. received optical power of user 1 for increasing number of
users..................................................................................................................139
Fig. 6.25. Performance of an O-CDMA system for increasing number of users
with transmission scheduling, aloha-CDMA, and worst case .........................140

xvi

Abstract

The advances in long haul transmission and optical reach have shifted the bottleneck
from the core network to metro and access networks. Optical access network is a
promising solution to the already congested access network, advocating the
fulfillment of the enormous future requirements of applications and Internet services
of the next-generation on demand.
Optical code division multiple Access (O-CDMA) systems are possible
strong candidate for future optical access network due to their enhanced data
privacy, flexibility, and simplicity of network control, especially when considering
the fine granularity of traffic, fine channel granularity; flexible bandwidth
management, and ability to support variable Quality-of-Service (QoS).
One major challenge in O-CDMA systems results from the square detection
in the optical receivers. Spreading sequences need to be designed in order to support
unipolar signaling, hence, limiting the number of codes for a certain code
parameters. In addition, the multiple-access-interference (MAI) caused by other
users, limits the maximum number of users that can simultaneously operate in the
system.
This thesis presents a detailed research on various system structures
alleviating the effects of MAI. This paper presents an analytical model quantifying
the MAI in the O-CDMA systems for various transmitter/receiver structures

xvii
including conventional receiver, hard limiting receiver, and code position
modulation (CPM) O-CDMA systems; relates the system performance to the MAI;
experimentally demonstrates the effects of MAI on the threshold level and a novel
technique to monitor the number of users in the system based on estimating the
amount of MAI in the system; demonstrates a novel technique “code position
modulation” and its variances “double pulse position modulation (2-PPM) and
differential pulse position modulation (DPPM)” to increase the spectral efficiency of
the system by a factor of 3; and finally introduces and demonstrates various
techniques in order to enhance the O-CDMA network performance by enabling
variable quality of service, variable bit rate, and interference avoidance.
The techniques presented in this thesis may potentially play key roles in
future dynamically reconfigurable optical code division multiple access systems and
networks.

1
Chapter 1
Introduction

Optical fiber communication systems use high carrier frequencies (~100 THz) in
near-infrared region of the electromagnetic spectrum and employ optical fibers as the
transmission media. Theses systems have been deployed since 1980 and
revolutionized the communication technology[2].The optical communication
technology was started by the invention of lasers in the early 1960. Erbium-Doped
Fiber Amplifier (EDFA) revolutionized the optical communication industry in the in
late 1979. Due to the wide gain bandwidth of the EDFA, the wavelength-division
multiplexing (WDM) channels can be simultaneously amplified and transmitted over
long distances. WDM enabled very high bit rates over a very long distance, such as
5.94 Tb/s (40 2 2 40 Gb/s) over 324 km [13], and 3.73-Tb/s (373 × 10-Gb/s, C+L
band) over 11,000 [19], 3-Tbit/s (300 × 11.6-Gbit/s, C+L band) over 7,380 km[111].
These advances in long haul transmission and optical reach shifted the
bottleneck from the core network to metro and access networks. One promising
solution to the already congested access network is optical access network. Optical
access networks are able to provide broadband to the users in order to fulfill the
enormous future requirements of next-generation on demand applications and
internet services. Two different types of architecture for the access points are: (1)
point-to-point, and (2) passive optical network (PON). Point-to-point access requires

2
an installation of optical transceiver for each customer resulting in a huge economic
barrier. PON uses a single transceiver with a splitter to serve up multiples of users
sharing the same bandwidth. As several users share the same fiber media, various
multiplexing scheme can be used in a PON[3].
Current time division multiplexing PON (TDM-PON) architectures are
economically possible, however, they suffer from bandwidth limitation, and
difficulty in scalability. One possible proposed solution is WDM-PON[35]. A
CDMA-PON may be a good alternative for future PON due to their enhanced data
privacy, flexibility, and simplicity of network control especially when considering
the fine granularity of traffic, fine channel granularity; flexible bandwidth
management, and ability to support variable Quality of Service (QoS).
This dissertation is structured as follows: Chapter 2 presents a brief overview
of O-CDMA systems. It discusses concept of different types of O-CDMA systems,
the optical orthogonal codes, and the problems associated with O-CDMA systems.
Chapter 3. provides a model to describe multiple access interference in O-CDMA
systems. The relationship of the system performance and the proposed model is then
explored, followed by various design issues and optimization factors to maximize the
number of users in an O-CDMA system. Chapter 4. experimentally demonstrate the
existence of an optimal decision threshold in an O-CDMA system and show its
relation to the number of active users. This chapter propose a scheme to enable
monitoring the threshold level. Chapter 5. introduces code position modulation for
OCDMA systems increasing the spectral efficiency, i.e. bit rate for a given chip

3
time, then experimentally demonstrate and analytically evaluate this method.
Chapter 6 introduces various applications where O-CDMA is able to enhance the
network performance. The applications “variable quality of service, variable bit rate,
and interference avoidance algorithm to avoid congestion collapse” are demonstrated
experimentally and analyzed by modeling.

4
Chapter 2
Optical CDMA

This chapter provides a brief perspective of the progress in the field of CDMA.
We then, provide a brief history of optical CDMA systems, followed by different
implementation method. We also explain the properties, and design of the optical
orthogonal codes.

2.1 History
Spread spectrum (SS) communication systems have been around since 1960. The
general idea of CDMA is modulating the data over a wideband carrier and as a result
of that making the signal partially insensitive to the data itself. Originally CDMA
systems were motivated by enhanced security and immunity to the interference and
jamming in the military application. CDMA technology served two main purpose in
military application: (1) to overcome the effects of jamming (2) to hide the signal
from eavesdropper, by transmitting the signal over a bandwidth many times wider
than the data bandwidth[63, 112].
By accelerating demand, in communication technology, for mobile and
personal communication several users required to share the same bandwidth. Several
multiplexing scheme were used to efficiently share the bandwidth. The obvious
candidates to enable frequency sharing were frequency and time. Frequency division

5
multiple access (FDMA) could divide the available frequency spectrum into some
frequency bins. Each bin is assigned to a user, and multiple access the same system
without interference from each other. With the same concept, time division multiple
access (TDMA) schemes divide the time axis into time slots, each assigned to a
single user to transmit its data.
Some of the spread spectrum techniques started later to become favourable
for multiple access in the commercial systems, and were named code division
multiple access (CDMA). Each users’ data is spread into a much wider spectrum
using a high chip rate code. By designing the codes to have certain properties, it is
possible to send multiple users’ data on the same frequency band and detecting the
signal at the receiver side provided that the receiver is aware of the transmitter
spreading sequence. The CDMA systems have shown to have certain advantages
such as easier planning the frequency allocation, overcoming the “near far effects”,
mitigation of fading, and soft hand off.
Generally spreading the signal can be achieved by several schemes:
Direct sequence: The data is directly encoded at a higher frequency. The codes are
pseudo random sequences generated pseudo-randomly, the receiver is aware of each
encoder’s code and can detect data by using a correlator
Frequency hopping: The data is rapidly switched between different frequencies
using a pseudo-random sequence, the receiver is aware of the encoder’s sequence to
follow the signal in each frequency

6
Time hopping: The data is transmitted in short bursts pseudo-randomly, and the
receiver is aware of the burst time.

2.2 Optical Code Division Multiple Access (O-CDMA) Systems
The idea of Optical CDMA was first suggested in 80's as an asynchronous secure
multiple access protocol for optical communications networks [94-96]. Optical
CDMA was introduced as an access strategy that does not require centralized
network management and thus, unlike conventional access strategies and can
efficiently provide the required bandwidth and connectivity in local access networks.
Although the potential of OCDMA has been recognized for many years, it has never
accomplished its true potential because of fundamental limitations.
In an O-CDMA system different user share both time and frequency and are
distinguished using a unique spreading sequence. Each user’s data is multiplied by
its spreading sequence, and then all the users are coupled into the shared channel. O-
CDMA system can be designed to support synchronous and asynchronous data
traffic. In the synchronous case high spectral efficiency can be achieved, however
the need for chip and bit-wise synchronization brings the necessity of global
synchronization. In this case the O-CDMA network is more complicated and less
secure[60, 113].
In asynchronous O-CDMA system there is not need for chip and bit-wise
synchronization between different users. This will bring simplicity in the receiver

7
design, robust network, and enhanced security, however to achieve large number of
users in this case large number of chip time and wavelength are necessary, which
will decrease the spectral efficiency of the asynchronous O-CDMA system.
To support asynchronous traffic the spreading sequence should be designed
such that
1. Each sequence should be distinguishable from any shifted version of itself.
2. Each sequence is distinguishable from a possibly shifted version of any other
sequences in the code set.
One-dimensional O-CDMA using optical orthogonal codes is very similar to
the classical O-CDMA, however despite conventional CDMA which utilizes bipolar
signaling [98, 99, 112], in optics only unipolar signaling can used due to the nature
of optical communication receivers, which are intensity receivers[83]. Due to this
fundamental limitation the spreading sequences can not be completely orthogonal .
This limits the maximum number of users in O-CDMA systems. One possible
technique to increase the number of users would be using time and wavelength.
Multi-wavelength or fast wavelength hopping scheme use wavelength as
another dimension to provide more number of users without increasing the number
of chip-times in an O-CDMA system [107]. In this method each users’ data bit is
subdivided into different small chips and then each chip is illuminated with a unique
wavelength, so the number of allowed code words increases without the need for
more chips per bit. Note that it is now possible to have the same time-sequence for

8
more than one user since different wavelength combinations may be used for each.
The increase in the number of simultaneously allowed users in this scheme is quite
remarkable. For example, if a one-dimensional code with n = 125 chips and weight,
w = 5 is able to support a maximum of 9 users with time-spreading on one
wavelength is expanded to include eight wavelengths, then the maximum number of
allowed users increases to >300.
There are different approaches to implement two-dimensional codes. One
approach is using fiber Bragg grating (FBG) [2, 11, 44, 100] arrays as an encoder
and decoder. General implementation of an OCDMA encoder and decoder for a 2-
dimensional code using FBGs is shown in Fig 2.1. Fiber Bragg gratings (FBGs) are
a convenient way to make the encoder/decoder scheme in an O-CDMA system. FBG
is a narrowband optical reflector that reflects the spectrum centers on the Bragg
wavelength[2, 83]. Hence arrays of FBG matching the appropriate code are capable
of encoding and decoding signals. Fig. 2.1 shows the use of FBGs as encoder in the
O-CDMA system. The spacing between different FBG’s in the array provides the
appropriate delay between chips. The decoder should be the same structure so that it
can line up all of the input coded chips on top of each other. It should also be noted
that if there are more than one grating in the array of FBG which reflects the same
wavelength, that wavelength will be reflected twice and will cause unwanted
interference. Due to this reason the codes with the limitation of at most one pulse per

9
wavelength are more favorable in the O-CDMA systems. This will bring another
degree of limitation on the number of codes in the code set.
Reflections
FBG Array
λ
3
λ
2
λ
1
O-CDMA Encoder Using FBG
λ
1
λ
1
λ
2
λ
2
λ
3
λ
3
λ
4
λ
4
λ
4
Stack of pulses
on different
wavelength
Encoded Signal Reflections
FBG Array
λ
3
λ
2
λ
1
O-CDMA Encoder Using FBG
λ
1
λ
1
λ
2
λ
2
λ
3
λ
3
λ
4
λ
4
λ
4
Stack of pulses
on different
wavelength
Encoded Signal

Fig 2.1. Using fiber Bragg grating as an O-CDMA encoder. Stack of pulses in
different wavelength is fed to the FBG array. Each wavelength is then reflected at by
its respective grating. The spacing between different FBG’s in the array are designed
to provides the appropriate delay between chips.

FBG’s in O-CDMA decoder/encoder schemes is shown with the usage of
both lasers and broadband sources. The latter is called spectral encoding. In the
spectral encoding O-CDMA systems the chip delay time is caused by physical space
between different Bragg gratings. Incoherent broadband sources [50] include those
of LEDs, super-luminescent diodes and erbium-amplified spontaneous emissions
(ASE Sourse). These sources offer broadband spectrum and low cost. FBGs are used
in different O-CDMA encoding schemes, including frequency hopping [41], direct
sequence [80]–[97], two-dimensional wavelength/time spreading [113]and amplitude
and/or phase spectral coding [110].
One limitation of using FBG as encoder and decoder is lack of tenability.
Moreover the spacing between adjacent channels in the arrays of FBG’s are limited

10
by the writing process. Due to these reasons it is the use of combination of array
waveguide grating and tunable delay line in O-CDMA system is of interest. Using
tunable delay lines was first proposed for coherent phase encoding O-CDMA system
[96]. Two-dimensional wavelength/time spreading O-CDMA encoder/can also be
implemented using tunable delay lines. Schematic of generic O-CDMA system using
tunable delay lines is shown in Fig. 2.2. In this method each bit is first modulated
using different laser colors. Then using a demultiplexer these wavelengths are
separated and delayed with respect to each other using tunable delay lines. The
encoded bit is shown in time domain.
DEMUX
λ
3
λ
2
λ
1
λ
4
τ
τ
τ
τ
Optical
Delay
Lines
λ
4
λ
3
λ
2
λ
1
Coupler
λ
1
λ
2
λ
3
λ
4
DEMUX
λ
3
λ
3
λ
2
λ
2
λ
1
λ
1
λ
4
λ
4
τ
τ
τ
τ
Optical
Delay
Lines
λ
4
λ
4
λ
3
λ
3
λ
2
λ
2
λ
1
λ
1
Coupler
λ
1
λ
2
λ
3
λ
4

Fig 2.2. Schematic of two dimensional O-CDMA system using Mux/Demux and
tunable delay lines as an encoder/decoder system. Stacks of pulses are split using the
Demux. Each pulse is delayed appropriately using the optical delay line.
A schematic of an O-CDMA system is shown in Fig. 2.3. An input data bit is
fed to the 2-D O-CDMA encoder. The encoder can be FBG or Mux/Demux base.
The encoder maps the incoming bit to its 2-D code matrix. The output of the encoder
is the 2-D code of this user satisfying the auto-cross correlation properties. All users
are multiplexed in a star coupler and send over the fiber channel. At the decoder

11
again the same structure is used to line up the users chip times on top of each other
and provide the autocorrelation peak. The decoder which is matched to the encoder
can line up the autocorrelation peak and correctly recover the data by thresholding,
while the decoder which does not have this information is unable to detect the data.
The output of this decoder is just MAI. Recently, there has been several
demonstration of 2-D Time-wavelength O-CDMA systems [6, 10, 38].
2D OCDMA
encoder
Input
data bit
λ
2
λ
3
λ
4
λ
1
t
1
t
2
t
3
t
4
Other
User
N×N
Decoder
User of
interest
Sample time
Sample time
Threshold
Threshold
Data out
Match
No match
Non-zero
cross-correlation at the
sample time due to a
code collision
High autocorrelation
peak due to code match
Bit Time
No data
2D OCDMA
encoder
Input
data bit
λ
2
λ
3
λ
4
λ
1
t
1
t
2
t
3
t
4
Other
User
N×N
Decoder
User of
interest
Sample time
Sample time
Threshold
Threshold
Data out
Match
No match
Non-zero
cross-correlation at the
sample time due to a
code collision
High autocorrelation
peak due to code match
Bit Time
No data

Fig 2.3. Schematic of an optical CDMA system. The input bit is fed through the 2D
O-CDMA encoder. The output of the encoder is the 2D O-CDMA matrix. All users
are multiplexed through a star coupler and transmitted through output fibers. The
user with the matched decoder can line up the autocorrelation peak and recover the
data by thresholidng. An unmatched decoder only sees MAI
2.3 Optical orthogonal codes
Optical Orthogonal Codes (OOC) are the spreading sequences used in O-CDMA
systems [94]. An OOC is a group of sequences of length n, constant weight w, and
maximum collision parameter(κ) _ satisfying the following two properties:

12
1. The Autocorrelation property: For every sequence x
t
in the OOC it should
satisfy:
.
1
0
κ
τ
≤
∑
−
=
+
n
t
t t
x x
kn ≠ τ
This Property guarantees that synchronization can be achieved in the asynchronous
system.
2. The Cross-correlation property: For every two sequences x
t
and y
t
in OOC they
should satisfy:
.
1
0
κ
τ
≤
∑
−
=
+
n
t
t t
y x

This property guarantees that the code of any given user is distinguishable
from other users and all possible shift of other users.
The set of all sequences satisfying the above conditions is called an OOC
sequence of (n,ω,κ), where n is the sequence length, ω is the weight of the code and
κ is the maximum collision parameter.
Example: C = {(1100100000000); (1010000100000)} is a OOC sequence
with (13, 3, 1) parameter which has only two codeword
One of the most important characteristics of the OOC codes is the size of the
family. Each user in a network is assigned a unique code, so the number of users is
limited by the number of codes. We call this the number of potential users. Apart
from maximum number of potential users, increasing the size of the code is
advantageous to provide another degree of security using code hopping.

13
Size of an OOC set is defined by P(n,ω,κ). The size of an OOC set is
restricted by the well-known Johnson bound [45]as:


















−
−
−
−
≤
κ ω
κ
ω ω
κ ω
n n
n P L
1
1 1
) , , (
Johnson bound only gives an upper bound for the maximum number of
possible code in an OOC code-set however in most cases the construction to achieve
those set does not exist.
Example: 1-D OOC size

Table 2.1. Code size for various 1 dimensional code sets using Johnson bounds
OOC Set (10,3,1) (40,3,1) (160,5,1) (160,5,2)
OOC size 1 6 7 413

As the above example shows, the size of the 1 dimensional OOC is extremely
small. We can only support only 7 users by using 160 chip times. This is far below
the required number of users in an optical network. In the (160,5,2) example above
we see a huge improvement in the size of the OOC by increasing κ, it should be
noted that increasing κ will increase the interference and hence decreases the number
of active users in the O-CDMA system. Moreover the tightness of Johnson bound for
κ>1 is not known, however there are many optimal or asymptotically optimal
constructions in the literature [26, 69, 70]. For example using the code (255,127,64)

14
the only know construction, which is optimal, gives only 1 code in the set, while the
Johnson bound is 1.36e22.
The main reason of having such small code dimensionality in O-CDMA
systems is the necessity of using unipolar signaling in contrast with regular CDMA
which bipolar signaling can be used

2.4 Two-dimensional optical Orthogonal Codes
In a 1-D O-CDMA system the data rate is equal to chip rate divided by the spreading
sequence length. We either need to go to higher chip-rates or lower bit-rates in order
to provide reasonable number of users in the system. As in fiber optic
communication systems the potential usable bandwidth is 25 THz the simplest way
to increase the number of user without increasing chip-rate is the usage of
wavelengths as another dimension and spread the signal over the wavelengths as
well [120].
The advantage of this approach is the reduction of the number of chip times
by use of different wavelengths. Moreover, there is no need to have auto- and cross-
correlation property for circular shifts of wavelengths, as the wavelengths are always
synchronized. So, increasing the number of wavelengths has a more significant
effect in comparison with increasing the number of chip times.

15
A 2-D OOC consists of arrays of constant weight {0,1}, which different rows
of the arrays correspond to different wavelengths, and the columns correspond to the
time slots. These arrays should satisfy auto- and cross-correlation properties in time:

λ
1
λ
2
λ
3
t
1
t
2
t
3
t
4
t
5
t
6
t
7
λ
1
λ
2
λ
3
t
1
t
2
t
3
t
4
t
5
t
6
t
7
λ
1
λ
2
λ
3
t
1
t
2
t
3
t
4
t
5
t
6
t
7
λ
1
λ
2
λ
3
t
1
t
2
t
3
t
4
t
5
t
6
t
7
λ
1
λ
2
λ
3
t
1
t
2
t
3
t
4
t
5
t
6
t
7
λ
1
λ
2
λ
3
t
1
t
2
t
3
t
4
t
5
t
6
t
7
λ
1
λ
2
λ
3
t
1
t
2
t
3
t
4
t
5
t
6
t
7
λ
1
λ
2
λ
3
t
1
t
2
t
3
t
4
t
5
t
6
t
7
λ
1
λ
2
λ
3
λ
1
λ
2
λ
3
t
1
t
2
t
3
t
4
t
5
t
6
t
7
t
1
t
2
t
3
t
4
t
5
t
6
t
7
λ
1
λ
2
λ
3
t
1
t
2
t
3
t
4
t
5
t
6
t
7
λ
1
λ
2
λ
3
t
1
t
2
t
3
t
4
t
5
t
6
t
7
t
1
t
2
t
3
t
4
t
5
t
6
t
7
λ
1
λ
2
λ
3
t
1
t
2
t
3
t
4
t
5
t
6
t
7
λ
1
λ
2
λ
3
t
1
t
2
t
3
t
4
t
5
t
6
t
7
t
1
t
2
t
3
t
4
t
5
t
6
t
7
λ
1
λ
2
λ
3
t
1
t
2
t
3
t
4
t
5
t
6
t
7
λ
1
λ
2
λ
3
t
1
t
2
t
3
t
4
t
5
t
6
t
7
t
1
t
2
t
3
t
4
t
5
t
6
t
7
λ
1
λ
2
λ
3
t
1
t
2
t
3
t
4
t
5
t
6
t
7
λ
1
λ
2
λ
3
λ
1
λ
2
λ
3
t
1
t
2
t
3
t
4
t
5
t
6
t
7
t
1
t
2
t
3
t
4
t
5
t
6
t
7
λ
1
λ
2
λ
3
t
1
t
2
t
3
t
4
t
5
t
6
t
7
λ
1
λ
2
λ
3
λ
1
λ
2
λ
3
t
1
t
2
t
3
t
4
t
5
t
6
t
7
t
1
t
2
t
3
t
4
t
5
t
6
t
7
t
1
t
2
t
3
t
4
t
5
t
6
t
7
λ
1
λ
2
λ
3
t
1
t
2
t
3
t
4
t
5
t
6
t
7
λ
1
λ
2
λ
3
λ
1
λ
2
λ
3
t
1
t
2
t
3
t
4
t
5
t
6
t
7
t
1
t
2
t
3
t
4
t
5
t
6
t
7

Fig. 2.4. Example of sub-optimal two-dimensional codes. This code is using 3
wavelength and 8 chip times and can support 7 codes.

1. The Autocorrelation property: For every array x
t
in OOC ,it should satisfy:
∑∑
− Λ
=
−
=
+
≤
1
0
1
0
) (
i
T
j
j i ij
x x κ
τ
kT ≠ τ
2. The Cross-correlation property: For every pair of arrays x
t
and y
t
in OOC, they
should satisfy
∑∑
− Λ
=
−
=
+
≤
1
0
1
0
) (
i
T
j
j i ij
y x κ
τ

16
In the above equations T stands for number of chip times, Λ is number of
wavelength, and κ the Maximum Collision Parameter. The set of all such arrays
build a 2-D (Λ,T ,ω,κ) OOC set. An example of 2-D OOC for a code size of
(3,6,3,1) is shown in Fig. 2.4.
The size of a two dimensional OOC set is defined by P(Λ,T,ω,κ). Johnson
bound provides us with an upper bound for the two-dimensional OOC set.


















−
− Λ
−
− Λ Λ
≤ Λ
κ ω
κ
ω ω
κ ω
T T
T P L
1
1
) , , , (
Again this bound gives only an upper bound for the maximum number of
possible code in an OOC code-set however in most cases the construction to achieve
those set does not exist. There has been lots of new research on finding tighter
bounds for OOCs [78, 79].
For the example above, the upper bound given by Johnson bound is:
P(3,6,3,1)=10. The optimal code-set based on function plot construction has seven
codes demonstrated in Fig. 2.4.
Table 2.2. Code size for various 2 dimensional code sets using Johnson bounds
OOC Set (8,10,3,1) (16,40,3,1) (32,160,5,1) (32,160,5,2)
OOC size 104 1701 8185 13972819

Table 2.2 shows that the number of potential users can be increased
enormously using two-dimensional codes, however the number of active users in an

17
O-CDMA system is highly dependent on the code weight for a specific receiver
design. For instance using conventional O-CDMA receiver the above code sets can
support at most 3,3,5, and 2 active users without error, so it is necessary to increase
the weight of the code which decreases the number of potential users consequently,
the number of potential users for increased weigh is demonstrated in table 2.3.
Table 2.3. Code size for various 2 dimensional code sets using Johnson bounds
OOC Set (8,10,8,1) (16,40,8,1) (32,160,16,1) (32,160,16,2)
OOC size 11 42 165 28071

As we discussed above, Johnson bound provides only an upper bound for the
size of the coder-set. If the upper bound is achievable, is generally a question of
code design. A code which can achieve the Johnson bound is called to be an optimal
code. A code that achieve Johnson bound as n goes to infinity is called
asymptotically optimal. There is a large research on code construction such as
algebraic constructions, recursive construction, and constant weight constructions [1,
14, 16-18, 21, 22, 24, 25, 30, 36, 42, 53, 56, 58, 59, 102, 116, 118, 120, 121].
2.5 Error in O-CDMA system
Several effects can cause bit errors in O-CDMA systems. Errors can occur due to
characteristics of the optical fiber medium. This effects are thermal noise, shot noise,
Amplifier Spontaneous Emission (ASE). These effects have been studied in [27, 28,
66, 84, 85, 104, 123]. Another physical layer effect which is due to the square

18
detection in the receiver in multi wavelength O-CDMA systems is beat noise. This
effects has been studied in [12, 29, 32, 62, 74, 108, 117].
These effects are negligible compared to the effect of multiple access
interference. MAI occurs as multiple users are transmitting in the system. After
correlation receiver, the main users’ pulses are aligned on top of each other to create
the autocorrelation peak. Other users (interferes) appear as cross correlation
(multiple access interference). An interference error causes a false positive detection
at a receiver. It means that the MAI can additively increase the level of the
transmitted “0” to be falsely detected as “1”.
Fig. 2.5. shows the concept of MAI. User “1” is the user of interest and
decoder correctly. The autocorrelation window is shown by dotted lines. Any user
which has a pulse in this window causes an interference. It is clear that user 2 does
not have any interference with user “1” while user 3, and 4 have 1 interference. In
this scenario if user 1 transmits a “0” bit it will be detected correctly as the two
interference from user 3, and 4 can not exceed the threshold. As it can be seen from
this figure, the amount of MAI is dependent of the delay within various users. For
instance, A delayed version of user 2 can shift is decorrleated pattern and cause MAI
with user “s. This effect the MAI a random process, which is the major difficulty in
analyzing the MAI, moreover MAI depends on the receiver structure[7, 87, 92, 93].
It should be noted that MAI is an inherent problem in O-CDMA systems and limit
the number of active users in the system. One technique to reduce the MAI in the
system is using hard limiters by limiting the amount of MAI in each time-

19
wavelength bin[46, 47, 55, 76, 81]. Another proposed method to reduce the MAI is
to use polarization as the 3
rd
dimension[55, 64, 65].
After Decoder of User 1
t
t
t
t
Bit
Tc
User 1
User 2
User 3
User 4
# of wavelength = 4
# Chip Times = 8
Weight = 4
Threshold
After Decoder of User 1
t
t
t
t
Bit
Tc
User 1
User 2
User 3
User 4
# of wavelength = 4
# Chip Times = 8
Weight = 4
Threshold

Fig. 2.5 Example of MAI, user “1” is the user of interest and user 2-4 are acting as
interferes

20
Chapter 3
Analytical Interference Model for 2-
Dimensional (Time-Wavelength)
Asynchronous O-CDMA Systems using
Various Receiver Structures

In this chapter, we describe a model that described the multiple access
interference (MAI) in O-CDMA systems. Using the model, we find the number of
active users in a system given the code parameters. We then explain a novel receiver
design which can increase the spectral efficiency of the O-CDMA system, and
compare the limits of spectral efficiency for these systems.

