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Advanced modulation, detection, and monitoring techniques for optical communication systems

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Advanced modulation, detection, and monitoring techniques for optical communication systems

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Content ADVANCED MODULATION, DETECTION, AND MONITORING TECHNIQUES FOR OPTICAL COMMUNICATION SYSTEMS by Vahidreza Arbab A Dissertation Presented to the FACULTYOFTHEUSCGRADUATESCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (ELECTRICAL ENGINEERING) May 2012 Copyright 2012 Vahidreza Arbab Dedication To my parents and my entire family and friends for their everlasting love, support, and understanding. ii Acknowledgements This work is the culmination of a long journey that I could never have completed without the patience, support, and guidance of many excellent people. First, I would like to thank my dissertation committee chairman and academic advisor, Professor Alexander A. Sawchuk, for his guidance, supervision, and in- sight that made the preparation of this thesis possible. I would also like to extend my great appreciation to Professor William H. Steier for serving on my disserta- tion and qualifying examination committees. In addition, I wish to express my deepest gratitude to Professor Behrokh Khoshnevis for serving on my disserta- tion and qualifying exam committees as well as contributing his time and effort to help me learn many invaluable life lessons. Furthermore, I am very grateful to my research co-advisor, Dr. Poorya Saghari, for his many contributions to this thesis. Since my first day at USC when he started to teach me how to use and operate lab equipment, he has continued his mentorship till this very day through insightful comments, suggestions, and research direction, as well as serving on my dissertation committee, in spite of his busy schedule at Avago Technologies. Imust,too,acknowledgemyfirstadvisoratUSCandchairmanofmyqualifying exam committee, Professor Alan E. Willner, who supervised and supported my research in the first four years and gave me the opportunity of working at OCLab from which I learned many invaluable lessons that will serve me for the rest of my life. Likewise, I wish to thank Professor John O’Brien and Professor Michelle Povinelli for their support and guidance during my qualifying examination. iii Similarly, I would like to express my sincere appreciation for advice I received from many excellent faculty members at USC. In particular, I would like to thank Professor Iraj Ershaghi, Professor Hossein Hashemi, Professor Massoud Pedram, and Professor Timothy Pinkston. I wish to express my special thanks to the associate chairman of Ming Hsieh EE-Systems, Professor Antonio Ortega, who contributed his efforts to address unforeseen problems. Also, I would also like to recognize Dr. Shahin Nazarian and Professor Kai Hwang, who trusted me as their teaching-assistant in several courses. I wish to express my heartfelt gratitude to Dr. Raymond Rakhshani as well, for his support, encouragement, and friendship during the past year. I would like to thank Professor Murat Uysal and my friend, Dr. Mohammad Mehdi Mansourirad, as well, for their wonderful collaboration in a project that appears in the fifth chapter of this thesis. I must also thank my M.Sc. thesis advisor at Sharif University, Professor Jawad A. Salehi, from whom I learned optical CDMA. Moreover, I want to acknowledge my previous colleagues at OCLab who helped me in the completion of the results presented in different parts of this thesis and other friends at USC for many years of insightful discussions and collabo- ration. Specifically, I would like to thank Paniz Ebrahimi, Irfan Fazal, Mahta Haghi, NarenderJayachandran, YannickKeith-Liz´ e, SaurabhKumar, TerryLewis, Yunchu Li, Scott Nuccio, Wei-Ren Peng, Xiaoxia Wu, Jeng-Yuan Yang, Omer Faruk Yilmaz, Yang Yue, Bo Zhang, and Lin Zhang. In addition, I wish to extend my appreciation to the staff of the electrical engineering department and the communication science institute at USC. In par- ticular, IwishtothankDianeDemetras, MillyMontenegro, TimBoston, Gerrielyn Ramos, Mayumi Thrasher, and Anita Fung for all their gracious help. I would also like to thank Margery Berti, Carolyn Suckow, and Tracy Charles from the Viterbi School of Engineering, and Ariel Suarez from the Office of International Services. iv I marvel at how lucky I was to have many wonderful friends who made this journey possible and pleasant for me in many ways; from guiding and helping me to be admitted at USC, to always being a great company and support during the hard times. I would like to thank all of them. Particularly, I wish I could thankSoroushAbbaspour,BehnamAmelifard,EhsanBarjasteh,PamchalFaroghi, Reza Gholizadeh, Ali Kamranzadeh, Damon Moazen, Reza Motaghian, Ehsan Pakbaznia, Arash Seifhashemi, Mahmood Shirooyeh, and Kasra Zamani. Above all, I am so thankful to my mother and father, Parvin Rohanni and Ahmad Arbab, and my sister and brother, Pegah and Vahab, for their uncondi- tionallove, trust, endlesssupport, encouragement, patience, andsomanysacrifices they made, one of which was bearing the physical distance between us so I can grow and succeed in my academic endeavors. Last but not least, I wish to thank my uncle, Reza Rohanni, and his family for being so much supportive and caring in all these past years. v Table of Contents Dedication ii Acknowledgements iii List of Figures ix Abstract xv Chapter 1: Background and Introduction 1 Chapter 2: Basics of Incoherent Optical CDMA 8 2.1 OpticalCDMASystems ........................ 11 2.2 Optical Orthogonal Codes ....................... 12 2.2.1 Two-DimensionalOpticalOrthogonalCodes ......... 15 2.2.2 Experimental Implementation of Optical Orthogonal Codes . 17 2.3 PerformanceAnalysisofOCDMASystems .............. 19 2.3.1 ModelofInterferenceinOCDMASystems .......... 22 2.3.2 Probability of Error in OCDMA Systems........... 24 2.4 SetupforOCDMAExperiments.................... 25 2.5 Conclusion................................ 26 Chapter 3: M-ary Modulation Formats in Optical CDMA 28 3.1 Pulse Position Modulation (PPM)-OCDMA ............. 29 3.2 Code Position Modulation (CPM)-OCDMA ............. 32 3.2.1 Experimental Demonstration of CPM-OCDMA ....... 34 3.3 Double Pulse Position Modulation (2-PPM)-OCDMA . ....... 37 3.3.1 Concept of 2-PPM-OCDMA.................. 39 3.3.2 Experimental Demonstration of 2-PPM-OCDMA ...... 40 3.4 Differential Pulse Position Modulation (DPPM)-OCDMA...... 43 3.4.1 DPPM-OCDMA System .................... 45 3.4.2 Experimental Demonstration of DPPM-OCDMA ...... 45 3.5 Conclusion................................ 48 Chapter 4: OCDMA in Local Area Networks 50 4.1 VariableQualityofServicewithOCDMA .............. 50 4.1.1 Multiple Pulse Position Modulation (MPPM)-OCDMA . . . 51 4.1.2 MPPM System Model and Experimental Setup ....... 53 4.1.3 MPPM-OCDMA Experimental Results and Discussion . . . 58 vi 4.2 InterferenceAvoidance(IA)AlgorithminOCDMA ......... 59 4.2.1 IAAlgorithminOCDMALANs................ 60 4.2.2 ExperimentalDemonstrationofIA-OCDMA ......... 64 4.3 Conclusion................................ 69 Chapter 5: Multiple-Bit Delay Detectionfor Phase ModulatedOp- tical Systems 70 5.1 OpticalDPSKSystems......................... 71 5.1.1 ConventionalDPSKDetection................. 74 5.2 Multiple-Bit Delay Detection (MBDD) for DPSK Signals ...... 76 5.2.1 MBDD-DPSKSystemModel ................. 77 5.3 PerformanceAnalysisofMBDD-DSPKDetectionAlgorithms.... 82 5.3.1 MBDD-DPSKwithOptimumDecisionRule ......... 83 5.3.2 MBDD-DPSKwithMajorityVoteDecisionRule....... 85 5.4 Conclusion................................ 90 Chapter 6: Optical Performance Monitoring withConstellationDi- agrams 91 6.1 TransmissionImpairmentsinOpticalFiberSystems......... 92 6.1.1 ChromaticDispersion(CD) .................. 92 6.1.2 PolarizationModeDispersion(PMD)............. 93 6.2 Conventional Methods in Optical Performance Monitoring (OPM) . 94 6.3 Constellation Diagram Monitoring of Phase Modulated Systems . . 96 6.3.1 EffectsofChromaticDispersionontheConstellationDiagrams100 6.3.2 Effects of First-Order PMD on the Constellation Diagrams . 102 6.4 AsynchronouslyGeneratedConstellation ...............103 6.5 Conclusion................................106 Chapter 7: Intensity Modulated Optical Multicarrier CDMA 108 7.1 MulticarrierTransmissionandOFDMinOpticalSystems......110 7.2 System Model of Intensity Modulated OMC-CDMA . . .......112 7.3 NoiseinOMC-CDMABasedPONS..................118 7.4 ModelofFiber-OpticIntensityChannel................119 7.5 PerformanceEvaluationofOMC-CDMA ...............121 7.6 Conclusion................................124 Chapter 8: Experimental Demonstration of Optical Multicarrier CDMA 126 8.1 BlockDiagramandExperimentalSetupofOMC-CDMA ......126 8.2 OMC-CDMAExperimentalResultsandDiscussion .........128 8.3 Conclusion................................130 Chapter 9: Optical Multicarrier CDMA with Asymmetrical Clip- ping 132 9.1 Model of OMC-CDMA with Asymmetrical Clipping . . .......133 9.2 BER Performance Analysis of OMC-CDMA with Clipping .....141 9.3 Conclusion................................142 vii 9.4 Analyticalderivationoftheparameters ................143 9.4.1 Formulationofthereceivedsymbol ..............144 9.4.2 Noisecharacterization .....................145 9.4.3 Calculationofaveragetransmittedopticalpower.......146 Chapter 10:Conclusion and Future Work 148 Glossary 152 Bibliography 154 viii List of Figures Figure 1.1 Thesis outilne ......................... 4 Figure2.1 Conceptofspreadspectrumsignals ............. 8 Figure2.2 ComparisonofFDMA,TDMA,andCDMAsystems..... 10 Figure 2.3 Block diagram of an OCDMA system with N pairs of users. 11 Figure 2.4 ExampleoftwoOOCswithparameters(13, 3, 1): (a)code- word is 1100100000000, (b) codeword is 1010000100000. . . 14 Figure 2.5 An example of two dimensional (2-D) OOC code-set .... 16 Figure 2.6 Active implementation of OOC using electrical components. 17 Figure 2.7 PassiveimplementationofOOCintheopticaldomainusing tappeddelaylines........................ 18 Figure 2.8 2-D OOC implemented in the optical domain with an FBG arrayandacirculator...................... 19 Figure 2.9 Experimental implementation of 2-D OOC using FBG ar- raysinthelab.......................... 19 Figure 2.10 Example of 2-D OCDMA encoder and decoder using cor- relationintheopticaldomain. ................ 20 Figure 2.11 An example of the MAI effect in OCDMA systems. .... 21 Figure 2.12 pmf of the interference for (a) (Λ,T,ω)=(20,8,15) and few active users, (b) (Λ,T,ω)=(64,40,31) and a large numberofactiveusers[88]................... 23 Figure 2.13 Probability of error versus code weight for different number of active users. In each figure, a fixed code length and numberofwavelengthshavebeenconsidered[88]. ..... 25 Figure 2.14 Experimentaldemonstrationof2-D(time-wavelength)OCDMA usingFBGarraysasCDMAencodersanddecoders. .... 26 Figure 3.1 An example of PPM symbol set capable of representing 3 bitspersymbol. ........................ 30 ix Figure 3.2 AnexampleofPPM-OCDMAencodingwithT = M.Each symbol carries 2 bits and there are two wavelengths in the OOC............................... 31 Figure 3.3 An example of CPM-OCDMA encoding. .......... 33 Figure 3.4 Experimental setup of CPM-OCDMA with 6 active users and using FBG arrays as CDMA encoders to generate 2-D OOCs with T =16,Λ=8,and ω=6............. 35 Figure 3.5 Fig. 5.4. (a) Modulated CPM data, distinct shifts of the auto-correlation peak represents the symbols (b) CPM- OCDMA encoded data, (c) decoded CPM-OCDMA data; thehorizontalscaleis1ns/div................. 36 Figure 3.6 Left: the encoded data of all users for 1 through 6 active users. Right: the decoded data of the user of interest along withtheMAI. ......................... 37 Figure 3.7 BER vs. received optical power of the user of interest for differentnumberofactiveusers. ............... 38 Figure 3.8 Block diagram of a 2-PPM-OCDMA system. ........ 39 Figure 3.9 Block diagram of a 2-PPM-OCDMA system. ........ 40 Figure 3.10 (a) 2-PPM symbols of the user of interest after modulator, (b) CDMA-Encoded symbols, (c) Decoded symbols when thereare5activeusers..................... 41 Figure 3.11 BER vs. received power of the user of interest for two cases ofsingleactiveuserand5activeusers. ........... 42 Figure 3.12 Power penalty of switching from CPM-OCDMA to 2-PPM- OCDMA............................. 43 Figure 3.13 Concept of DPPM signaling. ................. 44 Figure 3.14 Comparison of the average number of transmitted bits per symbol for different modulation techniques. ......... 44 Figure 3.15 Experimental setp of DPPM-OCDMA. ........... 46 Figure 3.16 Comparison of the required time to transmit the same bit sequence using OOK, CPM, and DPPM. .......... 47 Figure 3.17 (a) Encoded DPPM-OCDMA symbols, (b) Decoded sym- bols (single user), (c) Decoded symbols with 3 active users. 48 Figure 3.18 BER curves for different number of active users in the net- work vs. received power. ................... 49 x Figure 4.1 Examples of PPM, 2-PPM, and 3-PPM Symbols. Number ofpossiblesymbolsiswrittenbesideeachpattern. ..... 51 Figure 4.2 Number of bits per symbol for PPM, 2-PPM, and 3-PPM symbols versus the code length T(= M). .......... 52 Figure 4.3 A variable bit rate OCDMA network using PPM, 2-PPM and3-PPMformats....................... 52 Figure 4.4 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 pat- terns in the pulses and black pulses show MAI due to other usersinthenetwork. ..................... 54 Figure 4.5 ExperimentalsetupforavariablebitrateOCDMAnetwork using MPPM-OCDMA. .................... 56 Figure 4.6 (a) 3-PPM symbols, (b) PPM symbols, after the modula- tors. In each case, three symbols are shown and dotted lines separate adjacent symbols. . .............. 57 Figure 4.7 Decoded symbols and their eye diagrams: (a) PPM, (b) 3-PPM. Small pulses are the MAI from other users in the system. ............................. 58 Figure 4.8 Power penalty versus the number of PPM users to achieve various combinations of users operating at different bit rates. 59 Figure 4.9 (a) OCDMA network: The nodes are connected by trans- mit and receive (upstream, downstream) fibers to a passive star coupler to enable a shared medium LAN, (b) Block diagramofanIAnetworkinterfacecard. .......... 62 Figure 4.10 Top: fiber link after the decoder of the user of interest. Bottom: data is transmitted such that the auto-correlation isinthechiptimewiththeleastinterference......... 63 Figure 4.11 The normalized network throughput vs. normalized offered load for Aloha-CDMA and transmission scheduling. (a) Simulated traffic (b) Real traces of traffic from OC44 link. The throughput of the network does not collapse in high loads. The traffic model is Poisson arrivals with exponen- tially distributed packet lengths. ............... 65 Figure 4.12 Experimental setup for implementing IA-OCDMA...... 66 xi Figure 4.13 Bit sequence of ‘10110’ for (a) single user, (b) 3 users, and (c) 6 users. Eye diagram of the correlation for (d) single user, (b) multiple users with transmission scheduling, and (c)randomcase(ALOHA)................... 67 Figure 4.14 (a) BER vs. received optical power of user 1 for increasing numberofusers, (b)performanceofanOCDMAsystemfor increasing number of users with transmission scheduling, aloha-CDMA,andworstcase................. 68 Figure 5.1 Change of the output electrical fields in phase modulators andMZMs............................ 73 Figure 5.2 Phase modulation using MZM [32]. ............. 74 Figure 5.3 Conventional DPSK receiver ................. 75 Figure 5.4 Block diagram of optical DPSK system with multiple-bit delay detection (MBDD) receiver structure ......... 78 Figure 5.5 Block diagram of the optimum (LMSE) MBDD detector . . 85 Figure5.6 Blockdiagramofthemajorityvotedetector ........ 87 Figure 5.7 BERperformanceofthemajorityvotedetectorversusOSNR for different number of delay segments (M)with BT =4. AsM increasestheBERcurvegetsclosertotheBERcurve ofthecoherentdetection.................... 88 Figure 5.8 OSNR gain of the optimum MBDD detector and the ma- jority vote MBDD detector compared to the conventional DPSK receiver for different number of delay segments (as- suming ρ s BT)........................ 89 Figure 6.1 Optical performance monitoring techniques ......... 95 Figure 6.2 Experimental setup for two-tap asynchoronous sampling [4]. 96 Figure 6.3 Deformations of the two-tap aynchronous plot with CD [4]. 96 Figure 6.4 Block diagram of QPSK system with balanced detection constellation-diagrammonitor. CW:ContinuousWavelight source, RZ: Return to Zero, I: In-phase, Q: Quadrature, CD: Chromatic Dispersion, DGD: Differential Group De- lay, BPF: Band-Pass Filter, T: Delay (equal to the symbol time),A/D:AnalogtoDigitalconverter. .......... 97 Figure 6.5 An arbitrary sequence of I and Q, (a) without any type of fiber impairments, (b) constellation affected by CD only, (c) constellation affected only by DGD . . ......... 98 xii Figure 6.6 Received constellation diagrams of QPSK signal (a) with- outanytypeoffiberimpairments, (b)constellationaffected by CD only, (c) constellation affected only by DGD .... 98 Figure 6.7 Effect of DGD on DQPSK signals. . . ............102 Figure 6.8 Different constellations obtained at different times (15-ps CD). ..............................103 Figure 6.9 Effects of CD and DGD on the asynchronously generated constellation diagrams (a) CD Broadens the branches in constellationdiagrams,(b)DGDcreates4newsignalphases right in the middle of the initial signal phases, (c) the con- stellation diagram is symmetric with respect to the line I=Q.104 Figure 6.10 Simultaneous effects of CD and DGD on QPSK constella- tionpatterns. .........................105 Figure 6.11 Normalized distance of the emerged new phases from the center of the I/Q plane as a figure of merit to measure the amountofDGD.........................106 Figure 6.12 Normalized width of the constellation branch in the third quadrant.............................107 Figure7.1 ComparisonofthespectrumofWDMandOFDM......109 Figure7.2 HistoryofopticalOFDM[13]. ................109 Figure 7.3 Different multiple access techniques using subcarrier, time, andcodedivision. .......................111 Figure 7.4 Simplified concept of MC-CDMA showing that it is com- posedofOFDMandCDMA .................112 Figure7.5 BlockdiagramofOMC-CDMAsystem ...........113 Figure 7.6 Frequency response of a typical optical fiber for two fiber lengthsof50and100Km. ..................120 Figure 7.7 BER graphs consideing different number of active users . . 123 Figure7.8 BERgraphsfordifferentsymbolconstellations .......124 Figure 8.1 BlockdiagramofintensitybasedOMC-CDMAsystemwith MZM. CP: Cyclic Prefix, D/A: Digital to Analog, MZM: Mach-Zehnder Modulator...................127 Figure 8.2 BiasingMZMatquadraturepoint. Theslopeofthetangent line at the bias is β.......................128 xiii Figure 8.3 BER curves for different number of active users consider- ing both back-to-back and 70-km fiber link cases and cor- responding constellation diagrams . . ............129 Figure8.4 BERcurvesfordifferentQAMsymbolmappings ......130 Figure 8.5 Equalized received constellations of different QAM symbol mappings (a) R=7.5-Gb/s, (b) R=10-Gb/s, (c) R=12.5- Gb/s, (d) R=15-Gb/s.....................131 Figure 9.1 Block Diagram of IMDD OMC-CDMA with Asymmetrical Clipping. Inthetransmitteronlyuserk, andinthereceiver onlyuser1havebeenshown. ................136 Figure 9.2 Effects of asymmetrical clipping on the signal in time and subcarrierdomains ......................138 Figure9.3 BERgraphsfordifferentnumberofactiveusers ......143 Figure 9.4 Effects of constellation size on the BER ...........144 xiv Abstract Optical code division multiple access (OCDMA) systems have recently become a topic of interest for their potential application in access points and optical local area networks (LAN). In this thesis, we review OCDMA systems and their limita- tions, as well as various experimental techniques to increase the number of users and/or bit rate in a system or a network. These techniques include incorporating M-ary modulation formats, such as pulse position modulation (PPM), code posi- tion modulation (CPM), double-PPM (2-PPM), differential-PPM (DPPM), and multiple-PPM (MPPM). We also discuss and experimentally demonstrate variable quality of service (QoS) in OCDMA networks. Congestion collapse problems in OCDMA networks are reviewed, and we experimentally demonstrate the interfer- ence avoidance (IA) algorithm to overcome it. Advanced data modulation formats are playing an ever-increasing role within the optical communications community. For example, phase-shift-keying (PSK) providesbetterreceiversensitivityandtolerancetononlineareffects,andquadrature- PSK(QPS)andquadrature-amplitude-modulation(QAM)provideincreasedspec- tralefficiencyandtolerancetochromaticdispersion(CD).Weinvestigatemultiple- bit delay detection (MBDD) as an advanced technique for incoherent detection of xv optical differential-PSK (DPSK) signals in fiber-optic systems. We show that with a large number of delay segments and employing the optimum decision rule or the majority vote decision rule, the power efficiency asymptotically approaches the power efficiency of the coherent detection. Monitoring constellation diagrams of phase-modulated signals isalso presented as a new tool to visualize different effects of fiber impairments. Anewresearchtopicinopticalcommunicationscommunityisopticalfrequency division multiplexing (OFDM). We describe a multiple-access technique based on optical OFDM called optical multicarrier CDMA (OMC-CDMA) that has the advantages of both CDMA and OFDM. These advantages include high flexibility in serving multiple users and changing the transmitted baseband symbols without modification of the hardware, tolerance to dispersion, and simplified equalization. Analytical and experimental evaluations of OMC-CDMA are presented as well. We expect that the modulation, detection, and monitoring techniques pre- sentedinthisthesismaypotentiallyplaykeyrolesinfutureopticalcommunication systems and networks. xvi Chapter 1 Background and Introduction The idea of using glass fiber for communications is as old as telephone systems, but this idea had to wait for tens of years so the necessary components could emerge over the course of time. Optical communication technology was enabled by the invention of the laser in the late 1950’s. The invention of low loss optical fibers in the 1970’s was also a big step forward, but it was the invention of Erbium-Doped Fiber Amplifier (EDFA) that revolutionized the optical communication industry in the 1980’s. Before the invention of the optical amplifier, the regeneration of optical signals over long distances had to be in the electrical domain by converting the optical signal to an electrical signal, then amplifying the detected signal, and finally exciting another laser. However, after the invention of EDFA, the need for optical/electrical/optical conversion, which was the bottleneck of the speed in optical communication systems, was alleviated. Fiber-opticcommunicationsystemshavemanyadvantagesovertraditionalwireline communication systems, including: (1) High capacity: Optical fiber communication systems employ carrier fre- quencies around 193-THz in near-infrared region of the electromagnetic spectrum. Compared this number with GHz range of carrier frequency in traditional com- munication systems shows the potentially available high bandwidth of fiber-optic systems. Some recent demonstrations of