3.1 Analytical Interference Model for 2-Dimmensional O-CDMA
Systems
A key drawback for O-CDMA systems is the necessity of generating,
propagating, and detecting extremely short optical pulses during a specific chip time
(i.e. the time domain subdivision of a bit). These optical pulses must be generated in
such a way that: (i) there is sufficient orthogonality among the codes, and (ii) a large
number of users can be accommodated. This utilization of time-domain chips is
commonly referred to as a one-dimensional (1-D) O-CDMA [82, 94, 95]. One
approach for partially alleviating the limitations presented by these extremely small

21
chip times has been the introduction of a two-dimensional (2-D) O-CDMA
architecture, where each bit is sub-divided into a combination of chip times and a
discrete set of wavelengths [33, 107]. In 2-D O-CDMA, each user transmits a
sequence of ω pulses in specified wavelengths and time slots. The pattern of this
sequence is unique for each user and is called a 2-D O-CDMA optical orthogonal
code (2-D OOC) [77]. These patterns are designed to have a determined number of
maximum collisions for any time cyclic shift of the code, specified by the maximum
collision parameter (MCP), κ MCP is a parameter defined for optical orthogonal
codes (OOC), which is the maximum of cross-correlation and autocorrelation of the
codes within another code in the code set, while any two codes can have any cross-
correlation value less than or equal to MCP. As the number of users increases in the
O-CDMA network, the total number of collisions from all users to each of the codes
becomes a random number, which is referred to as multiple access interference
(MAI). This interference appears in the receiver as an unwanted signal that has the
potential of making transmitted “0”-bit to be incorrectly decoded as a “1”-bit. One
potential method for reducing MAI would be to implement hard limiting in the O-
CDMA receiver [75]. A hard-limiting receiver will only detect a maximum optical
power of a predetermined “unitary” level within each chip time-wavelength bin.
Subsequently, it limits the accumulated MAI in each time-wavelength bin as the
number of active users increases. Hard limiting receiver can be implemented in the
electronic domain after detection[31] or in the optical domain before detection[55].

22
Recently, several families of 2-D OOC have been reported. Some examples of
these include prime-hop codes[107], carrier-hopping prime codes [119], modified
quadratic congruence codes [115], prime/OOC codes [114], and algebraic code
constructions [77]. Because of the specific structure of 2-D OOCs, the number of
allowable codes is very limited, and therefore the objective of the above-mentioned
code constructions is to increase the code cardinality - number of potential users in
the O-CDMA system - while maintaining proper autocorrelation and cross-
correlation properties for a given code dimensions.
Due to the accumulated interference in the system, all of the codes within a
code set could not be used simultaneously (actively) in the O-CDMA network. The
number of possible active users in the system determines the system performance
under certain conditions. There have been some reports on the performance of the
conventional and hard limiting O-CDMA systems based on the number of active
users: (1) performance analysis based on probability distribution pattern of
interference using random code model for 1-D O-CDMA [7, 75, 122] (2) simulation
of the variance of the interference based on code parameters and then using Gaussian
assumption to calculate the BER [37, 67], (3) performance analysis based on specific
code construction [57, 68], and (4) finding an upper bound for probability of
error[68].
In this chapter, we describe a probabilistic model for O-CDMA systems that
determines the probability mass function (pmf) of the interference for a given code
dimensions, and specific number of active users based on a random code analysis

23
[91-93]. In this analysis, the specific code structures are not taken into the account,
but the general restrictions of OOCs are considered. The derived pmf can be used to
relate the code parameters to the system performance, or it can be used for other
applications where we need to know the interference distribution. One such
applications is to find the optimal threshold level in the receiver when there are a
certain number of active users in the system [86].
Moreover, while most of the works in the literature are focusing on only
system performance, we focus on finding the complete MAI statistics, and relating it
to the system performance. Most of the practical O-CDMA systems are using
specific codes which have maximally one pulse in each wavelength due to their
implementation simplicity. Consequently, the 1-D O-CDMA analysis results in the
literature cannot be generalized to this case trivially. In this section, we are mainly
interested in studying these systems. Although our focus in this section is on codes
with 1 pulse per wavelength, our method supports both general 1-D and 2-D O-
CDMA systems, which we have included all of them for the sake of completeness.
Moreover, the focus of this section is on the performance of the O-CDMA
network in the presence of interference; the results resemble the asymptotic
performance of the network when the signal to noise ratio approaches infinity. This
method has been widely used for performance analysis of O-CDMA systems [7]. We
then use the model to analyze the performance of the O-CDMA system using
different code parameters. In addition, we show that for a designated hardware setup,
which limits the number of chip times and wavelengths, we can optimize our code

24
construction using the free parameters weight and maximum collision parameter.
Optimization is performed in order to increase the number of active users while
maintaining a predetermined BER.

3.2 O-CDMA System Structure
In a general O-CDMA network, each user is assigned a unique signature code
where in any instant of time the O-CDMA transmitter generates an information bit
for a laser based optical OOK modulator. These pulses are then passed through the
O-CDMA encoder, which splits the pulse over small chips in time and a specified
wavelength to create the 2-dimensional-code matrix [107]. The general method to
create the 2 dimensional code matrix is to delay and recombine different chip times.
Experimental demonstration of O-CDMA encoders/decoders has been shown by (1)
using fiber Bragg gratings (FBGs)[40], and (2) demultiplexing the wavelength and
then recombining them by using specified delay times . In most reported cases, the
hardware will impose a limitation on the codes that there should be at most one pulse
per wavelength. At the receiver side, users receive the desired signal along with the
MAI from other users. Moreover, the performance of the system depends on the
amount of MAI, the receiver structure, and other noise sources (thermal, ASE and
beat-noise). In the following we ignore all noise sources in the system, which
resembles the system for very large SNR, and calculate the statistics of interference
for different receiver structures.

25
Encoded Signal
t
Interference
t
λ
1
λ
2
λ
3
Desired Signal
λ
1
λ
2
λ
3
DEMUX
Delay
line
Decoder
Fiber link
RX
Decision
Circuit
Sampling chip
User of
interest
# of 1’s >= w
# of 1’s < w
0
1
Received Data
Threshold
“1”
“0”
1
Received Data
Threshold
“1”
“0”
Interference
Bit
PLUS
Encoded Signal
t
Interference
t
Interference
t
λ
1
λ
2
λ
3
Desired Signal
λ
1
λ
2
λ
3
DEMUX
Delay
line
Decoder
Fiber link
RX
Decision
Circuit
Sampling chip
User of
interest
# of 1’s >= w
# of 1’s < w
0
1
Received Data
Threshold
“1”
“0”
1
Received Data
Threshold
“1”
“0”
Interference
Bit
Sampling chip
User of
interest
# of 1’s >= w
# of 1’s < w
0
1
Received Data
Threshold
“1”
“0”
1
Received Data
Threshold
“1”
“0”
Interference
Bit
PLUS

Fig. 3.1. Schematic of the conventional O-CDMA system: Encoded signal of
desired user along with interference is fed to the decoder and photo-receiver
resulting in autocorrelation peak along with MAI. Threshold detector detects “1”
autocorrelation is more than weight of the signal otherwise it detects “0”.

Fig. 3.1 shows the schematic of a conventional O-CDMA receiver where an
encoded O-CDMA signal is fed to an O-CDMA decoder; after the decoder, all pulses
are lined up on top of each other. The output of the decoder is then fed to a gating
system, which only picks up the stack of pulses on the appropriate chip.
Furthermore, the output of the photo-detector is then fed to a threshold detector. The
threshold detector should be set so that it is able to accommodate the worst-case
scenario, which is when the system has the maximum number of collisions. Taking
that into account, the threshold is set so that if the number of pulses is equal to or
greater than weight it will detect “1” and if the number of pulses is smaller than the
code weight it will detect “0”. In this case if the transmitted signal is “1” the output
is always one, but if the transmitted signal is “0” errors can occur when the amount
of interference is larger than weight.

26
(a)
(b)
λ
1
λ
2
λ
3
threshold
1
1
1
λ
1
λ
2
λ
3
t
1
t
2
t
4
t
3
t
5
Auto Correlation Peak
Decoding
λ
2
λ
2
λ
3
3
2
λ
1
λ
2
λ
3
t
1
t
2
t
4
t
3
t
5
Without Hard Limiter:
Interference > Autocorrelation
With Hard Limiter:
Interference < Autocorrelation
λ
3
λ
3
λ
2
λ
3
1
1
λ
1
λ
2
λ
3
t
1
t
2
t
4
t
3
t
5
Multiple Access Interference
Hard Limit
Numbers in each bin represent the number of pulses
User of interest
transmitting “1”
User of interest
transmitting “0”
threshold
threshold
λ
1
λ
2
λ
3
threshold
1
1
1
λ
1
λ
2
λ
3
t
1
t
2
t
4
t
3
t
5
Auto Correlation Peak
Decoding
λ
2
λ
2
λ
3
3
2
λ
1
λ
2
λ
3
t
1
t
2
t
4
t
3
t
5
Without Hard Limiter:
Interference > Autocorrelation
With Hard Limiter:
Interference < Autocorrelation
λ
3
λ
3
λ
2
λ
3
1
1
λ
1
λ
2
λ
3
t
1
t
2
t
4
t
3
t
5
Multiple Access Interference
Hard Limit
Numbers in each bin represent the number of pulses
User of interest
transmitting “1”
User of interest
transmitting “0”
threshold
threshold

Fig. 3.2. Hard-limiting concept.: Limiting each time-wavelength bin to a single
pulse decrease the MAI tremendously (grey squares are the bins that receiver
look at); (a) user of interest transmitting “1” in the absence of MAI (b) user of
interest transmitting “0” but MAI is present; conventional receiver detects “1”
and hard-limiter detects “0”

The general problem with the conventional receiver is that MAI can
accumulate in each time-wavelength bin. One way to avoid this problem is to limit
the amount of MAI in each time-wavelength bin to only one unit of optical or
electrical power, which is the method used in an optical or electrical hard-limiting
receiver implementation [31, 75]. Fig. 3.2(a) shows the user of interest transmitting
“1” and there is no interference. In this case, the decoder stacks up the dark bins and
sets the threshold as it is indicated in order to detect as many users as possible. In
Fig. 3.2(b) user of interest is transmitting “0”, however there is MAI from other
users. (The amount of MAI is represented as a number in each bin) the decoder still

27
stacks up the dark bins and compares it with the same threshold. In this case the
conventional receiver detects “1” erroneously, while hard limiting receiver limits the
interference to 1 unit in each bin and as a result of that it will detect “0” correctly.

3.3 Interference Model
Since there are different OOC constructions with their own structural specifications,
a general method to study OOC interference without considering the specific
construction is the probabilistic model based on random codes. In this section we
will find the analytical model for interference of the conventional and hard limiting
O-CDMA receivers with and without the constraint of having one pulse per
wavelength.
In the following probabilistic method we assume each user is assigned a Λ×T
array of {0,1} entries, where Λ and T are the numbers of wavelengths and chip times
respectively. The number of “1”s in each array is ω, and any column circular shift of
each two arrays are colliding in at most κ positions. In addition, the upper bound for
the number of code in the system for a given parameters are given by Johnson
bound[103, 120], or the bound from Omrani et al. for codes with at most one pulse
per wavelength[77]:
For general 2-D OOC:


















−
− Λ
−
− Λ Λ
≤
κ ω
κ
ω ω
T T
P L
1
1

28
For 2-D OOC with at most one pulse per wavelength


















−
− Λ
−
− Λ Λ
≤
κ ω
κ
ω ω
) (
1
) 1 ( T T
P L

The following analysis is based on the assumptions: (1) the system is
asynchronous; (2) the received signals are chip synchronous, which is a common
assumption in computing MAI. These two conditions imply that at any instant there
is a combination of different code-words aligned in time on the line, but columns of
each code-word is cyclically shifted by a random number.
We assume there are A+1 users transmitting data in the system with A+1 ≤ total
number of code- words. Moreover, the first A users are acting as interferers on the
A+1
st
user. We find a probability distribution on the amount of interference for a
given number A of interferers.
) Pr( h MAI =

Since users transmitting ”0” do not cause any interference, we assume that
”α” of the A interfering users are transmitting ”1” with probability P
α
at the time of
interest.

∑
=
= = =
A
send users of send users h MAI h MAI
0
) " 1 " A Pr( ) " 1 " | Pr( ) Pr(
α
α α

(3.1)

Assuming each user is transmitting “1” or “0” with probability β and 1-β then
α
β
α
β
α
α
α
−
−








= =
A
A
P send users ) 1 ( ) " 1 " Pr(

29
In practice β is 0.5 in communication systems.
In the following, we compute the probability of interference on a single user
when α other users are transmitting “1”. We define q(x) as the total number of code-
words having x ≤κ collisions with the specific 1s of the user of interest.
2-D OOC with no restriction: since there is no restriction on the placement of
1s we should choose ω-x locations out of ΛΤ−ω locations containing 0 for an
interferer, while there is only one choice for the colliding 1s, so (x) can be calculated
as:








−
− Λ
=
x
T
x q
ω
ω
) (

(3.2)

2-D OOC with not more than one pulse per wavelength: In this case we
cannot choose any ω-x location out of the ΛΤ−ω locations to assign to non-colliding
1s, since we need to enforce that the interferer be a code-word and not more than one
pulse per wavelength. So the interferer cannot have any non-colliding 1s in the
colliding wavelengths, which means the ω-x non-colliding locations should be
chosen from the Λ-x non-colliding wavelengths with the restriction that there are
maximally one pulse per wavelength, and there is no more collisions in these
remaining 1’s.
In other words, the remaining ω-x ones should be divided into two groups; one
group for the ones that are located in the same wavelength as the one in the original

30
code, and the other group in which ones are chosen from wavelengths not having one
in the original code. This can be done in:
∑
− −








− −
− Λ
−







 −
=
y
y x y
T
y x
T
y
x
x q
) (
) (
) 1 ( ) (
ω
ω
ω ω

The range of the summation is defined by: 0≤y ≤ω-x, and 0≤(ω-x)-y ≤Λ−ω. This
Inequality can be simplified to max(0,2ω-x-Λ ≤y ≤ω-x). So we can re-write the above
summation as:
y x y
x
x y
T
y x
T
y
x
x q
− −
∑
−
Λ − − =








− −
− Λ
−







 −
=
) (
) 2 , 0 max(
) (
) 1 ( ) (
ω
ω
ω
ω
ω ω

y x y
x y
T
y
T
x y
x
x q
− −
Λ − =








−
− Λ
−








−
−
=
∑
ω
ω
ω
ω
ω ω
) 1 ( ) (
) 2 , max(
(3.3)

Conventional O-CDMA receiver
Initially, we find the MAI probability distribution of one interferer. This is the
probability that the interferer collides with the original code in h locations where h is
less than or equal κ. Without loss of generality, we fix our user of interest (code). All
other codes with h collisions with the original code should have h ones exactly in
the same locations as the “1’s” in the original codes. These h ones can be chosen in








h
ω
ways. The remaining ω-k pulses can be chosen in q(h)

ways, where q(x) is
defined in equations 2.1, and 2.2. So the number of codes having exactly h collisions
with the user of interest is:

31
) ( interest of user with collision h having codes of Number h q
h








=
ω

The total numbers of favorable cases is all combinations with
κ ≤ h
:
) ( properties code random the satisfying codes of Number
0
h q
h
h
∑
=








=
κ
ω

We define the parameter P
1
to be the interference pmf of one interferer
transmitting 1-bit. Subsequently, the probability that the interferer is making h
collisions with the user of interest is:
) ' (
'
) (
) (
0 '
1
h q
h
h q
h
h P
h
∑
=
















=
κ
ω
ω

(3.4)

Now substituting q(x) from 3.3 and 3.4 into equation 3.5, we find the
probability distribution of interference from one interferer in two cases:

2-D OOC with no restriction:








−
− Λ
















−
− Λ








=
∑
=
' '
0 '
1
h
T
h
h
T
h
P
h
ω
ω ω
ω
ω ω
κ

(3.5)

32
2-D OOC with not more than one pulse per wavelength:
x
h x h
h
x
h x
h
T x h x
h
T
h
T x h x
h
T
h
P
)
1
1 (
'
'
) 1 (
'
)
1
1 (
) 1 (
) 2 , ' max( 0 '
'
) 2 , max(
1
−








−
− Λ








−
−
−








−








−
− Λ








−
−
−








=
∑ ∑
∑
Λ − = =
Λ − =
ω
ω ω
ω
ω
ω ω
ω
ω
ω
κ
ω
ω

(3.6)

The above equations are giving the probability of any user colliding with the
first user in h locations. Now assuming that there are totally i users interfering with
the original code transmitting 1, and also assuming that the interference distributions
of all different users are independent, we can convolve the above distribution i times
to find the distribution for interference of i interferers. The independence assumption
is quite reasonable for a large enough code-set, where
∗
refers to the convolution
operator:
i1 i1
PP*P
−
=

In other words P
i
is the distribution of MAI when there are i interferers
transmitting “1” and making interference with the user of interest:
1) ing transmitt are users i | Pr( ) ( h MAI h P
i
= =

When there are A interferers in the system transmitting “1” and “0” with
probability β and (1−β) respectively, using equation 3.1 we find the probability of
h collisions as:

33
κ β β
κ
A h h P
j
A
h MAI
i
A
h
j
j A j
,..., 0 ) ( ) 1 ( ) Pr( = −








= =
∑






=
−

The lower range of the summation is due to the fact that the upper bound of
maximum collision in the presence of i interferers transmitting 1 is iκ. Note that the
2-D with no restriction will result in 1-D OCDMA for the case Λ=1.
Hard Limiting Receiver:
In the following, a purely combinatorial method is used to find MAI distribution for
hard limiting receiver. Alternatively, the novel method of [23] for 1-D OOCs which
uses Markov chains can be generalized to 2-D codes too, which is not discussed
here. We assume (i) any interfering user can have at most one collision κ=1 with the
user of interest and (ii) there are A+1 active users in the system (A interfering users).
Note that in this section we are considering only κ=1 case for hard limiting receiver,
while there is no restriction on κ for hard limiting receiver. The interfering users can
make up to A collisions in ω different cells (a given t-λ location). Since we are using
a hard limiter, there can be at most one collision in each cell, and for that reason after
hard limiting, the maximum amount of possible collision will be max (Α,ω).
We assume that”α” of these active users are transmitting ”1”. We want to find
the number of ways that these α interferers cause x (x ≥h) collisions in h different
cells, so we choose x users out of these α users, and partition them into the h
partitions. Since users are assumed independent in this counting method, the

34
number of ways to do the partitioning is S(x,h) [105], where S(x,h) is the second type
Stirling number, calculated by:
1 ) 0 , 0 ( ; ) , 1 ( ) 1 , 1 ( ) , ( = − × + − − = S j i S j j i S j i S

Since x can vary from h to α, the whole count is a summation over x from h to
α. In addition, the h cells can be chosen out of ω pulses and since the collisions are
ordered, these h partitions can be permutated in h! ways. So the total number of the
codes that have h collisions in h of ω pulses with the user of interest is:
∑
=
−
















=
α
α
α ω
α
h x
x x
q q h x S
x h
h send users collisions h C ) 0 ( ) 1 ( ) , ( ! ) " 1 " | (

(3.7)

Where q(1) is the number of ways that a code can be chosen to have exactly
one collision with a specific pulse of the user of interest, q(0) is the number of codes
without any collision with the user of interest. Since 0 ≤ h ≤ ω, the probability of
having MAI equal to h provided α users transmitting “1” is:
∑
=
= =
ω
α
α
α
0
) " 1 " | (
) " 1 " | (
) " 1 " | Pr(
h
send users collisions h C
send users collisions h C
send users h MAI

Using equation (2) we can find the distribution of MAI as:
∑
∑
=
−
=
−








= =
A
h
A
h
A
send users collisions h C
send users s collision h C
h MAI
α
α α
ω
β β
α
α
α
) 1 (
) " 1 " | (
) " 1 " | (
) Pr(
0

(3.8)

35
The lower range of the summation is due to the fact that the upper bound of the
maximum collision in the presence of i interferers transmitting 1 is i.
Substituting q(x) in equation 3.7 by equations 3.2 and 3.3, we get C(h
Collisions | α users send ˝1˝) for OOC with no restriction, and OOC with not more
than one pulse per wavelength respectively. Then we can use these values in
equation 3.8 to MAI pmf in each case. Note that 1-D O-CDMA is a special case of
general 2-D O-CDMA ,using OOCs with no restriction, where Λ=1, in the function
q(x).

3.4 Probability Distribution of the interference
Fig. 3.3 shows the probability distribution of the interference for different number of
users and (Λ,Τ,ω)=(20, 8,15) and (Λ,Τ,ω)=(64, 40,31) in Fig. 3.3 (a) and (b),
respectively for conventional receiver. It should be noted that we have tried to
consider current practical systems and potentials of O-CDMA system in future, and
as a result of that, we show the examples with small and large code size. In both
cases, increasing the number of users increases the mean and variance of the
distribution. The tail of the curve goes up to the number of interfering users - number
of active user minus “1”- multiplied by κ . It is clear that increasing κ causes more
interference - increasing mean and variance - in the system and as a result of that a
reduction in the number of active users.

36
0 5 10 15 20
0
0.1
0.2
0.3
0.4
Interference
Probability
κ=1
κ=2
A=7
A=14
0 5 10 15 20
0
0.1
0.2
0.3
0.4
Interference
Probability
κ=1
κ=2
A=7
A=14

0 20 40 60
0
0.05
0.1
0.15
Interference
Probability
κ=1
κ=2
A=100
A=175
0 20 40 60
0
0.05
0.1
0.15
0
0.05
0.1
0.15
Interference
Probability
κ=1
κ=2
A=100
A=175

(a) (b)
Fig. 3.3. Pmf of the interference (number of collision induced from other users) for
code of size (Λ⋅Τ,ω)= (a) (20,8,15) (b) (64,40,31) for different number of active
users. When the code size and number of users increase the pdfs starts too look like
Gaussian

The only advantage of increasing κ in the system is increasing the number of
codes in the code-set (potential users), which may be a network requirement to
achieve a certain ratio of potential to active users. Fig. 3.3(a) shows the probability
distribution for small numbers of chip-times and wavelengths and an accordingly
small number of active users. In this case, the pmfs are not Gaussian-like, however
in Fig. 3.3(b), where the system can support 175 users, the pmfs become more like a
Gaussian shape, which is expected by central limit theorem. So we can conclude that
the Gaussian assumption is a reasonable assumption for large number of users and
code dimension, while it is not that accurate for small number of users and code
dimensions This is when most of practical interest lies in this region considering the
technology limitations.

37
Comparison of the pmfs of the system with hard limiting (WHL) and without
hard limiting (W/OHL), where both are using ( Λ,Τ,ω,κ)=(64,40,31,1) as code
parameters for 175 active users is depicted in Fig. 3.4. Using a hard limiter, tail of
pmf does not go beyond the code weight - unlike a conventional receiver in which
tail of pmf grows with an increase in the number of active users. However, the
probability of each point within zero and code weight is more in hard limiting
versus conventional system for fixed code and number of active users. Since the pmf
is bounded from both sides, the Gaussian assumption is not valid for the “with hard
limiter” (WHL) system. It is also clear that the mean and variance of the distribution
of the hard-limiting receiver system is decreased in comparison with conventional
receiver, which is the result of limiting the amount of interference in the receiver.

0 20 40 60 80
0
0.05
0.1
0.15
Active User: 175
With
HL
Without
HL
Tail of
WHL cuts
off at
weight
Interference
Probability
0 20 40 60 80
0
0.05
0.1
0.15
Active User: 175
With
HL
Without
HL
Tail of
WHL cuts
off at
weight
Interference
Probability

Fig. 3.4. Distribution of interference for the system with and without hard limiter for
175 active users  (Λ,Τ,ω,κ)=(64,40,31,1)

38
3.5 System Performance
We assume that an O-CDMA system with parameters (Λ, Τ, ω, κ) is used, and
there are A users transmitting data simultaneously. Let’s P
A
be the MAI pmf of this
system found as described in Section III, and the threshold level is set to th. The
error probability in this system is given by Pr(MAI>th), which can be computed as
following for both with and without hard limiting cases:
Conventional O-CDMA Receiver:

∑
−
=
=
κ ) 1 (
) (
A
th h
A A
h P BER

Hard Limiting receiver:

∑
=
=
ω
th h
A A
h P BER ) (

In following we assume that the amount of threshold is set to ω−0.5, which is
optimal if we have no knowledge about the number of active users. If we know how
many users are on the line, then the threshold can be set to a different optimal value
which can improve performance [86].
A. Conventional Receiver (Correlation Receiver)
A rough estimate of the maximum number of users that can transmit
simultaneously in a system is code weight. This means that – in the absence of other
noise sources – a system can operate free of interference error as long as the number
of active users is less than that of the code weight. As discussed before in the O-

39
CDMA systems, it is favorable to have at most one pulse per wavelength because
that code weight puts a limitation on the minimum number of wavelengths in the
system; moreover, there is a trade-off between the code weight and code cardinality.
Increasing the code weight decreases the number of codes (potential users) for a
fixed number of wavelengths and chip times. Fig. 3.5 shows lower bounds on code
dimensions for error free transmission that achieve 16, 32, 48, and 64 active users.
These graphs plot the minimum number of wavelengths and corresponding number
of chip-times for the error free operation such that the number of codes given by
Johnson bound [103] is greater than or equal to the number of active users
0 50 100 150 200
0
20
40
60
# of chip time
# of Wavelength (Λ)
ω=16
ω=32
ω=48
ω=64
Error Free
ω=A
ω: weight A: # of active user
0 50 100 150 200
0
20
40
60
# of chip time
# of Wavelength (Λ)
ω=16
ω=32
ω=48
ω=64
Error Free
ω=A
ω: weight A: # of active user

Fig. 3.5. Minimum number of wavelengths and chip times required for error
free signaling for various number of active users

The above analysis is based on the constraint that no errors should occur due to
interference. However, for large numbers of chip times and wavelengths, a

40
reasonable BER is achievable using a weight less than the number of active users.
This is due to the fact that in a large code set the error that occurs due to MAI may
be very small as a result of the probabilistic nature of the system. In this case, the
code weight becomes an important design parameter in an O-CDMA system.
Fig. 3.6(a) shows the number of potential users in an O-CDMA system using
OOC of size (64,100,ω,1) for different values of weight. Moreover, the number of
potential users falls drastically by increasing the code weight. This can result in a
situation where the limitation of the number of active users is the shortage of codes
instead of MAI.
Fig. 3.6(b) shows the effect of weight on the number of active users. It is clear
that because the number of wavelengths is 64, the code weight can be at most 64 as
well. As a result, for the interference-induced-error free transmission, the maximum
number of active users is 64. However, to achieve an interference-induced-error rate
of <1e-9, the system can support up to 150 active users which means 2.5 times
greater spectral efficiency in the O-CDMA system. Interestingly the largest number
of active users does not happen for weight 64, instead it happens for weight = 44.
That is because for weight greater than 44, the maximum number of active users is
limited by the number of potential users and not the amount of interference in the
link. It is also shown that by fixing the interference-induced-error to be less than 1e-
6, the peak of the curve is moved to lower weight. In this case, the maximum number
of active users is increased to 182 at weight 18. This shows that for lower accepted
BER, the optimum weight is restricted with MAI instead of the numbers of potential

41
users. Here, the optimum weight is 18, and consequently there are 1336 potential
users.