high capacity fiber-optic systems include 1 69.1-Tb/s over 240-km [94], 1.15-Tb/s over 3560-km [111], and 109-Tb/s over 16.7-Km [91]. (2) Low loss: Power loss in new fibers is less than 0.2-dB/Km which is much less than 5-dB/Km loss in coaxial cables, so fiber-optic transmission systems at- tenuate the signal 25 times less. Hence, the number of regenerators in an optical link is much fewer compared to an electrical wireline link in long-haul transmission and consequently the price of the whole system. (3) Low weight and size: Optical fibers are very light and have a small size compared to coaxial cables. This reduces the laying and maintenance cost. (4) Immunity to electromagnetic radiation: Sincethecarrierfrequencyin fiber-opticcommunicationsystemsisdifferentbyordersofmagnitudefromconven- tional wireless and wireline communication systems, electromagnetic interference from other sources does not affect optical communication systems. Moreover, this property of fiber-optic systems makes them robust to jamming. (5) Material cost: Optical fibers are made of glass which is much cheaper than metals used in wireline communications like copper. Recent advancements in fiber-optic technology have shifted the bottleneck from the core networks to metropolitan and access networks. Optical access networks are capable of providing high bandwidths for every single user in the network. Currently, around30millionsubscribersusefiber-to-the-home(FTTH)technology in Japan that enables them to access broadband internet. Since in a network a group of subscribers are interacting, there should be an algorithm to allocate the available channel resources to the active users and 2 prevent them from interfering with each other. In time division multiple access (TDMA) systems, each user is allowed to be active in certain allocated time slots and it can send and receive data over all available frequency bands. With a similar concept but in another dimension, in frequency division multiple access (FDMA) which its counterpart in optical systems is wavelength division multiple access (WDMA), the available frequency spectrum is divided between users, so each user can transmit and receive data all the time using its own frequency band. In code division multiple access (CDMA) technique, a unique spreading code is assigned to each user in the network, so all users can send and receive data at the same time and over the entire available frequency spectrum in the medium. Currently, optical TDMA and WDMA architectures are commercially avail- able; however, they have fundamental disadvantages including bandwidth limita- tions, synchronization, and difficult scalability. Moreover, a centralized control mechanism is necessary in aforementioned techniques. Optical CDMA (OCDMA) has recently gained attention due to its unique features such as enhanced through- put efficiency, data privacy, asynchronous nature, plug and play functionality, and simplicity of network control especially when considering the fine granularity of traffic, flexible bandwidth management, and ability to support variable quality of service (QoS). The outline of this thesis is shown in Fig. 1.1. Chapter 2, 3, and 4 are parts of the DARPA OCDMA program. In chapter 2, an introduction to CDMA systems is presented and the specific properties and limitations of incoherent OCDMA sys- tems are studied. It is shown that using 2-D OOCs enables increasing the number 3 Figure 1.1: Thesis outilne 4 of active users without reducing the bit rate or increasing the chip rate. Different methods of implementing optical orthogonal codes (OOC) are introduced and the advantage of each one is discussed. The method of modeling the interference is then reviewed and using the statistics of the MAI, an algorithm to calculate the BER performance is explained. The main contributions in this chapter address two concerns: (i) how to design the fiber-Bragg gratings (FBG)-OOCs consider- ing practical limitations and predefined requirements in milestones of the project, (ii) how to build an OCDMA experimental setup to serve as the foundation of experiments in the following chapters. In chapter 3, different M-ary OCDMA methods to increase the bit rate per user are introduced. First, pulse-position-modulation (PPM)-OCDMA is studied, but due to practical limitations, the CPM-OCDMA technique is introduced as a sub- optimal method, and it is experimentally demonstrated. It is shown that the bit rate significantly increases. In order to increase the bit rate further, double-PPM- OCDMA (2-PPM-OCDMA) and differential-PPM-OCDMA (DPPM-OCDMA) formats proposed and experimentally demonstrated. These techniques increase the bit rate approximately by a factor of 2 compared to CPM-OCDMA. Both techniques provide versatility such 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 2-PPM or DPPM schemes to oper- ate at a higher bit rate. The main contribution in this chapter is increasing the bit rate in OCDMA systems to meet the requirements of the milestone, without 5 decreasingthechiptimeorthenumberofactiveusersbyproposingandexperimen- tally demonstrating two new techniques of 2-PPM-OCDMA and DPPM-OCDMA [6, 7, 110]. In chapter 4, incoherent OCDMA in the physical layer of local area networks (LAN) is studied and potential functionalities of OCDMA to provide variable QoS to different subscribers in a network is investigated. The contributions are the proposal and experimental demonstration of variable QoS through multiple-PPM (MPPM)-OCDMA [11], as well as experimental demonstration of a scheduling algorithm named interference avoidance (IA) to reduce interference in OCDMA networks is experimentally demonstrated [84, 85]. It is shown the IA algorithm can dramatically enhance the throughput of OCDMA based LANs. In chapter 5, first, phase modulated optical communication systems are re- viewed and conventional detection techniques are studied. The performance of multiple-bit delay detection (MBDD) which is based on using several balanced detection segments with different delay values, using optimum and majority vote decision rules, are analytically formulated and it is shown the performance of the system with a high number of delay segments approaches the performance of a completely coherent detection scheme [5]. In chapter 6 that is part of the DARPA CORONET and NIST performance monitoring programs, first, different methods of optical performance monitoring are reviewed. The main contribution in this chapter is that for the first time, con- stellation diagrams of phase-shift-keying (PSK) signals are used as a new tool for visually monitoring fiber impairments [9]. It is shown that constellation patterns 6 deform in a fairly predictable way, such that the diagrams can be recognizably used to determine the amount of accumulated chromatic dispersion (CD) and dif- ferential group delay (DGD) [10]. In chapter 7, optical multicarrier transmission and orthogonal frequency divi- sion multiplexing (OFDM) are studied and a new CDMA technique with intensity modulation and direct detection, called optical multi-carrier CDMA, is proposed. It is shown that the system has a high flexibility in serving multiple users and changing the modulation format without modification of the hardware. The BER performance of the system in synchronous transmission considering common noise sources in passive optical networks is analytically derived. In chapter 8, the first experimental demonstration of OMC-CDMA in single mode optical fiber is presented. It is shown that with an electrical bandwidth of 2.5-GHz, OMC-CDMA is capable of supporting 256 users at a total bit rate of 15-Gb/s with almost no penalty in a 70-Km fiber-optic link [8]. In chapter 9, a modification to OMC-CDMA based on signal clipping is in- troduced and the BER performance of the system in downlink transmission is analytically evaluated in passive optical networks. Considering shot-noise and thermal noise of photo-receivers, a closed form expression to predict the overall BER of the system is presented. It is shown the system achieves a higher power efficiency compared to the OMC-CDMA systems without signal clipping at the price of a reduced spectral efficiency. 7 Chapter 2 Basics of Incoherent Optical CDMA Spread spectrum communication systems are based on modulating the data over a large bandwidth, usually orders of magnitude larger than the bandwidth of the original signal. The wideband nature of spread spectrum signals increases the tolerance of the system to noise, interference, eavesdropping, and jamming. The motivation and advantages of spread spectrum originated in military applications. Initial commercialization of spread spectrum started in the early 1980’s. One of the first commercial spread spectrum systems was Qualcomm’s OmniTRACS for communications to trucks. Figure 2.1: Concept of spread spectrum signals 8 CDMA is a spread spectrum technique that spreads the signal using a coded sequence of many short-length pulses (chips) shown in Fig. 2.1. The chip time is thedurationofa‘0’ora‘1’inthecodeword. CDMAallowsdifferentuserssimulta- neously have access to the same frequency spectrum. By contrast, TDMA divides the access of different users to the channel in the time domain, and FDMA divides it in the frequency domain. An analogy to multiple access is a room (channel) in which people want to talk to each other. In order to avoid confusion, people can take turns speaking (time division), speak at different pitches (frequency division), or speak in different languages (code division). CDMA is analogous to the last example where people speaking the same language can understand each other, but other languages are perceived as noise and rejected. Similarly, in communications, each group (pair) of users is given a shared code and many codes occupy the same channel, but only users associated with a particular code can communicate. The reason that spread spectrum is robust to eavesdropping and jamming is that any group (pair) of users is unaware of the codes of other groups (pairs), so they cannot detect other signals intended for other groups. Figure 2.2 shows the concept of CDMA and how it compares to TDMA and FDMA. Designing spreading codes with certain desired properties enables multiple users to transmit data on the same frequency band simultaneously over a shared medium, provided that the receiver is aware of the transmitter’s spreading code. In general, spreading the signal can be achieved by several schemes: Direct Sequence Spread Spectrum (DSSS): Data is directly encoded us- ing a high chip rate codeword. 9 Figure 2.2: Comparison of FDMA, TDMA, and CDMA systems. Frequency Hopping Spread Spectrum (FHSS): While encoding data us- ingahighchipratecodeword,thefrequencyofeachchipisalsoaltered. Asaresult, FHSS is a two-dimensional encoding using both time and frequency domains. Time Hopping Spread Spectrum (THSS): Data is not transmitted con- stantly, it is transmitted in short bursts according to the ones or zeros of a code- word. The idea of optical CDMA (OCDMA) was first suggested in the late 1980’s as an asynchronous secure multiple access protocol for optical communications net- works [83, 93]. OCDMA was introduced as an access method that does not require centralized network control and it can efficiently provide the required bandwidth and connectivity in a local access network (LAN). Although the advantages of OCDMA have been recognized for many years, it could not achieve its potential because of practical limitations until recently. 10 2.1 Optical CDMA Systems In Fig. 2.3, the general concept of an OCDMA system with N pairs of users is shown. OCDMAsystems can bedesigned to support synchronousor asynchronous data traffic. In the synchronous case, higher spectral efficiency can be achieved. However, the system requires global synchronization between different users, re- sulting in a more complicated and less secure architecture. Intheasynchronouscase,theOCDMAsystemdoesnotrequiresynchronization in the transmitter. As a result, the implementation of the system is easier, but in order to accommodate a large number of users in such systems, long CDMA codes and large number of wavelengths are required, which will decrease the spectral efficiency of the system. InordertoenableasynchronoustransmissiontheCDMAcodemustbedesigned such that (i) each codeword must be different than any circularly shifted version of itself and (ii) each codeword and all its possible shifted versions must be different thananyothercodewordsusedbyotherusersinthenetwork. Thefirstrequirement sets a condition for the auto-correlation property of the codewords, and the second one imposes another condition regarding the cross-correlation of the codewords. Figure 2.3: Block diagram of an OCDMA system with N pairs of users. 11 In incoherent optical communication systems, the receiver detects only the intensity of the received optical field, so bipolar signaling is not possible. As a result, the spreading sequences cannot be completely orthogonal in incoherent OCDMA systems. This limitation fundamentally separates OCDMA from non- optical CDMA. For example, with an identical code length, the maximum number of users in OCDMA systems is less than the number of users in regular CDMA sys- tems. In the next section the basic concept of the codewords which are appropriate for asynchronous OCDMA systems will be discussed. 2.2 Optical Orthogonal Codes In incoherent OCDMA systems, a unique signature code of length T from a set of OOCs is assigned to each user [93]. These codes have appropriate auto-correlation and cross-correlation properties that enable each user at the receiver side to distin- guish its own data among the encoded data of all active users. Each bit time, T b , is equally divided into T smaller chip times denoted by T c , and then a user’s signa- ture code specifies ω out of the T chips to contain an optical pulse with duration of T c ,where ω is the code weight. ThecommonmodulationformatinOCDMAsystemsisOOKinwhichforsend- ing a ‘1’ bit, a codeword is transmitted and for a ‘0’ bit, nothing is transmitted during the bit time duration. Because of the unipolar nature of the optical inten- sity based systems, the data of different users in OOK-OCDMA systems cannot be completely orthogonal, i.e., the correlations of the codewords cannot be zero. Hence, giving up the zero correlation, a new concept of threshold, called maximum 12 collision parameter, is defined for OOCs. This parameter which is denoted by κ, is the maximum allowed number of chip collisions of any codeword with the circu- larly shifted version of itself or other codewords. In summary, the mathematical conditions of the code sequences in a set of OOC that must be satisfied are [93]: 1. The auto-correlation property: For any arbitrary codeword c = [c(0),c(1),...,c(T −1)] the inequality T−1 i=0 c(i)c(i⊕τ) ≤ κ (2.1) must hold for every τ which is not an integer multiple of T. In (2.1), ⊕ is the modulus T summation operator. 2. The cross-correlation property: For any two codewords of denoted by c=[c(0),c(1),...,c(T − 1)] and d=[d(0),d(1),...,d(T − 1)], respectively, the inequality T−1 i=0 c(i)d(i⊕τ) ≤ κ (2.2) must hold for every integer value of τ. The set of all codewords satisfying the above conditions is denoted by (T,ω,κ). For example, C 1 = (1100100000000) and C 2 = (1010000100000) are the only two OOC’s of (T,ω,κ)=(13,3,1). These two codes are shown in Fig. 2.4. The number of codewords (which is also the maximum number of users) is called the cardinality of the OOC set and it is denoted by Φ(T,ω,κ). The upper bound on Φ(T,ω,κ) can be expressed by the following inequality 13 Figure 2.4: Example of two OOCs with parameters (13, 3, 1): (a) codeword is 1100100000000, (b) codeword is 1010000100000. Φ(T,ω,κ) ≤ 1 ω T −1 ω −1 ··· T −κ ω −κ . (2.3) This is called the Johnson bound [42]. It only gives an upper bound to the maximum number of possible codes in an OOC code-set and in most cases a code construction algorithm to achieve equality on the right side of (2.3) does not exist [74]. As observed, in order to increase the number of available codewords to provide service to more users in a network, the code length should be increased. In- creasing the code length while trying to maintain the bit rate unchanged requires using optical pulses with shorter duration, i.e., the chip time should be reduced. Since generating and detecting extremely short pulses are challenging, a method of increasing the number of codewords without changing the chip time is of great interest. One possible technique to overcome this issue is encoding data in both time and wavelength domains, which will be discussed as two dimensional (2-D) OCDMA in the next session. 14 2.2.1 Two-Dimensional Optical Orthogonal Codes IfinanOOCallω pulseshavethesamewavelength, theOCDMAcodeiscalledone dimensional (1-D), otherwise it is called a two dimensional (2-D) OCDMA system since it uses the wavelength domain as another dimension. Given a fixed code length, 2-D OCDMA systems can support more users than 1-D OCDMA systems [88]. Any 2-D OOC set can be represented with 4 parameters, (Λ,T,ω,κ), where Λ is the number of wavelengths. A 2-D OOC consists of an array of ones and zeros, whose rows correspond to different wavelengths, and the columns correspond to time slots. For example in Fig. 2.5, the code length is 7, the code weight is 3, the number of wavelengths is 3, and the maximum collision parameter is 1, so this OOC set is denoted by (3,7,3,1). 2-D OCDMA systems are similar to FHSS in wireless communication systems. Similarto1-DOOC,thereareauto-correlationandcross-correlationconditions for2-DOOCsaswell: 1. The autocorrelation property : For an arbitrary codeword c where c = ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ c(0,0) c(0,1) ··· c(0,T −1) c(1,0) c(1,1) ··· c(1,T −1) . . . . . . c(Λ−1,0) c(Λ−1,1) ··· c(Λ−1,T −1) ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ the inequality Λ−1 i=0 T−1 j=0 c(i,j)c(i,j ⊕τ) ≤ κ. (2.4) must hold for every integer value of τ which is not an integer multiple of T. 15 Figure 2.5: An example of two dimensional (2-D) OOC code-set 2. The cross-correlation property: For any two codewords c and d,the inequality Λ−1 i=0 T−1 j=0 c(i,j)d(i,j ⊕τ) ≤ κ. (2.5) must hold for any integer value of τ. The upper bound on the cardinality of a 2-D OOC code set (Λ,T,ω,κ)canbe expressed by the inequality Φ(Λ,T,ω,κ) ≤ Λ ω ΛT −1 ω −1 ··· ΛT −κ ω −κ . (2.6) Comparing (2.3) and (2.6) shows with the same T, ω,and κ, two dimensional OOC can potentially have a higher cardinality compared to one dimensional OOC. 16 2.2.2 Experimental Implementation of Optical Orthogonal Codes There are different methods to encode and decode data in OCDMA systems. The encoding/decoding can be accomplished in the electrical or the optical domain. The output of an OCDMA encoder is a 1-D or 2-D OOC. For example, Fig. 2.6 shows an active implementation of a 1-D OOC in the electrical domain, in which the output of the multiplier which is a switch controlled by the CDMA code, modulates the light according to the code c(t). The disadvantage of this method is that the chip time is limited by the minimum switching time of the electrical components. Figure 2.6: Active implementation of OOC using electrical components. A method of generating OOC in the optical domain is shown in Fig. 2.7, where the delay between OOC chips is implemented by various delays in fiber delay lines [93]. Since the weight of the OOC is ω, the number of required delay lines is ω.In this method which was initially used in the OClab, free space stages were required in order to fine-tune the delays between optical chips. As it can be observed this 17 method is passive. The disadvantage of this method is that in implementation of 2-D OOC, the system becomes very bulky. Figure 2.7: Passive implementation of OOC in the optical domain using tapped delay lines. ThebestsolutiontoimplementOOCusesFBGandcirculatorsasshowninFig. 2.8. In this passive encoding method, all wavelengths are transmitted together and are fed into an array of FBGs that implements the delays between the wavelengths using reflections [30]. Depending on the distance between the gratings in the FBG array, different delays between the wavelengths can be realized. For decoding, the same grating can be used, but the received signal must be fed into the other end of the grating. Figure 2.9 shows the experimental implementation of 2-D OOC using FBG arrays in the lab. In general, 2-D OOCs can have more than one chip of the same wavelength, i.e., a wavelength can appear more than once within a 2-D OOC. FBG arrays can be only used to implement the special case of 2-D OOCs with at most one chip per wavelength. In the experimental demonstrations, we have only considered this special case to simplify the practical implementation. 18 Figure 2.8: 2-D OOC implemented in the optical domain with an FBG array and a circulator. Figure 2.9: Experimental implementation of 2-D OOC using FBG arrays in the lab. 2.3 Performance Analysis of OCDMA Systems There are many different factors that affect the performance of an OCDMA sys- tem. The source of an error in transmission can be thermal noise or shot noise in the photo-receiver, amplifier spontaneous emission (ASE) noise generated in the optical amplifier, beat noise in photo-detection process, interference from other users, linear and nonlinear distortions due to propagation in the fiber, and so on. The effects of noise have been studied in [25, 18, 66, 63, 117]. 19 Figure 2.10: Example of 2-D OCDMA encoder and decoder using correlation in the optical domain. Since OCDMA is used in LANs, the effects of fiber impairments such as CD and PMD, which are only important in long-haul transmission, can be ignored. The effects of noise are also negligible compared to the effect of the multiple access interference(MAI).MAIistheresultofmultipleuserstransmittingsimultaneously in the system and its effect is generally more damaging than the noise because the encoded signals are allowed to have non-zero chip collisions. The amount of the MAI depends on the OCDMA detection technique [117]. In correlation receivers, with the decoder being the complement of the encoder, the optical chips from the encoded data go through the reverse process of encoding thatmakesallthechipswhichwerespreadintimetobealignedontopofeachother in one chip time. Figure 2.10 shows an example of CDMA encoding and decoding with a correlation receiver. The summation of the delays for each wavelength in the encoder and the decoder is constant. It should be noted that ignoring the noise makes the optical channel a Z- channel, i.e., there is no error when a ‘1’ is transmitted, and an error can only occur when a transmitted ‘0’ is interpreted as ‘1’ in the receiver. For example, an error occurs when the user of interest wants to transmit ‘0’, so it sends no signal 20 Figure 2.11: An example of the MAI effect in OCDMA systems. in the bit time duration, but the amount of the MAI from other users is so high that a false ‘1’ is detected as the signal of the user. Figure 2.11 shows the concept of the MAI. User 1 is the user of interest. User 1’s data is ‘0’, and user 2, user 3, and user 4 are transmitting ‘1’ using their own CDMA codes and with different delays with respect to the user of interest. In the fiber link, all the pulses from the users are added. The chip sequence that arrives at the user 1’s decoder will generate the MAI pattern at its output as illustrated in the figure. Since the MAI in the desired time, corresponding to the interval of user 1, is greater than the threshold, a false ‘1’ is detected. As observed from this example, reducing the number of users reduces the amount of the MAI. Therefore, the MAI is a major problem that limits the number of active users in incoherent OCDMA networks. Figure 2.11 also illustrates that the level of MAI depends on the delays of the different users. On the other hand, OOC code construction is difficult to formulate. Therefore, the MAI is a random 21 process which cannot be simply analyzed. There are some techniques to reduce the MAI such as using hard limiters [43, 44, 57, 73], or using three dimensional (3-D) OOC using polarization as the third dimension [65]. 