20 30 40 50 60
0
500
1000
1500
2000
weight
# of Potential users
20 30 40 50 60 20 30 40 50 60
0
500
1000
1500
2000
0
500
1000
1500
2000
weight
# of Potential users

020 40 60
0
50
100
150
200
# of of active users
BER<1e-9
BER<1e-6
weight
020 40 60 020 40 60
0
50
100
150
200
0
50
100
150
200
# of of active users
BER<1e-9
BER<1e-6
weight

(a) (b)
Fig. 3.6. OOC code of size (64,100,w, 1) (a) Number of potential users (b) Number
of active users to support BER<1E-9 and 1E-6

Fig. 3.7 shows the probability of error versus weight for different numbers of
active users for a fixed number of wavelengths and chip times. It is clear that
generally as the weight increases, the probability of error for a given number of
active users decreases. Fig. 3.7(a) shows that for a small number of wavelengths and
chip-times the BER of 1e-9 cannot be easily achieved. Fig. 3.7(b) shows that when
the code dimension increases, low BER can be accommodated for large numbers of
users.

42

Hard limiting Receiver
We use the interference model for the hard limiting receiver in order to
quantify its performance improvement over the conventional receiver. Fig. 3.8 shows
the number of active users that can be supported by the hard-limiting receiver for
varying BERs. As the code weight increases, the number of active users - supported
by the hard-limiting system - grows until it reaches to its maximum point. This point
corresponds to the optimum weight for any given code parameter set. The fall-off of
the curves is mainly due to the insufficient number of potential users, since the
number of active users cannot exceed the number of potential users. These curves
clearly illustrate that as the code weight increases, the number of active users
increase too, whereas, the number of potential users decreases. Moreover, the
optimal point depends on how much BER can be tolerated in the system.
Λ=16
T=8
Code Weight
Probability of error
A=8
A=12
A=16
A=20
Λ=16
T=8
Code Weight
Probability of error
A=8
A=12
A=16
A=20
Λ=48
T=32
A=24
A=36
A=48
A=64
Probability of error
Code Weight
Λ=48
T=32
A=24
A=36
A=48
A=64
Probability of error
Code Weight

(a) (b)
Fig. 3.7. Probability of error versus weight for different number of active users
for a fixed number of wavelength and chip time Vs. weight. as the weight
increases, the probability of error for a given number of active users decreases

43
0 20 40 60
0
100
200
300
400
500
MAX # of
potential users
Code Weight
# of Active Users
BER<1E-9
BER<1E-4
BER<1E-3
0 20 40 60
0
100
200
300
400
500
MAX # of
potential users
Code Weight
# of Active Users
BER<1E-9
BER<1E-4
BER<1E-3

Fig. 3.8. Maximum number of active users for a code with 64 wavelength, and
40 chip time for varying weight for different preset BER. Number of is limited
by MAI so the maximum number of users as code weight increases till it
reaches the code cardinality and from that point the number of users is limited
by the number of potential users in which increasing the code weight has the
reverse effect

Fig. 3.9 shows the increase in the number of active users in a system using a
hard limiter versus conventional receiver for different code parameters and varying
code weight. It also shows that increasing the number of wavelength in hard limiting
gain is more important than increasing the number of chip times. This is due to the
fact that for optimized code weight, a hard limiting receiver is mainly restricted to
the number of codes in the code-set instead of the interference; and number of
wavelengths is more important in increasing the number of codes.

44

Fig. 3.10 shows the probability of error vs. number of active users for the
conventional (WO/HL), and hard limiting system for 64 wavelengths and 40 chip
times and weight 15 and 31. The probability of error increases as the number of
active users increases in both cases, however, there is a significant improvement
when using the hard limiting receiver. Weight 31 is chosen in Fig. 3.10 as it is the
optimal weight for hard limiting receiver. This figure shows that at BER=1E-9, the
number of active users is increased from 69 users to 170 users.
% Increase in # of users
(64,40)
(32,20)
(30,140)
(16,20)
(32,20)
(30,140)
(64,40)
(32,20)
(16,20)
1
1.5
2
2.5
Code Weight
0 102030 4050
(30,140)
% Increase in # of users
(64,40)
(32,20)
(30,140)
(16,20)
(64,40)
(32,20)
(30,140)
(16,20)
(32,20)
(30,140)
(64,40)
(32,20)
(16,20)
1
1.5
2
2.5
Code Weight
0 102030 4050 0 102030 4050
(30,140)

Fig. 3.9. Hard-limiting based improvement ratio in number of active users for
codes with different (Λ,Τ) = (# of wavelengths, # of chip times) at the BER of
1e-9. Increasing the number of wavelength in hard limiting gain is more
important than increasing the number of chip times

45

3.6 Spectral Efficiency
Although the main motivation for using O-CDMA is not its spectral efficiency,
the spectral efficiency is a classical metric in evaluating any communication system.
In principle the spectral efficiency of an O-CDMA system is far less than the
equivalent WDM system [72]. This is due to the fact that the O-CDMA system uses
unipolar signalling, and as a result of that complete orthogonality within codes is
impossible. Study of spectral efficiency using different code constructions and
conventional receiver has been shown in [34, 72]. In this section, we show a general
method to find an upper bound of spectral efficiency for conventional and hard
limiting receivers; moreover, we propose some rules of thumbs for the choice of the
codes to find the best achievable spectral efficiency in the O-CDMA systems.
0 50 100 150 200 250
10
-30
10
-20
10
-10
10
0
w=31
w=15
WHL
W/OHL
Number of Active User
BER
# of WL: 64
# of chip time: 40
0 50 100 150 200 250
10
-30
10
-20
10
-10
10
0
w=31
w=15
WHL
W/OHL
Number of Active User
BER
# of WL: 64
# of chip time: 40

Fig. 3.10. Probability of error vs. # of active users for code weights 15,
and 31 (Λ=64, Τ=40). We can observe a significant improvement in
system performance using Hard limiting receiver

46
Unlike WDM, in the case of O-CDMA systems the spectral efficiency is not
only based on the wavelength spacing, but is also highly dependent on the choice of
codes to be used in the system. Spectral efficiency in an OCDMA system is defined
as:
α ΛΤ
= =
A
idth TotalBandw
b
R A
S
*

Where S is the spectral efficiency, A is the number of active users, R
b
is the bit
rate, and total bandwidth is the bandwidth used - considering the guard band
between different wavelengths. The second equality can be driven easily by plugging
in the wavelengths and channel spacing. Parameter α is defined as:
ChipRate
Spacing Wavelength
= α

In an O-CDMA system, parameters Λ, and Τ are given by hardware limitations,
and α depends on the system structure as well as the chip-rate of the system. It is
clear that the spectral efficiency is highly dependent on this parameter. Usually in
optical systems α of order of 2 is used, however, to increase the spectral efficiency
α of the order of one or smaller has been demonstrated experimentally using mode
locked lasers and narrowband filtering [9]. Given these parameters (Λ,Τ,α), the code
weight and maximum collision parameters should be optimized in order to maximize
the number of active users and consequently, the spectral efficiency. In the following
analysis the statistical model for the interference is considered to estimate the

47
number of active users in the system which uses 2-D OOC with maximum one pulse
per wavelength.
0
20
40 0
10
20
30
40
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
# of chip-times
# of wavelengths
Spectral Efficiency
0
20
40 0
10
20
30
40
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0
20
40 0
10
20
30
40
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
# of chip-times
# of wavelengths
Spectral Efficiency
0
20
40 0
10
20
30
40
0.02
0.04
0.06
0.08
0.1
0.12
0.14
# of chip-times
# of wavelengths
Spectral Efficiency
0
20
40 0
10
20
30
40
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0
20
40 0
10
20
30
40
0.02
0.04
0.06
0.08
0.1
0.12
0.14
# of chip-times
# of wavelengths
Spectral Efficiency

(a) (b)
Fig. 3.11. Maximum spectral efficiency achievable for the wavelengths and chip-
times in the range of 4 to 40 using conventional receivers (a)BER<1E-9
(b)BER<1E-3; all point are derived for optimum weight and MCP

Fig. 3.11(a) shows the maximum spectral efficiency achievable for the
asynchronous O-CDMA system using conventional receivers for optimised weight
and maximum collision parameter. For any given wavelength and chip time
combination, the optimum weight and maximum collision parameter is found in
order to maximize the number of active users for the BER set to <1e-9. In this curve,
the parameter α is assumed “1”. Increasing the number of active users generally
requires increasing the number of wavelengths and chip times. Spectral efficiency
decreases by the multiplication of number of wavelengths and chip times, whereas,
the increase in the number of active users by increasing chip times and wavelengths
is not quadratic. As a result, the spectral efficiency in the system decreases as the
number of desired active users increases. Fig. 3.11 (b) shows the same trend for

48
spectral efficiency while the BER in the system is set to 1E-3. In this case the floor
of the curve is higher.
Fig. 3.12(a) and (b) show the maximum achievable spectral efficiency for the
system using hard limiting receiver. The parameters α and MCP are both assumed to
be one and the optimization is done over the code weight. The figures also show that
by using hard limiting receiver, increasing the number of wavelength is more
effective than increasing the number of chip times. Moreover, by increasing the
number of wavelengths and chip times the spectral efficiency does not decrease with
the same rate as the conventional receiver.

0
20
40 0
10
20 30
40
0
0.05
0.1
0.15
0.2
0.25
# of chip-times
# of wavelengths
Spectral Efficiency
0
20
40 0
10
20 30
40
0
0.05
0.1
0.15
0.2
0.25
# of chip-times
# of wavelengths
Spectral Efficiency
0
20
40 0
20
40
0.1
0.15
0.2
0.25
0.3
0.35
# of chip-times
# of wavelengths
Spectral Efficiency
0
20
40 0
20
40
0.1
0.15
0.2
0.25
0.3
0.35
# of chip-times
# of wavelengths
Spectral Efficiency

(a) (b)
Fig. 3.12. Maximum spectral efficiency achievable for the wavelengths and chip-
times in the range of 4 to 40 using hard limiting receivers (a)BER<1E-9
(b)BER<1E-3; all point are derived for optimum weight

49
Chapter 4
Experimental and Theoretical Analysis of the
Optimum Decision Threshold for Varying
Numbers of Active Users in a 2D Time-
Wavelength Asynchronous O-CDMA System

In this chapter, we experimentally demonstrate the existence of an optimal
decision threshold in an O-CDMA system and show its relation to the number of
active users. We also demonstrate a monitoring scheme to estimate the number of
active users in an O-CDMA system using harmonics of RF clock tones.

4.1 O-CDMA Plug and Play Networks
One major advantage of optical code-division-multiple-access systems may is that
they are suitable for “plug-and-play” operations in a many-user optical local-area-
network (LAN) [94, 95]. This plug-and-play issue means that new users could be
added to the network by simply assigning a new code, and without any major
hardware changes to an existing network. Such a scenario implies that the normal
difficulties of optical network control and management are even more
challenging[48, 49].

50
In both one and two dimensional O-CDMA systems the pattern of the sequence is
unique to each user with proper auto and cross correlation properties to ensure the
detection of each user data in the presence of other users. These sequences are called
a 1-D or 2-D optical orthogonal codes (OOCs), which can be based on various code
design schemes [115, 119]. All users transmit to a star coupler which collects all the
data and broadcasts them simultaneously through the network to all users. At a
given user’s receiver, a decoder “stacks” the pulses as appropriate for that user’s
code, and after photo-detection, a threshold detector compares the signal to a pre-set
threshold, resulting in a “1” bit if all the chips are present, and a “0” bit otherwise.
Because there is a probability of multiple users transmitting at the same time, and
users are transmitted asynchronously with respect to each other, other user chips act
as “interference” to a receiver tuned to a particular code. The pattern of the
interference is random due to the asynchronous nature of O-CDMA in both 1-D and
2-D O-CDMA systems, and the probability distribution of the interference depends
on the number of active users in the system and code parameters which are: the
number of wavelengths, the number of chip times, code weight (number of pulses in
a time wavelength code matrix), and maximum collision parameter (a predefined
parameter for a given code-set, which sets the maximum amount of collision within
two codes in the code set – i.e., maximum allowable cross correlation between two
codes) [7, 92]. Furthermore, the electronic threshold must be set to a maximum value
to prevent false positive results. Fig. 4.1(a) shows an example of a system with 6
users, (user of interest and 5 interferes) where each user has code-weight 6 (6 pulses

51
per bit). In the worst case scenario 5 interferers can create a false autocorrelation
peak of weight 5. We must set the threshold at ~5.5 to ensure that only when all 6
intended chips are present will the system consider the signal as a “1” bit.
However, this does not result in an optimal bit-error-rate (BER) when the
number of transmitting users varies. An ideal threshold value for a system with 6
chips is “3”, at the middle between the “1” and “0” autocorrelation levels, when
there is only one user present. At this level, the BER is much improved, and shifting
the threshold level up or down results in degraded BER compared to this optimal
value. This is if the threshold level of ~5.5 is used in a single user system, noise
induced fluctuations give a small window of operation. This threshold, however, is
not used, as the presence of additional active users (i.e. interfering chips at the
decoder) will quickly cause bit errors resulting from the reduced threshold.
Knowledge of the number of active users enables a receiver to dynamically
adjust the decoder threshold level, which can provide a wider power margin to the
decoder/receiver setup. In fact, it has been shown theoretically that such adjustable
thresholding can potentially improve the performance of the O-CDMA network[60,
73]. One recent publication has postulated to monitor total system optical power in
order to determine the optimum threshold in an O-CDMA network [73]. However,
this method does not take into account the possibility of saturated erbium doped
fiber amplifiers (EDFAs) keeping power levels constant despite a change in the
number of active users, and does not demonstrate the technique in an experimental
O-CDMA system.

52
In this chapter, we demonstrate via simulation and experiment the effect of
changing the electronic threshold on an 11-chip, 6-wavelength, and 4-user O-CDMA
system [86, 88]. We vary the number of active users in the network, and for any
number of users, we find the minimum power to achieve the BER of 1E-9 by varying
the threshold level. The threshold level which corresponds to the minimum power is
the optimum threshold. We then fix the optical power at this minimum power, and
vary the threshold and determine the respective BER. We illustrate that the optimal
threshold value for an O-CDMA system varies with the number of active users, and
that use of a non-optimal threshold level can degrade the BER by four or more
orders of magnitude. For example, our experimental results show that using a
threshold level that is optimal for 2 active users - when only 1 user is active - can
result in a BER degradation of four orders of magnitude from 10
-9
to 10
-5
. We also
illustrate that the effect of changing the overlap (“collision” within users for 100 ps
collision, 50 ps collision, and no collision case”) between interfering user chips is
minimal compared to the effect that results from changing the total number of active
users in the system.
In addition, we also introduce and demonstrate a simple method for
monitoring the number of active users in a system, which makes possible for an O-
CDMA system to use dynamic thresholding; this occurs when the threshold changes
as the number of users transmitting in the system fluctuates. We show that the
power of certain RF harmonics is related to the total number of active users, and that
by measuring the power of one or more RF harmonics, the number of users can be

53
estimated - although not necessarily determined with 100% precision. Our
experimental results show that for an O-CDMA system using 11 chip times, 6
wavelengths, and with a code weight of 6 (6 pulses per bit), by adaptively changing
the threshold a receiver sensitivity improvement of >3 dB is achievable.
(a)
(b)
Chip time
Single user (No MAI)
Bit time
“1” Transmitted
Auto correlation
peak main user
Bit time
“0” Transmitted
Decision
Threshold
Multiple user
Error Margin
MAI from
other users
“1”
Error Margin
Varying
Decision
Threshold
Error Margin
“1”
Fixed
Decision
Threshold
Chip time
Single user (No MAI)
Bit time
“1” Transmitted
Auto correlation
peak main user
Bit time
“0” Transmitted
Decision
Threshold
Multiple user Multiple user
Error Margin
MAI from
other users
“1”
Error Margin
Varying
Decision
Threshold
Error Margin
“1”
Fixed
Decision
Threshold

Fig. 4.1. Concept: Effect of multiple access interference (MAI) on the error margin
for varying threshold (a) detected autocorrelation peak along with MAI from
interferers (b) detected autocorrelation peak of a single user
4.2 Effect of varying threshold in an O-CDMA system
A conceptual diagram of the O-CDMA output is shown in Fig. 4.1. In Fig. 4.1(a), the
auto-correlation peak of a user with weight 6 (6 pulses per bit time) along with
multiple access interference (MAI) from other user is shown, assuming that the user
has sent the pattern of “10”. In this case, the optimum point for the decision
threshold is shown to be in the middle of the auto correlation peak and the maximum

54
amount of MAI. The maximum amount of MAI depends on the number of users and
varies according to the asynchronous nature of the network. As illustrated in this
figure, having 5 interferers in the network the maximum amount of collision is
weight 5. It should be noted that the MAI has increased the level of the “0” bit and as
a result, the
optimum threshold is increased. In this case, the threshold is not in the
middle of the auto-correlation peak whereas in the absence of MAI the threshold
level should be set to the middle of auto-correlation peak. In Fig. 4.1(b), we show
two different scenarios, where a varying and fixed decision threshold are shown. It is
clear that the error margin for the varying decision threshold is much higher than the
fixed decision threshold. This confirms that fixing receiver threshold at the worst
case in an asynchronous O-CDMA network is not a wise choice- due to the
dynamics of the network. The reason is that the worst case dose not happens very
frequently, and setting the threshold at the worst case will result in the performance
degradation for most cases.
we performed simulations for different code sets in order to evaluate the
system scalability according to the number of users and size of the code,. The
simulation is done using both the exact analytical model of the interference to model
the MAI and asynchronous nature of the O-CDMA network, and with thermal noise
in the receiver.
For any given code, the s MAI statistic depend on the number of wavelengths
and chip times, code weight, maximum collision parameter, and number of active

55
users. Fig. 4.2 shows the probability distributions of MAI for a transmitted bit “0”
and a bit “1”. The code used in this graph has 16 wavelengths and 40 chip times. The
code weight is set to 16 (1 pulse per wavelength), and maximum collision parameter
is 1. It should be noted that the distributions depend on the number of active users
(A), more specifically the tail of the distribution grows as much as the number of
interferes (A-1). The probability distribution of the MAI for a transmitted bit “1” is
the shifted version of the probability distribution of the MAI for a transmitted bit “0”
with the amount of code weight, which is basically the amount of auto-correlation of
the user of interest. Note that these graphs are normalized to code weight.
Fig. 4.2(a) shows the probability distribution for 12 active users, and Fig.
4.2(b) shows the probability distribution for 20 active users. When there are 12
active users in the system, the two probability distributions are completely
disjointed. In this case, in the absence of other noise sources, there would be no
errors due to MAI by setting the threshold to the code weight. Fig. 4.2(b) shows the
distributions when the number of active users is greater than the code weight. In this
case, the probability distributions of a transmitted “0” and “1”-bit are not disjointed.
Therefore, the threshold should be set to minimize the addition of probability of “0”
detected as “1” and probability of “1” detected as “0”. In the presence of other noise
sources in both cases (a, and b), the bounded MAI probability distributions will be
convolved with the noise probability distribution, and therefore, the threshold varies
from weight and it should be designed accordingly. For a given hardware, the code
construction and its parameters are known beforehand, so the optimum threshold can

56
be designed by knowing of the number of active users in the network. The details of
the statistics of MAI are explained in [92, 93].
0 10 20 30
0
0.1
0.2
0.3
MAI
probability
P(MAI | 1)
P(MAI |0)
W=16
0 10 20 30
0
0.1
0.2
0.3
MAI
probability
P(MAI | 1)
P(MAI |0)
W=16

MAI
probability
P(MAI | 1)
P(MAI |0)
0 10 20 30 40
0
0.05
0.1
0.15
0.2
0.25
MAI
probability
P(MAI | 1)
P(MAI |0)
0 10 20 30 40
0
0.05
0.1
0.15
0.2
0.25
(a) (b)
Fig. 4.2. Simulation results for the probability of MAI for transmitted “0” bit
and “1” bit for a code with 16 wavelengths, 40 chip times, code weight 16, and
(a) number of active users 12, (b) number of active users 20

Our analytical model is based on the average asynchronous delays between
the entire active users in the network. In the simulation, for a given number of active
users, we change optical power and threshold level, and we calculate the respective
BER on this matrix. We choose a BER of 1E-9 as our baseline. We first find the
minimum power needed to achieve the error rate of 1E-9 for varying threshold
levels. According to this simulation, the respective threshold of the minimum power
is the optimum threshold. Using this calculated optical power, we vary the threshold
and record the variations in the BER as presented in Fig. 4.3. It should be noted that
the optical power used for varying number of active users in these graphs are

57
different, where they show some amount of power penalty as the number of users
increases.
Fig. 4.3(a) demonstrates our simulation results of BER vs. threshold level in
our system as the number of active users varies for the above mentioned code
parameters (16 wavelengths, 40 chip times, code weight 16). It is clear that by
increasing the number of users, the optimum threshold level increases as well. This
is due to the fact that by increasing the number of users, the level of the MAI will be
increased; therefore, the threshold should be set higher to avoid a “0”-bit to be
detected as “1”-bit. In Fig. 4.3, the threshold level is normalized to weight. For the
case of 1 user, the v-shape curve is symmetric; however, by increasing the number of
users, the curves become more asymmetric. This is due to the fact that the
probability distributions - as shown in Fig. 4.2 - are asymmetric, so in the lower part
of the V shape curves the degradation is mainly dominant by a “0” bit being detected
as “1” bit, and the upper part is mainly dominant by a “1” bit being detected as “0”
bit.
Fig. 4.3(b) illustrates the BER versus threshold for varying number of active
users for a code with 6 wavelengths, 11 chip times, and weight 6. This is the code
that we use in our experiment. In this case, the threshold is normalized for a signal,
which is between 0 volts and –1 volts, to follow the experiment. The power penalties
for A=2, 3, and 4 users are 1.4 dB, 3.1dB, and 5.3 dB correspondingly with respect
to the single user case. Comparison of these figures shows that a code with larger
size (number of chip times, wavelength and weight) can support more users;

58
however, the trends of optimum threshold remain almost the same when the numbers
of users increases. The same argument is valid for a fixed code size and varying
weight. If we increase the code weight, the autocorrelation peak increases. This
results in an increase in the number of active users supported by the system, thus the
higher shift of auto correlation peak for the added active users.
The experimental setup for our OCDMA system is shown in Fig. 4.4. In this
experiment, we use six lasers, at 1548, 1549.5, 1551.2, 1552.8, 1554.4, and 1556 nm,
couple them together, and modulate them at the chip rate 11 Gchip/s (bit rate is 1 G
bit/s) using a 2
9
-1 PRBS. After an EDFA, we split the signal between four branches,
each with a unique O-CDMA encoder, to represent 4 O-CDMA users. In each
encoder, we split the wavelengths using a demultiplexer, assign each wavelength
chip an appropriate time slot using optical delay lines, and recombine the
wavelengths. Each user is transmitted through different short lengths of fiber in
order to decorrelate the signals. All user branches are then sent through a delay line
followed by a polarization controller and then all four users are recombined using a
multiplexer, which resembles the O-CDMA node in the network. The manual delay
lines for each user enable checking the real nature of asynchronous O-CDMA system
by delaying different users with respect to each other, and achieve different amount
of collision in the system. We put a polarization controller on these paths in order to
decrease the effect of beat noise between different users. After the multiplexer, all
users are transmitted through a short length of fiber as the O-CDMA link and are
received by a photo-receiver.