2.3.1 Model of Interference in OCDMA Systems In order to model the MAI, instead of considering specific OOC structures, the model of general code with OOC restrictions is taken into account. Based on the general code model, a probability mass function (pmf) can be generated and using this pmf, the probability of error can be predicted [88]. In this section, only the results of the MAI model for 2-D OOCs with at most one chip per wavelength are presented. In [88] it has been shown that the pmf of the MAI can be calculated as follows, Prob(MAI = h)= A j= h κ A j β j (1−β) A−j P j (h) (2.7) where A is the number of active users, κ is the maximum collision parameter, β is the probability of sending ‘1’ which is usually equal to 0.5, and P j (h)= P 1 (h)∗P j−1 (h) which is recursively obtained is the distribution of the MAI when there are j interferers transmitting ‘1’ and making interference with the user of interest. P 1 (h) is the probability of one user colliding with the user of interest in h locations and is given by P 1 (h)= ( ω h ) (T−1) h ω x=max(h,2ω−Λ) ω−h x−h Λ−ω ω−x (1− 1 T ) x κ h =0 ( ω h ) (T−1) h ω x=max(h ,2ω−Λ) ω−h x−h Λ−ω ω−x (1− 1 T ) x . (2.8) 22 Figure 2.12: pmf of the interference for (a) (Λ,T,ω)=(20,8,15) and few active users, (b) (Λ,T,ω)=(64,40,31) and a large number of active users [88]. The pmf of the MAI for two different number of active users (A) with the OOC parameters of (Λ,T,ω)=(20,8,15) and (Λ,T,ω)=(64,40,31) are shown in Fig. 2.12(a) and 2.12(b), respectively. In each figure, two different values of κ=1 and κ = 2 have been considered. In both cases, increasing the number of users increases the mean and variance of the distribution. The tail of the curves cannot be greater than (A − 1)κ, which is the number of collisions multiplied by the number of interferers. It is observed that increasing κ creates more interference and increases the mean and variance of the MAI distribution, and consequently limitsthenumberofactiveusers. However,fromEq. (2.6),increasingκpotentially increases the number of codewords. Comparing 2.12(a) where Λ, T,and A are smaller than the parameters of Fig. 2.12(b) shows that the pmf becomes approximately Gaussian when the code length, number of wavelengths, and number of active users are large, which is in agreement with the central limit theorem (CLT). 23 2.3.2 Probability of Error in OCDMA Systems Using the MAI statistics obtained in the previous section, the probability of error, P e can be calculated. If P A is the pmf of the MAI in a system with A active users, and th is the threshold of deciding whether ‘0’ or ‘1’ has been transmitted, an error occurs when the MAI is greater than th. Therefore, the conditional probability of error is [88] P e|A = 1 2 (A−1)κ h=th P A (h). (2.9) Since transmitting a ‘1’ is error free, the 1 2 has appeared in Eq. (2.9). When a ‘1’ is transmitted, after the correlation receiver and in the absence of interference, the height of the correlation peak is ω, so it is assumed that the threshold th in units of chips is ω −0.5. This value of threshold is optimum when the receiver is not aware of the number of users in the system. If the receiver knows the number of active users, the optimum threshold that minimizes the bit-error rate (BER) will be different [89]. Using the above assumptions and Eq. (2.9) the BER has been calculated and plotted in Fig. 2.13. It can be observed the probability of error is generally de- creased when the weight is increased. In Fig. 2.13(a) the number of wavelengths and the code length are small compared to the parameters in Fig. 2.13(b). Com- paring the two figures it is concluded that when Λ×T increases, lower BER can be achieved even for large numbers of active users. 24 Figure 2.13: Probability of error versus code weight for different number of active users. In each figure, a fixed code length and number of wavelengths have been considered [88]. 2.4 Setup for OCDMA Experiments The experimental setup of an OCDMA system is shown in Fig. 2.14. The 2-D OOCs have been designed with Λ = 8 and T = 16. Therefore, 8 lasers are used to provide λ 1 through λ 8 . The 8 lasers are coupled together in the 8×1 coupler and are fed into the optical modulator. The electrical signal deriving the modulator is a sequence of pulses with the period of T ×T c . The duty cycles are 1/T and 0 for one and zero bits, respectively. Here in this experiment the chip rate is 1 Tc = 10- Gchips/s. The modulated signal is amplified using an EDFA, and then the signal is split between six branches, with each branch corresponding to a different user. In each of the six paths, there is an FBG array as the CDMA encoder that splits the wavelengths and assigns each wavelength the time slot based on the code. The CDMA-encoded data of the users are delayed by different values of τ 1 through τ 6 in different lengths of fiber in order to decorrelate the signals. At the 25 Figure2.14: Experimentaldemonstrationof2-D(time-wavelength)OCDMAusing FBG arrays as CDMA encoders and decoders. final stage of the transmitter, all the encoded and delayed signals are recombined through the 6×1 coupler. At the receiver, only the detection scheme of the user of interest has been shown. The received signal is amplified first and then enters the decoder that is the complement of the encoder in order to reconstruct the auto-correlation peak. Next, a photo-receiver detects the decoded optical signal and finally a threshold detectorsamplesthedataanddetermineswhetheritexceedsthedecisionthreshold or not. 2.5 Conclusion In this chapter, an introduction to CDMA systems was presented and then the specific properties and limitations of incoherent OCDMA systems were studied. 26 It was shown that 2-D OOC enables increasing the number of active users with- out reducing the bit rate or the chip time. Different implementations of OOCs were introduced and the advantage of each one was discussed. The method of modeling the interference was then presented and using the statistics of the MAI, the algorithm to calculate the BER performance was studied. The main contribu- tions in this chapter were (i) designing the FBG arrays to implement 2-D OOCs considering practical limitations and predefined requirements in the milestone of the project, (ii) building an OCDMA experimental setup that could serve as the foundation of experiments in the following chapters. 27 Chapter 3 M-ary Modulation Formats in Optical CDMA ThemotivationforusinganM-arymodulationformatistoincreasethebitrate. As discussed in the previous chapter, OOK-OCDMA is the simplest form of OCDMA in which for transmitting a ‘1’ bit, the OOC of the user is transmitted and for a ‘0’ bit, nothing is transmitted in one bit duration, thus, the bit rate of an arbitrary user in the network is R OOK-OCDMA = 1 T b = 1 T.T c bits/s. (3.1) Therefore, in order to increase the bit rate, the chip time, T c , or the code length, T, should decrease. However, according to Eqs. (2.3) and (2.6) that show the number of potential users increases with T, reducing the code length is not a good option. Keeping T unchanged forces T c to be reduced, but generating and detecting optical pulses with short duration is challenging. Moreover, the shorter the duration of an optical pulse, the more the fiber impairments such as CD distort the pulse. InthischapterweinvestigateothermethodstoincreasethebitrateinOCDMA systems without decreasing the optical pulse width or the code length. First, 28 we introduce PPM-OCDMA and describe its advantages and its limitations and difficulties regarding practical implementations. Then as a simplification of PPM, another method called code position modulation (CPM) is introduced and the performance of CPM-OCDMA is studied. Finally, in order to further increase the bit rate in OCDMA systems, two variations of CPM-OCDMA, namely 2-PPM and DPPM are introduced and the results of the experimental demonstrations are presented. 3.1 Pulse Position Modulation (PPM)-OCDMA One approach to increase the bit rate is increasing the transmitted bits per symbol inanOCDMAsystemusingmorecomplexmodulationschemes. Astraightforward method to increase the information rate in traditional non-multiple access systems is using PPM instead of OOK modulation. In PPM, each signaling time interval, T s , is divided into M equal time slots, and only one of these M time slots must contain a pulse. Therefore, there will be M distinct symbols, so each symbol is capable of representing log 2 M bits. Due to the increased signal processing requirements, the adaptation of this method to optics is not trivial. Figure 3.1 shows an example of PPM signaling. In this figure, each symbol time is divided into M = 8 time slots and the symbol number is the number of the time slot marked with the pulse. In this example, each symbol carries 3 bits and the pattern of framing every 3 bits into a PPM symbol is not unique. Some theoretical studies on using PPM techniques in OCDMA systems have been reported in [97, 98, 67, 54, 118], but the suggested systems have two major 29 Figure 3.1: An example of PPM symbol set capable of representing 3 bits per symbol. problems; Either they must use very short pulses or they require a cyclic code shifter in the transmitter that is difficult to implement. One way to implement PPM-OCDMA without reducing the chip time when T = M is to circularly shift the OOC within a symbol. For example, the CDMA-encoded sequence of symbol ‘1’ is just the OOC code, but the CDMA-encoded sequence of symbol ‘2’ is the OOC code with a cyclic shift of 1 time slot, and in general, in order to generate the CDMA-encoded sequence of the PPM symbol ‘x’, the OOC is shifted x − 1 times in units of the PPM time slots. An example of PPM-OCDMA is shown in Fig. 3.2 with M = 4, and an OOC with T =4,Λ=2,and ω = 2. Due to the 30 Figure 3.2: An example of PPM-OCDMA encoding with T = M.Eachsymbol carries 2 bits and there are two wavelengths in the OOC. fact that the encoding is done in a cyclic way, PPM-OCDMA is also called code cyclic modulation (CCM)-OCDMA. Since the properties of OOCs ensure that the auto-correlation and cross-correlation of the OOCs are bounded, the receiver can decode its own intended data by finding the location of the auto-correlation peak within a symbol. 31 For the case of T = M, the duration of each time slot is the same as the chip time, so the bit rate of a user in a PPM-OCDMA system is equal to R PPM-OCDMA = log 2 T T s = log 2 T TT c bits/s (3.2) which is log 2 T times the bit rate of OOK-OCDMA. Passive implementation of cyclic OOC encoders is not straightforward since it requires an optical buffer; hence, a sub-optimal method to avoid the cyclic shift is to allow the spreading code to leak into the next symbol [90]. Although in this case the MAI increases, it alleviates the difficulties in the practical implementation of PPM-OCDMA. In the next section, this method will be studied. 3.2 Code Position Modulation (CPM)-OCDMA In CPM-OCDMA, similar to PPM-OCDMA, input bits are first framed into PPM symbols where each symbol is represented by a specific time shift of the optical pulse. The difference of the two methods is that there is no cyclic code shifter in CPM-OCDMA, so an encoded CPM-CDMA symbol is just a regularly shifted version of the OOC. In general, with this method the complexity of the system is reduced at the price of increasing MAI. Even though the MAI increases, if the spreading codewords consist of OOCs with at most one pulse per wavelength, it is guaranteed that intersymbol-interference (ISI) does not occur in the transmitter. Figure 3.3 shows an example of a CPM-OCDMA system that takes 3 bits together to provide one symbol represented by the proper shift of the spreading 32 Figure 3.3: An example of CPM-OCDMA encoding. sequence. In this example, the input bit stream is ‘101001’, which corresponds to symbols S 7 and S 2 with the position encoding presented in Fig. 3.1. It can be observed that the encoded signal goes beyond its symbol boundaries. After the OCDMA decoder, the chip sequence is aligned on top of each other to create the auto-correlation peak at the correct position. The major differences of the MAI in CPM-OCDMA and OOK-OCDMA sys- tems are: (i) In OOK-CDMA no signal is transmitted for a ‘0’ bit, but in CPM- OCDMA, there is always a transmission in every symbol time, and (ii) since in CPM-OCDMA the adjacent symbols are allowed to leak into each other, the inter- ference from another user can become more than κ collisions. This may potentially increase the amount of the MAI in the system that limits the number of active 33 users. In [90] the complete analysis of CPM-OCDMA has been presented. The bit rate of the PPM-CDMA and CPM-CDMA systems are identical and obtained from Eq. (3.2). It should be noted that each user must be synchronous to its corresponding transmitter. Synchronizationcanbeachievedbytransmittingapredefinedpattern that is known by both sides of the system. It should be emphasized that this synchronization is only needed for each transmitter and receiver pair and different pair of users are asynchronous to each other. 3.2.1 Experimental Demonstration of CPM-OCDMA In this experiment, OOCs with Λ = 8 wavelength, T = 16 chip times, and code weight ω = 6 have been used. These codes have been designed based on the code construction algorithm in [74] and they can support 18 potential users. The codes have at most one pulse per wavelength. The experimental setup of a CPM- OCDMA system is shown in Fig. 3.4. Eight equally spaced lasers provide the 8 wavelengths required for the 2-D OOCs are coupled together and modulated using PPM data at the rate of 10-Gchip/s. After an EDFA, the signal is split between six branches, each with a unique FBG array OOC encoder. The encoded data of each user is transmitted through different lengths of fiber to decorrelate the signals and finally the encoded data of all six users are combined and sent to the fiber link. At the receiver, the received signal is amplified first and using the FBG array of the user of interest, the auto-correlation peaks are formed. A 34 Figure 3.4: Experimental setup of CPM-OCDMA with 6 active users and using FBG arrays as CDMA encoders to generate 2-D OOCs with T =16,Λ=8,and ω=6. photo-receiver detects the decoded symbols and a threshold detector determines whether the pulses exceed a certain value as the threshold. The chip rate is 10 Gchip/s, thus, the symbol rate is 1 Ts =10G/16 = 625 Msymbols/s. Since each symbol carries log 2 16 = 4 bits, the bit rate per user is 2.5 Gbits/s. It should be noted that using conventional OOK-OCDMA with the same chip rate, the bit rate would have been only 625 Mbits/s, according to Eq. (3.1). In the experiment, the 10 Gchip/s CPM encoded data is generated electroni- callyandthenisfedtothemodulator. Figure3.5(a)showstheCPMdataafterthe modulator. The dashed line shows the boundary of each symbol, and the position of each autocorrelation peak shows the transmitted symbol. Figure 3.5(a) shows the transmission of the bit steam {0000,1110,0010,1011,1001} which correspond 35 Figure 3.5: Fig. 5.4. (a) Modulated CPM data, distinct shifts of the auto- correlation peak represents the symbols (b) CPM-OCDMA encoded data, (c) de- coded CPM-OCDMA data; the horizontal scale is 1 ns/div. to the symbol stream {S 1 ,S 15 ,S 3 ,S 12 ,S 10 }. In Fig. 3.5(b) the CDMA-encoded symbols are shown. As observed, there is a chip in S 3 with double the height of other chips that originates from the fact that an encoded symbol can leak to the previous symbol. Although different symbols go out of their original boundaries of their symbol duration, due to complete orthogonality of the OOCs to its various time shifts, the transmitted data can be recovered without an additional power penalty. This property only holds for 2-D OOCs with at most one pulse (chip) per wavelength. Figure 3.5(c) shows the decoded sequence matches the original transmitted data. Figure3.6(left)showstheCDMA-encodeddataofallusersfordifferentnumber of active users. On the right side of the figure, the decoded signals of the user of interest are shown. It is observed that as the number of users increases the MAI increases too. However, the peaks of the original data are still above the MAI and detectable. The BER measurements are shown in Fig. 3.7. In this figure, the received optical power is the power of the user interest when the number of users increases in the network. It can be seen that increasing the number of users increases the power penalty. However, even with 6 active users the system is functioning and 36 Figure 3.6: Left: the encoded data of all users for 1 through 6 active users. Right: the decoded data of the user of interest along with the MAI. the data is recoverable with less than an 8 dB power penalty, compared to the case of no interferes. The power penalty is imposed by the increased MAI and other noise sources in the system. 3.3 Double Pulse Position Modulation (2- PPM)-OCDMA In the previous section, it was shown the bit rate per user could increase us- ing CPM-OCDMA. The motivation of using 2-PPM is to push increasing the bit rate even further without decreasing the chip time. In general, multiple PPM in which more than one time slot within the symbol time is marked, increases the 37 Figure 3.7: BER vs. received optical power of the user of interest for different number of active users. transmitted information per symbol time [7]. In this section, 2-PPM-OCDMA is studied. Since in 2-PPM systems, 2 out of T time slots are marked, the number of possible symbols is T(T − 1)/2. Therefore, the number of bits per symbol is log 2 T(T −1)/2 ≈2log 2 T −1, thus information that can be carried by a 2-PPM symbol is approximately 2 times of a CPM system. The bit rate per user in 2-PPM OCDMA is equal to R 2-PPM-OCDMA = log 2 T(T−1) 2 T s ≈ 2log 2 T −1 TT c bits/s. (3.3) Another application of 2-PPM-OCDMA is providing variable quality of service (QoS), i.e., some users can operate in 2-PPM-OCDMA mode with a higher bit rate while other users send their data using CPM-OCDMA. This application will be studied in the next chapter. 38 Figure 3.8: Block diagram of a 2-PPM-OCDMA system. 3.3.1 Concept of 2-PPM-OCDMA The block diagram of a 2-PPM-OCDMA system is presented in Fig. 3.8. First, the bit stream enters a bit-to-symbol converter. Then the 2-PPM symbols are fed to the OCDMA encoder, while marked slots determine the auto-correlation peaks. The code length is set equal to the number of time slots, resulting T c = T s /T; hence, the chip time in our system is the same as the chip time in OOK-OCDMA. We allow each encoded data to spread over the next symbol. This solves the problem of implementing cyclic code shifter structure. If the codes have at most one pulse per wavelength, it will be guaranteed that adjacent symbols do not interfere with each other. Error in transmission happens when the MAI or noise changes a zero slot to one. The MAI is shown by dark blocks. In order to find out the position of each auto-correlation peak in the symbol time, each receiver must be synchronous to its corresponding transmitter. 39 Figure 3.9: Block diagram of a 2-PPM-OCDMA system. 3.3.2 Experimental Demonstration of 2-PPM-OCDMA The experimental setup is shown in Fig. 3.9. We use 8 equally spaced lasers, couple them together and modulate them at 10 Gchip/s. The data provided to the modulator is 2-PPM data. After an EDFA, we split the signal between 5 branches, each with a unique OCDMA encoder, to generate data for 5 OCDMA users. The CDMA encoders are FBG arrays that implement the splitting of the wavelengths and assigning each wavelength an appropriate time slot. The CDMA- encoded data of each user is transmitted through different short lengths of fiber to decorrelate the signals and then all five users are recombined. At the receiver, the signal is amplified and with a second FBG array as the CDMA-decoder, the auto- correlation peak is reconstructed. A photo-receiver detects the decoded optical data and at the final stage, a threshold detector samples the data to determine whether it exceeds a certain decision threshold or not. In the experiment 2-D OOCs with 8 wavelengths were used, 16 chip times, and code weight 6. Our codes are based on code construction algorithm in [74] and can support 18 potential users. The main significance of this code construction is that it is optimal in terms of number of active users and it has at most one pulse per wavelength. The chip rate is 10 Gchip/s and the symbol rate is 625 MSymbols/s. 40 Figure3.10: (a)2-PPMsymbolsoftheuserofinterestaftermodulator,(b)CDMA- Encoded symbols, (c) Decoded symbols when there are 5 active users. Due to the 2-PPM factor for T = 16, or using Eq. (3.3), the equivalent bit rate peruseris4.75 Gbits/s which is 6.9 times of OOK-CDMA and 1.7 times of CPM- CDMA. Figure 3.10(a) shows the 2-PPM data after the modulator. The dashed lines show the boundaries of adjacent symbols, and the position of the auto-correlation peaks that determines the transmitted symbols is shown in each symbol. At the output of the CDMA-encoder, the encoded data of the symbols can leak to other symbol boundaries as shown in Fig. 3.10(b). It is very important to observe that even though different symbols are now out oftheiroriginalboundaries, duetothecompleteorthogonalityofanyOOCwithits shifted version, the data is recoverable without any additional degradation. This can be seen in Fig. 3.10(c) where the encoded data and the MAI of 4 other users is passed through the decoder and the original data is recovered. Another important observationisthatintheCDMA-encodedchipsequencetherearepulseswithtwice the amplitude of other pulses, the reason being a pulse from two adjacent symbols cancollide. However, becausethecodeshaveatmostonepulseperwavelength, the colliding pulses have different wavelengths and consequently they are completely separable in the decoder as shown by Fig. 3.10(c). 41 Figure 3.11: BER vs. received power of the user of interest for two cases of single active user and 5 active users. The BER curves as a function of received optical power of the main user are shown in Fig. 3.11. The number of active users is 5. It can be seen that increasing the number of users increases the power penalty. It should be noted that the MAI in 2-PPM-OCDMA systems is more than CPM-OCDMA. The amount of required extra power to switch from a CPM- OCDMA system to a 2-PPM-OCDMA system is shown in Fig. 3.12. It is im- portant to notice that even for a single user, Double-PPM requires about 3-dB more power. This is due to fact that 2-PPM symbols have two pulses and the power is split between them. Therefore, in order to have the same peak power as in the CPM symbols, the amount of required average power is twice as much is needed in CPM-OCDMA. Using 2-PPM-OCDMA in systems with a limited num- ber of codes can significantly increase the spectral efficiency, because there are always few users in the system so the MAI has not saturated the network. 42 Figure 3.12: Power penalty of switching from CPM-OCDMA to 2-PPM-OCDMA. 