59
4 6 8 10 12 14 16
Threshold
Normalized to code weight
A=1
A=5
A=10
A=15
8
6
4
2
-Log(BER)
4 6 8 10 12 14 16
Threshold
Normalized to code weight
A=1
A=5
A=10
A=15
8
6
4
2
-Log(BER)

-0.8 -0.6 -0.4 -0.2 0
10
8
6
4
2
0
A=1
A=2
A=3
A=4
Threshold(V)
A: Number of active users
-Log(BER)
-0.8 -0.6 -0.4 -0.2 0
10
8
6
4
2
0
A=1
A=2
A=3
A=4
Threshold(V)
A: Number of active users
-Log(BER)

(a) (b)
Fig. 4.3. Simulation results for threshold level vs. BER as the number of active
users is varied for (a) a code with 16 wavelengths, 40 chip times, code weight 16
(threshold is normalized to code weight) (b) a code with 6 wavelengths, 11 chip
times, code weight 6 (threshold is normalized for an electrical signal within –1 and
0 ; A is the number of active users

At the receiver, we amplify the received signal, demultiplex the wavelengths,
and use a second set of fiber delays to stack the chips to decode the data. The
decoder can be tuned to detect any of the transmitted users. After decoding, we use
an optical tap line for monitoring. In the main data path, a receiver detects the
decoded data, followed by a threshold detector that samples the data to determine
whether it exceeds a set decision threshold. In the monitoring path, we monitor the
RF components of the electrical spectrum. We see that the best correlation is
between the 5GHz component and the number of active users, and consequently by

60
using a threshold voltage control unit we can change the level of the decision
threshold.
The main concentration of this section is on the characterization of the effects
of the threshold with respect to MAI. In order to isolate the effects of MAI and beat
noise, polarization controllers are put on each user’s link to decrease the amount of
beat noise in the receiver by making the polarizations orthogonal to each other. It
should be noted that, the effect of beat noise is significant when the number of users
is close to the code-weight (auto correlation peak). Consequently, this effect is not
severe for our system having at most 3 users with code weight 6. The effects of
varying the polarization and beat noise respectively are mainly narrowing the V-
shape threshold curves.
Based on our experimental set up including the encoder/decoder scheme, we
use codes with 6 wavelengths, 11 chip times, weight 6, and maximum collision
parameter 1. The code construction has only one pulse per wavelength which is
suitable for delay-lines encoder/decoder schemes. These codes are designed based on
function plot A code construction [77]. The code cardinality (number of codes in the
code-set) is 11. This code construction provides an optimal code set, which means
that it achieves the maximum number of codes in the code set which can be achieved
using a matrix of 11 chip times and 6 wavelengths. However, not all of those users
could be used in the network simultaneously and accordingly, we use 4 of them for
our 4 active users. Due to the asynchronous nature of the network, all different

61
delays within users will be experienced, and so there is no significant distinction in
choosing different codes.
MOD
11
Gchip/s
λ
1
λ
2
λ
3
λ
4
λ
5
λ
6
6x1 coupler
User 1
4x1 coupler
t
t
t
RX BERT
Electronic Threshold
Detector
Users 2, 3 & 4
EDFA
DEMUX
λ
1
λ
2
λ
3
λ
4
λ
5
λ
6
T
1
T
2
T
3
T
4
T
5
T
6
Delays
Fiber Link
All Users
λ
1
DEMUX
λ
2
λ
3
λ
4
λ
5
λ
6
T
1
T
2
T
3
T
4
T
5
T
6
Delays
RX
Monitor (5G
Component)
Transmitter Link
Receiver
Threshold
Voltage
Control
MOD
11
Gchip/s
λ
1
λ
2
λ
3
λ
4
λ
5
λ
6
6x1 coupler
User 1
4x1 coupler
t
t
t
RX BERT
Electronic Threshold
Detector
Users 2, 3 & 4
EDFA
DEMUX
λ
1
λ
2
λ
3
λ
4
λ
5
λ
6
T
1
T
2
T
3
T
4
T
5
T
6
Delays
DEMUX DEMUX
λ
1
λ
2
λ
3
λ
4
λ
5
λ
6
T
1
T
2
T
3
T
4
T
5
T
6
Delays
Fiber Link
All Users
λ
1
DEMUX
λ
2
λ
3
λ
4
λ
5
λ
6
T
1
T
2
T
3
T
4
T
5
T
6
Delays
DEMUX DEMUX
λ
2
λ
3
λ
4
λ
5
λ
6
T
1
T
2
T
3
T
4
T
5
T
6
Delays
RX
Monitor (5G
Component)
Transmitter Link
Receiver
Threshold
Voltage
Control

Fig. 4.4. Experimental setup for the O-CDMA system (EDFA: Erbium doped
fiber amplifier , RX: photo receiver, BPF: Band-pass filter, MOD: modulator)
Fig. 4.5(a) shows the experimental results for 1, 2, and 3 users. In the
experiment it is not possible to check all different delays between all users, therefore,
the data is taken only for the situation where there is a complete collision between
two users, meaning that the BER is taken for a single user case. Then another user is
added with a fixed delay with respect to the first user having a complete collision
(100 ps pulse collision) with the first user. The third user is then added to the system
having a complete collision with the first user. In the experiment, for any number of
active users, we find the minimum power to achieve the BER of 1E-9 by varying the

62
threshold level. The threshold level which corresponds to the minimum power is the
optimum threshold. We then fix the optical power at this minimum power, and vary
the threshold and determine the respective BER. The experiment is done while the
electrical amplitude of the signal is fixed to 1 volt, using variable electrical
attenuators after the photo receiver. At this point, we keep the optical power constant
and vary the threshold and measure the BER of the system. Our threshold detector is
voltage controlled so by changing the control voltage the threshold level varies. It
should be noted that the optical power for different families of curves are different,
and subsequently BER of those families cannot be compared with each other for a
fixed threshold. The experiment clearly shows that the dynamic range of threshold is
less than what is suggested by the simulation, i.e. for 1 active user, the dynamic
range of the threshold is suggested to be 200 mV, whereas, in the experiment it is
less than 150 mV. It is also important to observe that as the number of users
increases the V shape curves get narrower, which leads to a less dynamic range and
higher sensitivity to the threshold. This is due to the fact that as the number of users
increases the cross correlation peak is higher and accordingly the threshold level is
set to a higher value, so the error margin gets narrower and the error rate becomes
more sensitive to the variation of threshold.
As an example, Fig. 4.5(a) shows that the ideal decision threshold when three
users are active (a level of ‘4’), results in a BER of ~10
-4
where only 1 user is active
– a BER three orders of magnitude smaller than that obtainable when the ideal
single-user threshold of ‘3’ is used. In addition, the optimum threshold for the 1 user

63
case cannot recover the 3 active user case at all. Therefore, a system that is able to
determine the number of active users at any given moment, and is able to use this
value to set the threshold, can result in significant BER improvement.
Fig. 4.5(b) shows BER vs. threshold while there are 2 active users in the
system as the collision between the two users varies. The rectangle curve shows the
variation of the BER vs. the threshold for two users, as there is no collision between
those users. The circle and triangle curves are taken for the cases of half collision
and full collision respectively. The variation of the voltage of the optimum threshold
is not significant, i.e. the optimum threshold of no-collision case causes a BER of
1E-8 in the full-collision case, however, as the amount of collision is increased, the
dynamic range of the threshold is decreased, specifically in low thresholds where the
main limitation is the amount of collision in comparison with higher thresholds,
which are limited by noise. Not much deviation is observed at thresholds higher than
optimum, since this region is limited by noise, rather than the amount of collision.

64
2
4
6
8
10
-0.8 -0.6 -0.4 -0.2
Threshold (V)
-Log(BER)
A=1
A=2
A=3
A= # of
Active Users
2
4
6
8
10
-0.8 -0.6 -0.4 -0.2
Threshold (V)
-Log(BER)
A=1
A=2
A=3
A= # of
Active Users

2
4
6
8
10
-0.7 -0.5 -0.3
No
Collision
Half
Collision
Full
Collision
Threshold (V)
-Log(BER)
.(a) (b)
Fig. 4.5. (a) Experimental results for BER vs. threshold level as the number of
active users is varied. (b) BER vs. Threshold level for 2 active users as the amount
of collision between the two users is varied.

6(a) shows the encoded bits of the user of interest, when the pattern of 11010 is sent,
and Fig. 4.6(b) shows the decoded data for the same pattern by a matched decoder.
Fig. 4.6(c) and (d) show the output of the first user when there are 2 and 3 users
present in the system. The additional noise in these two cases is due to beat noise.
The accumulated MAI is clearly visible in the bit patterns as the number of active
users increases. It is also clear that for a single user case the 1-bit level is fixed,
however, as the number of users increases, the level of the “1”-bit becomes variable;
because the collisions from other users can be at the same place as the main
autocorrelation, they are able to add up to this autocorrelation. This can be clearly
seen in the Fig. 4.6(d) where there are three users active in the system. In this figure,

65
the second “1”-bit has a lower level than the other two and therefore, the error
margin is increased for a transmitted “1”-bit. However, the dominant error factor is
when zero is sent, and as a result of this increase, (This can be seen where zero is
transmitted) the error margin over the “0” bits is decreased. Fig. 4.6(e) shows the
detected bit after the threshold detector when 3 users are active in the system.

(a)
user1 encoded
11 1 00
user1 encoded user1 encoded
11 1 00

(c)
user1 & user2 user1 & user2

(b)
User 1 decoded
1 ns
User 1 decoded
1 ns

(d)
User 1 decoded (Users 2&3 present) User 1 decoded (Users 2&3 present)
(e)
User 1detected (Users 2&3 present)
11 1 00
User 1detected (Users 2&3 present)
11 1 00

Fig. 4.6. (a) Encoded O-CDMA data of user 1 when the pattern 11010 is sent. (b)
Decoded O-CDMA data of the first user (c) Decoded O-CDMA data of the first
user with one interferer (d) Decoded O-CDMA data of the first user with two
interfere. (e) 1 Gbit/s decoded data after threshold detection.

Fig. 4.7 shows our BER results as we vary the decision threshold. In Fig.
4.7(a), the system is set up for 2 active users, and the threshold is optimized to
provide minimum BER when 2 users are active (triangles). One user is then

66
deactivated, and the BER is taken again without changing the threshold, resulting in
the curve denoted by circles. In all cases, the electrical voltage after the photo
receiver is kept constant using electrical attenuator after photo receiver. We then re-
adjust the threshold to the optimal value for a single active user to achieve a ~1.8 dB
sensitivity improvement in comparison with the fixed threshold single user case.
Fig. 4.7(b) shows the same effect for the 3-user case – the threshold is
optimized for minimum BER when 3 users are active, and BER curves are taken for
the cases of 1, 2, and 3 users. We then adaptively optimize the threshold for 2 users,
and show a 3.6 dB sensitivity improvement in the 2-user curve over the 3-user-
threshold case. When we optimize the threshold for the single user case, we obtain a
3 dB increase in sensitivity compared to a single active user with the 3-user
threshold. It should be noted that the data has been taken for the full collision (all
interfering users are colliding with the main user with maximum collision, which is
the “worst case”), so considering the statistics of the O-CDMA system, the power
penalty variations would be varying with different asynchronous delays.

67
3
4
5
6
7
8
9
10
-20 -19 -18 -17 -16 -15 -14
2 users
Fixed
Threshold
Optimum
Threshold
1 users
Log(BER)
Received Optical Power
3
4
5
6
7
8
9
10
-20 -19 -18 -17 -16 -15 -14
2 users
Fixed
Threshold
Optimum
Threshold
1 users
Log(BER)
Received Optical Power

3
4
5
6
7
8
9
10
-20 -18 -16 -14 -12 -10
3 users
2 users 1 users
Opt Th.
Fix Th.
Log(BER)
Received Optical Power
3
4
5
6
7
8
9
10
-20 -18 -16 -14 -12 -10
3 users
2 users 1 users
Opt Th.
Fix Th.
3
4
5
6
7
8
9
10
-20 -18 -16 -14 -12 -10
3
4
5
6
7
8
9
10
-20 -18 -16 -14 -12 -10
3 users
2 users 1 users
Opt Th.
Fix Th.
Log(BER)
Received Optical Power

(a) (b)
Fig. 4.7. Bit-error-rate curves for the case of (a) threshold fixed for 2 active
users, then re-optimized for a single user and (b) threshold fixed for 3 active
users-two users and single user are taken, and then re-optimized for one or two
active users. Adaptive threshold results in significant sensitivity enhancement.

4.3 Monitoring the number of active users in an O-CDMA system
Recently, the whole topic of monitoring optical channels in an optical network has
taken on increased significance due to the desire to know the physical-state-of-the-
network for proper control and management [51]. For example, the cost-effective
measuring of the presence and quality of optical wavelength-division-multiplexed
(WDM) channels may be crucial to robust operation. Evidently, any set of optical
channels can be detected and measured electronically for any desired qualities, but
this brute-force approach may not be cost effective.

68
.
Electrical Spectrum Time domain Signal
RF Component
1 Bit
t
RZ Signal
Chip time
Autocorrelation
(User of interest)
Decreased
RF Component
1 Bit
t
MAI (Other
users)
f
f
(a)
Single User
(b)
Multiple User
Electrical Spectrum Time domain Signal
RF Component
1 Bit
t
RZ Signal
Chip time
Autocorrelation
(User of interest)
Decreased
RF Component
1 Bit
t
MAI (Other
users)
f
f
(a)
Single User
(b)
Multiple User

Fig. 4.8. Conceptual diagram of our RF tone monitoring scheme: Increasing the
number of active users will cause the harmonics of RF component to drop

To our knowledge, such monitoring issues have not yet been pursued
aggressively in the context of an O-CDMA system. Specifically, there may be a
keen desire to monitor the number of active users in the network, which is quite
challenging in an O-CDMA network, since all users share the same time and
frequency space and are only separated by orthogonality in code space. Knowledge
of the instantaneous number of active users brings the following key benefits: (i) it
provides crucial information for network control and management. For instance, the
network control and management system can use this information to determine,
statistically, whether the network can handle additional users, and the approximate
increase in data errors as a result, and (ii) it enables the receiver to dynamically re-

69
adjust the decoder threshold level which can provide a wider power margin to the
decoder/receiver setup
Fig. 4.8 shows a conceptual diagram of our active user-monitoring scheme
(under the assumption that at least one user is active). In a single user case - after the
decoder - the chip-time/wavelength pulses of the user are aligned on top of each
other and the post-detection signal resembles an RZ signal with a duty cycle equal to
the bit-rate divided by the chip-rate (Fig. 4.8(a)). In this scenario, we have strong RF
harmonics in all multiples of the bit-rate frequency. As the number of active users in
the system increases, the original RZ signal is detected along with shifted bits from
other users. As the “extra-user” data has passed through the decoder for a non-
matching user, their pulses are not aligned on top of each other so they are spread all
over the bit period. In addition, the increasing number of pulses may cause the main
“peak” pulse power to drop as EDFAs are often set for constant output power, and
this power is now split between all user pulses. This is a signal which is not an RZ
signal anymore and it is spread over time, so the bandwidth is less, resulting in
decreased RF tone power. The relation between the RF tones and number of users is
not a linear relation. This is because of the asynchronous nature of the O-CDMA
system, in which, different asynchronous delays can cause different scenarios.

70
Sample points (Variable delays between users)
Relative RF powers (dB)
2 users
3 users
4 users
1 users
-14
-12
-10
-8
-6
-4
-2
0
Samples
Sample points (Variable delays between users)
Relative RF powers (dB)
2 users
3 users
4 users
1 users
-14
-12
-10
-8
-6
-4
-2
0
Samples

Fig. 4.9. 5 GHz RF tone power vs. number of active users.

Fig. 4.9. shows the relative measured RF power of the 5 GHz component for
various delays between asynchronous users for the cases of 1, 2, 3, and 4 active
users. We measure the RF power for all harmonics of the spectrum, and the best
correlation between RF power and the number of active user in the system comes
with the 5 GHz components. The number of points increases with the number of
active users, as more delay configurations are possible with the number of active
users are increased (more delay combination between different users). This figure
shows that there is a clear distinction in the range of the RF power as the number of
active users changes from 1 to 2, and to 3. It can be seen that there is a clear
distinction between the one (~0 dB), two (~-4 to -6 dB) and three (~-7 to -10 dB)
user cases, however, for some specific delays, the RF power levels for 3 and 4 active
users overlap slightly. This is due to the asynchronous delays between users where in
some cases, the delays in a 4 user case resembles that of a 3 user case. We believe

71
(a)
(b)

Fig. 4.10. RF spectra for the case of (a) single user and (b) 4
users present

this is not a significant issue, particularly for high-user-count O-CDMA systems, as
the RF power level top spectrum shows the 5 GHz component when there is only 1
user active (5 GHz tone at -23 dBm) and the bottom where there are 4 users active
(~-38 dBm), with need not precisely determine the number of users, but rather
estimate it within a small range, such that the threshold level can be placed near an
optimal point (sub-optimal estimation). It should also be noted that the results are for
up to 4 users and for higher user count, the code set should be larger (more number
of chip time, wavelength, and weight) and for such a system we anticipate that more
numbers of users can be detected using this method. Fig. 4.10(a) shows the RF
spectrum for two cases – the the 5 GHz component level changing by ~15 dBm.

72
Chapter 5
M-ary Modulation in O-CDMA Systems to
Increase the Spectral Efficiency

In this chapter, we introduce a novel modulation scheme for OCDMA systems which
increases the spectral efficiency, i.e. bit rate for a given chip time. This modulation
scheme is called code position modulation (CPM) and uses different time shifts of
the spreading sequence assigned to each user to transmit M-ary information. In the
following we demonstrate some variations of CPM.

5.1 Experimental Demonstration of Code Position Modulation in
2-D O-CDMA Systems
In non-multiple-access systems, Pulse Position Modulation (PPM) provides a
straightforward method for increasing bit rate [93]. In PPM, each signaling interval,
T
s
, is divided into M equal slots and only one of these M slots must contain a pulse.
Therefore, there are M different symbols capable of representing Log
2
M bits so the
bit rate would be (Log
2
M)/T
s
.
There have been some theoretical studies to include M-ary modulations on
O-CDMA systems. One suggestion was to use different codes as different symbols
[20]. The major problem of this method is the scaling of the hardware with
increasing symbol/bits, and the lack of proper number of codes. Other methods tries

73
to take the advantages of PPM in OCDMA systems in [39, 71, 101, 124]., but the
suggested systems have some inherent problems: (1) they have to use very short
pulses, (2) they require a cyclic code shifter in the transmitter that is difficult to
implement, (3) they are limited to a specific code construction, and (4) the proposed
methods are not shown experimentally. One paper has shown the experimental
encoding-decoding of PPM in O-CDMA without relating it to system performance
[15]. In this section, we demonstrate a PPM-OCDMA with 6 active users that has a
simple structure and does not require extremely short pulses.
In this section ,we propose and demonstrate code position modulation (CPM)
scheme that has the potential of increasing the number of active users in a 1-D or 2-
D O-CDMA asynchronous system while maintaining the same bandwidth utilization.
We use different time shifts of the incoming code to provide an additional degree of
freedom for encoding more data within each code, i.e. each time shift represents a
symbol. In this case having T chip times (the number of different shift equals to the
number of chip times), we have T different shifts representing T different symbols,
as a result of that we can send log
2
T bits of information using the same spectrum. In
this case adjacent symbols can leak into each other after spreading, however we
show that by using specific code structures “one pulse per wavelength” the original
sequence is recoverable.
We experimentally demonstrated an O-CDMA system using 8 wavelength,
16 chip times, and code-weight 6 and we enable 6 active users operating at BER
<1E-9 with bit rate 2.5 Gb/s using 10Gchip/s pulses.

74
Data = 1
PPM
Data = 011 Data = 010 Data = 001 Data = 000
Data = 111 Data = 110 Data = 101 Data = 100
(send nothing)
Data = 0
OOK
Bit Time
Symbol Time
Chip time
Data = 1
PPM
Data = 011 Data = 010 Data = 001 Data = 000
Data = 111 Data = 110 Data = 101 Data = 100
Data = 011 Data = 010 Data = 001 Data = 000
Data = 111 Data = 110 Data = 101 Data = 100
(send nothing)
Data = 0
OOK
Bit Time
Symbol Time
Chip time
Fig. 5.1. Autocorrelation peak of the OCDMA appears in different chip times to
represent different symbol

5.1.1 Code-Position Modulation
In conventional O-CDMA systems, the presence or absence of the signal marks a 1
or a 0 respectively. In the CPM O-CDMA system, an input bit stream is fed to a bit
to symbol converter. Each symbol is represented by a specific time shift of the
spreading sequence, which after the decoder creates the different shifts of the
autocorrelation peak within the symbol time. The result after O-CDMA decoder is
the various position of the autocorrelation peak holding the symbol information.
Thus the size of the message alphabet under CPM is T and to send the ith symbol in
the modulation alphabet, the transmitter sends the ith shift along the time-axis of the
its 2-D spreading code. This has been shown in Fig. 5.1.
Fig. 5. 2. shows an example of a system which takes 3 bits together to
provide 1 symbol represented by the proper shift of the spreading sequence. In this
example, the imput bit stream is “101001” , which corresponds to symbols S
5
S
1
. In

75
order to transmit these symbols two different shifts of the spreading sequence are
transmitted. It can be seen that each encoded signal goes beyond its boundaries.
After the decoder, these chips are aligned on top of each other to create the
autocorrelation peak at the right position which then can be decoded as the sequence
of symbols.
While CPM can be employed in conjunction with either a 1-D or 2-D O-
CDMA systems, the discussion here will focus on the 2-D case. The spreading code
of each user in a 2-D OCDMA system with Λ wavelengths and T time slots, can be
visualized as a 2-D (Λ×T) {0, 1} array. Let T
c
denote the chip time, corresponding to
the duration of a time slot and a chip rate of 1/T
c
chips per second. The duration T
s
of
a message symbol is then given by T
s
=TT
c
.
Each user must be synchronous to its corresponding transmitter. This can be
achieved by transmitting a predefined pattern which is known by the both sides of
the system. It should be emphasized that this synchronization is only needed for each
transmitter and receiver pairs, but different users are asynchronous to each other.

76
S
5
S
1
S
5
S
1
101001
101 001
Input Bit
Stream
Bits to
Symbols
O-CDMA
Encoder
O-CDMA
Decoder
Symbols
to Bits
Encoding is in the different phase
shifts of the peak
Other users
T
1
T
2
T
3
T
4
T
5
T
6
T
7
T
8
λ
1
λ
3
λ
2
Data = 001(S
1
) Data = 011 (S
5
)
T
1
T
2
T
3
T
4
T
5
T
6
T
7
T
8
T
1
T
2
T
3
T
4
T
5
T
6
T
7
T
8
λ
1
λ
3
λ
2
Data = 001(S
1
) Data = 011 (S
5
)
T
1
T
2
T
3
T
4
T
5
T
6
T
7
T
8
Peaks are spread they can leak into
another adjacent symbol
Output Bit
Stream
S
5
S
1
S
5
S
1
101001
101 001
Input Bit
Stream
Bits to
Symbols
O-CDMA
Encoder
O-CDMA
Decoder
Symbols
to Bits
Encoding is in the different phase
shifts of the peak
Other users
T
1
T
2
T
3
T
4
T
5
T
6
T
7
T
8
λ
1
λ
3
λ
2
Data = 001(S
1
) Data = 011 (S
5
)
T
1
T
2
T
3
T
4
T
5
T
6
T
7
T
8
T
1
T
2
T
3
T
4
T
5
T
6
T
7
T
8
λ
1
λ
3
λ
2
Data = 001(S
1
) Data = 011 (S
5
) Data = 001(S
1
) Data = 011 (S
5
)
T
1
T
2
T
3
T
4
T
5
T
6
T
7
T
8
T
1
T
2
T
3
T
4
T
5
T
6
T
7
T
8
λ
1
λ
3
λ
2
Data = 001(S
1
) Data = 011 (S
5
)
T
1
T
2
T
3
T
4
T
5
T
6
T
7
T
8
Peaks are spread they can leak into
another adjacent symbol
Output Bit
Stream

Fig. 5.2. CPM O-CDMA: Each symbol is represented by a time shift of the
spreading sequence, the time shift will be translated as the position of
autocorrelation peak within the symbol time after the receiver

5.1.2 Experimental Results
The experimental setup for our OCDMA system is shown in Fig. 5.3. We use eight
equally spaced lasers, couple them together and modulate them at 10 Gchip/s. The
data provided to the modulator is the PPM data. After an EDFA, we split the signal
between six branches, each with a unique O-CDMA encoder, to generate data for 6
O-CDMA users. Each encoder is based on an FBG (fiber Bragg grating) technology
which implements the splitting of the wavelengths and assigning each wavelength
chip an appropriate timeslot. Each user is transmitted through different short lengths
of fiber to decorrelate the signals and then all six users are recombined. At the
receiver, we amplify the received signal, demultiplex the wavelengths and use a
second set of fiber delays to stack the chips to decode the data. At the receiver, a

77
photo-receiver detects the decoded symbols followed by a threshold detector that
samples the data to determine whether it exceeds a set decision threshold.
User 1
T-λ FBG
Encoder λ
1
λ
8
MOD
10 Gchip/s
CPM Encoded
Data
8x1 coupler
EDFA
1X6 Splitter
Tunable Delay
Line
τ
User 1
User 6
6X1 Coupler
τ
Decoder
BERT Rx
Threshold
Detector
User 1
T-λ FBG
Encoder λ
1
λ
8
MOD
10 Gchip/s
CPM Encoded
Data
8x1 coupler
EDFA
1X6 Splitter
Tunable Delay
Line
τ
User 1
User 6
6X1 Coupler
τ
Decoder
BERT Rx
Threshold
Detector

Fig. 5.3. CPM system: input bit stream is converted to symbols, each symbol is
represented by various time shifts of the peak.

In our experiment we used the codes with 8 wavelength, 16 chip times, and
code weight 6. Our codes are based on code construction function Plot B [77]. and
they can support 18 potential users. Our code construction is optimal in terms of the
number of code-sets and has at most one pulse per wavelength. The chip rate is 10
Gchip/s and the symbol rate is 625 Msymbol/s. Due to the CPM enhancement factor,
the equivalent bit rate is 2.5 Gbit/s. It should be noted that for the conventional O-
CDMA system using the same chip rate and supporting 2.5 Gbit/s there were only 4
chip times which could limit the number of users.

78
1 12 15 10 3 1 12 15 10 3

112 15 10 3 112 15 10 3

1 12 15 10 3 1 12 15 10 3

(a) (b) (c)
Fig. 5.4. (a) modulated CPM data, various shifts of the autocorrelation peak
represents the symbols (b) CPM-OCDMA encoded data (c) decoded CPM-
OCDMA data ; the scale is 1 ns/div

The 10 Gchip/s CPM encoded data is generated electronically and then is fed
to the modulator. Fig. 5.4 shows the CPM data after the modulator. The dashed line
shows the boundary of each symbol, and the position of each autocorrelation peak
shows the transmitted symbol. Fig. 5.4(a) shows the transmission of the bit steam
0001’1111’0011’1100’1010’ which correspond to the symbol stream 1,15,3,12, and
10 noting that each symbol is carrying 4 bit information. (Each symbol is encoded in
the relative shift of the autocorrelation peak.) This symbol stream is then fed to each
encoder. In the output of the encoder, the encoded data of each symbol can leak to
other symbol boundaries as shown in Fig. 5.4(b). This is very important to observe
that although different symbols are now out of their original boundaries and leaking
together, due to the complete orthogonality of the each user’s data to its various time
shifts the data is recoverable without any additional degradation. This property only
holds if the codes have at most one per wavelength. This can be seen in the figure
4(c) where the encoded data is passed through the decoder and the original data is
recovered. It should also be noted that here we show an extreme case where the

79
symbol 15 is followed by 3 and as a result of that the encoded symbol 15 is
completely leaked into symbol 3 and sill the decoder can recover the data. Another
important observation is that in the encoded stream there is a pulse twice the size of
other pulses, this has happened when a pulse from encoded stream 15 and 3 are
colliding, however due to the fact that our codes have the properties of being one
pulse per wavelength the colliding pulsed have to be from different wavelengths and
as a result of that they are completely separable in the decoder as shown by Fig.
5.4(c).
(1)
(2)
(3)
(4)
(5)
(6)

Fig. 5.5. (left) shows the encoded data of the user of interest for 1 thought 6
users. (right) the decoded version of the same signal along with the
interference: as the number of users increase the traffic on the link becomes
more regulated.

80
Fig. 5.5 (left) shows the encoded data of the user of interest for 1 thought 6
users. At the right side of this figure we can see the decoded version of the same
signal along with the interference. From the encoded signals we can see that as the
number of users increase the traffic on the link becomes more regulated. This will
basically means that as the number of users increases the MAI fill on the empty
spaces. By observing the decoded signal we can wee that the level of MAI is
increasing, however, the autocorrelation peak is detectible.
. Fig. 5.6 shows our BER measurement. It should be noted that the analysis
above was not considering the optical effects, and were only showing the trends of
increase in spectral efficiency for asymptotic behavior (when signal to noise ratio
reaches infinity). In order to show that the system can experimentally work in the
presence of various optical effects, we need to show the BER performance of the
system. In this figure, the received optical power is the power of the user interest
when the number of users increases in the O-CDMA system. It can be seen that by
increasing the number of users the power penalty increases, however the 6 users
were recoverable with less than 8 dB power penalty. Power penalties are due to
increased MAI and additional noises in the system, which reduces the eye opening.