3.4 Differential Pulse Position Modulation (DPPM)-OCDMA Another technique to increase the bit rate in regular non-multiple-access systems is differential-PPM (DPPM). This technique has been already reported for an indoor wireless infrared application [101] and it is considered as a more spectrally efficient scheme than regular PPM. In DPPM, information is encoded in the time difference between two consecutive ‘1’ time slots instead of the position of the ‘1’ within a symbol time. This modulation format results in variable-length symbols with a duration less than or equal to the CPM symbols, thus in average, less time is needed for transmitting the data. In Fig 3.13, the concept of DPPM signaling 43 Figure 3.13: Concept of DPPM signaling. Figure 3.14: Comparison of the average number of transmitted bits per symbol for different modulation techniques. and bit rate improvement is shown. The average symbol time to transmit data using DPPM is obtained as T ave,DPPM = T c T (1+2+···+T)= (T+1)T c 2 = (T+1)T s 2T ≈ T s 2 . (3.4) 44 Since there are T possible symbols, the number of bits per symbol is log 2 T, and using (3.4), the bit rate of DPPM signaling is equal to R DPPM-OCDMA = 2T log 2 T (T+1)T s bits/s, (3.5) that is slightly higher than 2-PPM signaling. In Fig. 3.14, the number of bits per symbol for PPM (or CPM), 2-PPM, and DPPM are shown and compared. 3.4.1 DPPM-OCDMA System The concept of DPPM-OCDMA is similar to CPM-OCDMA and the only differ- ence is that in DPPM information is in the time difference of consecutive auto- correlation peaks, while in CPM-OCDMA information is transmitted according to the position of the auto-correlation peaks. In DPPM-OCDMA first log 2 T input bits are mapped to one of T possible symbols such as Fig. 3.13, which results in variable symbol time. The OCDMA encoder then splits the auto-correlation peaks and assigns a specific chip time to each wavelength to build the 2-D OOC. It should be noted that the encoded symbols will leak to adjacent symbols. In the previous section we showed that by using OOCs with one pulse per wavelength, the transmitted data is recoverable. 3.4.2 Experimental Demonstration of DPPM-OCDMA The experimental setup that is shown in Fig. 3.15 is similar to the CPM case with a slight difference in the input electrical pulses. In Fig. 3.16 an example of 45 Figure 3.15: Experimental setp of DPPM-OCDMA. transmission of similar bits using OOK, PPM, and DPPM is shown. In this figure, the original bits are first converted to the CPM symbols ‘20594’ where each digit shows the position of the time slot containing the auto-correlation peak as shown in Fig. 3.16(b). Then by omitting the zero slots from the beginning of the PPM symbols, DPPM symbols are obtained which are shown in Fig. 3.16(c). It can be seen that using DPPM, it takes 2.5-ns to transmit the five symbols while for the same 5 symbols with CPM the transmission time is 8-ns, and for OOK it takes 32-ns. Figure 3.16 shows the encoded symbols of a single user for the pattern. Due to the variable length of the symbols, the encoded chips have different amplitudes. This is because each encoded symbol leaks into the adjacent symbols and the chip times of these symbols add up together. This effect is more severe for smaller symbols such as 2, 0, and 5. However, as our OCDMA spreading 46 Figure 3.16: Comparison of the required time to transmit the same bit sequence using OOK, CPM, and DPPM. codes have at most one pulse per wavelength the high power pulses consist of different wavelengths, so they can be separated in the decoder. Figure 3.17(a) shows the CDMA-encoded DPPM and in Fig. 3.17(b) the de- coded auto-correlation peaks when there is no interfering active user is in the system are shown. Figure 3.17(c) shows the decoded data along with the MAI from 2 other interfering users (3 active users). The BER curves for different number of users are shown in Fig. 3.18. Using DPPM, we were able to achieve 3 simultaneous users so this modulation method is considerable when the number of users is low and the MAI is not a limiting factor. Moreover, this modulation format can be used with other OCDMA schemes to provide variable QoS in a net- work, for example allowing a user to transmit more information using DPPM while other users operate at a lower bit rate using OOK-OCDMA or CPM-OCDMA. In 47 Figure 3.17: (a) Encoded DPPM-OCDMA symbols, (b) Decoded symbols (single user), (c) Decoded symbols with 3 active users. this particular experiment, the bit rate is equal to 4.71 Gbit/s which is 7.53 times of the bit rate in OOK-OCDMA and 1.88 times of CPM-OCDMA, using the same codes and bandwidth. 3.5 Conclusion In this chapter, different M-ary OCDMA methods to increase the bit rate per user were introduced. First, PPM-OCDMA was studied, but because the im- plementation of a cyclic code shifter is not trivial, the CPM-OCDMA technique was introduced as a sub-optimal method, and was experimentally demonstrated. It was shown that the bit rate significantly increases. In order to increase the bit rate further, 2-PPM-OCDMA and DPPM-OCDMA modulation formats were studied and experimentally demonstrated. These techniques increase the bit rate approximately by a factor of 2 compared to CPM-OCDMA. It was concluded that 48 Figure 3.18: BER curves for different number of active users in the network vs. received power. if the number of active users is small in a system and the MAI is not the limiting factor, 2-PPM and DPPM can increase the spectral efficiency. In order to perform an accurate evaluation of the performance of the 2-PPM system in terms of the capacity and spectral efficiency, further investigations are required in future. With DPPM-OCDMA, a slightly higher bit rate than 2-PPM-OCDMA was achieved but the MAI severely limited the performance of the system. Therefore, thenumberofsimultaneouslyactiveusersin2-PPM-OCDMAismorethanDPPM- OCDMA. Both techniques provide versatility such that when there is low traffic demandinthenetwork, forexamplewhensomeusersarenotactiveinthenetwork, ausercanbenefittheavailablebandwidthandswitchto2-PPMorDPPMschemes to operate at a higher bit rate. 49 Chapter 4 OCDMA in Local Area Networks In this chapter, some capabilities of OCDMA in the physical layer of LANs are studied. First, it is shown by experimental demonstration that variants of the PPM technique can provide variable QoS in OCDMA LANs. In the second part, a scheduling algorithm to reduce the MAI in OCDMA networks is experimen- tally demonstrated. It is shown the IA algorithm can dramatically enhance the throughput of OCDMA based LANs. 4.1 Variable Quality of Service with OCDMA Providing variable QoS for different users in OCDMA networks has been an inter- esting topic for research; for example some structures have been recommended in [87, 55]. The major problem of these suggested systems is that they do not have a fixed optical platform. In other words, in order to change the quality of service using the aforementioned techniques, users must adjust their signature code or bit rate, whereas the system we present here offers a variable bit rate which can be translated into variable QoS without changing the parameters of the optical setup, including encoders/decoders, chip rate, pulse width, and optical spectrum. 50 Figure 4.1: Examples of PPM, 2-PPM, and 3-PPM Symbols. Number of possible symbols is written beside each pattern. 4.1.1 Multiple Pulse Position Modulation (MPPM)- OCDMA It was discussed in previous chapters that with the position of the auto-correlation peak within a symbol time as an additional degree of freedom for encoding in- formation, we were able to demonstrate PPM techniques to increase the number of bits per symbol [86, 6]. If the code length is M, the symbol time is divided into T equal intervals, one of which will be marked by the auto-correlation peak. Therefore, there are T possible symbols, representing log 2 M bits in each signaling time. It was also shown that with 2-PPM signaling, the bit rate could be enhanced even more. [6, 7, 110]. In general, with multiple-pulse-position modulation (MPPM) in which more than one time-slot in a symbol time is marked, the number of bits per symbol is larger. If the number of marked time-slots in a symbol duration is N, the number 51 Figure 4.2: Number of bits per symbol for PPM, 2-PPM, and 3-PPM symbols versus the code length T(= M). Figure 4.3: A variable bit rate OCDMA network using PPM, 2-PPM and 3-PPM formats. of available symbols is equal to the number of ways one can choose N time-slots out of a total of M time-slots. Therefore, the bit rate is R = log 2 M N T s bits second ,(4.1) where T s is the symbol time. In this section, we have used MPPM with three different values of N =1,2, and 3 in order to implement PPM, 2-PPM, and 3-PPM, respectively, as shown in 52 Fig. 4.1. Similar to the previous chapter, the code length is equal to the number of time-slots in a symbol, i. e., T = M. In Fig. 4.2, the number of bits per symbol is plotted for the three cases as the function of code length, M. It should be emphasized that the code length is fixed, so in order to adjust the bit rate, the transmission scheme is changed by moving vertically to one of the three graphs of Fig. 4.2. The general concept of the OCDMA network with users operating simultaneously at different bit rates is illustrated in Fig. 4.3. This is the first experiment to demonstrate a variable bit rate OCDMA network. It will be shown that the price of providing a high QoS for some users in the system is reducing the number of total active users. 4.1.2 MPPM System Model and Experimental Setup The block diagram of an MPPM-OCDMA system is illustrated in Fig. 4.4. First, input bits enter a bit-to-symbol converter, which in this example changes the bits to 3-PPM symbols. Next, the 3-PPM symbols enter the OCDMA encoder. Each marked time-slot is encoded in the order that is launched into the encoder. For 3-PPM-OCDMA, according to the delays between the three pulses in the original 3-PPM symbol, there will be three different shifts of the OCDMA code in the time domain. Since the codes have at most one pulse per wavelength, spreading the encoded data over the next symbol will not cause ISI and it is guaranteed that adjacent symbols do not interfere with each other [88]. 53 Figure 4.4: 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. 54 At the receiver side, the user decodes the data and extracts 3-PPM symbols. If the level of MAI or noise is high, it can potentially cause an originally empty time- slot to be falsely detected a marked time-slot. Finally, a bit to symbol converter extracts the transmitted bits. The experimental setup is shown in Fig. 4.5. Ten different lasers provide the ten wavelengths used in the OOCs. Two pulse pattern generators (PPGs) simultaneously generate two different multiple pulse position patterns but with the same chip time. For example, PPG 1 generates PPM symbols while PPG 2 generates 3-PPM symbols. The symbols from the two PPGs are fed into two separate 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 other users with 3-PPM symbols, shown as group 2 users. The outputs of the modulators are shown in Fig. 4.5 where adjacent symbols are separated with dotted lines. TheCDMA-encodedsymbolsaretransmittedthroughdifferentlengthsofshort fibers that make the signals become uncorrelated. The CDMA-encoded signals from all users are combined and sent to the fiber. At the receiver side, each user correlates the incoming optical signals with its own OCDMA 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 demaps the decoded symbol into ‘0’ or ‘1’ bits. 55 Figure 4.5: Experimental setup for a variable bit rate OCDMA network using MPPM-OCDMA. 56 Figure 4.6: (a) 3-PPM symbols, (b) PPM symbols, after the modulators. In each case, three symbols are shown and dotted lines separate adjacent symbols. In the experiment, we have used a code set with 16 chip times, 10 wavelengths, and a weight of 6. We have used the algorithm in [75] for designing the codes. Our encoders and decoders are FBG arrays that split the wavelengths and assign each wavelength an appropriate chip time [30]. The chip rate is set to 10-Gchips/s and since it takes 16 chip-times to transmit one symbol (M = 16), the symbol rate is equal to 10−G/16 = 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, resepectively. Therefore, if a user desires a higher bit rate, it can modify its input electrical signal from PPM to 2-PPM or 3-PPM, without requiring any modification to the rest of the setup. 57 Figure 4.7: Decoded symbols and their eye diagrams: (a) PPM, (b) 3-PPM. Small pulses are the MAI from other users in the system. 4.1.3 MPPM-OCDMA Experimental Results and Discus- sion We have implemented different number of users operating with different symbol types. Forexample, Fig. 4.6showstheinitial1-PPMand3-PPMsymbolsafterthe modulators and in Fig. 4.7, the same decoded symbols at the receiver side along with the MAI (small pulses) are shown. It can be observed that the data is still detectable because the autocorrelation peaks are larger than the MAI. With this combination, we were able to simultaneously accommodate one 3-PPM-OCDMA user and three PPM-OCDMA users, with BERs less than 10 −9 . Since the 3-PPM user operates at a higher bit rate, it transmits more pulses into the network, and as a result, it generates approximately three times more MAI compared 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 4.8. 58 Figure 4.8: Power penalty versus the number of PPM users to achieve various combinations of users operating at different bit rates. We have considered another scenario in which two users transmit 2-PPM sym- bols and four other users transmit PPM symbols. The PPM users are added one by one to the network and the power penalty is measured and shown in Fig. 4.8. Another combination that is demonstrated is one 2-PPM user along with five PPM users. As seen from Fig. 4.8, adding a higher bit-rate user in the system reduces the number of potential lower bit-rate users. Our scheme provides ver- satility when there is low traffic demand in the network, for example when some users are not active, a user can take over the available bandwidth and switch to a higher order PPM scheme to operate at a higher bit rate. 4.2 Interference Avoidance (IA) Algorithm in OCDMA A critical limitation of OCDMA networks is the reduction of throughput when many users are simultaneously trying to transmit over a common medium, thereby 59 producing extreme congestion at high network loads. In fact, networks can suffer from congestion collapse in which the network throughput can actually begin to decrease when traffic exceeds a threshold and it eventually approaches to zero under extremely high loads, i.e., when several users transmit simultaneously, their packetsandhencetheircode-wordsoverlap[89,45]. Whentheopticalpulsesinthe codewordoverlap, theirpowerwillbeadded, thusopticalpulsesfromonecodeword may be detected by receivers tuned to other codewords. As a result, a receiver may incorrectly detect other users’ code-words, resulting in packet transmission errors [45]. These false positive errors increase with offered load, resulting in congestion collapse. Recently, there has been a theoretical report on an OCDMA network protocol called IA that helps managing congestion and maintains a relatively-high through- put even under extreme loads [45, 46]. Also the stability and throughput of optical CDMA networks using various protocols are analyzed in [56]. They showed how the saturation throughput degrades with code sharing. In the context of packet radio networks, the throughput of a generic CDMA based packet switched network is analyzed [82]. To our knowledge, there have been no reports of experimental demonstrations of a network protocol that avoids congestion collapse for OCDMA systems. 4.2.1 IA Algorithm in OCDMA LANs Figure 4.9(a) shows a shared medium operating based on packet switched optical CDMA LAN in which several nodes are connected to a passive optical coupler 60 to form an all optical broadcast network. The star coupler is a passive optical element with all inputs connected to all outputs. Each node in the network is allocated an optical CDMA codeword, which is a sequence of zeroes and ones that are transmitted asynchronously. When a node is ready to transmit, it tunes its transmitter to the receiver’s codeword and sends the data into the shared medium. Without using a media access control (MAC) protocol, each user transmits its data whenever the packet is ready. This is called Aloha-CDMA that can lead to congestion collapse in OCDMA networks. The problem of throughput collapse in optical CDMA LANs is conceptually similar to the problem of throughput collapseinsingle-channelshared-mediumnetworks. Single-channelshared-medium networks without MAC (Aloha networks) suffer from throughput collapse at high offered load because of collisions between packets. Carrier sensing multiple access (CSMA) and its variants [107] have been proposed as solutions to this problem. In order to alleviate this problem, using IA media access protocol is proposed. IA is a distributed, contention based MAC protocol for broadcast shared-medium in OCDMA LANs [45]. It improves throughput of the network at high offered load by estimating the state of the line and scheduling transmission times to reduce packet loss due to interference errors. IA is a contention MAC mechanism that prevents throughput collapse in optical CDMA networks at high offered load. It consists of two stages of state estimation and transmission scheduling. State estimation is a process in which a node estimates state of the link at one point and at a certain time using state observations obtained from possibly 61 Figure 4.9: (a) OCDMA network: The nodes are connected by transmit and receive (upstream, downstream) fibers to a passive star coupler to enable a shared medium LAN, (b) Block diagram of an IA network interface card. different point(s) on the line at some possibly different time(s). The estimated state is used as the input to a transmission-scheduling algorithm. Transmission scheduling is the process by which a node with an estimate of the state of the line and a codeword to transmit, calculates the best time to transmit data at the moment that possible packet losses due to interference are minimized. A simplified block diagram of an OCDMA node is also shown in Fig. 4.9(b). When a packet arrives at the receive fiber, it is split 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 the appropriate transmission delays based on this information. Afterestimationofadelay, aschedulertunesthetunabledelaylines(TDL)and sends a signal to the transmitter. The OCDMA transmitter sends the scheduled packet on the transmit fiber. The concept of the state estimation and scheduling 62 Figure 4.10: Top: fiber link after the decoder of the user of interest. Bottom: data is transmitted such that the auto-correlation is in the chip time with the least interference. algorithmisshowninFig. 4.10. Inordertoaccomplishthestateestimationwefirst pass the traffic from the line through the decoder of the user of interest. This is the traffic seen by the receiver end. We then detect the data using multiple threshold detectors. The best time to transmit the data is obtained by finding the position within the received data with minimum detected interference. The transmission scheduler selects the marked chip with the lowest MAI and then delays the packet and transmits the autocorrelation peak. It should be noted because each packet consists of several bits the state of the link remains unchanged for a long duration. In [45], an IA based OCDMA network was modeled using discrete event based packet simulator. The simulator modeled multiple nodes on a broadcast shared 63 medium OCDMA LAN. The normalized offered load is the arrival rate (in pack- ets/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 trans- mission 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. 4.11(a). The results show that the as the offered load increases the throughput of Aloha-CDMA tends to zero, while the use of the transmission scheduling algorithm prevents throughput degradation. Fig. 4.11(b) shows the congestion collapse when simulations were performed with traffic traces obtained from a real network link to understand the impact of real packet arrival times. Traffic traces from a single OC48 [81] link were used. Several of these traces were merged to generate traffic of different of- fered loads. The packet sizes, source addresses, and destination addresses were preserved during merging. The results indicate that the performance is similar to that of the Poisson arrivals/exponentially distributed model, indicating that it was a reasonable choice for analysis. 4.2.2 Experimental Demonstration of IA-OCDMA TheexperimentalsetupforourOCDMAsystemisshowninFig. 4.12. Wecombine eight wavelengths and modulate them at 10 Gchip/s. After an EDFA, we use OCDMA encoder to encode the data and then use a variable delay line to vary the 64 Figure 4.11: The normalized network throughput vs. normalized offered load for Aloha-CDMA and transmission scheduling. (a) Simulated traffic (b) Real traces of traffic from OC44 link. The throughput of the network does not collapse in high loads. The traffic model is Poisson arrivals with exponentially distributed packet lengths. time delay of the user. Each encoder is an FBG array. This data is transmitted through a short length of fiber and then combined in a star coupler with 5 other users. At the receiver, the received signal is first amplified and then another FBG array is used as the CDMA decoder. A photo-receiver detects the decoded optical data and a threshold detector samples the data to determine whether it exceeds a certain decision threshold or not. 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 [75, Plot B] and they can support 18 potential users. The codes have at most one pulse per wavelength. The chip rate is 10 Gchip/s and the corresponding bit rate is 625 Mbit/s. Fig. 4.13(a), (b), and (c) show the bit pattern of 10110 for 1, 3, and 6 users. The additional MAI is due to the additional active users. In Fig. 4.13(c) the MAI is very high as they are 6 users transmitting. From this figure, it is 65 Figure 4.12: Experimental setup for implementing IA-OCDMA. observed that by delaying the transmission time of the user of interest we can find a position to optimize the performance of the system. Figure 4.13(d) shows the eye diagram of the auto-correlation function for a single user. The auto-correlation resembles an RZ signal with 1/16 ratio as there are 16 chip-times. Figure 4.13(e) 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 auto-correlation can move to any point of time. In this case, the position of the auto-correlation is optimized, resulting in a clear eye. Fig. 4.13(f) shows a random delay of the user which causes severe eye closure. Figure 4.14(a) shows the BER curves for different number of active 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 66 Figure 4.13: Bit sequence of ‘10110’ for (a) single user, (b) 3 users, and (c) 6 users. Eye diagram of the correlation for (d) single user, (b) multiple users with transmission scheduling, and (c) random case (ALOHA). the optimized delay up to 6 users are recoverable with less than a 4-dB power penalty. In order to compare the performance of the IA algorithm with aloha CDMA given a certain number of users and the state of the link, we change the delay of the user of interest until the optimum delay is obtained. The optimum delay corresponds to the BER of 10 −10 with the least optical power. As this point, we do not change the optical power. Then, we change the delays of different users to emulate different states of the link and we also vary the delay of the user of interest to emulate Aloha-CDMA. The average BER resembles the Aloha-CDMA. The results are shown in Fig. 4.14(b). It should be noted that the respective point for different number of users are achieved for different values of the optical power. Results show that in the worst case the BER of system drops below 1 −3 for the cases of 5 and 6 active users. Moreover, using Aloha-CDMA the performance drops as the users increase in the network, while with the IA algorithm we can 67 Figure 4.14: (a) BER vs. received optical power of user 1 for increasing number of users, (b) performance of an OCDMA system for increasing number of users with transmission scheduling, aloha-CDMA, and worst case maintain the desired performance regardless of an increase in the number of users. It is also important to mention that we are only scheduling the user of interest. This schedule depends on the statistics of other users. However, in the experiment we changed delays of all interfering users randomly and then by delaying the user of interest, we were able to schedule and the measured the penalties for the user of interest. The other observation is that if each user attempts to optimize its own transmission timing, it might hurt other users in the network. The simulation showed that although this effect might be partially true, at the equilibrium point the performance of all users is better by avoiding the congestion collapse. 68 4.3 Conclusion In this chapter, some capabilities of OCDMA in physical layer of LANs were studied. It was shown by experimental demonstration that various pulse posi- tion modulation techniques can enable variable QoS in OCDMA LANs. In the other section, a scheduling algorithm to reduce interference (MAI) in an OCDMA network was experimentally demonstrated. It was shown the IA algorithm can enhance the throughput of OCDMA based LANs. 69 Chapter 5 Multiple-Bit Delay Detection for Phase Modulated Optical Systems Intensity modulation-direct detection (IM/DD) systems are commonly employed in optical communication systems due to their simplicity and low cost. However, it is known that phase modulation is more robust to amplitude fluctuations (i.e., ad- ditivenoise)anddistortions(i.e., nonlinearitiesthatonlyaffecttheamplitude)and it can provide a higher spectral efficiency. As a result, they bring some power sav- ings; for example, binary phase-shift-keying (BPSK) is 3-dB more power efficient than conventional amplitude-shift-keying (ASK) in an additive white Gaussian noise (AWGN) channel. Both coherent and incoherent detection schemes have been proposed for de- modulation of phase-modulated signals. A coherent detection scheme has a better performance but requires a local oscillator with carrier recovery in the receiver that increases the complexity and cost of the system. However, with incoherent detection, the complexity is reduced at the price of some power penalties. In differential phase-shift-keying (DPSK), input bits are encoded in the phase difference of consecutive transmitted symbols and the received signal in past re- placesthe coherent local oscillator in thereceiver and acts astherelativefrequency and phase reference for demodulating current symbol [32, 61, 26]. In optical fibers, 70 demodulation of DPSK symbols can be simply implemented by a delay line inter- ferometer (DLI) followed by a balanced photoreceiver[32]. Compared to the OOK modulation, differential detection provides a 3-dB increase in the receiver’s sen- sitivity, but it is not as power efficient as a homodyne coherent detection system [61]. Inordertoincreasethepowerefficiencyofdifferentialdetection, MBDDscheme has been proposed in [26] for non-optical systems. In this chapter, first the basics of optical phase modulated systems and DPSK are presented, and then the perfor- mance of MBDD in optical DPSK systems is analytically formulated. Assuming a high optical signal-to-noise ratio (OSNR), an optical bandpass filter with a large bandwidth, and negligible laser phase noise, the detection problem under the opti- mum decision rule and the majority vote decision rule is studied. It is shown that the performance of MBDD system employing either of the decision rules asymp- totically approaches the performance of the coherent receiver when the number of delay segments gets large. Using numerical calculations, a closed form expression is presented to approximate the BER performance of the majority vote detection as a function of the number of delay segments, OSNR, and the bandwidth of the optical bandpass filter [5]. 5.1 Optical DPSK Systems Although BPSK with coherent detection has a better performance compared to DPSK with balanced detection, the receiver structure for DPSK is much simpler. 71 In DPSK, information is transmitted in the differential phase of the optical carrier in consecutive signals. The complex electric field of an ideal laser is E(t)= Aexp(jω c t), (5.1) where A is the complex amplitude, and ω c is the radial frequency of the laser. The most straightforward method to modulate the phase of a laser is using a phase modulator which produces an output electrical field proportional to the input electrical field and exponentially related to the applied voltage, i.e., E o (t)= E(t)exp[jπ V(t) V π ], (5.2) where V π is the amount of the required DC voltage corresponding to a π phase shift. Due to the exponential relationship, a small change in the applied voltage could change the phase dramatically, which makes the phase modulator super- sensitive. Therefore, in practice MZM modulators that consist of two electrodes are preferred for generating DPSK signals [32]. In an MZM, input light is split and travels in two separate equal paths with an electrode in each path. One or two voltages are applied to one or both of the electrodes in order to modulate the light by changing the index of refraction. At the end, light from the two paths are recombined. Thus, the output electric field of an MZM is [37] E o (t)= E(t) 2 exp[jπ V 1 (t) V π ]+exp[jπ V 2 (t) V π ] , (5.3) 72 Figure 5.1: Change of the output electrical fields in phase modulators and MZMs. where V 1 (t)and V 2 (t) are the applied voltages to the two electrodes. If V 1 (t)= V 2 (t), the scheme will be the same as a phase modulator, and for V 1 (t)= −V 2 (t)= V(t)/2 the output electric field is E o (t)= E(t)cos π V(t) 2V π . (5.4) As observed, the phase is either 0 or π depending on whether the Cosine term is positive or negative. The maximum output power with the phases of 0 and π occur when V(t)=0and V(t)=2V π , respectively. Unlike the phase modulator, the amplitude of the output field in the MZM depends on the applied voltages. Figure 5.1 compares output electrical fields of phase modulators and MZMs. It should be noted that with appropriate voltages of V 1 (t)and V 2 (t) in dual-arm MZMs, different QAM modulation format can be generated [37]. In Fig. 5.2 the principle of phase modulation using MZM is shown. The intensity dips in the modulated signal correspond to the transitions in the drive voltage. Ignoring these dips, the configuration shown in the figure can generate non-return-to zero (NRZ) phase modulated signals. Using a second MZM as the signal carver, return-to-zero (RZ) pulses can be generated [32]. 73 Figure 5.2: Phase modulation using MZM [32]. It should be noted that the two levels of the driving signal correspond to the input bits in simple BPSK modulation. In DPSK, the phase is modulated relative to the phase of the previous signal so input bits must be encoded first using DPSK encoder which is a simple XOR gate with a one bit delay feedback [32]. 5.1.1 Conventional DPSK Detection TheconventionalDPSKreceiveriscomposedofadelay-lineinterferometerfollowed by a balanced photo-detector, as shown in Fig. 5.3. The received field is split and then mixed with the field of the previous signal. If the phase of the previous field is 74 Figure 5.3: Conventional DPSK receiver φ 0 and the phase of the current received field is φ 1 , considering only the baseband and constant amplitudes (e.g. ideal NRZ), the outputs of the DLI are E + = j A 2 exp(jφ 0 )+exp(jφ 1 ) E − = A 2 exp(jφ 0 )−exp(jφ 1 ) . (5.5) The balanced photo-detector detects the optical power of the two fields and gener- ates an electrical current proportional to the difference of the two detected powers. Assuming an ideal photo-detector, the generated electrical current is i = |E + | 2 −|E − | 2 = A 2 4 |exp(jφ 0 )+exp(jφ 1 )| 2 −|exp(jφ 0 )+exp(jφ 1 )| 2 = A 2 cos(φ 1 −φ 0 ). (5.6) Therefore, if the phase difference is φ 1 −φ 0 = 0, the output current is A 2 ,and if the phase difference is π, the output current is −A 2 . As observed, the receiver detects the signal based on the phase of the previous signal, which is in agreement with the DPSK-encoded bits at the transmitter. 75 5.2 Multiple-Bit Delay Detection (MBDD) for DPSK Signals The MBDD structure is based on the observation of the received signal over more than two symbol time intervals. Thus, in addition to comparing the current signal with the received signal in the last symbol time, multiple preceding symbols are used as references for demodulation of the current symbol, so MBDD can com- pensate for the additive noise of the system as if a repetitive error correcting code has been used. The application of MBDD in fiber-optic systems is studied in [71, 112], and the experimental verifications are presented in [48, 49, 50, 21]. Considering the re- cent advanced methods in integrating optical DPSK modulation components[119], MBDD can be a potential solution to reduce the complexity of the receiver circuits by shifting some of post processing tasks such as error correction [105] from the electrical domain, which inherently is the barrier of increasing the data rate, to the optical domain, while maintaining similar performances[49, 21]. It has been argued that with a large number of delay segments in MBDD systems, the overall performance tends towards the performance of a completely coherent detection system [26] if the carrier frequency fluctuations are very small compared to the symbol time [52]. 76 5.2.1 MBDD-DPSK System Model Figure 5.4 illustrates the MBDD scheme under consideration. The receiver has M delay branches, so each received signal is interfered with M preceding signals to demodulate the current bit. It should be noted that for M = 1 the scheme reduces to the conventional DPSK receiver. The baseband equivalent of the signal (optical field) at the input of the receiver in Fig. 5.4 is Y k (t)= √ Pd k +n(t) , kT <t<kT +T, (5.7) where P is the average received power of the modulated optical field, T is the bit time, and d k ∈{−1,1} is the differentially encoded input bit in the k th bit interval. In (5.2.1), n(t) represents the ASE noise after the ideal optical bandpass filter. The ASE noise is modeled as a complex, zero mean, additive white Gaussian process[32] with variance N 0 /2 for both its in-phase and quadrature components. Therefore, if the bandwidth of the optical filter is B (Hz), the variance of n(t) for its real and imaginary parts is equal to σ 2 def = N 0 B/2. The bandwidth of the filter is large enough so it can pass the signal without creating any distortions or ISI [76, 24]. Later in this chapter, it is assumed that BT = 4. The effect of oscillator phase noise on the performance of DPSK systems employing MBDD receiver structure was studied in [52]. It has been shown that MBDD structure enhances the performance of differential detection only when the coherence time of the carrier is much longer than the bit duration [50]. Therefore, it is assumed 77 Figure 5.4: Block diagram of optical DPSK system with multiple-bit delay detection (MBDD) receiver structure 78 that a narrow linewidth laser has been used as the light source, so the impact of phase noise is neglected in our calculations. In the MBDD scheme, the power of the received signal is first equally divided into M branches. Using M DLIs, each signal is interfered with the signal received in i bit duration in the past, with 1 ≤ i ≤ M. Therefore, if demodulation in the M th bit duration is targeted, the output of the DLI in the i th branch is z ± i (t)= 1 2 √ M ⎡ ⎣ Y M (t)±Y M−i (t) ⎤ ⎦ = √ P 2 √ M ⎡ ⎣ d M ±d M−i +p(t)±p(t−iT) +jq(t)±jq(t−iT) ⎤ ⎦ (5.8) where n(t) has been replaced by its normalized in-phase and quadrature compo- nents p(t)and q(t), i.e., n(t)= √ P[p(t)+ jq(t)]. These processes are i.i.d and real with the probability distribution of N(0,σ 2 /P). In (5.8), + and − indices correspond to the constructive and destructive ports of the DLI, respectively. Assuming a nonlinear square-law detection process with perfect responsitivity, the photocurrents at the outputs of each detector are I ± i (t)= z ± i (t) 2 . ASE is the major noise source in the system, so other types of noise such as shot noise and thermal noise are neglected in the analysis [32]. It should be noted that with this assumption, increasing the number of delay segments does not change the overall signal to noise ratio, since the signal power and the noise power are both divided 79 among the M DLIs. The generated photocurrents are subtracted in balanced detectors, so the output of the i th balanced detector is given by r i (t)= I + i (t)−I − i (t) = P M ⎡ ⎣ d M d M−i +d M p(t−iT)+d M−i p(t) +p(t)p(t−iT)+q(t)q(t−it) ⎤ ⎦ . (5.9) The first term in (5.9) contains the desired information, i.e., the differential in- formation between the current bit d M and the received bit in i bit duration ago, d M−i . The remaining terms are undesired signal-noise and noise-noise beat terms. It should be noted that all terms in (5.9) are uncorrelated since it has been as- sumed an ideal optical bandpass filter with a large bandwidth has been employed before the receiver. OSNR is defined as the ratio of the energy of the signal to the energy of the noise after the optical filter and is denoted by ρ s = PT 2ασ 2 ,where α is a correction factor and approximately equal to 1 for BT ≥ 4 [24, Eq. (9)] (It should be noted that B IF in [24] is equivalent to B/2 here). The random variable after the integration and sampling is r i = (M+1)T MT r i (t)dt = PT M ⎛ ⎝ d M d M−i +d M p i +d M−i p 0 +n pi +n qi ⎞ ⎠ , (5.10) 80 where p i = 1 T (M−i+1)T (M−i)T p(t)dt are i.i.d Gaussian with zero mean and variance of 1/2ρ s . The last two terms in (5.10) are associated with noise-noise beat terms and both are obtained by integration of the product of two independent Gaussian random processes (integral of the last two terms in (5.9)). It is shown in [24, Eq. (16)] that these terms are zero mean with the variance equal to βBT 4α 2 ρ 2 s ,where β is another correction factor and approximately equal to 1 for BT ≥ 4. After multiplying (5.10) by M √ ρs PT d M−i , the decision variables are given by r i = √ ρ s d M +d M p i + p 0 + n i , 1 ≤ i ≤ M (5.11) where p i = d M−i √ ρ s p i and p 0 = √ ρ s p 0 are i.i.d with probability distribution of N(0,1/2). In (5.11), n i = d M−i √ ρ s (n pi + n qi ) is zero mean with the variance of βBT 2α 2 ρs and it consists of Gaussian quadratic terms with a distribution that is equivalent to subtraction of pairs of Chi-Square random variables [15]. Moreover, n i ’s are correlated to each other in general, and they are also correlated to p i ’s and p 0 . However,thesecorrelationscanbeneglectedundertheassumptionofwideband optical filtering and n i ’s can be approximated by Gaussian random variables if OSNR is high [76, 24, 14]. If the optical channel has memory, i.e., when employing a narrowband optical bandpass filter or considering dispersion impairments, the most accurate method of calculating the BER performance of DPSK systems considering the ASE noise with post detection electrical filtering is via the Karhunen-Lo` eve (KL) expansion method[109]. This method is a semi-analytical approach based on calculation of 81 moment-generating function and saddle-point approximation and does not result in a closed form expression for probability of error. 5.3 Performance Analysis of MBDD-DSPK De- tection Algorithms The detection problem is estimating d M based on the observation set { r i :1 ≤ i ≤ M}. From(5.11), eachobservationiscomposedoffourterms: √ ρ s d M is the desired signal term, p i represents the Gaussian noise added to the signal in i bit duration ago, p 0 is the Gaussian noise added to the current signal, and n i is associated to noise-noise beating in photo-detectors. Since the current signal is interfered with M preceding signals, p 0 is present in all the observations. In this section, the optimum decision rule is derived in the first part and its probability of error is calculated. In the second part, the majority vote decision rule is stud- ied and using numerical calculation, the corresponding BER performance will be presented. In order to evaluate the performance of the MBDD structure, it is necessary to consider the performance of the coherent detection scheme as a reference. In coherent detection, the decision variable is c=Real T Y k (t)dt (5.12) 82 which has the probability distribution of N( √ PTd k ,αN 0 BT/2). Therefore, the probability of error in coherent detection is P e coherent = Q 2ρ s (5.13) where Q(.) is the tail probability of the standard normal distribution. 5.3.1 MBDD-DPSK with Optimum Decision Rule The optimum detector is the linear least mean-square error (LMSE) estimator since it is assumed that the distribution of all the undesired terms is Gaussian. Therefore, the covariance matrix of the observations is K ˜ r =E (˜ r−μ ˜ r )(˜ r−μ ˜ r ) † =( 1 2 + βBT 2α 2 ρ s )I M×M + 1 2 J M×M , (5.14) with ˜ r=[˜ r 1 ˜ r 2 ... ˜ r M ] † and μ ˜ r =E{˜ r} = √ ρ s d M J M×1 , (5.15) 83 where I is the identity matrix, and J is the unit matrix. Using the log-likelihood ratio test, the decision rule to estimate d M is given by (˜ r+μ ˜ r ) † K −1 ˜ r (˜ r+μ ˜ r ) 1 ≷ -1 (˜ r−μ ˜ r ) † K −1 ˜ r (˜ r−μ ˜ r ) ⇒ M i=1 r i 1 ≷ -1 0 (5.16) where K −1 ˜ r = 2α 2 ρ s α 2 ρ s +βBT (I− α 2 ρ s α 2 (1+M)ρ s +βBT J). (5.17) The block diagram of the optimum detector is shown in Fig. 5.5. From (5.11) it can be observed that M i=1 r i has the probability distribution of N(Md M √ ρ s , M 2 + M 2 2 + βMBT 2α 2 ρ s ). (5.18) Therefore, the probability of error for the optimum detector is given by P e optimum = Q ⎛ ⎝ 2Mρ s M+1+ βBT α 2 ρs ⎞ ⎠ , (5.19) which in limit approaches the performance of the coherent receiver as M ap- proaches infinity according to (5.13). In (5.19), setting M = 1 which corresponds to the conventional DPSK receiver, and α = β ∼ =1(for BT ≥ 4), results in the same expression for probability of error as in [76, Eq. (23)] (replace E b /η and W in [76] by ρ s and B/2, respectively). For the sake of simplicity, hereafter in this chapter it is assumed that α = β=1. 84 Figure 5.5: Block diagram of the optimum (LMSE) MBDD detector 5.3.2 MBDD-DPSK with Majority Vote Decision Rule In practice, implementation of the LMSE receiver is challenging for optical sys- tems since it requires very high speed electrical components such as adders and analog-to-digital (A/D) converters to perform the required post-detection tasks [105]. Therefore, the majority vote decision rule has been suggested as a sub- optimal detection method in MBDD systems and various implementations of it were studied and experimentally demonstrated in [48, 49, 50]. The block diagram of the majority vote detector is illustrated in Fig. 5.6. In this method, based on each r i , an individual and independent decision is made in each delay branch, and the final decision for decoding d M is performed by selecting the decision that has been made most among all the M individual branches. So in majority vote detection, soft post-processing is avoided and consequently, the required electronic circuits is realizable by simple high speed mixed signal logic gates such as current-mode logic (CML) circuits [1]. It should be noted that 85 multiplication of two bipolar signals followed by a zero threshold slicer is the same as using an XOR logic gate operating on the binary equivalent of the signals [48]. If it is assumed that the common noise term p 0 in (5.11) is known, all the r i ’s will be i.i.d with probability distribution of N(d M √ ρ s +˜ p 0 , 1 2 + BT 2ρ s ), (5.20) so the conditional probability of error in each delay branch is P e| ˜ p 0 = Q( √ ρ s +˜ p 0 1/2+BT/2ρ s ). (5.21) In majority vote detection, if among M individual decisions, at least (M+1)/2 of them are incorrect (M is odd), the final decision will be incorrect. Therefore, the probability of error is equal to P e majority vote | ˜ p 0 = M k= M+1 2 M k ⎛ ⎝ P e| ˜ p 0 ⎞ ⎠ k ⎛ ⎝ 1−P e| ˜ p 0 ⎞ ⎠ M−k . (5.22) Using [103, Eq. (6)], equation (5.22) can be also written as M! ( M+1 2 !) 2 B P e| ˜ p 0 (M + 1,M+1)whereB x (a,b) is the incomplete Beta function. The probability density function (pdf) of p 0 is known, i.e., f ˜ p 0 ( p 0 )= 1 √ π e − ˜ p 0 2 , so averaging over all possible 86 Figure 5.6: Block diagram of the majority vote detector values of p 0 results in the unconditional probability of error. Therefore, the BER in majority vote decision rule is P e majority vote = 1 √ π M k= M+1 2 M k ∞ −∞ ⎡ ⎣ Q ⎛ ⎝ √ ρ s +˜ p 0 1/2+BT/2ρ s ⎞ ⎠ ⎤ ⎦ k · ⎡ ⎣ 1−Q ⎛ ⎝ √ ρ s +˜ p 0 1/2+BT/2ρ s ⎞ ⎠ ⎤ ⎦ M−k e − ˜ p 0 2 d p 0 . (5.23) Analytical simplification of (5.23) is not straightforward, but the results can be evaluated using numerical methods and computer. The BER graphs versus OSNR are plotted in Fig. 5.7 for different values of M, assuming BT = 4. Compared to the conventional receiver (M = 1), a significant improvement in the BER can be observed; for instance, at the BER of 10 −9 , the MBDD scheme with M=3,5, and 7 is respectively 1.4-dB, 2-dB, and 2.3-dB more power efficient. Computing (5.23) with large values of M shows that in the limit, the performance of the majority vote detector approaches the performance of the coherent receiver, but at a lower rate compared to the optimum detection. 87 Figure 5.7: BER performance of the majority vote detector versus OSNR for different number of delay segments (M)with BT =4. As M increases the BER curve gets closer to the BER curve of the coherent detection. Assuming ρ s BT (thus, ignoring BT 2ρs for the moment), the amount of OSNR gain in MBDD compared to the conventional DPSK receiver is plotted in Fig. 5.8 for both cases of the optimum and majority vote detectors. As expected, the OSNR gain of MBDD with the optimum detector is higher than the OSNR gain of MBDD with the majority vote detector. It can be observed that the maximum penalty of using the majority vote detector instead of the optimum detector is about 0.4-dB for M = 3. Using the results of Fig. 5.8 and curve fitting, it can be verified that the OSNR gain of the majority vote detection scheme compared 88 Figure 5.8: OSNR gain of the optimum MBDD detector and the majority vote MBDD detector compared to the conventional DPSK receiver for different number of delay segments (assuming ρ s BT). the conventional DPSK receiver is equal to 10Log 2M+1.2 M+2.2 . Thus, (5.23) can be approximated by P e majoirty vote ≈ Q ⎛ ⎝ (2M+1.2)ρ s M+2.2+ 1.6BT ρs ⎞ ⎠ ; M=1,3,5,.... (5.24) It should be emphasized that the results are valid only when OSNR is not low, a wideband optical bandpass filter has been used in the system, and the coherence time of the laser is much longer than the bit time duration. 