81
4
5
6
7
8
9
10
-26 -24 -22 -20 -18 -16
Received Optical Power of the user
of interest (dBm)
-Log (BER)
1 2 3 4 5 6
Number of active users
4
5
6
7
8
9
10
-26 -24 -22 -20 -18 -16
Received Optical Power of the user
of interest (dBm)
-Log (BER)
1 2 3 4 5 6
Number of active users

Fig. 5.6. BER vs. received optical power

5.2 Analytical Model for PPM O-CDMA Systems
There have been recent reports of further enhancing the “efficiency” by employing
pulse-position modulation (PPM), in which the number of bits-per-symbol will
increase to >1 [101]. The added degree-of-freedom with PPM is that the
autocorrelation peak can appear in any of the chip times, and this time location
carries added information. One key limitation of PPM is that optical chips are
allowed to leak into the adjacent symbol times, thus changing the dynamic of the
MAI produced by other users. Although PPM and its variants have been
demonstrated experimentally, there has been no analysis that shows the increased
MAI and its limitation on the number of users.

82
In this section, we derive an analytical model that provides the full statistics
of the probability distribution of MAI in an O-CDMA network that uses PPM. Our
results show that the effect of increased MAI in PPM is almost like MAI in
conventional OCDMA with twice the number of users. We also show that overall
increase using PPM OCDMA is up to ~3X increase in spectral efficiency as
compared to conventional OCDMA. We also compare various code sets and show
different trends of system performance and code parameters.

5.2.1 Mathematical Model
There has been an interest in providing M-ary modulation formats in O-CDMA
systems, in order to increase the bit-rate and/or number of users in an O-CDMA
system. Such techniques include: (1) using M different codes as M different symbols
[71], (2) Code cyclic modulation (CCM), in which each symbol is transmitted using
a different cyclic shifts of the encoded O-CDMA signal,[54, 101] and (3) PPM (or
CPM) in which each symbol is transmitted using time shift of the encoded signal
[39, 71, 101, 124]. In conventional O-CDMA systems, the presence or absence of
the signal marks a 1 or a 0 respectively. In the PPM O-CDMA system, each symbol
is represented by a specific time shift of the spreading sequence, which after the
decoder creates the different shifts of the autocorrelation peak within the symbol
time.

83
The major differences of the MAI of the PPM and OOK OCDMA systems
are: (1) there is a transmission for 0 symbols, and (2) as adjacent symbols are
allowed to leak into each other, the MAI within two users can be more than 1
collision. This may increase the amount of MAI in the system resulting in the
limitation of the number of users. So to evaluate the global system performance we
first need to find the number of active users that can transmit with a certain error rate
and using that find the spectral efficiency of the system. In order to provide a model
to describe the performance of the O-CDMA system using PPM, we need to use a
probabilistic model based on code parameters under general optical orthogonal codes
(OOC) limitations. It should be noted that the focus of this section is on the
performance of the O-CDMA network in the presence of interference so the results
resemble the asymptotic performance of the network when the signal to noise ratio
approaches infinity [7]. There has also been other reports on analysis of the M-ary
OCDMA system performance based on an specific code set [57, 67].
Let's assume there are two users A and B in the system, and we need to find
the pmf of MAI that B creates on A. We assume the users are chip synchronous,
while they are not symbol synchronous. In PPM system we need to correlate the
output of channel in every single chip time. In other word we have a sliding window
which the correlation detection is done. This is shown in Fig. 5.7 along with 3
possible position of the 3 consecutive symbols of the interfere which can collide with
the window of interest. Let's assume we need to compute the interference in window
A, which has a time delay δ chip times relative to the reference point T=0. Let's set

84
this reference time equal to the symbol clock of user B. Without loss of generality
we can assume 0 ≤δ ≤Τ−1.

Now three consecutive symbols of user B can cause interference in the
window A: (1) The symbol B
L
which was started during the symbol time [-T,0).
Depending on what symbol was transmitted a tail of length τ
L
, 0 ≤τ
L
≤Τ−1 of this
symbol can be extended in time interval [0,T) and cause interference with window A.
(2) The symbol B
P
which starts during the symbol time [0,T) with a delay equal to τ
P

, 0 ≤ τ
P
≤Τ−1. (3) The symbol B
N
which will start in the interval [T,2T) with a delay
τ
N
, , 0 ≤τ
N
≤Τ−1 from T.
Pmf of MAI for the conventional OCDMA which assumes the duration of
interference is of maximum time T is derived in several papers for example [93]. Let
Symbol (window)
of interest
Window A
B
L
B
P
B
N
-T 0 2T T
τ
L
τ
P
τ
N
δ
possible
position
of 3
symbol of
the
interferes
Symbol (window)
of interest
Window A
B
L
B
P
B
N
-T 0 2T T
τ
L
τ
P
τ
N
δ
possible
position
of 3
symbol of
the
interferes

Fig. 5.7. The upper window shows the correlation window and the lower shows
various possible positions of 3 possible symbols that can collide with the
correlation window

85
call this pmf p
T
(h)=Pr{some interferer of length T causes h units of
interference}.Now we need to find p
τ
(h)in which the duration of interference is
reduced to τ, τ ≤Τ . If we assume spreading sequences as random codes with
maximum collision restriction as it is assumed in [93] then the probability of having
collision equal to h ≠0 scales with τ/T, while probability of having 0 collision
increases:



= + −
≠
=
0 ), 0 ( / ) / 1 (
0 ), ( /
) (
h P T T
h h P T
h p
T
T
τ τ
τ
τ
We can compute P
BL
(h), P
BP
(h),and P
BN
(h) for a given set {δ,τ
L
,τ
P
,τ
N
}:
) ( ) (
) ( ) (
) ( ) (
) , 0 max(
) , 0 max(
h p h P
h p h P
h p h P
N
P
L
BN
T BP
BL
τ δ
τ δ
δ τ
−
− −
−
=
=
=

Let's assume the interferences caused by B
L
, B
P
, and B
N
, has independent
pmfs, which can be justified when the code dimension increases and there are many
interferers in the system then:
BN BP BL
B
MAI
P P P P
N P L
∗ ∗ =
τ τ τ δ , , ,

Where * is convolution operator. In order to compute pmf of MAI in general
we should average it on δ,τ
L
,τ
P
,τ
N
:

86
∑∑∑∑
∑∑∑∑
−
=
−
=
−
=
−
=
−
=
−
=
−
=
−
=
=
=
1
0
1
0
1
0
1
0
, , , 4
1
0
1
0
1
0
1
0
, , ,
1
) , , , (
TT T T
B
MAI
B
MAI
N P L
TT T T
B
MAI
B
MAI
LPN
N P L
LP N
N P L
P
T
P
pr P P
δτ τ τ
τ τ τ δ
δτ τ τ
τ τ τ δ
τ τ τ δ

Assuming there are independent users B
1
, B
2
, …, B
s
interfering with user A,
we can compute the over all pmf of MAI recursively as:
1 2 1 2 1
,..., , ,..., ,
−
∗ =
S S S
B B B
MAI
B
MAI
B B B
MAI
P P P

Fig. 5.8 shows pmf of MAI for a code with 24 wavelength, 32 chip times, and
weight 18 for 10 and 20 interferers. The pmf tail goes all the way to three times
maximum collision parameter (in this case 1), as there can be at most 3 collisions
0 10 20 30 40 50 60
0
0.05
0.1
0.15
0.2
0.25
Interference
Probability
# of λ: 24
# of chip time: 32
Code Weight:18
A:# of active users
PPM O-CDMA
A=10
A=20
0 10 20 30 40 50 60
0
0.05
0.1
0.15
0.2
0.25
Interference
Probability
# of λ: 24
# of chip time: 32
Code Weight:18
A:# of active users
PPM O-CDMA
A=10
A=20

Fig. 5.8. Probability distribution of interference in PPM O-CDMA as the number of
users increase

87
within each two users. In Fig. 5.9 the same graphs are plotted against conventional
OCDMA in logarithmic Y axis. In this figure solid lines show PPM model, while
dotted lines show conventional OCDMA system (OOK-OCDMA). In order to make
a better comparison, we have shown the pmf of the conventional OCDMA for
10,20,30 and 40 interferers, and the pmf of the PPM OCDMA for 10, and 20
interferers for the same code-set. It can be seen that the pmf of the interference for
PPM OCDMA is almost equal to the OOK OCDMA for twice the number of users.
It should be emphasized that although the pmfs look the same, the tail of the PPM
goes beyond the conventional OCDMA.

0 10 20 30 40
10
-20
10
-15
10
-10
10
-5
10
0
OOK
OCDMA
PPM
OCDMA
A=10
A=20
A=30
A=40
A=10
A=20
A: # of
Active users
Interference
Probability
0 10 20 30 40
10
-20
10
-15
10
-10
10
-5
10
0
OOK
OCDMA
PPM
OCDMA
A=10
A=20
A=30
A=40
A=10
A=20
A: # of
Active users
Interference
Probability

Fig. 5.9. Comparison of probability distribution of interference in OOK OCDMA for
number of active users (10,20,30,40) and PPM (10,20). Rule of Thumb: pmf of PPM
is close to pmf of OOK with twice the number of users

88
5.2.2 Performance Analysis
System performance depends on the receiver structure. The receiver used in the
following, chooses a threshold, and if finds only one peak above the threshold
decodes to that data and can't decode on other cases. Let’s set the threshold to code
weight. Since the only degradation assumed on the line is MAI, so we always receive
a peak for the original data, so an error occurs if we receive a false peak. Since the
MAI distribution for all chip times is the same, probability of a false peak is given
by:
) ( ) 1 (
) (
) ( ) (
3
,
int
3
,
h P T Pe
i chiptime on peak false pr Pe
h P i chiptime on peak false pr
S
th h
S
PPM MAI
erest userof i
S
th h
S
PPM MAI
∑
∑
∑
=
≠
=
− ≤
≤
⇒ =

Where, s is the number of interferers.
10 20 30 40 50
10
-20
10
-15
10
-10
10
-5
10
0
(24,32,18)
(24,64,18)
(32,32,24)
(32,64,24)
BER
(# of λ, # of chip times, code weight)
# of active users
10 20 30 40 50
10
-20
10
-15
10
-10
10
-5
10
0
(24,32,18)
(24,64,18)
(32,32,24)
(32,64,24)
BER
(# of λ, # of chip times, code weight)
# of active users

Fig. 5.10. BER vs. number of active users

89
Fig. 5.11 shows BER vs. number of active users for several code parameters.
It is clear that by increasing number of users for any code set the BER degrades.
Comparison of these two curves shows that increasing the number of wavelength
and/ or chip times reduce the MAI and respectively improve the respective BER.
One important design parameter in OCDMA systems is code weight. Fig. 5.12 shows
BER vs. code weight for a fixed code space (24 wavelengths, 32 chip times). We
show that increasing code weight results in performance enhancement. As we have
discussed all M-ary formats increase the bit per symbol transmission of O-CDMA
while limit the number of active users due to the increased MAI.
10 20 30 40 50
10
-20
10
-15
10
-10
10
-5
10
0
(24,32,18)
(24,64,18)
(32,32,24)
(32,64,24)
BER
(# of λ, # of chip times, code weight)
# of active users
10 20 30 40 50
10
-20
10
-15
10
-10
10
-5
10
0
(24,32,18)
(24,64,18)
(32,32,24)
(32,64,24)
BER
(# of λ, # of chip times, code weight)
# of active users

5 10 15 20 25
10
10
10
-5
10
0
-15
-10
Code Weight
BER
# of wavelength:24
# of chip time:32
A=7
A=14
A: number of
active users
5 10 15 20 25
10
10
10
-5
10
0
-15
-10
5 10 15 20 25
10
10
10
-5
10
0
-15
-10
10
10
10
-5
10
0
-15
-10
Code Weight
BER
# of wavelength:24
# of chip time:32
A=7
A=14
A: number of
active users

Fig. 5.11. BER vs. number of active
users: Increasing code size improves
the performance
Fig. 5.12. BER vs. code weight:
Increasing code weight improves the
system performance

In order to compare different type of O-CDMA systems the best comparison
metric is spectral efficiency which is defined as: S=A*R
b
/(BW) where A is the
number of users, R
b
is the bit rate, and bandwidth is the total bandwidth occupied
with all wavelengths. The number of users that can be supported is calculated using

90
the analytical model explained above. Fig. 5.13 shows the relative spectral efficiency
of CCM and PPM to conventional OCDMA. Both cases have more than up to ~3
times the spectral efficiency with respect to OOK O-CDMA. Spectral efficiency of
PPM is less than CCM by a small fraction, while it has extremely simpler hardware.
It should be noted that CCM OCDMA is theoretically suggested in[54], but
due to the complexity of structure, it has not been experimentally demonstrated.

10 20 30 40 50 60 70
180%
200%
220%
240%
260%
280%
# of chip times
% Increase in spectral
efficiency over OOK O-CDMA
CCM
PPM
# of wavelength: 24
code weight 18
10 20 30 40 50 60 70
180%
200%
220%
240%
260%
280%
# of chip times
% Increase in spectral
efficiency over OOK O-CDMA
CCM
PPM
# of wavelength: 24
code weight 18

Fig. 5.13. % increase of PPM and CCM vs OOK. Both PPM and CCM achieve
higher spectral efficiency with respect to OOK.

Fig. 5.14 shows the percentage increase in spectral efficiency using CPM
method compared to OOK O-CDMA. A simple estimation of the percentage increase
in spectral efficiency is log
2
(T)/2, as the bit/symbol is increased by log
2
(T), and the
number of active users is reduced by a factor of 2 (twice traffic on the link due to
always transmitting). The analysis from the modeling shows a less increase in
spectral efficiency. It also shows that the increase in spectral efficiency decreases

91
more as the number of chip times increase. This is due to the following two reasons:
(1) the increased tail of the MAI due to CPM, and (2) the CPM receiver needs to
sample on every chip time, while the conventional receiver only sample at the
autocorrelation peak. So, by increasing the number of chip times, unlike
conventional receiver, our receiver needs to sample in all those chip times. This will
increase the probability of error and limits the number of users respectively.

20 30 40 50 60
# of chip times
% Increase in spectral
efficiency over OOK O-CDMA
180%
200%
220%
240%
260%
280%
300%
CPM
(Modeling Results)
Log
2
(T)/2
20 30 40 50 60
# of chip times
% Increase in spectral
efficiency over OOK O-CDMA
180%
200%
220%
240%
260%
280%
300%
CPM
(Modeling Results)
Log
2
(T)/2

Fig. 5.14. % increase of PPM vs OOK and the ideal curve. (1) ideal case: log
2
(T)/2,
as the bit/symbol is increased by log
2
(T), and the number of active users is reduced
by a factor of 2 (2).Modeling. The increase in spectral efficiency decreases more as
the number of chip times increase because of the increased tail of the MAI due to
CPM, and sampling on every chip times

92
5. 3 Demonstration of Double Pulse Position Modulation (2-PPM)
in Time-Wavelength Optical CDMA Systems
In non-multiple-access systems, Pulse Position Modulation (PPM) provides a
straightforward method for increasing bit rate. In PPM, each signaling interval, Ts, is
divided into M equal slots and only one of these M slots must contain a pulse.
Therefore, there is M different symbols capable of representing Log2M bits so the bit
rate would be (Log2M)/Ts. Multiple PPM (MPPM), in which N out of M slots are
marked, can further increase the bit rate approximately by a factor of N. An MPPM
system with N=2 is called Double-PPM (2-PPM) and it can transmit Log2(M(M-
1)/2) bits/symbol [106].
In this section, we demonstrate a 2-PPM-OCDMA with 5 active users that
has a simple structure and does not require extremely short pulses[5].

5.3.1. 2-PPM Concept
The block diagram of the system is shown in Fig. 5.15. First, the bit stream is fed
into a bit to symbol converter that maps several bits to a specific symbol. Then, the
2-PPM symbol is fed to the OCDMA encoder, while marked slots represent the
autocorrelation peaks. The code length is set equal to the number of slots (F=M),
resulting Tc=Ts/M. So the chip time will be exactly the same as an OOK-OCDMA
system, which is far more than the chip times in [39]. We allow each encoded
symbol to spread over the next symbol. This solves the problem of implementing

93
cyclic code shifter. The signature codes have at most one pulse per wavelength, so it
will be guaranteed that adjacent symbols of a user do not interfere with each other.
At the receiver point, the OCDMA decoder correlates the received signal with its
own signature code every Tc seconds. These auto- correlation peaks form 2-PPM
symbols every Ts seconds and finally the symbol to bit converter extracts the bits
based on the position of autocorrelation peaks. Each user must be synchronous to its
corresponding transmitter. This can be achieved by transmitting a predefined pattern
that is known by the both sides of the system. It should be emphasized that this
synchronization is only needed for each transmitter and receiver pairs, but different
users are asynchronous to each other.

Fig. 5.15. 2-PPM-OCDMA System. Different wavelengths are shown by
different patterns and multiple access interference (MAI) is shown by black
pulses. Error in transmission happens when MAI or noise changes a zero slot to
one.

94
The experimental setup is shown in Fig. 5.16. We use eight equally spaced
lasers, couple them and modulate them at 10 Gchip/s. The encoded 2-PPM symbols
are sent to the modulator. After an EDFA, we split the signal between five branches,
each with a unique OCDMA encoder, to generate the input data for the five users.
We have used FBGs as encoders that split the wavelengths and assign an appropriate
timeslot to each wavelength. Then each user’s encoded data is transmitted through
different short lengths of fiber to uncorrelate the signals and then all users’ signlas
are recombined together through a coupler. At the receiver, we amplify the received
signal, demultiplex the wavelengths, and use the second set of FBGs to stack the
chips and decode the data. A photo-receiver detects the decoded symbols and finally
a threshold device examines the output of the photo receiver to determine if the slot
is one or zero.

Fig. 5.16. Experimental Setup

In our experiment, the codes have 8 wavelengths, 16 chip times, and a weight
of 6. Our codes are based on code construction algorithm in [77] and can potentially
support 18 users. The main significance of this code construction is that in terms of

95
number of active users, it is optimal, and the codes have at most one pulse per
wavelength. The chip rate is 10 Gchips/s and the symbol rate is 625 Msymbols/s.
Due to the 2-PPM factor, for M=16 the equivalent bit rate is 4.75 Gbits/s which is
6.9 times of OOK-OCDMA and 1.7 times that of PPM-OCDMA.

Fig. 5.17. (a) 2-PPM symbols (b) Encoded symbols (c) Decoded symbols with 5
active users

5.3.2 2- PPM Experimental Result
Fig. 5.17(a) shows the 2-PPM data after the modulator. The dashed lines show the
boundaries of adjacent symbols, and the position of peaks in each symbol is shown
on top of the signaling intervals. At the output of the encoder, the encoded symbol
can leak across the other encoded symbol boundaries as shown in Fig. 5.17(b). It is
very important to observe that although different symbols are now out of their
original boundaries and merging, due to the complete orthogonality, the data is
recoverable without any additional degradation. This can be seen in Fig. 5.17(c)

96
where the encoded data along with multiple access interference of four other users is
passed through the decoder and the original data is recovered. It is also important to
note that in the encoded stream there are pulses with twice the amplitude of other
pulses. This happens when a pulse from two adjacent encoded symbols collide;
however, because our codes have at most one pulse per wavelength, the colliding
pulses have different wavelengths and consequently they are completely separable in
the decoder as shown in Fig. 5.17(c).

Fig. 5.18. (a) 2-PPM symbols (b) Encoded symbols (c) Decoded symbols with 5
active users

The BER curve as a function of the received optical power of the main user is
depicted in Fig. 5.18 while 4 other users are active in the system. It should be noted
that 2-PPM-OCDMA would suffer more from MAI than PPM-OCDMA and OOK
OCDMA. The amount of required extra power to switch from a PPM-OCDMA
system to a 2-PPMOCDMA system is shown in Fig. 5.18. It is important to notice

97
that even for a single user, 2-PPM requires 3dB more power. This is because 2-PPM
symbols have two pulses with the power split between them. Therefore, in order to
have the same peak power as PPM symbols, the amount of required average power is
twice as much as needed in PPM symbols. Using 2-PPM-OCDMA in systems with a
limited number of active users can significantly increase the spectral efficiency,
because in such systems MAI is not a imitating factor. Moreover, 2-PPM-OCDMA
technique can serve as a mean for variable quality of service (QoS), i.e., some users
can operate in 2-PPMOCDMA mode while the other users send their data using
PPM-OCDMA or OOK-OCDMA.

Fig. 5.19. (a) 2-PPM symbols (b) Encoded symbols (c) Decoded symbols with 5
active users
5.3.3 10GB/S 2-PPM
As we discussed before 2-PPM is an effective way to increase the Symbol/Bit or
equivalently the Bit rate of an O-CDMA system. In this section, we explain a high

98
bit rate O-CDMA system using 2-PPM. In this project, the objective is to provide a
10Gb/s O-CDMA system supporting 8 users. If we want to use the conventional O-
CDMA to support the specified bit-rate and number of users, we need to generate
chip rates of 160 Gchip/s, which is not available using lasers and off-shelf
modulators.
(a)

(b)
(1,5) (2,10) (6,9) (1,5) (2,10) (6,9)

(c)
Fig. 5.20. (a) 2PPM encoded data of user (chip rate 24 Gchip/sec) (b) decoded data
– single user: boundaries of each symbol is shown with dotted lines. Two peaks
within each symbol time represents the transmitted symbol (c) eye diagram of the
received autocorrelation

In our experiment we used the codes with 12 wavelength, 16 chip times, and
code weight 8. Our code construction is optimal in terms of the number of code-sets
and has at most one pulse per wavelength. The chip rate is 24 Gchip/s and the
symbol rate is 1.5 Gsymbol/s. Due to the 2-PPM enhancement factor, the equivalent
bit rate is 10 Gbit/s. It should be noted that for the conventional O-CDMA system
using the same chip rate and supporting 10 Gbit/s there were only 1 chip times which

99
could not represent an O-CDMA signal. The experimental set up is the same as the
experimental set up explained above with 12 wavelengths.
(a)

(b)

(c)
Fig. 5.21. (a) 2PPM encoded data of all user (chip rate 24 Gchip/sec) (b) decoded
data of user of interest along with 7 interferers. Boundaries of each symbol is shown
with dotted lines. The autocorrelation peak is higher than the MAI from other users
(c) eye diagram of the received autocorrelation

Fig. 5.20 shows the encoded data of the 2-PPM signal. As it can be seen the
encoded data has 3 different peak level. This is due to the fact that different symbols
can leak into each other and because of having two peaks within one symbol, this
can cause a 3 level signal. However, if we use codes with at most one pulse per
wavelength the colliding peaks are from different wavelength and can be separated
in the decoder. The output of the decoder is shown in Fig. 5.20(b). Two peaks within
each symbol time represents the transmitted symbol such as (1,5). There can be 120
different transmitted symbols. The eye diagram of the recovered data is shown in
Fig. 5.20(c). Fig. 5.19(a) shows the encoded data of 8 users transmitting at the same
time. The noise like O-CDMA data is clear from this figure. Fig. 5.21(b) shows the

100
decoded autocorrelation peak of the same bits. The level of MAI is a lot higher while
the autocorrelation peak is still clear. Fig. 5.21(c) shows the eye diagram of the 8-
user case. We can see an open eye in the presence of the MAI.

Fig. 5.22. BER Vs. received optical power

Fig. 5.22 shows the BER vs. received optical power of the user of interest.
Fig. 5.22 shows the BER as the number of users increases. As we can see the there is
very small amount of penalty for 2, and 3 users, while the penalty starts to ramp up
when the number of users exceed 4. This is due to the fact the for less than 3 users
the probability that different pulses of MAI add up to each other is very low while
for 4 users and more at least at one position those MAI adds up which will degrade
the BER performance. Fig. 5.23 show the power penalty as the number of users
increase. Other issue to be mentioned is that these BERs are taken for an snap shot
of the network. (for one set of delays). While varying delays within different users
will effect the performance, we expect them to have the same trends.

101
0
1
2
3
4
5
6
02 4 6 8 10
# of users
Power Penalty (dB)
0
1
2
3
4
5
6
02 4 6 8 10
# of users
Power Penalty (dB)

Fig. 5.23. power penalty Vs number of users in the system

5.4 Differential-Pulse-Position-Modulation (DPPM) in OCDMA
Networks to Achieve Higher Data-Rate/User
Several methods have been reported that attempt to increase the bit-rate per user
given a finite number of chip times. We consider the potential for an even greater
increase over regular PPM in data-rate by demonstrating differential-pulse-position-
modulation (DPPM) in an OCDMA network. DPPM had previously been reported
for indoor infrared wireless application [124], and is considered a more
temporally/spectrally efficient coding scheme than regular PPM. In DPPM codes, the
information bits are coded into the difference of delay between two consecutive “1”
chips instead of the position of the “1” chip in the symbol hence producing variable
symbol lengths thereby increasing the data rate even further. In this section, we have
demonstrated the ability to modulate and receive OCDMA signals using the DPPM
format and to improve data rate by a factor of 8 [43] .

102

5.4.1 Differential-Pulse Position modulation (DPPM)
In 2D OCDMA networks, both time and wavelength domains are shared between
different users by assigning orthogonal codes to each user. The codes are a two
dimensional time wavelength matrix satisfying auto/cross correlation properties.
Fig. 5.24 shows the concept of DPPM-OCDMA. In this technique: first
Log
2
M input bits are mapped to one of M different symbols, then each symbol is
encoded as a time difference between each pulse with its previous pulse. The unit of
this time difference is the number of chip times between two pulses. Fig. 5.24 shows
an example of an O-CDMA system using 4 wavelengths and 16 chip times. Using
these 16 chip times, we can achieve 16 symbols; therefore every 4-bit sequence is
mapped to one symbol. In this example the input bit sequence of “0010 0110 0001”
is first mapped to the symbols “261” which is represented by the difference in the
pulses. Each of these pulses, which consist of 4 different wavelengths, is then fed to
an O-CDMA encoder. The O-CDMA encoder then assigns a specific chip time to
each wavelength to build the 2-dimentional-code matrix. It should be noted that the
number of chip times are still 16 so the encoded symbols will leak to adjacent
symbols. We show that by using one pulse per wavelength spreading OCDMA
codes, the autocorrelation is completely recoverable. In an OCDMA network
multiple users are combined to each other at the star coupler and transmitted to all
users; each user can recover its information using the matched decoder. It can be

103
seen in Fig. 5.24 that in the DPPM-OCDMA 3 symbols are transmitted while only
1.25 bits are transmitted in regular OCDMA in the same transmission time.