89 5.4 Conclusion In this chapter, the performance of the MBDD receiver structure in optical DPSK systems was evaluated and it was shown that with a large number of delay seg- ments and employing the optimum decision rule or the majority vote decision rule, the power efficiency asymptotically approaches the power efficiency of the coherent detection. The BER performance of the MBDD with the optimum decision rule was analytically derived and with the aid of numerical computations, a closed form equation was presented to estimate the BER performance of the MBDD systems employing majority vote decision rule. It was also shown that in a memoryless channel, implementing the majority vote detection instead of the optimum detec- tion is more practical when considering the complexity of required post-detection circuits, but it imposes a small power penalty. 90 Chapter 6 Optical Performance Monitoring with Constellation Diagrams Optical performance monitoring of a data signal is of great interest for systems that have impairments changing over time. A desirable attribute of a monitor is to determine the specific impairment that is degrading the data signal. Moreover, it mightbebeneficialforthemonitortoaccommodatedifferentadvancedmodulation formats and be asynchronous and not require exact clocked timing. In general, it is well known that the eye diagram which can be generated by an oscilloscope after detection is a powerful diagnostic tool for evaluating system performance. In this chapter, it is shown how CD and DGD change constellation diagrams, and using different figure of merits in asynchronously generated constellation dia- grams, the amount of impairments is quantified. It is shown that I/Q plots deform in a fairly predictable way, such that the patterns can be recognizably used to de- termine the amount of accumulated impairments. 91 6.1 Transmission Impairments in Optical Fiber Systems In fiber-optic transmission systems there are many different impairments such as amplifier noise, amplifier distortion and transients, CD, PMD, fiber nonlinear- ity induced distortion and crosstalk (self-phase-modulation (SPM), cross-phase- modulation(XPM), four-wave mixing (FWM), stimulated Rayleigh, and Brillouin scattering), optical filter distortion, and linear crosstalk [53]. Both CD and PMD broaden the optical pulse, thus creating ISI and limiting the bit rate-distance product. 6.1.1 Chromatic Dispersion (CD) CD makes different spectral components of an optical pulse to propagate at dif- ferent speeds, thus broadening the optical pulse in the time domain. An optical pulse at time t and distance z may be represented as E(t,z)= A(t,z)exp j(ωt−βz) (6.1) where A(t,z) is the complex envelope of the optical pulse, ω is the angular fre- quency, and β is the propagation constant. The source of CD is that β is not constant and it depends on the frequency. Hence, the more accurate way of its 92 representation is β(ω) which can be expanded around the center frequency of the optical pulse using Taylor series, β(ω)= β 0 +(ω −ω 0 )β 1 + 1 2 (ω −ω 0 ) 2 β 2 +··· (6.2) where β m = d m β dω m | ω=ω 0 . As observed, the group velocity which is the propagation speed of the complex envelope is v g = 1 β 1 . The parameter β 2 is the dispersion of the group velocity and the source of CD and it can be written as β 2 = − 1 2π λ 2 c D (6.3) where D is the dispersion parameter in units of ps/nm/km. The group velocity distortion (GVD) is the product of the dispersion parameter and the fiber length, i.e., GVD= DL (ps/nm). The impulse response of the fiber with CD is [106] h(t)= e j π 4 sign(ξ) T b π|ξ| exp −j t T b 2 (6.4) where ξ = −2β 2 LR 2 b is the normalized dispersion index, R b =1/T b is the pulse rate, and T b is the pulsewidth. 6.1.2 Polarization Mode Dispersion (PMD) In an ideal optical fiber, the core has a perfectly circular cross-section. In this case, the fundamental mode has two orthogonal polarizations that travel at the same speed. The signal that is transmitted over the fiber is randomly polarized, 93 i.e., a random superposition of these two polarizations, but that does not matter in an ideal fiber because the two polarizations would propagate identically. In a realistic fiber, however, there are random imperfections that break the cir- cular symmetry, causing the two polarizations to propagate with different speeds. In this case, the two polarization components of a signal will slowly separate, e.g., causing pulses to spread and overlap. By definition, the polarization with slower speed is polarized along the slow axis and the polarization with faster speed is polarized along the fast axis. Since the fiber imperfections are random, the pulse spreading effects correspond to a random walk, and thus have a mean called DGD which is given by Δτ = D PMD √ L (6.5) where D PMD is the PMD parameter measured in units of ps/ √ Km. With only the first order PMD, the pulse shape in the fast and slow axis is not distorted. 6.2 Conventional Methods in Optical Perfor- mance Monitoring (OPM) There are different methods of optical performance monitoring. These methods are shown in the chart of Fig. 6.1. Monitoring can be done in the time or the frequency domain. CD and PMD cause optical pulses to be broaden, so in the frequency domain the power and the phase of the main frequency component of the clock or the signal are changed. Based on this general property, various techniques such as RF-tone monitoring [68, 69, 70, 115], pilot tone monitoring 94 Figure 6.1: Optical performance monitoring techniques [39], in-band frequency monitoring [16], optical filtering [113, 116], and optical homodyne techniques [3] have been developed. In the time domain, based on the synchronous or asynchronous sampling of the signal, different measures such as anaylzing the histogram of the signal amplitude [35] can be performed. One of the advanced time-domain methods is a clever adaptation of the eye di- agram to asynchronously generate a new type of diagram in optical on-off-keying (OOK) systems [27, 4]. This asynchronous diagram is fairly straightforward to generate and will deform in generally predictable ways by different types of im- pairments, i.e., CD, PMD, and OSNR. The experimental setup of this method is shown in Fig. 6.2. In this method, a two dimensional of diagram based on the samples of the signal is plotted. The change in the diagram can be associated with an amount of CD. In Fig. 6.3 the deformations of the plot based on CD is shown. Although, this is a creative method for monitoring CD, it does not address differ- ent types of dispersion, especially in advanced modulation formats. In the next section, our method which is a time-domain monitoring technique is discussed and analyzed. 95 Figure 6.2: Experimental setup for two-tap asynchoronous sampling [4]. Figure 6.3: Deformations of the two-tap aynchronous plot with CD [4]. 6.3 Constellation Diagram Monitoring of Phase Modulated Systems Advanced data modulation formats are playing an ever-increasing role within the optical communications community. For example, phase-shift-keying (PSK) pro- vides better receiver sensitivity and tolerance to nonlinear effects, and quadrature- PSK (QPSK) and quadrature-amplitude-modulation (QAM) provide increased spectral efficiency and tolerance to chromatic dispersion. Our proposed moni- toring algorithm is a time-domain technique to evaluate the constellation diagram for both cases of synchronous and asynchronous sampling. In advanced modulation formats, a common way of portraying the signal is plotting constellation diagrams on the I (in-phase) and Q (quadrature) plane. Different data signal degradations will impact the I/Q constellation diagrams, 96 Figure 6.4: Block diagram of QPSK system with balanced detection constellation-diagram monitor. CW: Continuous Wave light source, RZ: Return to Zero, I: In-phase, Q: Quadrature, CD: Chromatic Dispersion, DGD: Differential Group Delay, BPF: Band-Pass Filter, T: Delay (equal to the symbol time), A/D: Analog to Digital converter. 97 Figure 6.5: An arbitrary sequence of I and Q, (a) without any type of fiber im- pairments, (b) constellation affected by CD only, (c) constellation affected only by DGD Figure6.6: ReceivedconstellationdiagramsofQPSKsignal(a)withoutanytypeof fiber impairments, (b) constellation affected by CD only, (c) constellation affected only by DGD and understanding the impact on the constellation shape can be quite valuable for system diagnostics. A technique based on constellation diagram was used to measure the phase noise of light sources[28]. However, there have been little reported results on different types of deformations in constellation diagrams that would occur due to fiber impairments, such as CD and PMD. We presented a method to monitor CD and DGD in (D)QPSK systems based on the constellation diagram using synchronous sampling of the received signal [9]. In [10] we showed theeffectsofdispersiononanasynchronouslygeneratedconstellationdiagram, and based on this method, an artificial neural network (ANN) technique to monitor CD and DGD was reported in [38]. 98 In order to analyze the effect of CD and PMD on constellation diagrams, the QPSK system shown in Fig. 6.4 is considered. A continuous wave (CW) laser is modulated by two data streams of I and Q through a parallel I/Q dual-arm modulator. The optical signal is then carved using a Mach-Zehnder modulator (MZM) to obtain a return-to-zero (RZ) QPSK signal. Then the fiber impairments are induced by a CD and a DGD emulator followed by an Erbium-doped fiber amplifier (EDFA) and a bandpass filter (BPF) to filter the out of band noise. The monitor consists of two DLIs, one with a 45 o and the other one with a −45 o phase shift, followed by two balanced photo-receivers. The constellation diagrams are obtained by sampling the electrical I and Q signals using an A/D. OptSim software is used to simulate the QPSK system and the constellation diagrams are plotted offline in MATLAB. The amount of CD and DGD can be controlled by changing the parameters of the emulator. In order to examine only the effects of fiber impairments, a continuous wave (CW) laser with a narrow linewidth (10-KHz) is used as the light source. In a QPSK system with a bit rate of 40-Gb/s, the symbol rate, i.e., the rate of I and Q data, is 20-Gbaud/s, so the outputs of the photo-receivers are sampled every integer multiples of 50-ps. Two random bit sequences of length 1024 are transmitted as the I and Q signals and the received samples form the constellation diagram. In the first step, three scenarios have been considered: (i) a link without any type of impairments, (ii) a link only with DGD and without CD, (iii) a link only with CD and without DGD. 99 Fig. 6.5 shows the effects of CD or DGD on an arbitrary snapshot of the signal. The corresponding constellation diagrams are illustrated in Fig. 6.6. In the ideal case, in which the transmitted symbols are perfectly modulated and there is no significant distortion or noise in the link and the samples are taken at the maximum eye opening instant, the constellation diagram consists of 4 points in the four quadrants of the I/Q plane. 6.3.1 Effects of Chromatic Dispersion on the Constellation Diagrams The effects of CD on the constellation is shown in Fig.6.6(b). As observed, CD splits the constellation points, resulting in four clouds in the four quadrants. In ordertoanalyzethiseffect, itshouldbenotedthatCDspreadsthesignalandcause ISI. For example, 20-ps of accumulated CD in a 20-GBaud/s system extends the pulse over two symbol durations, and 40-ps of CD spreads the pulse over 6 symbol duration [106]. If S i (t)= E(t)exp(jπ d i 4 ) is the transmitted signal, with E(t) being the electrical field and d i ∈{±1±3} as one of the four possible symbols, we define y(t)= S i (t)∗h(t)and y k (t)= y(t)[u(t−T −kT)−u(t−kT)], where h(t)isthe impulse response of the channel with CD presented in [106]. Therefore, in the k th symbol time, the signal at the input of DLI is R k (t)= y k (t)e jπ d k 4 + L−1 n=1 y n (t)e jπ d k−n 4 (6.6) 100 where L is the length of symbol spread due to CD. The first term is the desired signal, and the second term is ISI. Based on the central limit theorem, as L in- creases, ISI can be interpreted as an additive Gaussian noise, so the filtering effect of the DLI can further influence the signal since a DLI can be viewed as two filters with the same input; the constructive port, acts like a lowpass filter and the de- structive port, has a highpass effect on the signal [22]. Therefore, the fluctuations caused by ISI which can be interpreted as noise, will be suppressed more by the constructive port compared to the destructive port. This asymmetry between the two ports appears in the 4 quadrants of the I/Q plane. Therefore, the effect of CD on the constellation diagram is more noticeable in the third quadrant where both destructive ports, i.e., highpass ports of the DLIs, are active. However, this asymmetry in different quadrants of the constellation is not apparent for small values of CD. In [9], error-vector-magnitude (EVM) (or normalized deviation) was used as a figure of merit to quantify the amount of impairments. An arbitrary detected symbol k can be represented by the pair of I and Q coordinates, (I k ,Q k ) and EVM which is the variance of the vector s k =(I k ,Q k ) is a measure that shows how much a symbol is spread in the I/Q plane or how large the constellation cloud is. For the symbol type d, the mean vector is defined as s d = 1 N d N d k=1 (I k ,Q k ), where N d is the number of d type symbols. Therefore, EVM is given by EVM = 1 N d |s d | 2 N d k=1 s k −s d 2 , (6.7) which exponentially increases with the amount of accumulated CD [9]. 101 Figure 6.7: Effect of DGD on DQPSK signals. 6.3.2 Effects of First-Order PMD on the Constellation Di- agrams The effect of DGD on the constellation is illustrated in Fig.6.6(c) where a DGD of 35-ps is considered. It can be observed that DGD splits each constellation point into points in the complex plane. The same snapshot in the time domain from the I and Q signals, affected only by DGD, is shown in Fig. 2(c), where the corresponding samples are numbered in the figure. Unlike CD, the pattern does not look like a cloud, the reason being that DGD simply cause a shift between the signal’s components in fast and slow polarizations, without broadening pulses [23]. Fig. 6.7 shows DGD makes parts of the optical fields in the two polarizations to overlap. As a result, the fields are coherently added in the overlapping region. Therefore, new phases will emerge after the signal propagates through the fiber; for example, if the phase of the first signal is 135 o and the subsequent symbol has a phase of 45 o , due to the vector summation, the new phase of 90 o is generated in the region that the two polarizations overlap. If the amount of DGD increases, the overlap time increases too. As a result the magnitude of the constellation diagram along the new phases increases as well. 102 Figure 6.8: Different constellations obtained at different times (15-ps CD). 6.4 Asynchronously Generated Constellation It has been shown that the shape of a constellation diagram depends on the sam- pling time [9]. Figure 6.8 illustrates three constellation diagrams obtained at three different sampling times. The second constellation is obtained by sampling at the maximum eye opening, but any shift from the optimum time that can be created by a simple clocking jitter changes the constellation. Therefore, it is desirable to use a monitoring technique that is independent of the sampling time [10, 38]. If the monitor is not locked to the reference clock and all the received samples are plotted in one I/Q plane, patterns like in Fig. 6.9 are obtained. As discussed in section 2, CD broadens the width of the branches in constellation diagrams by creating constellation clouds in I/Q plane, while the effect of DGD is symmetrical bycreating4newsignalphasesinthemiddleofthe4originallytransmittedphases. In summary, DGD has a symmetric effect on the constellation, while CD has an asymmetric effect. This asymmetry depends on whether I and Q are positive or negative. As illustrated in Fig. 6.9(c), the constellation is symmetric to the I = Q line. On the other hand, it can be observed the signal variations are smoother in the region where I +Q> 0 compared to the region where I +Q< 0 due to the asymmetric filtering effects of the constructive and destructive ports of 103 Figure 6.9: Effects of CD and DGD on the asynchronously generated constella- tion diagrams (a) CD Broadens the branches in constellation diagrams, (b) DGD creates 4 new signal phases right in the middle of the initial signal phases, (c) the constellation diagram is symmetric with respect to the line I=Q. DLI. A combination of different values of CD and DGD is illustrated in Fig. 6.10 where CD increases from left to right and DGD increases from top to bottom. An important observation is that the effects of CD are suppressed when DGD increases. The reason is that coherent interference of the signal along the fiber due to DGD resembles a low pass effect, i.e., in addition to the 90 o phase steps, DGD creates 45 o steps in between which make signal transitions smoother and relaxes the bandwidth constraints, thus, suppressing effects of CD. As shown in the previous section, the amount of DGD is proportional to the magnitude of the new phases. In Fig. 6.11, considering different values of CD, the normalized magnitudes of these new phases which are the maximum distance of the constellation diagram in I and Q direction from the center of the plane, are plotted versus DGD. As observed, this parameter is almost independent of the amount of CD. In Fig. 6.12, the normalized width of the branch of the constellation in the third quadrant, which is the most sensitive quadrant to CD, is plotted versus CD. 104 Figure6.10: SimultaneouseffectsofCDandDGDonQPSKconstellationpatterns. Unlike Fig. 6.11, the curves are different for different values of DGD. It can be observed that more DGD in the link reduces the slope of the curves. Hence, in order to measure CD from the constellation diagram, the amount of DGD must be evaluated first, and then the amount of CD can be estimated using the curve corresponding to the estimated DGD. 105 Figure 6.11: Normalized distance of the emerged new phases from the center of the I/Q plane as a figure of merit to measure the amount of DGD. 6.5 Conclusion In this chapter, the basics of optical performance monitoring were discussed and different conventional methods were listed. It was shown that constellation dia- gram can be used as a time-domain monitoring technique suitable for the channels with advanced modulation formats. The effects of CD and DGD on constella- tion diagrams of (D)QPSK signals were studied. It was shown that synchronously generated constellation is sensitive to the sampling time, so asynchronous con- stellation diagrams which are obtained similar to eye diagrams are more desirable in monitoring fiber impairments. The amount of accumulated impairments was estimated using specific features in deformations of the constellation diagrams. 106 Figure 6.12: Normalized width of the constellation branch in the third quadrant. 107 Chapter 7 Intensity Modulated Optical Multicarrier CDMA Orthogonal frequency division multiplexing (OFDM) is used in many wireless or wiredcommunicationsystemssinceitisaneffectivemethodtoavoidorcompensate dispersion effects, especially in systems with high spectral efficiency [13, 20, 95, 102]. Since OFDM is based on processing of digital data, another advantage of OFDM is that it is capable of providing more accurate signal processing and filtering blocks compared to conventional techniques that rely on analog filtering [13]. Since in OFDM, data is transmitted on many narrowband subcarriers, the symbol duration is much longer than conventional systems. As a result, for the same length of the channel response, the relative effect of ISI is less for OFDM systems in general. This advantage is even more highlighted in optical OFDM systems because the dispersive effect of CD is inversely proportional to the square of the symbol duration. The residual ISI can be avoided by inserting a guard interval in the time domain between adjacent symbols called cyclic prefix (CP) [13]. In WDM systems data is also transmitted on many different carriers using sev- eral light sources with different wavelengths but in optical OFDM there is only one 108 Figure 7.1: Comparison of the spectrum of WDM and OFDM. Figure 7.2: History of optical OFDM [13]. light source. The main difference of WDM and OFDM is that in OFDM, subcar- rier multiplexing and demultiplexing are carried out with fast-Fourier-transform (FFT) and inverse-FFT (IFFT) in the digital domain. This feature makes OFDM a highly spectrally-efficient technique because the orthogonal subcarriers overlap in the frequency domain [13]. In WDM since multiple lasers are used, there are unused frequency bands between the carriers and the carrier spacing is much larger than subcarrier spacing in OFDM. Figure 7.1 shows the difference of WDM and OFDM in the frequency domain. 109 Figure 7.2 shows the historical development of OFDM [13]. Although OFDM is a very new topic in optical communications, there are many theoretical and experimental papers to evaluate OFDM in different optical systems such as free space optical communications [33, 34], single mode optical fiber [96, 99, 40, 41], multimode optical fiber [62, 58], and plastic optical fiber [59]. In this chapter, implementation of optical multicarrier-CDMA (OMC-CDMA) in single mode fiber with intensity modulation and direct detection (IMDD) is explained in details and considering the shot-noise and thermal noise of the photo- receiver, the BER performance of the system is analytically derived. 