0010,0110,0001
DPPM
Encoder
2 6 1
t
1 6 2
OCDMA code length (16 chips)
t
OCDMA code length (16 chips)
1
1
OCDMA
Encoder
Conventional OCDMA DPPM-OCDMA
λ1
λ2
λ3
λ4
λ1
λ2
λ3
λ4
λ1
λ2
λ3
λ4
λ1
λ2
λ3
λ4
λ1
λ2
λ3
λ4
λ1
λ2
λ3
λ4
λ1
λ2
λ3
λ4
λ1
λ2
λ3
λ4
1 6 2
OCDMA
Encoder
0010,0110,0001
DPPM
Encoder
2 6 1
t
1 6 2 1 6 2
OCDMA code length (16 chips)
t
OCDMA code length (16 chips)
1
1
OCDMA
Encoder
Conventional OCDMA DPPM-OCDMA
λ1
λ2
λ3
λ4
λ1
λ2
λ3
λ4
λ1
λ2
λ3
λ4
λ1
λ2
λ3
λ4
λ1
λ2
λ3
λ4
λ1
λ2
λ3
λ4
λ1
λ2
λ3
λ4
λ1
λ2
λ3
λ4
1 6 2 1 6 2
OCDMA
Encoder

Fig. 5.24. Comparison of Conventional OCDMA with PPM OCDMA

DPPM-OCDMA increases the transmitted information per symbol time by
encoding the information in difference of the consecutive bits. The data transmission
rate in DPPM-OCDMA compare to conventional OCDMA is increased by:
1
log 2
2
+
=
N
N
Rate Increase
N

Where N is the number of OCDMA chip times.

104

5.4.2 Experimental Setup and Results
Experimental setup for our OCDMA network is shown in Fig. 5.25. We use eight
equally spaced lasers, couple them together and modulate them with DPPM coded
data at 10 Gchip/s. After an EDFA, we split the signal into 3 branches, each with a
unique O-CDMA encoder, to generate data for 3 O-CDMA users. Each encoder
consists of a circulator and a multi array of linear FBG written on a single fiber with
spacing between the FBGs designed to assign each wavelength chip an appropriate
timeslot. Each user is then transmitted through different short lengths of fiber to
decorrelate the signals and then all three users are recombined. At the receiver, we
decode the signal using an FBG array, which has the reverse delays of the
corresponding encoder. Finally, a photoreceiver detects the decoded data followed
λ
1
λ
2
8x1
MOD
1x3
10 Gchip/s
DPPM Encoded
Data
λ
8
1x3
FBG 1
FBG 2
FBG 3
OCDMA Encoders
Decoder for user 1
RX
Decision
circuit
EDFA
FBG
BERT
λ
1
λ
2
8x1
MOD
1x3
10 Gchip/s
DPPM Encoded
Data
λ
8
1x3
FBG 1
FBG 2
FBG 3
OCDMA Encoders
Decoder for user 1
RX
Decision
circuit
EDFA
FBG
BERT

Fig. 5.25. Experimental Set up

105
by a threshold detector that samples the data to determine whether it exceeds a set
decision threshold.
(a)
single user
encoded
symbols
(b)
single user
decoded
symbols
(c)
3-user decoded
symbols
20 5 9 4
20 5 9 4
20 5 9 4
20 5 9 4 20 5 9 4
20 5 9 4 20 5 9 4
20 5 9 4 20 5 9 4

Fig. 5.26. Demonstration of variable symbol length in DPPM

In our experiment we used codes with 8 wavelengths, 16 chip times, and a
code weight of 6. Our codes are based on the code construction and they can support
18 potential users. Our code construction is optimal in terms of the number of code-
sets and has at most one pulse per wavelength. The chip rate is 10 Gchip/s and the
symbol rate is 625 M-symbol/s. Due to the DPPM enhancement factor, the
equivalent bit rate is 5 Gbit/s. Fig. 5.26(a) shows the encoded symbols of a single
user for a pattern of “20594”. Due to the variable length of the symbols, the encoded
chips have different amplitude. This is due to the fact that each symbol leaks into the
adjacent symbols and the chip times of these symbols add together. This effect is
more severe for smaller symbols such as 2, 0, and 5. However, as our O-CDMA
spreading codes are at most one pulse per wavelength the added pulses consist of

106
different wavelengths, so they can be separated in the decoder. Fig. 5.26(b) shows
the decoded autocorrelation peak of a single user. The autocorrelation peaks of
different symbols have equal power, which confirms that the pulses are separated
properly. Fig. 5.26(c) shows the autocorrelation of the first user along with 2 other
interfering users.
Fig. 5.27 compares DPPM to conventional O-CDMA, and PPM. In these
figures, the pattern of “20594” is transmitted using the above-mentioned method. It
is shown that for 5 symbols transmitted using DPPM, it takes 2.5 nsec, while for the
same 5 symbols in PPM the transmission time is 8 nsec, and for OCDMA .it would
take 30 nsec to transmit the corresponding 20 bits.

(a) DPPM

(b) PPM

(c) Regular
OCDMA
20 5 9 4
2.5 ns
20 5 9 4
2.5 ns

0 2594
8 n s
0 2594
8 n s

0010 0 0 0 0 0 1 0 1 1 0 0 1 0 1 00
30 n s
0010 0 0 0 0 0 1 0 1 1 0 0 1 0 1 00
30 n s

Fig. 5.27. DPPM, PPM and conventional OCDMA transmission time comparison

The tradeoff of using DPPM–OCDMA is achieving higher data rate while
increasing multiple access interference due to reduction in the symbol time interval.

107
We were able to achieve 3 users with ~4dB power penalty compared to the single
user case (Fig. 5.28). This modulation method is especially valuable for higher user
count cases where the number of orthogonal codes and not the MAI is the network-
limiting factor. Additionally, this modulation format can be used in conjunction with
regular OCDMA transmission to enable variable quality of service in the network by
allowing higher data rates to some users while not overwhelming the system with the
additional MAI by transmitting all users at the DPPM rate.
3
4
5
6
7
8
9
10
-22 -20 -18 -16 -14 -12 -10
Received O ptical Pow er (dBm)
1 user
2 users
3 users
3 users eye
1 user eye
3
4
5
6
7
8
9
10
-22 -20 -18 -16 -14 -12 -10
Received O ptical Pow er (dBm)
1 user
2 users
3 users
3 users eye
1 user eye

Fig. 5.28. BER measurements and Eye diagrams

108
Chapter 6
O-CDMA Networks

In this chapter, we introduce Optical CDMA networks. We then introduce various
applications which O-CDMA can enhance the network performance. The
applications explained are variable quality of service, variable bit rate, and
interference avoidance algorithm to avoid congestion collapse.

6.1 Optical CDMA Networks
The Internet "backbone" is made up of fiber optic technology due to its enormous
bandwidth. However, connection to the backbone has been done through copper-
based technologies like twisted pair and DSL or Hybrid Fiber Coax cable, which
have limited bandwidth, which will create a bottleneck between the end user and
backbone. Recently, some providers begin to deliver fiber to the end user to
eliminate this bottleneck.
There are two different types of architecture to reach the fiber to the end user:
(1) point t point, (2) passive optical network (PON). Point-to-point access requires
an installation of optical transceiver for each customer. PON uses a single
transceiver with a splitter to serve up multiples of users sharing the same bandwidth.
As several users share the same fiber media, carious multiplexing scheme can be
used in a PON.

109
The proposed methods are: TDM, asynchronous transfer mode (ATM), and Ethernet
protocol, WDM [52].

Provider
Star
Coupler
1
2
3
End User
Upstream
downstream
Provider
Star
Coupler
1
2
3
End User
Upstream
downstream

Fig. 6.1. A typical Fiber to the Home (FTTH) network topology.

A CDMA-PON is a good alternative for future PON due to their enhanced
data privacy, flexibility, and simplicity of network control especially when
considering the fine granularity of traffic in local-area-networks (LANs), fine
channel granularity; flexible bandwidth management, and ability to support variable
Quality of Service (QoS). There has been such proposals to use O-CDMA as
multiplexing technique in the future PON systems [3].
One possible network architecture may be a star topology. The optical
CDMA LAN is constructed using single mode fiber and a passive optic coupler. The
passive optic coupler connects all the nodes on the network. The head end of the
network and the residential nodes are connected by fiber to the coupler. Fig. 6.1
shows a diagram of the future O-CDMA LAN.

110
6.2 Variable Quality of Service to Increase the Number of Users
in an O-CDMA Network

Optical code-division-multiple-access (O-CDMA) has generated a fair amount of
interest recently due to its potential for rapid deployment of new users based on code
assignments as well as the potential for enhanced privacy. CDMA has become quite
popular for kilo- or mega-bit/sec wireless systems for which the number of chips can
be in the hundreds, such that many users could then be accommodated via many
orthogonal codes. Unfortunately, Gbit/s optical systems strain to accommodate a
large number of chip times and thus cannot accommodate a large number of
orthogonal codes (i.e., potential users). Therefore, a key technical challenge has
been to devise solutions so that more users can be accommodated in an optical
CDMA network.
Variable QoS can mean that transmitted data will be assigned different levels
of network resources to guarantee unambiguous arrival at a destination. Typically, a
network would guarantee a lower probability of packet loss for a higher QoS.
Variable QoS enables a network, that cannot give the best QoS to all users, to divide
the appropriate resources and give higher and lower priority to a certain user classes.
If we apply this concept to O-CDMA, we can give a stronger code to a user of higher
priority and a weaker code to a user of lower priority, enabling the O-CDMA
network to: (i) provide variable QoS to its customers, as is common in many

111
networks, and (ii) have a larger set of orthogonal codes, with some stronger and
more weaker. Recently, a publication shows the use of variable weight in the O-
CDMA system, however the analysis of the system and network throughput is not
yet explored [8].
In general, O-CDMA operates as follows [119]. A data bit is encoded by
dividing the bit into many smaller chip times. Each user has a code that determines
which of the chip times would have energy. Each user’s code weight is the total
number of chip times that can have energy. The higher-weight codes can be
considered as being stronger and enable data recovery, but use more of the total
available network “code space.” In our scheme, we ascribe higher-weight codes to
the higher QoS channels and lower-weight codes to the lower QoS channels. This
division of code resources enables a network to provide QoS and to accommodate
more users.
In this section, we show a complete analytical model to describe the
performance of an O-CDMA system using variable weights in the system. Our
model is applicable to both 1-D and 2-D O-CDMA networks. We show that using
this method the number of users in the network can be increased while a predefined
performance for some of users is satisfied. Finally, we show that for a system using
64 wavelength and 40 chip times, by choosing proper weights for the different
services we can quadruple the number of users while maintaining the throughput of
high QoS users to be almost one.

112
t
Interference from
other users
t
High QoS users
Higher
Autocorrelation
Encoded data
Passive Star
Coupler
Decoded data
Low QoS users
Low weight
t
Low QoS users
Lower
Autocorrelation
t
High QoS users
High weight t
t
Interference from
other users
t
High QoS users
Higher
Autocorrelation
Encoded data
Passive Star
Coupler
Decoded data
Low QoS users
Low weight
t
Low QoS users
Lower
Autocorrelation
t
High QoS users
High weight t

Fig. 6.2. Concept of Variable QoS: Codes with higher weight has higher
autocorrelation peak so better MAI resistance

6.2.1 Concept of variable Quality of Service
Fig. 6.2 shows the concept of variable QoS using variable weight. Encoded bits of
two users are shown with weight 6 and 3. These encoded bits are combined with
other users (interference) in a star coupler. At the decoder the code with higher
weight has higher autocorrelation which makes it more robust to both MAI and
various noises in the network.
The varying weight also increases the numbers of users as well as providing
the variable QoS in the network. Fig. 6.3(a) shows the number of codes for varying
weight and code-set using 64 wavelengths and 40 chip times in the O-CDMA
network. It can be seen that the number of users for codes with smaller weight are
much larger than the numbers of codes with higher weight. Fig. 6.3(b) shows that for
a certain numbers of users the BER is much smaller for the higher weight code(48).

113

6.2.2 Analytical Interference Model For Variable QoS
In order to provide a model to describe the performance of the O-CDMA system
with multiple weight in the system, we need to use a probabilistic model based on
code parameters. This method is only based on the code parameters and is
independent of the code constructions. This modeling does not consider the optical
effects, and it is only based on code/transmitter/receiver structure, which resembles
the asymptotic performance of the network when the signal to noise ratio approaches
infinity. This method has been widely used to model the performance of O-CDMA
systems[7, 54, 93].
Code Weight
10 20 30 40 50
0
200
400
600
800
# of Potential Users
High QoS
region
High
Number
codes
Code Weight
10 20 30 40 50
0
200
400
600
800
0
200
400
600
800
# of Potential Users
High QoS
region
High
Number
codes

40 60 80 100
10
-15
10
-10
10
-5
# of active users
BER
Lower QoS
weight=24
Higher QoS
weight=48
40 60 80 100
10
-15
10
-10
10
-5
10
-15
10
-10
10
-5
# of active users
BER
Lower QoS
weight=24
Higher QoS
weight=48
(a) (b)
Fig. 6.3 (a) number of codes in a 2-D O-CDMA system for varying weight: lower
weights correspond to larger numbers of users as higher weight corresponds to
smaller number of users(b) BER vs. numbers of active users for weights 24, and 48:
A higher code weight corresponds to lower BER

114
The code parameter are (Λ,Τ,ω
1
,ω
2
) , where Λ is the number of wavelengths,
T is the number of chip times, and w
1
,w
2
are the are the weights of the codes (i.e. the
number of pulses in the code) with the high and low QoS respectively.
We assume there are Α(ω
1
)+Α(ω
2
) users transmitting data in the system. We
find a probability distribution on the amount of interference for a given number of
interferers as Prob(MAI=h).
In the following, we compute the probability of interference on a single user
when α other users are transmitting “1”. We define q
ij
(x) as the total number of code-
words of QoS type j having x ≤κ collisions with the specific 1s of the code of QoS
type i.
In the following, we find the interference distribution for code of type j with
weight ω
j
.
2-D OOC with no restriction: since there is no restriction on the placement of
1s we should choose w
j
-x locations out of ΛΤ−ω
ι
locations containing 0 for an
interferer, while there is only one choice for the colliding 1s, so q
ij
(x) can be
calculated as:








−
− Λ
=
x
T
q
j
i
ij
ω
ω

2-D OOC with not more than one pulse per wavelength: Due to the hardware
restrictions this type of codes are used in a real systems. In this case we cannot
choose any ω
j
-x locations out of ΛΤ−ω
ι
locations to assign to non-colliding 1s, since

115
we need to enforce that the interferer be a codeword, and not have more than one
pulse per wavelength. So the interferer cannot have any non-colliding 1s in the
colliding wavelengths, which means the ω
j
-x non-colliding locations should be
chosen from the ω
i
-x non-colliding wavelengths with the restriction that there are
maximally one 1 per wavelength, and there is no more collisions in these remaining
1’s. This can be done in:
y
j
i
x y
i
x ij
T y x y
x
T
T
x q
j i
j i
j
)
1
1 (
) 1 (
) (
) min(
) , max(
−








−
− Λ








−
−
−
=
∑
+
Λ − + =
ω
ω ω
ω ω
ω ω
ω

It should be note that, due to the hardware restrictions the codes with
maximum one pulse per wavelength are generally used in O-CDMA networks.
By this we can compute the probability of k collision caused by only one user as:
) " 1 " int Pr( ng transmitti j type of erferer one only with collision k P
ij
=
∑
=
















=
κ
ω
ω
0
) (
) (
r
ij
i
ij
i
ij
r q
r
k q
k
P

Now, assuming there are totally A(ω
i
)+A(ω
j
) users interfering with the
original code, and the interference distributions of all different users are independent,
then we can convolve the above pmf i times to find the pmf for interference of
A(ω
i
)+A(ω
j
) interferers. Note that distribution of interference condition on ω
i
and ω
j

are different and both can be calculated from above.
1 2 1 2 1
,..., , ,..., ,
− + +
∗ =
j i j j i
A A A
MAI
A
MAI
A A A
MAI
P P P

116
System performance depends on the receiver structure. The receiver used in
the following, chooses a threshold, and if finds only one peak above the threshold
decodes to that data and can't decode on other cases. Let’s set the threshold to code
weight. Since the only degradation assumed on the line is MAI, so we always receive
a peak for the original data, so an error occurs if we receive a false peak. Since the
MAI distribution for all chip times is the same, probability of a false peak is given
by:
) ( ) 1 (
) (
) ( ) (
,
int
,
h P T Pe
i chiptime on peak false pr Pe
h P i chiptime on peak false pr
S
th h
S
PPM MAI
S
erest userof i
S
th h
S
PPM MAI
∑
∑
∑
=
≠
=
− ≤
≤
⇒ =

Where, the second inequality is driven by union bound, and s is the number
of interferers. It should be noted that the threshold in the equation above is usually
around the coder weight. Fig. 4. shows the pmf of the distribution for high and low
QoS (code weight) users. As the BER is measured by the integration of tail of the
distribution from code weight to the number of interferers, the associated BER of the
high QoS users is a lot smaller than the lower QoS users.
We use the analytical results to evaluate various code sets. We calculate the
BER of the user of interest for varying numbers of users of both weights. The
resulting BER curves are 3 dimensional BER curves; using these BERs the regions
supporting a specified error rate is calculated. In the Fig. 6.4(a) the high QoS curve

117
Average # of user Qos(2)
0 50 100 150 200 250 300
0
20
40
60
80
Average # of user Qos(1)
BER<1E-9
BER<1E-3
(QoS 1)
Average # of user Qos(2)
0 50 100 150 200 250 300 0 50 100 150 200 250 300
0
20
40
60
80
0
20
40
60
80
Average # of user Qos(1)
BER<1E-9
BER<1E-3
(QoS 1)

Average # of user Qos(2)
Average # of user Qos(1)
0 50 100 150 200 250 300
0
20
40
60
80
BER<1E-3
BER<1E-9
(QoS 2)
Average # of user Qos(2)
Average # of user Qos(1)
0 50 100 150 200 250 300
0
20
40
60
80
0 50 100 150 200 250 300
0
20
40
60
80
0
20
40
60
80
BER<1E-3
BER<1E-9
(QoS 2)

(a) (b)
Fig. 6.4. (a) the maximum numbers of users of QoS(1) vs, varying numbers of users
with QoS(2) for the user of interest of both types. (b) the maximum achievable
number of users for different code sets. This curves are drawn for 2 different BER
for High QoS and Low QoS users

represents the maximum numbers of achievable users of high QoS (w
1
=48) vs. the
number of users of low QoS (w
2
=24) for the specified BER of 1E-9 when the user of
interest is the high the QoS user. The first part of the curve shows the code limitation
of 71 for weight 48. By increasing the users of QoS(2) the number of users of type
one drops. The low QoS curve shows the same effect with BER<1E-3. It is clear that
the number of users supported by the low QoS user is less. Fig. 6.4(b) shows the
maximum number of users for different weights. In this graph the maximum number
of users achievable using the set of (w
1
, and w
2
) is drawn under the above
constraints. The code-sets using weights of 64, and 32 can not support more than 40
of high QoS users due to the limitation of number of codes and it is clear that the
maximum number of users increases going to the 64, and 24. This is due to the fact

118
that the code with 32 is still high in performance so it doesn’t have so many users
and it adds up to the interference. The code-sets of weights 48, and 24 can support
more users of weight 64 however for less users of low QoS.

6.2.3 Analysis of the network performance
The performance of the variable weight based QoS is evaluated in a network.
Consider a network consisting of a large number of users transmitting
asynchronously. Let the arrivals of packets to the network be Poisson and the lengths
of the packets (service times) be exponentially distributed. The number of users
transmitting simultaneously may be found using the arrival rate and the service time.
The throughput of the network is defined as fraction of packets that are transmitted
without error. The throughput for a given number of transmitting users may be found
using the BER as calculated in the previous section.
A1= Average # of user of high QoS
0 10 20 30 40 50
0.9992
0.9994
0.9996
0.9998
1
Average # of high QoS users
Throughput of high QoS user
A2= 200
A2= 150
A2=100
A1= Average # of user of high QoS
0 10 20 30 40 50
0.9992
0.9994
0.9996
0.9998
1
Average # of high QoS users
Throughput of high QoS user
A2= 200
A2= 150
A2=100

Average # of low QoS users
Throughput of low QoS user
A1= 50
A1= 30
A1= 10
0 50 100 150 200
0.5
0.6
0.7
0.8
0.9
1
A2= average # of user of low QoS
Average # of low QoS users
Throughput of low QoS user
A1= 50
A1= 30
A1= 10
0 50 100 150 200
0.5
0.6
0.7
0.8
0.9
1
A2= average # of user of low QoS

(a) (b)
Fig. 6.5. Throughput of the network based on percent of packet loss for (a) high
QoS user (b) low QoS user : The throughput of user type 1 does not degrade as
fast as that of user type 2

119
Fig. 6.5. shows the result of network throughput for a network with two
different types of users. Fig. 6.5(a) shows the throughput of users of type 1 when
different number of users of type 2 are transmitting. Fig. 6.5(b) shows the throughput
of users of type 2 when different number of users of type 1 are transmitting. From
the graphs it is clear that the throughput of user 1 does not degrade as fast as that of
user 2.
We see that by setting the conditions: (1) throughput of high QoS > .999 (2)
low QoS >0.7, average of 230 users can transmit which is around 4 times of the
number of users with only weight 48. (57 users for fixed BER<1E-9)

6.2.4 Experimental Results
We showed the feasibility of V-QoS O-CDMA using through an experiment. Due to
the limitations of the setup, we were not able to emulate the network performance for
varying number of users and variable asynchronous delays within users. It should be
noted that the theoretical results above mainly describes the network as the load
increases, which is for very large number of users, which is not feasible to
experiment in the LAB environment. So, we just showed the feasibility of having
variable code weight in the system and their respective performances.
The experimental setup for our OCDMA system is shown in Fig. 6.6. We use
six equal space lasers, couple them together and modulate them at 11 Gchip/s (1

120
Gbit/s). After an EDFA, we split the signal between four branches, each with a
unique O-CDMA encoder, to generate data for 4 O-CDMA users. In each encoder,
we split the wavelengths using a demultiplexer, assign each wavelength chip an
appropriate timeslot using optical delay lines, and recombine the wavelengths. In
order to generate the variable QoS codes, we block some of wavelengths in the
encoder so that only a certain number of wavelengths pass the encoder and make the
appropriate code. Each user is then transmitted through different short lengths of
fiber to decorrelate the signals and then all four users are recombined. At the
receiver, we amplify the received signal, demultiplex the wavelengths and use a
second set of fiber delays to stack the chips to decode the data. In the case of the
weight of user of interest less than 6, we block the missing wavelengths paths in the
decoder. After decoding, a receiver detects the decoded data followed by a threshold
detector that samples the data to determine whether it exceeds a set decision
threshold.

RX
BERT
Electronic Threshold
Detector
λ
1
DEMUX
λ
2
λ
3
λ
4
λ
5
λ
6
T
1
T
2
T
3
T
4
T
5
T
6
Delays
Receiver
MOD
11
Gchip/s
λ
1
λ
2
λ
3
λ
4
λ
5
λ
6
6x1 coupler
User 1
4x1 coupler
t
t
t
Users 2, 3 & 4
EDFA
DEMUX
λ
1
λ
2
λ
3
λ
4
λ
5
T
1
T
2
T
3
T
4
T
5
T
6
Delays
Fiber Link
All Users
Transmitter Link
Variable weight
Codes:
6 wavelength
11 chip-times
variable weight
λ
6
RX
BERT
Electronic Threshold
Detector
λ
1
DEMUX
λ
2
λ
3
λ
4
λ
5
λ
6
T
1
T
2
T
3
T
4
T
5
T
6
Delays
Receiver
MOD
11
Gchip/s
λ
1
λ
2
λ
3
λ
4
λ
5
λ
6
6x1 coupler
User 1
4x1 coupler
t
t
t
Users 2, 3 & 4
EDFA
DEMUX
λ
1
λ
2
λ
3
λ
4
λ
5
T
1
T
2
T
3
T
4
T
5
T
6
Delays
Fiber Link
All Users
Transmitter Link
Variable weight
Codes:
6 wavelength
11 chip-times
variable weight
λ
6

Fig. 6.7. Experimental Setup

121
In our experiment we used the codes with 6 wavelength, 11 chip times, and
variable code weight. The code weight used in this experiment were code weight 4
as the lower quality of service, and the code weight 6 were used as higher quality of
service. Our code construction is optimal in terms of the number of code-sets and has
at most one pulse per wavelength. The chip rate is 11 Gchip/s and the symbol rate is
1 Gbit/s.

High QoS User
4
3 2
1
3
4
5
6
7
8
9
10
-27 -26 -25 -24 -23 -22 -21
3
4
5
6
7
8
9
10
-27 -26 -25 -24 -23 -22 -21
4
3 2
1
Log (BER)
Optical Power
High QoS User
4
3 2
1
3
4
5
6
7
8
9
10
-27 -26 -25 -24 -23 -22 -21
3
4
5
6
7
8
9
10
-27 -26 -25 -24 -23 -22 -21
3
4
5
6
7
8
9
10
-27 -26 -25 -24 -23 -22 -21
3
4
5
6
7
8
9
10
-27 -26 -25 -24 -23 -22 -21
4
3 2
1
Log (BER)
Optical Power

Low QoS User
4 3
2 1
3
4
5
6
7
8
9
10
-26 -24 -22 -20 -18 -16
-
3
4
5
6
7
8
9
10
-26 -24 -22 -20 -18 -16
-
4 3
2 1
Log (BER)
Optical Power
Low QoS User
4 3
2 1
3
4
5
6
7
8
9
10
-26 -24 -22 -20 -18 -16
3
4
5
6
7
8
9
10
-26 -24 -22 -20 -18 -16
-
3
4
5
6
7
8
9
10
-26 -24 -22 -20 -18 -16
3
4
5
6
7
8
9
10
-26 -24 -22 -20 -18 -16
-
4 3
2 1
Log (BER)
Optical Power

(a) (b)
Fig. 6.8. System performance for 1 high QoS user (code weight 6) and 3 low QoS
user (weight 4) for (a) high QoS user is detected(b) low QoS user is detected : The
high QoS user exhibits a smaller amount of power penalty for increasing number
of users

In our experiment, we used one user with code weight 6 as the high QoS user
and 3 other users with code weight 4 as the low QoS users. Fig. 6.8 shows the BER
results for these two users. Fig. 6.8 (a) show the BER vs. received optical power high

122
QoS user is detected. We can see that as the number of users increase this user shows
small power penalty. This is due to the fact that the autocorrelation peak of this user
is very high with respect to the low QoS users. Fig. 6.8 (b) shows the performance of
the low QoS user for the increasing number users. Clearly this user suffers more for
larger number of users. It should be emphasized that the number of codes available
for lower QoS user is 31, while they are only 13 high QoS codes available.

6.3 Variable Bit Rate Optical CDMA Networks Using Multiple
Pulse Position Modulation
As we discussed in chapter 4, using the position of the autocorrelation peak within a
symbol time as an additional degree of freedom for encoding information, we
demonstrated Code Position-Modulation (CPM) to increase the number of bits per
symbol without using narrow pulses[89]. If the code length is M, the symbol time is
divided into M equal slots that the autocorrelation peak can occupy. Therefore, we
have M different symbols, representing log
2
M bits in each signaling time. The idea is
similar to the Pulse-Position-Modulation (PPM) technique in non-multiple access
systems (Fig. 6.9).

123
M
M
3






M
2






M
1






2-PPM
PPM
3-PPM
M
M
3






M
2






M
1






2-PPM
PPM
3-PPM

Fig. 6.9. Examples of PPM, 2-PPM, and 3-PPM Symbols. Number of possible
symbols is written beside each pattern.