7.1 Multicarrier Transmission and OFDM in Optical Systems CDandPMDinsinglemodefibers(SMF)broadenstransmittedpulsesandcreates ISI, thus the length of an uncompensated link is limited to a relatively short range, especially in high speed links since the amount of accumulated CD scales with squareofthesignal’sbandwidth[47]. Opticalorelectricaldispersioncompensation cansuppressCDimpairmentstosomeextent[20,47],butthefundamentalsolution is to use advanced transmission techniques such as OFDM [96, 99, 40, 41, 17]. IMDD systems are commonly employed in optical communication systems due to their simplicity and low cost. Therefore, optical OFDM with IMDD has the advantage of using a simple PD as the receiver while coherent optical OFDM requiresacoherentdetectionscheme,whichmakesthereceivercomplex. Moreover, 110 Figure 7.3: Different multiple access techniques using subcarrier, time, and code division. sensitivity to laser phase noise is a challenge in coherent optical OFDM systems [79, 100]. In [60, 80], optical orthogonal frequency multiple access (OFDMA) was intro- duced as a technique that is capable of allocating the channel to different users in passive optical networks (PONs) with advantages of OFDM. This scheme is an FFT-based subcarrier multiplexing (SCM) in which a number of subcarriers are assigned to an optical network unit (ONU) depending on the required bandwidth of that ONU. The disadvantage of this method is that the total bandwidth of the channel is not efficiently utilized when some ONUs are not active in the network. In contrast, in CDMA networks, different users communicate at the same time and over the same bandwidth in a shared medium since unlike TDMA or WDM, a time slot or a frequency band is not permanently allocated to a certain user that can be frequently inactive [93, 92, 110]. Multicarrier-CDMA (MC-CDMA) is the combination of CDMA and OFDM and it has been extensively studied and implemented in wired and wireless radio 111 Figure 7.4: Simplified concept of MC-CDMA showing that it is composed of OFDM and CDMA communication systems [36]. In Fig. 7.3 different multiple access techniques using three dimensions of time, subcarrier (frequency), and code have been shown; since in MC-CDMA different users are distinguished in the code domain, they can be ac- tive all the time and over all subcarriers. In [8], we reported the first experimental demonstration of intensity modulated OMC-CDMA in standard SMF (SSMF). The simplified block diagram of OMC-CDMA is shown in Fig. 7.4. It is shown how OMC-CDMA can be realized by combining CDMA and OFDM. There are U activeusersinthenetworkeachwithauniqueCDMAcode. Ideally, thecodeshave high auto-correlation and low cross-correlation, so after the signals from different users are combined in the fiber channel, each user in the receiver can decode its own data. 7.2 System Model of Intensity Modulated OMC- CDMA The block diagram of OMC-CDMA system is illustrated in Fig. 7.5. In this figure, an arbitrary user k is shown in the transmitter while in the receiver side, without 112 Figure 7.5: Block diagram of OMC-CDMA system 113 loss of generality, user 1 has been only shown. The user k’s bit stream denoted by b k is first mapped to a quadrature amplitude modulation (QAM) symbol s k .In QAM mapping, in order to minimize the BER, Gray coding must be used. Then N copies of s k are multiplied by the CDMA spreading code of user k denoted by c k = {c k [0],c k [1],...,c k [N −1]} where N is the code length. The CDMA-encoded symbol X k = {X k [0],X k [1],...,X k [N −1]} = s k ·c k along with its complex con- jugate (c.c.) X ∗ k enter the IFFT block with N c =2N + 2 inputs and outputs, where N c is the number of subcarriers. The additional c.c. part is necessary in order to obtain a real-valued signal at the output of the IFFT block [31, 108, 12]. The other two extra subcarriers are assigned to DC (subcarrier 0) and Nyquist (subcarrier N +1) frequencies which cannot be used for data transmission. The outputs of the IFFT block are x k [n]= 1 √ N c N m=1 X k [m−1]exp(j 2πmn N c )+c.c. , 0 ≤ n ≤ N c −1, (7.1) which can be considered as the samples of x k (t)= 2 √ N c N m=1 Re X k [m−1]exp(j 2πmt T s ) (7.2) at t = nT c where T c = T s /N c is the chip time and T s is the symbol time. In order to preserve orthogonality of subcarriers, T s is equal to the inverse of the frequency gap between subcarriers. So if the available lowpass bandwidth is B (Hz), the symbol time is T s = N c /2B=(N+1)/B. 114 After the IFFT, samples are serialized through the parallel-to-serial (P/S) con- verter and a cyclic prefix (CP) is added to the signals. The duration of the CP denoted by T CP must be greater than duration of the impulse response of the channel. Therefore, the total signaling time of one symbol is T sig = T s + T CP . Figure 7.5 shows how the CP is added to the original samples. The number of the CP samples is N CP = T CP /T c where x is the smallest integer greater than x. The outputs of (P/S) are then combined with signals from other users, so the input to the digital-to-analog (D/A) converter is v[n]= U k=1 x k [n], where U is the number of active users, and the signal at the output of D/A is denoted by v(t). V[m] is also defined as the FFT of v[n], therefore V[m]= U k=1 X k [m]= s 1 c 1 [m]+ U k=2 s k c k [m]. (7.3) It should be noted that in downlink transmission all users are synchronous, so the CDMA-encoded symbols of different users can be combined before the IFFT block. Before modulation, a DC bias of V 0 is added to v(t) to guarantee that signal is positive and in the linear range of the modulator. Therefore, the total electrical signal at the input to the directly-modulated laser (DML) is V 0 +v(t). Thus, the output power of the DML is p(t)= β[V 0 +v(t)], where β is the quantum efficiency of the DML. The transfer function of the DML is shown in Fig. 7.5. The minimum threshold of the input electrical signal to derive the DML v th can be ignored [108]. At the receiver, the generated photocurrent is y(t) ≈ ρ[p(t)∗h(t)]+z(t), where h(t) is the impulse response of the channel, ρ is the responsitivity of the PD, and 115 z(t) is the additive noise. An approximation is used in the above equation since CD for intensity channels is approximately linear only when the DC bias is high [17]. Moreover, since in PONs the reaching distance is small, linear approximation is reasonable. The output of the PD is sampled every T c seconds and deserialized through the serial to parallel (S/P) converter. If synchronization is perfect and the CP duration is sufficient, the input to the FFT block after removing the CP is y[n]= y(nT c )= ρβ(V 0 H 0 +v[n]⊗h[n])+z[n] , 0 ≤ n ≤ N c −1, (7.4) where h[n]= h(nT c ) is the discrete-time impulse response of the channel, ⊗ is the circular convolution operator, H 0 is the DC gain (loss) of the channel, and z[n]= z(nT c ) is the discrete-time samples of the noise. The useful outputs of the FFT block are then given by V[m]= ρβH[m]V[m]+Z[m] , 0 ≤ m ≤ N −1, (7.5) where H[m]= H(j 2π(m+1) Ts ) is the complex gain of the channel at subcarrier m+1, H(j2πf) is the Fourier transform of h(t), and Z[m] is the FFT of z[n]. Only the first half of the FFT outputs is adequate for further processing since the other half is the complex conjugate of the first half. The equalizer is composed of N complex gains {F[m]:0 ≤ m ≤ N −1} corre- spondingtotheN usefulsubcarriers. Thesegainsareconstantlyupdatedbasedon channel estimation techniques to compensate for linear distortions, so the outputs oftheequalizerareF[m] V[m]. WedefinetheparameterF 2 = H 2 0 N−1 m=0 |F[m]| 2 /N 116 which can be considered as the average energy of equalizer taps and it will be used later in BER estimation. The outputs of the equalizer are sent to the CDMA decoder. For instance, user 1 correlates the received samples with its own assigned code c 1 . The decoded signal of user 1 can be written as N−1 m=0 F[m] V[m]c ∗ 1 [m]and after substituting V[m] from (7.3) in (9.5) and dividing the whole expression by A 1,1 ρβ,thedecodedsymbolofuser1isequalto s 1 = s 1 + 1 A 1,1 U k=2 A 1,k s k +z 1 , (7.6) where A i,j = N−1 m=0 c i [m]c ∗ j [m]H[m]F[m]. (7.7) In (9.11), the first term is the desired signal, the second term is the MAI, and the third term is noise obtained as follows z 1 = 1 A 1,1 ρβ N−1 m=0 F[m]c ∗ 1 [m]Z[m]. (7.8) With zero-forcing equalizer F[m]= 1 H[m] and the orthogonality of users is pre- served, so this method is also called orthogonality-restoring-combining (ORC)[36]. In this case, A 1,1 is the auto-correlation of user 1’s code and A 1,k is the cross- correlation of user 1’s code with the codeword of user k. However, according to (9.22), ORC amplifies noise in subcarriers with low gain. At the final stage, the QAM symbols are demapped into sequence of 0 and 1 bits, { b 1 }. 117 The bit rate per user is R b = log 2 M T sig = Blog 2 M N +N CP /2+1 , (7.9) where M is the constellation size of QAM symbols. In many families of CDMA codes, the total number of available code-words is qual to the code length N [36]. Therefore, the global bit rate of the whole network is R = NR b ≈ Blog 2 M when N N CP . Walsh-Hadamard (WH) codes are completely orthogonal in synchronous systems, e.g., in downlink transmission. Therefore, using WH codes and assuming |c k [m]| = 1, results is A 1,1 = N,and A 1,k =0for k = 1, i.e., the MAI term becomes zero. It should be noted that if channel estimation is not perfect, the cross-correlation terms become non-zero and increasing the number of users increases the MAI and degrades the performance of the system. 7.3 Noise in OMC-CDMA Based PONS In PONs, there is no optical amplifier so noise is added to the system only in the photo-receiver. The two types of noise in the photo-receiver are the shot-noise and thermal noise [108]. If the average received optical power is P r , the variance of the shot-noise current is i 2 sh =2qρP r B, (7.10) 118 where q is the electron charge. Thermal noise of the circuit is independent of the signal’s power and it is modeled by a zero-mean Gaussian current with a variance of i 2 th = S 2 th B, (7.11) where S th is the power spectral density (PSD) of thermal noise. Therefore, z 1 in eq. (9.22) can be modeled by a Gaussian distribution with zero mean and variance of σ 2 z = (2qρP r +S 2 th )B (A 1,1 ρβ) 2 N−1 m=0 |c[m]| 2 |F[m]| 2 = (2qρP r +S 2 th )B N(ρβ) 2 F 2 H 2 0 . (7.12) 7.4 Model of Fiber-Optic Intensity Channel In general, the optical fiber channel response to power signals is not linear. How- ever, in [17] it is shown that SMF intensity channel can be modeled by a linear system if the DC bias is large with frequency response of H(ω) = cos( 1 2 ω 2 β 2 l), (7.13) where β 2 is the second order propagation constant defined in (6.3), and l is the length of the fiber. The linearity assumption is even more realistic in PONs due to the small length of the fiber link. Figure 7.6 illustrates the absolute value of the channel response. 119 Figure 7.6: Frequency response of a typical optical fiber for two fiber lengths of 50 and 100 Km. In our calculations we include fiber loss in the transfer function, so H 0 =10 −αl , where α is the optical power loss (dB) per unit length and |H[m]| which is the absolute value of the channel’s gain at subcarrier m+1 is equal to |H[m]|=10 − αl 10 cos 2β 2 l( πB N+1 ) 2 (m+1) 2 . (7.14) It should be noted that V[m] was transmitted on subcarrier m+1so ω is replaced by 2πB m+1 N+1 in (7.13) to obatin (9.15). The duration of the channel’s impulse response is |D|lc(2B)/f 2 c [64] where |D| =2πcβ 2 /λ 2 c is the dispersion parameter, c is the speed of light, f c is the emission frequency of the DML, and λ c is the emission wavelength of the DML. Therefore, N CP = |D|lc(2B) 2 /f 2 c ! . (7.15) 120 7.5 Performance Evaluation of OMC-CDMA It can be verified that E{v[n]}=0if E{s k } = 0, so the average transmitted optical power is P 0 = βV 0 and the average received optical power is P r = H 0 P 0 . In order to determine the value of V 0 , it is necessary to know the minimum neg- ative amplitude of v[n]. Unfortunately, there is no exact model to predict this parameter. According to [72], |v[n]| is bounded by √ 2NUmax|s k |. This bound accounts even for the cases that rarely occur, so with this value, which corre- sponds to the worst case scenario as the bias of the DML, the power efficiency is extremely reduced. On the other hand, the increased bias results in an increased average received optical power, and consequently more shot noise. This is the main disadvantage in IMDD multicarrier systems without peak-to-average power ratio (PAPR) reduction. However, there are different techniques to overcome this problem such as signal clipping [108, 12] or constantly updating the DML’s bias [114], which are out of the scope of this chapter. A clipping technique will be discussed in chapter 8. If QAM symbols are from a square constellation of size M,max|s k | 2 = γσ 2 s where γ = 3 √ M( √ M −1) 2( √ M+1) , (7.16) 121 andσ 2 s = E{|s k | 2 }istheaverageenergyofsymbols. From(9.11)andrecallingthat ORC eliminates MAI, SNR = σ 2 s /σ 2 z . Using P 0 = β √ 2NUγσ s and eq. (9.14), the SNR can be written in terms of the average transmitted optical power as follows, SNR = Nρ 2 β 2 σ 2 s (2qρH 0 P 0 +S 2 th )B F 2 H 2 0 = ρ 2 P 2 0 2γU(10 αl/10 )(2qρP 0 +10 αl/10 S 2 th )BF 2 . (7.17) In order to calculate the BER, the results of calculations in [108] is used which state in a square constellation with Gray-mapped symbols, BER = 2(1−1/ √ M) Log 2 M erfc ⎛ ⎝ 3SNR 2(M −1) ⎞ ⎠ . (7.18) Typical values of the parameters are, ρ=0.8A/W, S th =16pA/ √ Hz, α=0.2 dB/Km, and |D| = 17 ps/nm.Km ( or β 2 =21.7(ps) 2 /Km at λ c = 1550 nm). The bandwidth is B=2.5 GHz which relaxes the DML and receiver constraints in PONs [8, 31]. With these parameters F 2 ≈1and N CP = 1. Assuming 16-QAM modulation, the BER curves are plotted for different number of active users in Fig. 7.8. Even though there is no MAI, increasing the number of active users degrades the performance of the system. The reason is that with more users in the system, the peak value of |v[n]| is increased, so P 0 mustbeliftedupinorder to avoid clipping lower peaks of the signal. In Fig. 7.8(b), the number of active users is 64, and the BER curves are plotted for different QAM symbol constellations. It should be noted that the global bit rate is respectively 5, 10, 20, and 40-Gb/s for constellation sizes of 4, 16, 64, 122 Figure 7.7: BER graphs consideing different number of active users and 256. There are two reasons that increasing M deceases the performance. First, with the same symbol energy, the peak value of |v[n]| linearly increases with the constellation size at the slope of γ based on the given bound, so P 0 must be increasedtooinordertoavoidsignalclipping. Thesecondreasonisthatwithfixed signal energy, increasing the constellation size reduces the Euclidean distance of the symbols and consequently increases the probability of error. 123 Figure 7.8: BER graphs for different symbol constellations 7.6 Conclusion In this chapter, the structure of OMC-CDMA system with IMDD was explained in details and it was shown that the system is highly flexible since adding a user in the network or changing the QAM symbols can be simply performed in the digital domain. Considering the shot-noise and thermal noise of photo-receivers, a closed form expression for the BER performance was analytically derived. The results showed that increasing the constellation size reduces the performance of the system; however, the global bit rate is increased. It was also shown in spite of eliminating MAI with ORC in synchronous download transmission, increasing the 124 numberofactiveusersdegradestheperformanceofthesystemduetotheincreased peak value of the signal and avoiding signal clipping. In future research, in order to increase the power efficiency, PAPR reduction techniques for OMC-CDMA can be investigated. 125 Chapter 8 Experimental Demonstration of Optical Multicarrier CDMA In previous chapter the basics of OMC-CDMA was discussed. In this chapter implementation of optical OMC-CDMA in optical fiber with QAM symbols in the baseband is presented in details and with experimental demonstration the functionality of the system is verified. It is shown that the system is capable of supporting 256 users with the global bit rate of 15-Gb/s using 2.5-GHz electrical bandwidth. Due to some practical problems, the experiment is slightly different from the system in chapter 7 since instead of using a DML, an MZM has been used. 8.1 Block Diagram and Experimental Setup of OMC-CDMA The block diagram of the OMC-CDMA system is illustrated in Fig. 8.1. The only difference of this system from the system in chapter 7 is that the output of D/A, v(t), derives an MZM biased at the quadrature point as shown in Fig. 8.2. The DC bias shifts the signal to the operating point with minimum nonlinearity. The 126 Figure 8.1: Block diagram of intensity based OMC-CDMA system with MZM. CP: Cyclic Prefix, D/A: Digital to Analog, MZM: Mach-Zehnder Modulator 127 Figure 8.2: Biasing MZM at quadrature point. The slope of the tangent line at the bias is β. output power of MZM for the first signaling time is obtained from the following equation, p(t) ≈ β[V 0 +v(t)] , 0<t<T s (8.1) where β is the slope of the MZM characteristic function at quadrature point. Equation 8.1 models the small signal approximation since the transfer function is approximated by a line with slope β. The rest of the system operates similar to the previous chapter. 8.2 OMC-CDMA Experimental Results and Discussion TheBERcurvesareobtainedbyaveragingovertheBERofallactiveusers. Figure 8.3 shows the BER curves and the corresponding constellation diagrams for three 128 Figure 8.3: BER curves for different number of active users considering both back- to-back and 70-km fiber link cases and corresponding constellation diagrams different number of active users with N = 64. It can be observed that there is almost no penalty after 70-Km SMF compared to the back to back case. As the number of users is increased from 4 to 64, less than a 2-dB penalty is observed. In Fig. 8.4, BER curves for different constellation sizes are presented for U = N = 256. As the constellation size increases, due to a higher spectral efficiency, the bit rate increases accordingly, but on the other hand the performance of the system is degraded. The corresponding equalized received constellation diagrams are also shown in Fig. 8.5 along with their global bit rate obtained from eq. 9.10. It can be observed that OMC-CDMA functions as a highly flexible system since adjusting the bit-rate can be accomplished in digital domain via changing the QAM symbol mapping, or the code length without the need to modify the software. Moreover, OMC-CDMA can provide variable quality of service (QoS), 129 Figure 8.4: BER curves for different QAM symbol mappings for example, based on the required bit rate, different users in the network can employ different QAM symbol mappings independent of each other. 8.3 Conclusion In this chapter, OMC-CDMA system was experimentally demonstrated and it was shown that with an electrical bandwidth of 2.5-GHz, OMC-CDMA was capable of supporting 256 users at a total bit rate of 15-Gb/s with almost no penalty in a 70-Km fiber-optic link. 130 Figure 8.5: Equalized received constellations of different QAM symbol mappings (a) R=7.5-Gb/s, (b) R=10-Gb/s, (c) R=12.5-Gb/s, (d) R=15-Gb/s 131 Chapter 9 Optical Multicarrier CDMA with Asymmetrical Clipping Since intensity is a non-negative quantity, before the DML a DC bias is added to the signal [31, 108] in order to guarantee the negative parts of the signal are not clipped. Thus, the amount of this DC value must be greater than the absolute value of the negative peak. Since the DC value does not carry data, the power efficiency in analog and multicarrier optical systems is less than optical coherent systems. In optical multicarrier CDMA, the power efficiency is even decreased further since there is no exact model to predict the DC value and instead, a bound regarding the worst case scenario is considered similar to chapter 7. It should be noted that increasing the DC value of optical intensity results in an increased average received optical power, and consequently more shot-noise in the PD. In [12, 34] however, it was shown in an IMDD OFDM system, if a DC value is not added to the signal before the DML, only the even subcarriers are distorted, so data can be transmitted on odd subcarriers. Since in this method only the positive amplitueds of the signal after the IFFT are preserved and the nagative amplitudes are removed or clipped, it is called asymmetrically-clipped OFDM (AC-OFDM). The disadvantage of this method is that it reduces the spectral efficiency. 132 In this chapter, a new OMC-CDMA technique for IMDD optical communica- tion systems based on signal clipping is introduced and the BER performance of the system in downlink transmission is analytically evaluated in SSMF. Consider- ing the shot-noise and thermal noise of photo-receivers, a closed form expression to predict the overall BER of the system is presented. It is shown that the proposed system has a high flexibility in serving multiple users and changing the modu- lation format while it also achieves a higher power efficiency compared to the OMC-CDMA systems without signal clipping at the price of reducing the spectral efficiency. 9.1 Model of OMC-CDMA with Asymmetrical Clipping The block diagram of OMC-CDMA system with asymmetrical clipping is illus- trated in Fig. 9.1. In the figure, an arbitrary user k is shown in the transmitter while in the receiver side, without loss of generality, only user 1 has been shown. The user k’s bit stream denoted by b k is first mapped to a QAM symbol s k .Then N copies of s k are multiplied by the CDMA spreading code of user k denoted by c k = {c k [1],c k [1],...,c k [N]}, (9.1) 133 where N is the code length. The CDMA-encoded symbol is X k = s k ·c k = {X k [1],X k [1],...,X k [N]}. (9.2) X k along with its complex conjugate (c.c.), X ∗ k , enter the IFFT block with N c inputs and outputs, where N c =4N is the number of subcarriers. It is shown in [12] that if the negative amplitudes of OFDM signals are clipped withanonlineardevicewiththetransferfunctionofanidealrectifier, thenonlinear effect of clipping distorts the even subcarriers only, and the magnitude of data on the odd subcarriers is halved as illustrated in Fig. 9.2. Therefore, X k and X ∗ k can be only transmitted on odd subcarriers in a way to maintain the conjugate symmetry in the frequency domain, so X k [m]isonsubcarrier2m − 1, X ∗ k [m]is on subcarrier N c − 2m + 1, and all the even subcarriers are nulled as shown at the input to the IFFT block in Fig. 9.1. The outputs of the IFFT block are then given by x k [n]= 1 √ N c N m=1 X k [m]exp(j 2π(2m−1)n N c )+c.c. for 0 ≤ n ≤ N c −1, (9.3) which can be considered as the samples of x k (t)= 2 √ N c N m=1 Re{X k [m]exp(j2π(2m−1)t/T s )} (9.4) 134 at t = nT c where T c = T s /N c is the chip time and T s is the symbol time. In order to preserve orthogonality of subcarriers, T s should be equal to the inverse of the frequency gap between subcarriers. So if the available lowpass bandwidth is B (Hz), the symbol time is T s = N c /2B=2N/B. After the IFFT, samples are serialized through the P/S and a CP is added to the sequence. The duration of the CP, T CP must be greater than duration of the impulse response of the channel. Therefore, the total signaling time of one symbol is T sig = T s +T CP . Figure 9.1 shows how the CP is added to the original samples. The number of the CP samples is N CP = T CP /T c . The outputs of P/S are then combined with signals from other users, so the input to the D/A converter is v[n]= U k=1 x k [n], and the signal at the output of D/A is denoted by v(t). V[m] is also defined as the FFT of v[n], so it is 0 in even subcarriers, and in odd subcarriers it is obtained as V[2m−1] = U k=1 X k [m] , 1 ≤ m ≤ N. (9.5) It should be noted that in downlink transmission all users are synchronous, so the CDMA-encoded symbols of different users can be combined after the CDMA decoder and unlike the general case in Fig. 7.4, only one OFDM transmitter would be adequate. The input-to-output transfer function of the DML is shown in Fig. 9.1. The minimum deriving electrical signal shown as v th is usually small and can be ignored [108, 12]. This model leads to an ideal rectifier with the slope of β, the quantum 135 Figure 9.1: Block Diagram of IMDD OMC-CDMA with Asymmetrical Clipping. In the transmitter only user k, and in the receiver only user 1 have been shown. 