Chapter 4 also reported Double-Pulse-Position Modulation (2-PPM) to further
enhance the per user bit rate with a fixed chip time [4]. In general, Multiple-Pulse-
Position Modulation (MPPM) in which more than one slot is marked by an
autocorrelation peak can increase the transmitted information per symbol. If the
number of pulses in a symbol time is equal to N, the number of symbols will be
equal to the number of ways in which we can choose N slots out of a total of M slots.
In this section, we have used MPPM with N equal to 1, 2, or 3 to implement PPM, 2-
PPM, and 3-PPM, respectively (Fig. 6.9). The number of bits per symbol is plotted
for N=1,2,3 as a function of code length, M, in Fig. 6.10. It should be emphasized
that the code length is fixed but by varying the transmission scheme we change the
bit rate (Fig. 6.11). To our knowledge, this is the first experimental setup in which
users with variable bit rates operate simultaneously.

124
PPM
2-PPM
3-PPM
Bits per sym bol
20 40
Increasing B it R ate
60
Code Length

Fig. 6.10. Number of bits per symbol for PPM, 2-PPM, and 3-PPM symbols versus
the code length, M.
Providing variable quality of service (QoS) for different users in an OCDMA
network has been an interesting topic of research and some structures have been
recommended [61, 87, 109], but the major problem of the suggested systems is that
they don't have a fixed optical platform. In other words, in order to change the
quality of service in those systems, a user should change his signature code or bit
rate whereas our reported system offers a variable bit rate which can be translated
into variable quality of service without changing the parameters of the optical setup
which includes encoders/decoders, chip rate, pulse width, and optical spectrum. We
will show that the price of achieving a high bit rate user in the system is reducing the
number of total active users.

125
2-PPM Data
middle bit rate
OCDMA Network
PPM Data;
low bit rate
3-PPM Data;
high bit rate
2-PPM Data
middle bit rate
OCDMA Network
PPM Data;
low bit rate
3-PPM Data;
high bit rate

Fig. 6.11. A variable bit rate OCDMA network using PPM, 2-PPM and 3-PPM
formats. With a fixed symbol time, but different number of bits/symbol, variable
bit rate is achievable.

6.3.1 Concept and Experimental Setup
The block diagram of an MPPM-OCDMA system is represented in Fig. 6.12. First,
the bits are fed into a bit to symbol converter. We have considered 3-PPM symbols
in this example. The 3-PPM symbols are fed to the OCDMA encoder. Each marked
slot is encoded in the order that it has been launched into the encoder. For 3-PPM-
OCDMA, there will be three signature codes shifted in time, according to the delays
between the three pulses in the original 3-PPM symbol. We allow the. Since our
codes have at most one pulse per wavelength, spreading the encoded data over the
next symbol will not cause Inter-Symbol-Interference and it is guaranteed that
adjacent symbols do not interfere with each other.
At the receiver side, the user decodes the data and extracts the 3-PPM
symbols. When MAI or noise is so high that it can change a zero slot larger than the
threshold, we will have error in the system. Finally, a bit to symbol converter
extracts the transmitted bits.

126
Input Bits
OCDMA
Encoder
Other
users
3-PPM Symbol
T
s T
s
Bits to
Symbol
Converter
Symbol
to Bits
Converter
OCDMA
Decoder
Output Bits
threshold
Input Bits
OCDMA
Encoder
Other
users
3-PPM Symbol
T
s T
s
Bits to
Symbol
Converter
Symbol
to Bits
Converter
OCDMA
Decoder
Output Bits
threshold

Fig. 6.12. Block diagram of an MPPM-OCDMA system with N=3 (3-PPM-
OCDMA). It is assumed that codes have a weight of 4. Different wavelengths are
shown with different patterns in the pulses and black pulses show MAI due to other
users in the network. Ts is the symbol time.

The experimental setup is shown in Fig. 6.13. Ten lasers have been used to
provide ten different wavelengths. We have used two pulse pattern generators
(PPGs) to simultaneously generate two different multiple pulse position patterns.
For example, PPG#1 generates PPM symbols while PPG#2 generates 3-PPM
symbols, but their chip rates are identical. The symbols from the two PPGs are fed
into two modulators whose output signals are launched into two sets of OCDMA
encoders. For instance, the modulator#1 feeds a certain number of users with PPM
symbols, shown as group#1 users, and modulator#2 feeds the remaining users with
3-PPM symbols, shown as group#2 users. The outputs of the modulators are shown
in Fig. 6 where adjacent symbols are separated with dotted lines.

127
Encoder
λ
Splitter
τ
τ
Encoder
10
10x1
Coupler
τ
τ
Rx Rx
1x2 Splitter
X -PPM Symbols
MOD#2
10 Gchip/s
10 Gchip/s
Y-PPM Symbols
10 Gchip/s
MOD#1
Encoder
Splitter
τ
τ
Encoder
τ
τ
group 2
users
group 1
users
2x1 Coupler
Splitter
BERT Rx
Threshold
Detector
Rx
Encoder
τ
τ
Encoder 1
τ
τ
Rx
Decoder
Rx
X-PPM
MOD#
10 Gchip/s
10 Gchip/s
-
10 Gchip/s
MOD#
Encoder
τ
τ
Encoder
τ
τ
group
users
group
users
2x1 Coupler
Splitter
Rx Rx
Receivers
PPG#1
PPG#2
Decoder
delay
line
delay
line
Threshold
Detector
Coupler Coupler
BERT
1x2 Splitter
λ
1
EDFA
EDFA
Encoder
λ
Splitter
τ
τ
Encoder
10
10x1
Coupler
τ
τ
Rx Rx
1x2 Splitter
X -PPM Symbols
MOD#2
10 Gchip/s
10 Gchip/s
Y-PPM Symbols
10 Gchip/s
MOD#1
Encoder
Splitter
τ
τ
Encoder
τ
τ
group 2
users
group 1
users
2x1 Coupler
Splitter
BERT Rx
Threshold
Detector
Rx
Encoder
τ
τ
Encoder 1
τ
τ
Rx
Decoder
Rx
X-PPM
MOD#
10 Gchip/s
10 Gchip/s
-
10 Gchip/s
MOD#
Encoder
τ
τ
Encoder
τ
τ
group
users
group
users
2x1 Coupler
Splitter
Rx Rx
Receivers
PPG#1
PPG#2
Decoder
delay
line
delay
line
Threshold
Detector
Coupler Coupler
BERT
1x2 Splitter
λ
1
EDFA
EDFA
Fig. 6.13. Experimental setup for a variable bit rate OCDMA network

The encoded symbols are transmitted through different lengths of short fibers
that make the signals uncorrelated and then all the users are coupled together. At the
receiver side, each user correlates the incoming optical signal with its own decoder
to extract the symbols. A photo-receiver detects the decoded data and a threshold
detector samples the data to determine whether it exceeds a certain decision
threshold or not. Based on the position of the detected autocorrelation peaks in each
symbol time, the receiver extracts the encoded bits.
In our experiment, we have used a code set with 16 chip times, 10
wavelengths, and a weight of 6. We have used the algorithm in [77] for designing the
codes. Our encoders and decoders are fiber bragg gratings that split the wavelengths
and assign each wavelength an appropriate chip time [33]. The chip rate is set to 10
Gchips/s and since each symbol takes 16 chips, the symbol rate is equal to 625
Msymbols/s. Therefore, for PPM-OCDMA (N=1), 2-PPM-OCDMA (N=2), and 3-
PPM-OCDMA (N=3), the corresponding bit rates are 2.5, 4.3, and 5.7 Gbits/s. As it

128
is seen, if a user requires a higher bit rate, it can switch its pattern from PPM to 2-
PPM or 3-PPM without modification to the rest of the setup.

(a)

(b)

Fig. 6.14. (a) PPM symbols, (b) 3-PPM symbols, after the modulators.
In each case three symbols are shown and adjacent symbols are
separated by dotted lines.

6.3.2 Results and Discussion
We have implemented different number of users operating with different symbol
types. For example, Fig. 6.14. shows the initial 1-PPM and 3-PPM symbols right
after the modulators and in Fig. 6.15, the same decoded symbols at the receiver side
along with MAI (small pulses) are shown. It can be observed that the data is still
detectable because the autocorrelation peaks are larger than the MAI. In this
combination, we have been able to get one user using 3-PPM-OCDMA with a bit-
error rate (BER) less than 1e-9, and three other users using PPM-OCDMA with
BERs less than 1e-9. Since a user operating at the higher bit rate, for example the 3-

129
PPM user, transmits more pulses into the system, it will generate approximately
three times more MAI to a PPM user. Therefore, in the presence of a 3-PPM user in
the network, we could not increase the number of PPM users more than three. The
power penalty for one 3-PPM user and different number of PPM users is shown in
Fig. 6.16.

Fig. 6.15. (a)Decoded PPM symbols (b) Decoded 3-PPM symbols and their eye
diagram. Small pulses are multiple-access-interference (MAI) due to other users in
the network.

Two users using 2-PPM and four other users using PPM could also be
achieved. The PPM users are added one by one in the system and the power penalty
is measured and shown in Fig. 6.16. Another combination we could achieve was one
2-PPM user and 5 other PPM users. As it is seen from Fig. 6.16, adding a higher bit
rate user in the system reduces the number of potential low bit rate users. Our
scheme provides versatility in that when there is low traffic demand in the network,
for example when some users are not active in the network, a user can benefit the
available bandwidth and switch to higher-PPM to operate at a higher bit rate.

130

12 3 4 5
1
2
3
4
5
6
7
8
9
10
Number of PPM users
Power Penalty (dB)
one 2-PPM user
in the system
two 2-PPM users
in the system
one 3-PPM user
in the system
12 3 4 5
1
2
3
4
5
6
7
8
9
10
Number of PPM users
Power Penalty (dB)
one 2-PPM user
in the system
two 2-PPM users
in the system
one 3-PPM user
in the system

Fig. 6.16. Power penalty versus the number of PPM users to achieve various
combinations of users operating at different bit rates

6.4 Experimental Demonstration of an Interference-Avoidance-
Based Protocol for O-CDMA Networks
A critical limitation of O-CDMA networks is the reduction of throughput when
many users are attempting to transmit simultaneously over the same medium,
thereby producing extreme congestion at high network loads. In fact, networks can
suffer from “congestion collapse,” in which the network throughput can actually
approach zero under extremely high loads i.e. when several users transmit
simultaneously, their packets and hence their code-words overlap[49]. When the
optical pulses in the codeword overlap, their optical power is added. Optical pulses
from one codeword may be detected by receivers tuned to other code-words. As a

131
result receivers may falsely detect their code-words resulting in packet errors. These
false positive errors increase with offered load, resulting in throughput collapse.
Recently, there has been a theoretical report on an O-CDMA network
protocol called interference avoidance (IA) that helps manage congestion and
maintains a relatively-high throughput even under extreme loads[48]. The proposed
media access protocol is interference avoidance. The protocol consists of two
different functionalities, state estimation and transmission scheduling. State
estimation is a mechanism by which nodes on the network estimate the state of the
line. Transmission scheduling is a mechanism by which nodes use the estimated state
to schedule their transmissions to avoid packet losses due to interference. To our
knowledge, there have been no reports of experimental demonstrations of a network
protocol that avoids congestion collapse for O-CDMA systems.
In this section, we propose and demonstrate a transmission scheduling
algorithm. We use an O-CDMA network supporting 6 users. Each user utilizes a
code-set of 16 chip-times, 8 wavelength, and code-weight 6 [90]. We demonstrate
the transmission scheduling by delaying each user’s traffic to have the least
interference with the line traffic and show the increase in system performance by
orders of magnitude. In order to establish a comparison with Aloha-CDMA, we
transmit the data with random delays and take an average over various line states.
Results from the measurements show that transmission scheduling can provide
orders of magnitude improvement in bit error rate.

132
O-CDMA
Node
Star
Coupler
O-CDMA
Node
O-CDMA
Node
O-CDMA
Node
Star
Coupler
O-CDMA
Node
O-CDMA
Node

Fig. 6.17. O-CDMA network: The nodes are connected by transmit and receive
(upstream, downstream) fibers to a passive star coupler to enable a shared medium
LAN.

6.4.1 Interference Avoidance
Fig. 6.17 shows a shared medium, packet switched optical CDMA LAN in which
several nodes are connected to a passive optical coupler to form an all optical
broadcast network. The star coupler is a passive optical element with all inputs
connected to all outputs. Each node on the network is allocated an optical CDMA
codeword, which is a sequence of zeroes and ones that are transmitted
asynchronously. When a node wants to transmit, it tunes its transmitter to the
receiver's codeword and transmits.
Without using a media access protocol each user starts to transmit whenever
the packet is ready. This is called Aloha-CDMA, which leads to congestion collapse
in an O-CDMA network. In order to alleviate this problem, the use of a media access
protocol "Interference Avoidance (IA)" is proposed. IA is a contention media access

133
control mechanism that prevents throughput collapse in optical CDMA networks at
high offered load. It consists of state estimation and transmission scheduling. State
estimation is a mechanism by which nodes on the network estimate the state of the
line. Transmission scheduling is a mechanism by which nodes use the estimated state
to schedule their transmissions to avoid packet losses due to interference.

Optical CDMA
Receiver
Transmit
buffer
State
estimation
module
Transmission
scheduling
module
Optical CDMA
Encoder
Transmit
fiber
Receive
fiber
Optical CDMA
Receiver
Transmit
buffer
State
estimation
module
Transmission
scheduling
module
Optical CDMA
Encoder
Transmit
fiber
Receive
fiber

Fig. 6.18. Block diagram of an Interference Avoidance(IA) network interface card
(NIC)

A simplified block diagram of an O-CDMA node is also shown in Fig. 6.18.
When a packet arrives on the receive fiber, it splits between two different paths. In
one path, it is decoded by the optical CDMA receiver and written to the receive
buffer. The other path is used to estimate the state of the link. The transmission
scheduling algorithm calculates Based on this information, the transmission
scheduling block calculated the appropriate transmission delay tunes the tunable

134
delay lines (TDLs) and signals the transmitter. The optical CDMA transmitter
transmits the packet on the transmit fiber.

State of the link after user’s decoder
Delay the autocorrelation and transmit it to
guarantee the least amount of interference
Transmitted
autocorrelation
Least interference:
Optimum scheduling
State of the link after user’s decoder
Delay the autocorrelation and transmit it to
guarantee the least amount of interference
Transmitted
autocorrelation
Least interference:
Optimum scheduling

Fig. 6.19. Upper: link after the decoder of user of interest. Lower: the data is
transmitted such that the autocorrelation is in the chip time with least interference

The concept of the state estimation and scheduling algorithm is shown in Fig.
6.19. In order to accomplish the state estimation we first pass the traffic from the line
through the decoder of the user of interest. This is the traffic as it is seen by the
receiver end. We then detect the date using multiple threshold detectors. The
minimum interference detected here is the best position to transmit the
autocorrelation peak. Now the transmission scheduler delays the packet so that the
autocorrelation transmits in the designated chip-time “Minimum interference”. The
transmission scheduler chooses the marked chip as the lowest MAI and then delays
the packet and transmits the autocorrelation peak. It should be noted that as each

135
packet consists of several bits, the state of the link remains constant for a long
duration.

Fig. 6.20. The normalized network throughput vs. normalized offered load for
Aloha-CDMA and transmission scheduling. The results are based on simulation.
The throughput of the network does not collapse in high loads The traffic model is
Poisson arrivals with exponentially distributed packet lengths.

In [48], an IA based optical CDMA network was modeled using discrete
event based packet simulator The simulator modeled multiple nodes on a broadcast
shared medium optical CDMA LAN. The normalized offered load is the 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. The arrival
rate is defined as the aggregate rate at which packets arrive to all the nodes for
transmission on the network. 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 multiplied by the normalized offered
load. The result of the simulation is shown in Fig. 6.20. The results show that the as

136
the offered load increases the throughput of Aloha-CDMA tends to zero, while the
use of the transmission scheduling algorithm prevents throughput degradation.

6.4.2 Experimental Result
The experimental setup for our O-CDMA system is shown in Fig. 6.21. We use
eight equal space lasers, couple them together and modulate them at 10 Gchip/s.
After an EDFA, we use O-CDMA encoder to encode the data and then use a variable
delay line to vary the time delay of the user. Each encoder is based on an FBG
technology which implements the splitting of the wavelengths and assigning each
wavelength chip an appropriate timeslot. This data is transmitted through a short
length of fiber and then combined in a star coupler with 5 other users. At the
receiver, we amplify the received signal and use a second set of fiber delays to stack
the chips to decode the data. At the receiver, a photo-receiver detects the decoded
User 1
T-λ FBG
Encoder
λ
1
λ
8
MOD
10 Gchip/s
Encoded Data 8x1 coupler
EDFA
User 1
Variable
Delay
Decoder
BERT Rx
Threshold
Detector
Users 2:6
Link
User 1
T-λ FBG
Encoder
λ
1
λ
8
MOD
10 Gchip/s
Encoded Data 8x1 coupler
EDFA
User 1
Variable
Delay
Decoder
BERT Rx
Threshold
Detector
Users 2:6
Link

Fig. 6.21. Experimental setup

137
data followed by a threshold detector that samples the data to determine whether it
exceeds a set decision threshold.

In our experiment we used the codes with 8 wavelength, 16 chip times, and
code weight 6. Our codes are based on code construction function Plot B [77]. and
they can support 18 potential users. Our code construction is optimal in terms of the
number of code-sets and has at most one pulse per wavelength. The chip rate is 10
Gchip/s and the corresponding bit rate is 625 Mbit/s.
Fig. 6.22 (a) shows an eye diagram of a correlation signal when only one user
is presented on the link. Fig. 6.22(b) shows the transmitted bit pattern of 10110. It is
clear that in the absence of other users there is no MAI thus the eye is completely
open.
(a)
100ps
Auto correlation
peak
100 ps/div

(b)

Bit Pattern 10110
800 ps/div

Fig. 6.22. Eye diagram of the correlation for (a) single user (b) bit
pattern of 10110

138

Fig. 6.23 (a) shows the eye diagram of the autocorrelation function of a
single user. The autocorrelation resembles an RZ signal with 1/16 ratio as there are
16 chip-times. Fig. 6.23(b) shows the eye diagram of the main user along with
multiple interferers. It is clear that by varying the transmission delay of this user, the
autocorrelation can move to any point of time. In this case the position of the
autocorrelation is optimized resulting in an open eye. Fig. 6.23(c) shows a random
delay of the user which causes severe eye closure.
Fig. 6.24 shows the BER curves for increasing number of users. As we added
more users to the network, we examined the link interference pattern and optimized
the transmission delay of the user of interest. It is clear that using the optimized
delay up to 6 users are recoverable with less than 4dB power penalty.
(a)
(b)
(c)

Fig. 6.23. Eye diagram of the correlation for (a) single user (b) multiple
user using transmission scheduling (c) random case

139

In order to compare the performance of the IA algorithm with aloha CDMA,
we first fixed the number of users and the state of the link. We then vary the delay of
the user of interest to find the optimum delay which can achieve the BER of 1E-10 at
the least possible optical power, at this point we fixed the optical power and changed
the delay of different users to emulate different link state and then vary the user of
interest delay to emulate the Aloha CDMA. The average BER resembles the Aloha-
CDMA. The results are shown in Fig. 6.25. It should be noted that the respective
point for different number of users are achieved for different optical power. Results
show that in worst case the BER of system drops below 1E-3 for 5 and 6 users.
Moreover using Aloha-CDMA the performance drops as the number of users
increases in the network, while using IA algorithm we can maintain the desired
performance for increasing number of users.
3
4
5
6
7
8
9
10
-26 -25 -24 -23 -22 -21 -20
Number of users:
1 2 3 4 5 6 X
Received optical power of user of interest
-log (BER)
3
4
5
6
7
8
9
10
-26 -25 -24 -23 -22 -21 -20
Number of users:
1 2 3 4 5 6 X
3
4
5
6
7
8
9
10
-26 -25 -24 -23 -22 -21 -20
Number of users:
1 2 3 4 5 6 X
Received optical power of user of interest
-log (BER)

Fig. 6.24. BER vs. received optical power of user 1 for increasing
number of users

140
3
4
5
6
7
8
9
10
01 23 45 67
Number of Users
-log (BER)
IA
Aloha
CDMA
Worst
Case
3
4
5
6
7
8
9
10
01 23 45 67 01 23 45 67
Number of Users
-log (BER)
IA
Aloha
CDMA
Worst
Case

Fig. 6.25. Performance of an O-CDMA system for increasing number of
users with transmission scheduling, aloha-CDMA, and worst case

141
Chapter 7
Conclusion

Optical CDMA has been studied for years. Various system structures and code
constructions have been developed. Recently, there has been an interest on
experimental evaluation of the O-CDMA systems and utilizing their unique
properties in network. Several application has been proposed to utilize the O-CDMA
systems, while the current progress in access networks has provided the motivation
for experimentally evaluating system structures to enable large number of users at
higher bit rate and analyzing various O-CDMA networks advances such as
flexibility, and simplicity of network control, fine channel granularity; flexible
bandwidth management, and ability to support variable Quality of Service (QoS) to
enable future O-CDMA access networks.

In this dissertation, we present a detailed study on optical CDMA systems
and networks:
(i) We established a probabilistic model for the interference in O-CDMA
systems using a conventional and hard limiting receiver, which relates the code
parameters to the system performance. This model does not depend on a specific
code structure, and the knowledge of the code parameters suffices the performance
analysis. We also showed that for a pre-specified hardware, (number of chip times,

142
and wavelengths) code weight becomes an important design parameter to maximize
the number of users. We showed that hard limiting receiver increases the number of
active users, and by optimizing code weight, a hard limiting receiver can support all
of the codes in the code set.
(ii) We experimentally demonstrated the effect of varying threshold on the
performance of the O-CDMA system. We first demonstrated the existence of the
optimum threshold via simulation and experiment and then, we showed the
relationship of the optimum threshold to the number of active users. We showed that
the BER vs. threshold curves are V-shaped, and by increasing the number of active
users the optimum threshold grows and the V-shape curves get narrower. Moreover,
we demonstrated a dynamic scheme for monitoring the number of active users in an
asynchronous O-CDMA system by measuring the power levels of various RF clock
tone harmonics. We showed that by using the half chip-rate frequency and
monitoring the RF power, we can estimate the number of active users in the system.
(iii) We introduce a novel modulation scheme “pulse position modulation”
for OCDMA systems which increases the spectral efficiency, i.e. bit rate for a given
chip time. This modulation scheme utilizes the different time shifts of the spreading
sequence as transmit M-ary information. We showed that using this method the
spectral efficiency can be increased up to threefold. We also introduced variations of
CPM, such as 2PPM and DPPM. Finally, We experimentally demonstrated an O-
CDMA system with 8 users each operating at 10Gbit/s at BER of <1E-9 using
2PPM.

143
(iv) we introduces various O-CDMA applications to enhance the network
performance. We demonstrated a method using variable weight to enable variable
quality of service. This method can provide a higher number of users, while certain
users have high quality of service. We also demonstrated a method to provide
variable bit rate in O-CDMA systems utilizing MPPM systems. Finally, we
demonstrated the interference avoidance algorithm in O-CDMA networks to avoid
congestion collapse.

144

References
[1] R. J. R. Abel and M. Buratti, "Some progress on (v,4,1) difference families
and optical orthogonal codes," Journal of Combinatorial Theory, Series A,
vol. 106, pp. 59-75, 2004.
[2] G. P. Agrawal, Fiber-Optics Communication Systems, 1997.
[3] B.-g. Ahn and Y. Park, "A symmetric-structure CDMA-PON system and its
implementation," Photonics Technology Letters, IEEE, vol. 14, pp. 1381 -
1383 2002.
[4] V. R. Arbab, P. Saghari, M. Haghi, R. Omrani, A. E. Willner, and P. V.
Kumar, "Demonstration of Double Pulse Position Modulation (2-PPM) in
Time-Wavelength Optical CDMA Systems," presented at Optical
Communication. ECOC . European Conference on, Cannes, France, 2006.
[5] V. R. Arbab, P. Saghari, M. Haghi, R. Omrani, A. E. Willner, and P. V.
Kumar, "Experimental Demonstration of Double Pulse Position Modulation
(2-PPM) in Time-Wavelength Optical CDMA Systems " presented at
European Conference on Optical Communication, IEEE/ECOC 2006.
[6] S. Ayotte, M. Rochette, J. Magne, L. A. Rusch, and S. LaRochelle,
"Experimental demonstration and simulation results of frequency encoded
optical CDMA," presented at IEEE International Conference on
Communications Paris, France, 2004.
[7] M. Azizoglu, J. A. Salehi, and Y. Li, "Optical CDMA via temporal codes,"
Communications, IEEE Transactions on, vol. 40, pp. 1162 – 1170, 1992.
[8] V. Baby, C.-S. Bres, L. Xu, I. Glesk, and P. R. Prucnal, "Demonstration of
differentiated service provisioning with 4-node 253 Gchip/s fast frequency-
hopping time-spreading OCDMA," Electronics Letters, vol. 40, pp. 755 - 756
2004.
[9] V. Baby, I. Glesk, R. Runser, R. Fischer, Y.-K. Huang, C.-S. Bres, W.
Kwong, T. Curtis, and P. Prucnal, "Experimental Demonstration and
Scalability Analysis of a 4-Node 102Gchip/sFast Frequency-Hopping Time-
Spreading Optical CDMA Network," in Lasers and Electro-Optics Society
2004 Annual Meeting, LEOS, 2004.

145
[10] V. Baby, I. Glesk, R. J. Runser, R. Fischer, Y.-K. Huang, C.-S. Bres, W. C.
Kwong, T. H. Curtis, and P. R. Prucnal, "Experimental demonstration and
scalability analysis of a four-node 102-Gchip/s fast frequency-hopping time-
spreading optical CDMA network," IEEE Photonics Technology Letters, vol.
17, pp. 253-255, 2005.
[11] H. V. Baghdasaryan, D. M. Meghavoryan, and N. K. Uzunoglu, "Optical
CDMA system based on amplifying fiber Bragg gratings chain," presented at
Transparent Optical Networks, 2000 2nd International Conference on, 2000.
[12] T. M. Bazan, D. Harle, and I. Andonovic, "Beat noise limits of 2-D time
spreading-wavelength hopping optical CDMA networks," 2005.
[13] S. Bhandare, D. Sandel, B. Milivojevic, A. Hidayat, A. A. Fauzi, H. Zhang,
S. K. Ibrahim, F. Wust, and R. Noe, "5.94-Tb/s 1.49-b/s/Hz (40/spl
times/2/spl times/2/spl times/40 Gb/s) RZ-DQPSK polarization-division
multiplex C-band transmission over 324 km," Photonics Technology Letters,
IEEE, vol. 17, pp. 914 - 916 2005.
[14] S. Bitan and T. Etzion, "Constructions for optimal constant weight cyclically
permutable codes and difference families," Information Theory, IEEE
Transactions on, vol. 41, pp. 77-87, 1995.
[15] C.-S. Bres, I. Glesk, R. J. Runser, T. Banwell, P. R. Prucnal, and W. C.
Kwong, "Novel M-ary architecture for optical CDMA using pulse position
modulation," Lasers and Electro-Optics Society, 2005. LEOS 2005. The 18th
Annual Meeting of the IEEE, pp. 982 - 983 2005.
[16] M. Buratti, "A powerful method for constructing difference families and
optimal optical orthogonal codes," Designs, Codes and Cryptography, vol. 5,
pp. 13-25, 1995.
[17] M. Buratti, "Powerful method for constructing difference families and
optimal optical orthogonal codes," Designs, Codes, and Cryptography, vol. 5,
pp. 13, 1995.
[18] M. Buratti, "Cyclic designs with block size 4 and related optimal optical
orthogonal codes," Designs, Codes, and Cryptography, vol. 26, pp. 111-125,
2002.

146
[19] J.-X. Cai, D. G. Foursa, C. R. Davidson, Y. Cai, G. Domagala, L. L. H. Li,
W. W. Patterson, A. N. Pilipetskii, a. M. Nissov, and N. S. Bergano, "A
DWDM Demonstration of 3.73 Tb/s over 11,000 km using 373 RZ-DPSK
Channels at 10Gb/s " presented at Optical Fiber Communication Conference.
OFC 2003.
[20] C. Chang, G. Yang, and W. C. Kwong, "Wavelength-time codes with
maximum cross-correlation function of two for multicode-keying optical
CDMA," Journal of Lightwave Technology, vol. 24, pp. 1093 - 1100 2006
[21] Y. Chang, R. Fuji-Hara, and Y. Miao, "Combinatorial constructions of
optimal optical orthogonal codes with weight 4," Information Theory, IEEE
Transactions on, vol. 49, pp. 1283-1292, 2003.
[22] Y. Chang and Y. Miao, "Constructions for optimal optical orthogonal codes,"
Discrete Mathematics, vol. 261, pp. 127-139, 2003.
[23] Y. Chen, "CDMA Fiber-Optics Systems with optical hard limiter," Lightwave
Technology, Journal of,, pp. 950-958, 2001.
[24] W. Chu and C. J. Colbourn, "Optimal (n,4,2)-OOC of small orders," Discrete
Mathematics, vol. 279, pp. 163-172, 2004.
[25] W. Chu and C. J. Colbourn, "Recursive constructions for optimal (n, 4, 2)-
OOCs," Journal of Combinatorial Designs, vol. 12, pp. 333-345, 2004.
[26] F. R. K. Chung, J. A. Salehi, and V. K. Wei, "Optical orthogonal codes:
design, analysis and applications," Information Theory, IEEE Transactions
on, vol. 35, pp. 595-604, 1989.
[27] T. Demeechai, "Noise-limited performance of spectral-amplitude-coding
optical CDMA in fibre-optic radio highway networks," Optoelectronics, IEE
Proceedings-, vol. 152, pp. 269-273, 2005.
[28] T. Demeechai, "On noise-limited performance of noncomplementary
spectral-amplitude coding optical CDMA systems," Communications, IEEE
Transactions on, vol. 54, pp. 29-31, 2006.
[29] T. Demeechai and A. B. Sharma, "Beat noise in a non-coherent optical
CDMA system," presented at Communication Systems, 2002. ICCS 2002.
[30] I. B. Djordjevic and B. Vasic, "Combinatorial constructions of optical
orthogonal codes for OCDMA systems," Communications Letters, IEEE, vol.
8, pp. 391-393, 2004.

147
[31] P. G. Ebrahimi, D.; Sahin, A.B.; Starodubov, D.S.; Willner, A.E.;,
"Experimental demonstration of multiple-wavelength hard limiting receiver
for reducing MAI noise in a 2-D time and wavelength O-CDMA system " in
Optical Communication. ECOC . European Conference on. Rimini, Italy,
2003
[32] A. G. Elmeligy, M. S. El-Sowehy, H. M. H. Shalaby, and E. A. El-Badawy,
"Effect of both shot and beat noises on the performance of a 2D optical
CDMA correlation receiver," presented at Circuits and Systems, 2003.
MWSCAS '03. Proceedings of the 46th IEEE International Midwest
Symposium on, 2003.
[33] H. Fathallah, L. A. Rusch, and S. LaRochelle, "Passive optical fast
frequency-hop CDMA communications system," Lightwave Technology,
Journal of,, vol. 17, pp. 397 - 405, 1999.
[34] T. Frederick and E. H. Sargent, "Optimizing Spectral Efficiency in
Multiwavelength Optical CDMA System," Communications, IEEE
Transactions on, vol. 51, 2003.
[35] A. Fu-Tai, D. Gutierrez, K. Kyeong Soo, L. Jung Woo, and L. G. Kazovsky,
"SUCCESS-HPON: A next-generation optical access architecture for smooth
migration from TDM-PON to WDM-PON," Communications Magazine,
IEEE, vol. 43, pp. S40-S47, 2005.
[36] R. Fuji-Hara and Y. Miao, "Optical orthogonal codes: their bounds and new
optimal constructions," Information Theory, IEEE Transactions on, vol. 46,
pp. 2396-406, 2000.
[37] R. M. Gagliardi and H. Taylor, "Code sequences and code matrices for
CDMA fiberoptic systems," USC Rep. CSI-91-08-01, 1991.
[38] S. Galli, R. Menendez, P. Toliver, T. Banwell, J. Jackel, J. Young, and S.
Etemad, "Experimental results on the simultaneous transmission of two 2.5
Gbps optical-CDMA channels and a 10 Gbps OOK channel within the same
WDM window," presented at Optical Fiber Communication Conference.
OFC Anaheim, CA, United States, 2005.
[39] I. Garrett, "Pulse-Position Modulation for Transmission over Optical Fibers
with Direct or Heterodyne Detection," IEEE Trans. Communication, vol. 31,
1983.

148
[40] I. Glesk, V. Baby, C.-S. Bres, X. L. Xu, S. Rand, and P. R. Prucnal,
"Experimental demonstration of a 2.5Gbps incoherent 2D OCDMA system "
in Lasers and Electro-Optics. (CLEO). Conference on, 2004.
[41] R. A. Griffin, D. D. Sampson, and D. A. Jackson, "Coherence coding for
photonic code-division multiple access networks," Lightwave Technology,
Journal of, vol. 13, pp. 1826-1837, 1995.
[42] L. Guu-Chang and T. E. Fuja, "Optical orthogonal codes with unequal auto-
and cross-correlation constraints," Information Theory, IEEE Transactions
on, vol. 41, pp. 96-106, 1995.
[43] M. Haghi, P. Saghari, V. R. Arbab, P. Ebrahimi, and A. E. Willner,
"Differential-Pulse-Position-Modulation (DPPM) in OCDMA Systems to
Achieve Higher Data-Rate/User " European Conference on Optical
Communication, IEEE/ECOC 2006.
[44] H. Jen-Fa and H. Dar-Zu, "Fiber-grating-based optical CDMA spectral
coding with nearly orthogonal M-sequence codes," Photonics Technology
Letters, IEEE, vol. 12, pp. 1252-1254, 2000.
[45] S. Johnson, "A new upper bound for error-correcting codes," Information
Theory, IEEE Transactions on, vol. 8, pp. 203-207, 1962.
[46] C. Jun-Jie and Y. Guu-Chang, "CDMA fiber-optic systems with optical hard
limiters," Lightwave Technology, Journal of, vol. 19, pp. 950-958, 2001.
[47] W. Jyh-Horng and W. Jingshown, "Synchronous fiber-optic CDMA using
hard-limiter and BCH codes," Lightwave Technology, Journal of, vol. 13, pp.
1169-1176, 1995.
[48] P. Kamath, J. D. Touch, and J. A. Bannister, "Algorithms for interference
sensing in optical CDMA networks," IEEE International Conference on
Communications (ICC), vol. 3, pp. 1720 - 1724, 2004.
[49] P. Kamath, J. D. Touch, and J. A. Bannister, "The need for media access
control in optical CDMA networks," INFOCOM vol. 4, pp. 2208 - 2219,
2004.
[50] M. Kavehrad and D. Zaccarin, "Optical code-division-multiplexed systems
based on spectral encoding of noncoherent sources," Lightwave Technology,
Journal of, vol. 13, pp. 534-545, 1995.

149
[51] D. C. Kilper, R. Bach, D. J. Blumenthal, D. Einstein, T. Landolsi, L. Ostar,
M. Preiss, and A. E. Willner, "Optical performance monitoring," Lightwave
Technology, Journal of,, vol. 22, pp. 294 - 304, 2004.
[52] K. S. Kim, "On the evolution of PON-based FTTH solutions," Informatics
and Computer Science: An International Journal,, vol. 149, pp. 21-30 2003.
[53] Z. Kostic and E. L. Titlebaum, "The design and performance analysis for
several new classes of codes for optical synchronous CDMA and for
arbitrary-medium time-hopping synchronous CDMA communication
systems," Communications, IEEE Transactions on, vol. 42, pp. 2608-2617,
1994.
[54] P. V. Kumar, R. Omrani, J. Touch, A. E. Willner, and P. Saghari, "A Novel
Optical CDMA Modulation Scheme: Code Cycle Modulation," in IEEE
GLOBECOM. San Francisco, USA, 2006.
[55] S. Kumar, P. Saghari, P. Ebrahimi, M. Haghi, V. R. Arbab, and A. E. Wilner,
"Experimental demonstration of all-optical "missing chip detection" to
alleviate near-far effect in O-CDMA systems," presented at Optical Fiber
Communication Conference, 2006. OFC 2006.
[56] W. C. Kwong and Y. Guu-Chang, "Design of multilength optical orthogonal
codes for optical CDMA multimedia networks," Communications, IEEE
Transactions on, vol. 50, pp. 1258-1265, 2002.
[57] W. C. Kwong and Y. Guu-Chang, "Extended carrier-hopping prime codes for
wavelength-time optical code-division multiple access," Communications,
IEEE Transactions on, vol. 52, pp. 1084 - 1091, 2004.
[58] W. C. Kwong and Y. Guu-Chang, "Multiple-length multiple-wavelength
optical orthogonal codes for optical CDMA systems supporting multirate
multimedia services," IEEE Journal on Selected Areas in Communications,
vol. 22, pp. 1640-7, 2004.
[59] W. C. Kwong, Y. Guu-Chang, V. Baby, C. S. Bres, and P. R. Prucnal,
"Multiple-wavelength optical orthogonal codes under prime-sequence
permutations for optical CDMA," Communications, IEEE Transactions on,
vol. 53, pp. 117-23, 2005.
[60] W. C. Kwong, P. A. Perrier, and P. R. Prucnal, " Performance comparison of
asynchronous and synchronous code-division multiple-access techniques for
fiber-optic local area networks," Communications, IEEE Transactions on,
vol. 39, pp. 1625-1634, 1991.

150
[61] W. C. Kwong and G.-C. Yang, "Design of multilength optical orthogonal
codes for optical CDMA multimedia networks," Communications, IEEE
Transactions on, vol. 50, pp. 1258- 1265, 2002.
[62] H. Lundqvist and G. Karlsson, "On error-correction coding for CDMA
PON," Lightwave Technology, Journal of, vol. 23, pp. 2342-2351, 2005.
[63] Marvin K. Simon, J. K. Omura, R. A. Scholtz, and B. K. Levitt, Spread
Spectrum Communications Handbook, 1994.
[64] J. E. McGeehan, S. M. R. M. Nezam, P. Saghari, T. H. Izadpanah, A. E.
Willner, R. Omrani, and P. V. Kumar, "3D time-wavelength-polarization
OCDMA coding for increasing the number of users in OCDMA LANs,"
presented at Optical Fiber Communication Conference, 2004. OFC 2004.
[65] J. E. McGeehan, S. M. R. M. Nezam, P. Saghari, A. E. Willner, R. Omrani,
and P. V. Kumar, "Experimental demonstration of OCDMA transmission
using a three-dimensional (time-wavelength-polarization) codeset,"
Lightwave Technology, Journal of, vol. 23, pp. 3282-3289, 2005.
[66] M. Meenakshi and I. Andonovic, "Effect of physical layer impairments on
SUM and AND detection strategies for 2-D optical CDMA," Photonics
Technology Letters, IEEE, vol. 17, pp. 1112-1114, 2005.
[67] A. J. Mendez, R. M. Gagliardi, V. J. Hernandez, C. V. Bennett, and W. J.
Lennon, "Design and Performance Analysis of Wavelength/Time (W/T)
Matrix Codes for Optical CDMA," Lightwave Technology, Journal of,, vol.
21, pp. 2524-2533, 2003.
[68] S.-S. Min and Y.-H. Won, " Upper-bounds on bit error rate of OCDMA
systems using the time spreading/wavelength hopping codes," Lasers and
Electro-Optics Society 2000 Annual Meeting, LEOS, vol. 2, pp. 814 - 815,
2000.
[69] O. Moreno, P. V. Kumar, L. Hsiao-feng, and R. Omrani, "New constructions
for optical orthogonal codes, distinct difference sets and synchronous optical
orthogonal codes," presented at Information Theory, 2003. Proceedings.
IEEE International Symposium on, 2003.
[70] O. Moreno, Z. Zhen, P. V. Kumar, and V. A. Zinoviev, "New constructions
of optimal cyclically permutable constant weight codes," Information Theory,
IEEE Transactions on, vol. 41, pp. 448-455, 1995.

151
[71] E. Narimanov, W. C. Kwong, Y. Guu-Chang, and P. R. Prucnal, "Shifted
carrier-hopping prime codes for multicode keying in wavelength-time O-
CDMA," IEEE Transactions on Communications, vol. 53, pp. 2150 - 2156
2005
[72] E. K. H. Ng and E. H. Sargent, "Mining the Fiber-Optic Channel Capacity in
the Local Area: Maximizing Spectral Efficiency in Multi-Wavelength Optical
CDMA Networks," in IEEE International Conference on Communications
(ICC), 2001.
[73] E. K. H. Ng and E. H. Sargent, "Optimum threshold detection in real-time
scalable high-speed multi-wavelength optical code-division multiple-access
LANs," Communications, IEEE Transactions on, vol. 50, pp. 778-784, 2002.
[74] B. Ni, J. S. Lehnert, and J. Zhang, "Impact of beat noise on an incoherent
OCDMA system with temporal spreading," presented at Signals, Systems and
Computers, Conference on, 2004.
[75] T. Ohtsuki, "Performance analysis of direct-detection optical asynchronous
CDMA systems with double optical hard-limiters," Lightwave Technology,
Journal of,, vol. 5, pp. 452 - 457, 1997.
[76] T. Ohtsuki, K. Sato, I. Sasase, and S. Mori, "Direct-detection optical
synchronous CDMA systems with double optical hard-limiters using
modified prime sequence codes," Selected Areas in Communications, IEEE
Journal on, vol. 14, pp. 1879-1887, 1996.
[77] R. Omrani, E. Elia, and P. V. Kumar, "New Constructions and Bounds for 2-
D Optical Orthogonal Codes Sequences, and Their Applications," in SETA.
KOREA, 2004.
[78] R. Omrani and P. V. Kumar, "Improved constructions and bounds for 2-D
optical orthogonal codes," presented at Information Theory, 2005. ISIT 2005.
Proceedings. International Symposium on, 2005.
[79] R. Omrani, O. Moreno, and P. V. Kumar, "Improved Johnson bounds for
optical orthogonal codes with λ > 1 and some optimal constructions,"
presented at Information Theory, 2005. ISIT 2005. Proceedings. International
Symposium on, 2005.
[80] T. Pfeiffer, B. Deppisch, M. Kaiser, and R. Heidemann, "High speed optical
network for asynchronous multiuser access applying periodic spectral coding
of broadband sources," Electronics Letters, vol. 33, pp. 2141-2142, 1997.

152
[81] W. Ping and L.-N. Tho, "2-D optical CDMA networks using MWPM, double
hard limiters and modified carrier-hopping prime sequences," Lightwave
Technology, Journal of, vol. 23, pp. 2902-2913, 2005.
[82] P. R. Prucnal, M. A. Santoro, and T. R. Fan, "Spread spectrum fiber-optic
local area network using optical processing," Lightwave Technology, Journal
of,, vol. 4, pp. 547–554, 1986.
[83] R. Ramaswami and K. N. Sivarajan, Optical Networks, A Practical
Perspective: Morgan Kaufman Publishers, 2002.
[84] M. Razavi and J. A. Salehi, "Statistical analysis of fiber-optic CDMA
communication systems. I. Device modeling," Lightwave Technology,
Journal of, vol. 20, pp. 1304-1316, 2002.
[85] M. Razavi and J. A. Salehi, "Statistical analysis of fiber-optic CDMA
communication systems. II. Incorporating multiple optical amplifiers,"
Lightwave Technology, Journal of, vol. 20, pp. 1317-1328, 2002.
[86] P. Saghari, R. G. H. Abrishami, E. Pakbaznia, J. E. McGeehan, S. M. R. M.
Nezam, and A. E. Willner, "Experimental Evaluation of the Optimum
Decision Threshold for Varying Numbers of Active Users in a 2-D time-
wavelength Asynchronous O-CDMA System " in Lasers and Electro-Optics.
(CLEO). Conference on, 2005
[87] P. Saghari, R. Ghilzadeh, P. Kamath, R. Omrani, A. E. Willner, J. A.
Bannister, J. D. Touch, and P. V. Kumar, "Analytical Model of Variable
Quality of Service to Increase Number of Users in an O-CDMA Network,"
presented at Optical Communication. ECOC . European Conference on,
Glasgow, UK, 2005.
[88] P. Saghari, R. Gholizadeh, H. Abrishami, E. Pakbaznia, J. E. McGeehan, R.
Motaghian, and R. E. Willner, "Experimental evaluation of the optimum
decision threshold for varying numbers of active users in a 2D t-/spl lambda/,
asynchronous O-CDMA system," presented at Lasers and Electro-Optics,
2005. (CLEO). Conference on, 2005.
[89] P. Saghari, M. Haghi, V. R. Arbab, S. Kumar, R. Gholizadeh, A. E. Willner,
P. V. Kumar, and J. D. Touch, "Experimental Demonstration of Code
Position Modulation in an OCDMA System to Increase the Number of
Users," presented at Lasers and Electro-Optics. (CLEO). Conference on,
Long Beach, CA, 2006.

153
[90] P. Saghari, P. Kamath, V. Arbab, M. Haghi, A. E. Willner, J. A. Bannister,
and J. D. Touch, "Experimental Demonstration of an Interference-
Avoidance-Based Protocol for O-CDMA Networks," presented at Optical
Fiber Communication Conference, 2006. OFC 2006.
[91] P. Saghari, R. Omrani, P. Ebrahimi, A. E. Willner, and P. V. Kumar,
"Doubling the number of active users in a 2-D t-λ O-CDMA network using a
hard limiting receiver," presented at Optical Communication,. ECOC 2005.
31st European Conference on, 2005.
[92] P. Saghari, R. Omrani, A. E. Willner, and P. V. Kumar, "Analytical
interference model for 2-dimensional (time-wavelength) asynchronous
OCDMA systems," Optical Fiber Communication Conference. OFC vol. 2
pp. 493 - 495, 2004.
[93] P. Saghari, R. Omrani, A. E. Willner, and P. V. Kumar, "Analytical
interference model for two-dimensional (time-wavelength) asynchronous O-
CDMA systems using various receiver structures " Lightwave Technology,
Journal of, vol. 23, pp. 3260- 3269, 2005.
[94] J. A. Salehi, "Code division multiple-access techniques in optical fiber
networks—Part I: Fundamental principles," Communications, IEEE
Transactions on, vol. 37, pp. 824–833, 1989.
[95] J. A. Salehi and C. A. Brackett, "Code division multiple-access techniques in
optical fiber networks—Part II: Systems performance analysis,"
Communications, IEEE Transactions on, vol. 37, pp. 834–842, 1989.
[96] J. A. Salehi, A. M. Weiner, and J. P. Heritage, "Coherent ultrashort light
pulse code-division multiple access communication systems," Lightwave
Technology, Journal of, vol. 8, pp. 478-491, 1990.
[97] D. D. Sampson, M. Calleja, and R. A. Griffin, "Crosstalk performance of
coherent time-addressed photonic CDMA networks," Communications, IEEE
Transactions on, vol. 46, pp. 338-348, 1998.
[98] R. Scholtz, "The Origins of Spread-Spectrum Communications,"
Communications, IEEE Transactions on [legacy, pre - 1988], vol. 30, pp.
822-854, 1982.
[99] R. A. Scholtz, "SPREAD SPECTRUM CONCEPT," Communications, IEEE
Transactions on, vol. CM-25, pp. 748-755, 1977.

154
[100] C. Seunghwan, L. Chung-Keun, K. Youngmin, L. Yongjun, S. Seung-Woo,
and L. Byoungho, "A simply tunable optical CDMA encoder/decoder for
two-dimensional cyclic permutable codes," presented at Optical Fiber
Communication Conference.OFC, 2006.
[101] H. M. H. Shalaby, "Direct detection optical overlapping PPM-CDMA
communication systems with double optical hardlimiters," Journal of
Lightwave Technology, vol. 17, pp. 1158-1165, Jul. 1999.
[102] M. Shikui and C. Yanxun, "A new class of optimal optical orthogonal codes
with weight five," Information Theory, IEEE Transactions on, vol. 50, pp.
1848-50, 2004.
[103] N. J. A. Sloane and F. J. MacWilliams, The theory of error correcting codes
North-Holland Mathematical Library, 1989.
[104] E. D. J. Smith, P. T. Gough, and D. P. Taylor, "Noise limits of optical
spectral-encoding CDMA systems," Electronics Letters, vol. 31, pp. 1469-
1470, 1995.
[105] R. P. Stanley, Enumerative Combinatorics, vol. 1, 2000.
[106] H. Sugiyama and K. Nosu, "MPPM: a method for improving the band-
utilization efficiency in optical PPM," Lightwave Technology, Journal of,
vol. 7, pp. 465-472, 1989.
[107] L. Tan¢cevski and I. Andonovic, "Hybrid wavelength hopping/time
spreading schemes for use in massive optical LANs with increased security,"
Lightwave Technology, Journal of,, vol. 14, pp. 2636–2647, 1996.
[108] L. Tancevski and L. A. Rusch, "Impact of the beat noise on the performance
of 2-D optical CDMA systems," Communications Letters, IEEE, vol. 4, pp.
264-266, 2000.
[109] N. G. Tarhuni, T. O. Korhonen, E. Mutafungwa, and M. S. Elmusrati,
"Multiclass optical orthogonal codes for multiservice optical CDMA
networks," Lightwave Technology, Journal of, vol. 24, pp. 694 - 704 2006.
[110] P. C. Teh, P. Petropoulos, M. Ibsen, and D. J. Richardson, "Phase encoding
and decoding of short pulses at 10 Gb/s using superstructured fiber Bragg
gratings," Photonics Technology Letters, IEEE, vol. 13, pp. 154-156, 2001.

155
[111] G. Vareille, F. Pitel, and J. F. Marcerou, "3 Tbit/s (300×11.6 Gbit/s)
transmission over 7380 km using C+L band with 25 GHz spacing and NRZ
format,," presented at Optical Fiber Communication Conference. OFC 2001.
[112] A. J. Viterbi, CDMA: Principles of Spread Spectrum Communication, 1995.
[113] N. Wada, H. Sotobayashi, and K. Kitayama, "2.5 Gbit/s time-
spread/wavelength-hop optical code division multiplexing using fibre Bragg
grating with supercontinuum light source," Electronics Letters, vol. 36, pp.
815-817, 2000.
[114] S. P. Wan and Y. Hu, "Two-dimensional optical CDMA differential system
with prime/OOC codes," Photonics Technology Letters, IEEE, vol. 13, pp.
1373–1375, 2001.
[115] Z. Wei, H. Shalaby, and H. Ghafouri-Shiraz, "Modified quadratic congruence
codes for fiber Bragg-grating-based spectral-amplitude-coding optical
CDMA systems," Lightwave Technology, Journal of,, vol. 19, pp. 1274–
1281, 2001.
[116] C. Wensong and S. W. Golomb, "A new recursive construction for optical
orthogonal codes," Information Theory, IEEE Transactions on, vol. 49, pp.
3072-6, 2003.
[117] W. Xu and K. Kitayama, "Analysis of beat noise in coherent and incoherent
time-spreading OCDMA," Lightwave Technology, Journal of, vol. 22, pp.
2226-2235, 2004.
[118] G.-C. Yang and T. E. Fuja, "Optical orthogonal codes with unequal auto- and
cross-correlation constraints," Communications, IEEE Transactions on, vol.
41, pp. 96-106, 1995.
[119] G.-C. Yang and W. C. Kwong Prime Codes with Applications to CDMA
Optical and Wireless Boston, MA, 2002.
[120] G. C. Yang and W. C. Kwong, "Performance Analysis of Multiwavelength
CDMA and WDMA+CDMA for fiber optic Networks," Communications,
IEEE Transactions on, pp. 1426-1434 1997.
[121] C. Yanxun, R. Fuji-Hara, and M. Ying, "Combinatorial constructions of
optimal optical orthogonal codes with weight 4," Information Theory, IEEE
Transactions on, vol. 49, pp. 1283-92, 2003.

156
[122] S. Zahedi and J. A. Salehi, "Analytical comparison of various fiber-optic
CDMA receiver structures," Lightwave Technology, Journal of, vol. 18, pp.
1718-1727, 2000.
[123] S. Zahedi and J. A. Salehi, "Performance analysis for various fiber-optic
CDMA receiver structures," presented at Global Telecommunications
Conference, 2000. GLOBECOM . IEEE, 2000.
[124] S. Zahedi, J. A. Salehi, and M. Nasiri-Kenari, "M-Ary Infrared CDMA for
Indoors Wireless Communications," Proceeding of IEEE PIMRC, pp. 6-10,
Sept. 2001.

Asset Metadata

Creator Saghari, Poorya (author)

Core Title Techniques for increasing number of users in dynamically reconfigurable optical code division multiple access systems and networks

School Andrew and Erna Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Electrical Engineering

Publication Date 11/16/2006

Defense Date 10/27/2006

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

Tag oai:digitallibrary.usc.edu:usctheses,OAI-PMH Harvest,optical cdma,optical communication

Language English

Advisor Willner, Alan E. (committee chair), Huang, Ming-Deh (committee member), O'Brien, John D. (committee member)

Creator Email saghari@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-m162

Unique identifier UC191555

Identifier etd-Saghari-20061116 (filename),usctheses-m40 (legacy collection record id),usctheses-c127-31483 (legacy record id),usctheses-m162 (legacy record id)

Legacy Identifier etd-Saghari-20061116.pdf

Dmrecord 31483

Document Type Dissertation

Rights Saghari, Poorya

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 uscdl@usc.edu

Abstract (if available)

Abstract The advances in long haul transmission and optical reach have shifted the bottleneck from the core network to metro and access networks. Optical access network is a promising solution to the already congested access network, advocating the fulfillment of the enormous future requirements of applications and Internet services of the next-generation on demand.