136 efficiency of the DML. In order to simplify the equations, the clipped electrical signal of the DML is defined by v c (t)= v(t)+|v(t)| 2 , (9.6) so the output power of the DML is p(t)= βv c (t). Moreover, v c [n]= v c (nT c )= U k=1 x k [n]+| U k=1 x k [n]| 2 (9.7) is defined as the discrete samples the clipped signal, and V c [m] is defined as the FFT of v c [n]. At thereceiver, thegenerated photocurrent isy(t) ≈ ρ[p(t)∗h(t)]+z(t), where h(t) is the impulse response of the channel, ρ is the responsitivity of the PD, and z(t) is the additive noise. An approximation is used in the above equation since CD in optical intensity channels is approximately linear only when the DC component of the signal is high [17]. The output of the PD is sampled every T c seconds and deserialized through the S/P. If synchronization is perfect and the CP duration is sufficient, the input to the FFT block after removing the CP is y[n]= y(nT c )= ρβ(v c [n]⊗h[n])+z[n] , 0 ≤ n ≤ N c −1, (9.8) where h[n]= h(nT c ) is the discrete-time impulse response of the channel, ⊗ is the circular convolution operator, H 0 is the the DC gain (loss) of the channel, and 137 Figure 9.2: Effects of asymmetrical clipping on the signal in time and subcarrier domains z[n]= z(nT c ) is the dicrete-time samples of the noise. The outputs of the FFT block are then given by Y[m]= ρβH[m]V c [m]+Z[m] , 0 ≤ m ≤ N c −1, (9.9) where H[m]= H(j2πm/T s ) is the complex gain of the channel at subcarrier m, H(j2πf) is the Fourier transform of h(t), and Z[m] is the FFT of z[n]. Since V c [m] is the FFT of the clipped version of v[n], it is concluded that V c [m]= V[m]/2for odd values of m. Thus, we define the odd outputs of the FFT as R[m]= Y[2m−1] = ρβ H[2m−1]V[2m−1] 2 +Z[2m−1] , 1 ≤ m ≤ N. (9.10) It should be noted that only the odd subcarriers in the first half of the FFT outputs, whichisthequarteroftheoutputs, areneededforfurtherprocessingsince 138 the even subcarriers are distorted and the other half are the complex conjugate of the first half. The equalizer is composed of N complex gains {F[m]:1 ≤ m ≤ N} corre- sponding to the N useful subcarriers. These gains are constantly updated based on channel estimation techniques to compensate for linear distortions, so the out- puts of the equalizer are F[m]R[m]. The outputs of the equalizer are sent to the CDMA decoder. For instance, user 1 correlates the received samples with its own assigned code c 1 . In the last section, it is shown that the decoded symbol of user 1 is equal to s 1 = s 1 + 1 A 1,1 U k=2 A 1,k s k +z 1 , (9.11) where A i,j = N m=1 c i [m]c ∗ j [m]H[2m − 1]F[m]. In (9.11), the first term is the desired signal, the second term is the MAI, and the third term is noise. With ORC or which is the same as zero-forcing equalizer F[m]= 1 H[2m−1] and theorthogonalityofusersispreserved[36]. Inthiscase, A 1,1 istheauto-correlation of user 1’s code and A 1,k is the cross-correlation of user 1’s code with the codeword of user k. However, according to (9.22), ORC amplifies noise in subcarriers with low gain. At the final stage, the QAM symbols are demapped into sequence of 0 and 1 bits, { b 1 }. The bit rate per user is the number of transmitted bits of one user in each signaling time, which is obtained as follows, R b = Blog 2 M 2N +N CP /2 , (9.12) 139 where M is the constellation size of QAM symbols. In many families of CDMA codes, the total number of available code-words is qual to the code length N [36]. Therefore, the global bit rate of the whole network is NR b ≈ Blog 2 M/2when N N CP . WH codes are completely orthogonal in synchronous systems, e.g., in downlink transmission. Therefore, using WH codes and assuming |c k [m]| = 1, results is A 1,1 = N,and A 1,k =0for k = 1, i.e., the MAI term becomes zero and (9.11) is simplified to s 1 = s 1 +z 1 . (9.13) Itshouldbenotedthatifchannelestimationisnotperfect, thecross-correlation terms become non-zero and increasing the number of users increases the MAI and degrades the performance of the system. In the last section of this chapter it is shown z 1 in eq. (9.11) can be modeled by a Gaussian distribution with zero mean and variance of σ 2 z = 4(2qρP r +S 2 th )BF 2 Nρ 2 β 2 |H 0 | 2 , (9.14) whereF 2 whichcanbeconsideredastheaverageenergyofequalizertapsisdefined in (9.25). 140 In order to find the impulse response of the discrete channel, H[m], which the channel’s gain at subcarrier m, ω in (7.13) is replaced by mπB/N,so H[m]= H 0 cos ⎡ ⎣ β 2 l 2 ( πBm N ) 2 ⎤ ⎦.(9.15) 9.2 BER Performance Analysis of OMC-CDMA with Clipping It is shown in the last section that the average transmitted optical power is P 0 = U/4πβσ s , so the average received optical power is P r = H 0 P 0 . Therefore, the SNR from (9.14) can be written as SNR = Nρ 2 β 2 |H 0 | 2 σ 2 s 4(2qρH 0 P 0 +S 2 th )BF 2 = Nπρ 2 |H 0 | 2 P 2 0 U(2qρH 0 P 0 +S 2 th )BF 2 = Nπρ 2 P 2 r U(2qρP r +S 2 th )BF 2 . (9.16) From (9.12), in order to operate at the same bit rate as the bit rate in chapter 7 and 8, the bandwidth must be approximately doubled. Therefore, B is replaced with 2B in previous equations, hence, SNR 2B = Nπρ 2 |H 0 | 2 P 2 0 2U(2qρH 0 P 0 +S 2 th )BF 2 . (9.17) The BER is calculated similar to chapter 7 from (7.18). 141 Typicalvaluesoftheparametersare, ρ=0.8A/W,S th =16pA/ √ Hz, α=0.2 dB/Km, and |D| = 17 ps/nm.Km ( or β 2 =21.7(ps) 2 /Km at λ c = 1550 nm). The bandwidth is B=2.5 GHz which relaxes the DML and receiver constraints in PONs [8, 31]. With these parameters F 2 ≈1and N CP = 1. Assuming rectangular 16-QAM modulation, the BER curves are plotted for different number of active users in Fig. 9.3. Even though there is no MAI, increasing the number of active users degrades the performance of the system. The reason is that with more users in the system, P 0 must be lifted up to maintain the same performance, and on the other hand, increasing P 0 increases the shot noise. InFig. 9.4, thenumberofactiveusersis64, andtheBERcurvesareplottedfor different QAM symbol constellations. It should be noted that the global bit rate is respectively 5, 10, 20, and 40-Gb/s for constellation sizes of 4, 16, 64, and 256. As it can be observed, increasing the constellation size decreases the performance of thesystemsincewithafixedsignalenergy, increasingtheconstellationsizereduces the Euclidean distance of the symbols and consequently increases the probability of error. 9.3 Conclusion In this chapter, intensity modulated OMC-CDMA with asymmetrical clipping in optical communication systems was introduced and the BER performance of the system in synchronous transmission of PONs was analytically derived in a closed form expression. It was shown that the proposed system has a high flexibility in serving multiple users and changing the modulation format while it also achieves a 142 Figure 9.3: BER graphs for different number of active users higher power efficiency compared to the OMC-CDMA systems without signal clip- ping. The effects of increasing the number of users and changing the constellation size were also investigated. 9.4 Analytical derivation of the parameters In this section, analytical derivation of the parameters and formulation of the system used in BER calculations are presented. 143 Figure 9.4: Effects of constellation size on the BER 9.4.1 Formulation of the received symbol Using (9.5) and (9.10) it can be seen that R[m]= ρβH[2m−1] U k=1 X k [m]/2+Z[2m−1]. (9.18) Therefore, the decoded signal of user 1 is obtained as follows s 1 = N m=1 F[m]R[m]c ∗ 1 [m] = N m=1 F[m] ⎛ ⎝ ρβH[2m−1] U k=1 X k [m]/2 +Z[2m−1] ⎞ ⎠ c ∗ 1 [m]. (9.19) 144 Since U k=1 X k [m]= s 1 c 1 [m]+ U k=2 s k c k [m], (9.19) can be written as s 1 = ρβ 2 s 1 N m=1 F[m]H[2m−1]c 1 [m]c ∗ 1 [m] + ρβ 2 U k=2 s k N m=1 F[m]H[2m−1]c k [m]c ∗ 1 [m] + N m=1 F[m]Z[2m−1]c ∗ 1 [m]. (9.20) Defining A i,j = N m=1 c i [m]c ∗ j [m]H[2m−1]F[m] results in the following expression for the decoded symbol of user 1, s 1 = ρβ 2 A 1,1 s 1 + ρβ 2 U k=2 s k A 1,k + N m=1 F[m]Z[2m−1]c ∗ 1 [m]. (9.21) Without changing the notation of s 1 , dividng (9.21) by ρβA 1,1 /2 results in (9.11) where z 1 = 2 A 1,1 ρβ N m=1 F[m]c ∗ 1 [m]Z[2m−1]. (9.22) 9.4.2 Noise characterization Accordingto[108], z[n]in(9.8)isconsideredwhiteandGaussianwiththevariance of σ 2 z[n] =(2qρP r + S 2 th )B. Since Z[m] is the FFT of z[n] with the normalizing factor, Z[m] is also Gaussian with the same variance. Using (9.22), it can be seen that there are N uncorrelated noise terms in the N subcarriers are added. Thus, the variance of z 1 is σ 2 z = 4 A 2 1,1 ρ 2 β 2 N m=1 |F[m]| 2 |c 1 [m]| 2 σ 2 z[n] . (9.23) 145 Since it is assumed that the code words are composed of 1 and −1, |c 1 [m]| 2 =1, and A 1,1 = N. Therfore, (9.23) can be written as σ 2 z = 4σ 2 z[n] N 2 ρ 2 β 2 N m=1 |F[m]| 2 , (9.24) which is the same as (9.14) with the following definition, F 2 = |H 0 | 2 N N m=1 |F[m]| 2 . (9.25) 9.4.3 Calculation of average transmitted optical power According to (9.3), the discrete samples of the electrical signal before the DML can be rewritten as v[n]= U k=1 x k [n] = 1 √ N c N m=1 U k=1 X k [m]exp(j 2π(2m−1)n N c )+c.c. = 2 √ N c N m=1 U k=1 Re X k [m]exp(j 2π(2m−1)n N c ) . (9.26) If the number of users is high, using CLT, samples of v[n] are Gaussian with mean μ v =E{X k } = 0 and the variance of σ 2 v = 2 N c N m=1 U k=1 σ 2 X k , (9.27) 146 where σ 2 X k is the energy of CDMA-coded symbols. Since X k [m]= s k c k [m]and |c k [m]| = 1, it is concluded that σ 2 X k = σ 2 s which is the energy of initial QAM symbols. Therefore, (9.27) is simplified to σ 2 v = 2 N c NUσ 2 s = Uσ 2 s 2 . (9.28) Since v c [n] is the clipped version of v[n], similar to (9.6), v c [n]=(v[n]+|v[n]|)/2, thus the average of v c [n]is μ vc = E{v[n]}+E{|v[n]|} 2 = 1 2 E{|v[n]|} = 1 2 ∞ −∞ |v| √ 2πσ v exp(− v 2 2σ 2 v )dv = σ v √ 2π = " U 4π σ s . (9.29) Therefore, the average transmitted optical power is obtained as follows P 0 = βμ vc = " U 4π βσ s . (9.30) 147 Chapter 10 Conclusion and Future Work In chapter 2, an introduction to CDMA systems was presented and the specific properties and limitations of incoherent OCDMA systems were studied. It was shownthatwith2-DOOCsthesystemcanaccommodatemoreactiveuserswithout reducing the bit rate or the chip time. Different methods of implementing OOC were introduced and the advantage of each one was discussed. A brief review of how to model OCDMA systems was also presented. Finally, the experimental demonstration of OOCs and 2-D OCDMA system were explained. The synchronization problem in 1-D OOK-OCDMA has been stdudied in [51] and probabilities of the required overhead time to synchronize pairs of users in transmitter and receivers sides of the system were formulated as a function of OOC parameters and number of active users. Similarly, a good research topic for the future could be modeling and studying synchronization requirements in 2-D OCDMA systems. Therearenumber ofother topicsthat areinteresting for futureresearch suchas studying 3-D OCDMA systems and studying the effects of CD on the performance of 1-D and 2-D OCDMA systems for detection and synchronization processes. In chapter 3, different M-ary OCDMA methods to increase the bit rate per user were introduced. The chapter started with PPM-OCDMA, but considering practical limitations, CPM-OCDMA was introduced as a sub-optimal method and 148 experimentally demonstrated. CPM-OCDMA resulted in a significant increase in the bit rate. Moreover, 2-PPM and DPPM-OCDMA formats were proposed and experimentally demonstrated to further increase the bit rate. It was shown the two latter techniques can increase the bit rate approximately by a factor of 2 compared to PPM or CPM-OCDMA. Modeling CPM and PPM-OCDMA have been already reported in [90]. A re- search topic in future could be modeling 2-PPM and DPPM-OCDMA systems, considering the general code assumption. New techniques might be investigated that use optical devices to achieve all optical cyclic code shifter that enables re- alizing PPM-OCDMA and consequently reducing the MAI due to overlapping. Similar to OOK-OCDMA, synchronization in M-ary OCDMA formats could be of research interest. In chapter 4, incoherent OCDMA in the physical layer of LANs was stud- ied and potential functionalities of OCDMA to provide variable QoS to different subscribers in a network were investigated. It was shown by experimental demon- strationthatvariouspulsepositionmodulationtechniquescanenablevariableQoS in OCDMA LANs. In the second part, a scheduling algorithm to reduce interfer- ence in an OCDMA network was experimentally demonstrated. It was shown the IA algorithm can significantly enhance the throughput of OCDMA based LANs. Several interesting topics for further research include developing new MAC protocols to achieve highly dynamic reconfigurable OCDMA LANs considering advantages and limitations of OCDMA systems. 149 In chapter 5, first, phase modulated optical communication systems were re- viewed and conventional detection techniques were studied. The performance of multiple-bit delay detection (MBDD) which was based on using several balanced detection segments with different delay values, using optimum and majority vote decision rules, were analytically formulated and it was shown the performance of the system with a high number of delay segments approaches the performance of a completely coherent detection scheme. There are several topics for additional research in this area, such as considering effects of CD, PMD, and fiber nonlinearity on the performance of DPSK systems with MBDD detection. Similar techniques to MBDD such as convolutional coding and the Viterbi algorithm with soft decoding can be interesting projects in future. In chapter 6 different methods of optical performance monitoring were re- viewed. It was shown that constellation diagram can be used as a time-domain monitoring technique suitable for the channels with advanced modulation formats. TheeffectsofCDandDGDonconstellationdiagramsofDQPSKsignalswerestud- ied. It was shown that synchronously generated constellation is sensitive to the sampling time, so asynchronous constellation diagrams which are obtained similar to eye diagrams are more desirable in monitoring fiber impairments. The amount of accumulated impairments was estimated using specific features in deformations of the constellation diagrams. The next step in this chapter could be experimental demonstration of the con- stellation monitoring which can be easily realized using ordinary lab equipments. Further research can be conducted on simultaneous effects of CD and PMD with 150 fibernonlinearitiesonconstellationpatterns, andmonitoringnon-idealtransmitter and receiver that can potentially change constellation diagrams. In chapter 7, 8, and 9, optical multicarrier transmission and OFDM were stud- ied and OMC-CDMA as a multiple access system with a high flexibility in serving multiple users and changing the modulation format were proposed and experi- mentally demonstrated. It is shown that with an electrical bandwidth of 2.5-GHz, OMC-CDMA is capable of supporting 256 users at a total bit rate of 15-Gb/s with almost no penalty in a 70-Km fiber-optic link. A modification to OMC-CDMA using signal clipping was also introduced. The BER performance of both systems in a downlink synchronous transmission, considering shot-noise and thermal noise of photoreceivers, was analytically evaluated in passive optical networks. OMC-CDMA is a new area and there are opportunities for further analyti- cal, modeling, and experimental research. The next project can be experimental demonstration of OMC-CDMA with asymmetric clipping. Asynchronous trans- mission with OMC-CDMA can be a great modeling project, as well. The effects of employing other CDMA codes such as m-sequence or Gold codes on the per- formance of OMC-CDMA for synchronous and asynchronous transmission cases can be studied in future. These last three chapters were based on IMDD. Hence, an interesting untouched project is studying and implementing OMC-CDMA with coherent modulation and detection. 151 Glossary 1-D OCDMA one dimensional OCDMA 2-D OCDMA two dimensional OCDMA 2-PPM double pulse position modulation A/D analog to digital ANN artificial neural network ASE amplifier spontaneous emission BER bit error rate BPF bandpass filter BPSK binary PSK CCM code cyclic modulation CD chromatic dispersion CDMA code division multiple access CLT central limit theorem CML current mode logic CP cyclic prefix CPM code position modulation CSMA carrier sensing multiple access CW continuous wave D/A digital to analog DGD differential group delay DLI delay line interferometer DML directly modulated laser DMT digital multi-tone DPPM differential pulse position modulation DPSK differential phase shift keying DSL digital subscriber loop DSSS direct sequence spread spectrum EDFA Erbium doped fiber amplifier EVM error-vector-magnitude FBG fiber-Bragg grating FDMA frequency division multiple access FFT fast Fourier transform FHSS frequency hopping spread spectrum FTTH fiber to the home GVD group velocity distortion IA interference avoidance IFFT inverse fast Fourier transform 152 ISI intersymbol interference KL Karhunen-Lo´ eve LAN local area network LMSE least mean-square error MAC media access control MAI multiple access interference MBDD multiple-bit delay detection MC-CDMA multicarrier CDMA MPPM multiple pulse position modulation MZM Mach-Zehnder modulator NRZ non-return to zero OCDMA optical code division multiple access OFDM orthogonal frequency division multiplexing OMC-CDMA optical multicarrier CDMA ONU optical network unit OOC optical orthogonal code OOK on-off keying OPM optical performance monitoring ORC orthogonality-restoring-combining OSNR optical signal-to-noise ratio P/S parallel to serial PAPR peak-to-average power ratio PMD polarization mode dispersion PMF probability mass function PON passive optical network PPG pulse pattern generator PPM pulse position modulation PSD power spectral density PSK phase shift keying QAM quadrature amplitude modulation QoS quality of service RX receiver RZ return to zero S/P serial to parallel SCM subcarrier multiplexing SMF single mode fibers SPM self phase modulation SSMF standard single mode fibers TDL tunable delay line TDMA time division multiple access THSS time hopping spread spectrum TX transmitter WDMA wavelength division multiple access WH Walsh-Hadamard XPM cross phase modulation 153 Bibliography [1] M. Alioto and G. Palumbo, “Modeling and optimized design of current mode MUX/XOR and D flip-flop,” IEEE Trans. Circuits and Syst. II: Analog and Dig. Sig. Process.,vol. 47, no. 5, pp. 452–461, May 2000. [2] F. E. Alsaadi and J. M. H. Elmirghani, “MC-CDMA Indoor Optical Wireless System,”proc. Globecom Conf., pp. 2455-2460 2007. [3] A. Amrani, G. Junyent, J. Prat, J. Comellas, I. Ramdani, V. Sales, J. Rold´ an, and A. Rafel,“Performance Monitor for All-Optical Networks Based on Homo- dyne Spectroscopy,”IEEE Photon. Tech. Lett.,vol. 12, no. 11, pp. 1564-1566, 2000. [4] T. B. Anderson, S. D. Dods, E. Wong, and P. M. Farell, “Asynchronous mea- surement of chromatic dispersion from waveform distortion, ”proc. OFC Conf., paper OWN4, Anaheim, CA, 2006. [5] V. R. Arbab, M. M. M. Rad , M. Uysal, and P. Saghari, “Performance Eval- uation of Multiple-Bit Delay Detection with Majority Vote Decision Rule in Optical DPSK Systems,” proc.Globecom conf., Houston, TX, 2011. [6] 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-WavelengthOpticalCDMASystems,”proc.ECOCConf.,paperTu4.2.5, Cannes, France, 2006. [7] V. R. Arbab, P. Saghari, M. Haghi, P. Ebrahimi, and A. E. Willner, “Increas- ing the bit rate in OCDMA systems using pulse position modulation tech- niques,”Optics Express, vol. 15, no. 19, pp. 12252-12257, 2007. [8] V. R. Arbab, W.-R. Peng, X. Wu, and A. E. Willner, “Experimental Demon- stration of Multicarrier-CDMA for Passive Optical Networks,”proc. ECOC Conf., paper. We.1.F.1, 2008. [9] V. R. Arbab, X. Wu, L. C. Christen, J.-Y. Yang, T. Dennis, P. Williams, and A. E. Willner, “Analysis of Fiber Dispersion Effects on Phase Modulated Signals Using Constellation Diagram,”proc. OFC Conf., paper J.Th.A45, San Diego, CA, 2009. 154 [10] V. R. Arbab, X. Wu, A. E. Willner, and C. L. Weber, “Optical Perfor- mance Monitoring of Data Degradation by Evaluating the Deformation of an Asynchronously Generated I/Q Data Constellation,”proc. ECOC Conf.,paper P3.23. Vienna, Austria, 2009. [11] V. R. Arbab, P. Saghari, Narender M. J., and A. E. Willner, “Variable Bit Rate Optical CDMA Networks Using Multiple Pulse Position Modulation,” proc. OFC Conf., Anaheim, CA, 2007. [12] J. Armstrong, B. J. C. Schmidt, D. Kalra, H. A. Suraweera, and A. J. Low- ery, “Performance of asymmetrically clipped optical OFDM in AWGN for an intensity modulated direct detection system,”proc. Globecom Conf., 2006. [13] J. Armstrong, “OFDM for Optical Communications,” J. Lightwave Technol., vol. 27, pp. 189-204, 2009. [14] N. S. Avlonitis and I. Tomkos, “Fast method for Q factor estimation in delay line demodulated DPSK optical communications systems,”proc. Int’l Conf. Transparent Optical Networks, pp. 1–4, Azeros, Portugal, Jun. 2009. [15] N. S. Avlonitis and E. M. Yeatman, “Performance evaluation of optical DQPSK using saddle point approximation,”J. Lightwave Technol., vol. 24, no. 3, pp. 1176–1185, Mar. 2006. [16] L. Baker-Meflah, S. Savory, B. Thomsen, J. Mitchell, and P. Bayvel, “In- Band OSNR Monitoring Using Spectral Analysis After Frequency Down- Conversion,” Photonics Tech. Letters, vol.19, no.2, pp.115–117, Jan.15, 2007. [17] D. Barros and J. M. Kahn, “Comparison of Orthogonal Frequency-Division Multiplexing and On-Off Keying in Amplified Direct-Detection Single-Mode Fiber Systems,”J. Lightwave Tech. , vol. 28, pp. 1811–1820, 2010. [18] T. M. Bazan, D. Harle, and I. Andonovic, “Beat noise limits of 2-D time spreading-wavelength hopping optical CDMA networks,”proc. Int’l Conf. Wireless and Optical Communications Networks, Dubai, UAE, 2005. [19] Z. Benyuan, L. Xiang, S. Chandrasekhar, D. W. Peckham, R. Lingle,“Ultra- Long-Haul Transmission of 1.2-Tb/s Multicarrier No-Guard-Interval CO- OFDM Superchannel Using Ultra-Large-Area Fiber,”Photonics Tech. Lett., vol. 22, pp. 1041–1135, 2010. [20] H. Blow, “Electronic dispersion compensation,” proc. OFC Conf.,paper O.M.G5, Anaheim, CA, 2007. [21] L. Christen, Y. K. Liz´ e, S. Nuccio, X. Liu, M. Nazarathy, and A. E. Willner, “DPSK error correction using multi-bit detection for enhanced sensitivity and compensation of impairments,”proc. OFC Conf., paper J.Th.A50, Anaheim, CA, 2007. 155 [22] L. Christen, S. Nuccio, Y. K. Liz´ e, A. E. Willner, and L. Paraschis, “Simul- taneous balanced DPSK demodulation of multiple 40 Gbit/s WDM channels using a single periodic FBG,”proc. CLEO Conf., paper CMJJ3, Baltimore, MD, 2007. [23] L. Christen, Y. Liz´ e, S. Nuccio, A. E. Willner, and L. Paraschis, “Variable rate, multi-format receiver design for 10 to 40 Gb/s DPSK and OOK for- mats,”Optics Express, vol. 16, pp. 3828–3833, 2008. [24] M.T.CoreandH.H.Tan, “BERforopticalheterodyneDPSKreceiversusing delaydemodulationandintegrationdetection,” IEEE Trans. Commun.,vol.50, no. 1, pp. 21–30, Jan. 2002. [25] T.DemeechaiandA.B.Sharma,“Beatnoiseinanon-coherentopticalCDMA system,”proc. Communication Systems,, vol.2, pp.899–902, 2002. [26] D. Divsalar and M. K. Simon, “Multiple symbol differential detection of MPSK,” IEEE Trans. Commun.,vol. 38, pp. 300–308, 1990. [27] S. D. Dods, T. B. Anderson, K. Clarke, M. Bakaul, and A. Kowalczyk, “Asyn- chronous Sampling for Optical Performance Monitoring,”proc. OFC Conf., pa- per O.M.M5, Anaheim, CA, 2007. [28] C. Dorrer, C. R. Doerr, I. Kang, R. Ryf, J. Leuthold, P. J. Winzer, “Measure- ment of Eye Diagrams and Constellation Diagrams of Optical Sources Using Linear Optics and Waveguide Technology,”J. Lightwave Technol., vol.23, pp. 178–186, 2005. [29] T. N. Duong, C. Milion, N. Genay, E. Grard, V. Rodrigues, J. R. Burie, M. do Nascimento, K. Bougueroua, F. van Dijk, B. Charbonnier, J. Le Masson, M. Ouzzif, P. Chanclou, A. Gharba, “Very High Bit Rate Transmission for NGPON using AMOOFDM Direct Modulation of Linear Laser,”proc. OFC conf., paper O.Tu.O3, 2010. [30] H.Fathallah, “Passiveopticalfastfrequency-hopCDMAcommunicationssys- tem,” J. of Lightwave Tech., vol. 17, no. 3, pp. 397–405, 1999. [31] R. P. Giddings, X.Q. Jin, H.H. Kee, X.L. Yang and J.M. Tang, “Real-time implementation of optical OFDM transmitters and receivers for practical end- to-end optical transmission systems ”Elec. Letters, vol. 45, pp. 800–802, 2009. [32] A. H. Gnauck and P. J. Winzer, “Optical Phase-Shift-Keyed Transmission,” J. Lightwave Technol.,vol. 23, no. 1, pp. 115–130, Jan. 2005. [33] O. Gonzalez, R. Perez-Jimenez, S. Rodriguez, J. Rabadan, and A. Ayala, “Adaptive OFDM system for communications over the indoor wireless optical channel,”IEE Proc.Optoelectron., vol. 153, pp. 139-144, 2006. [34] J. Grubor, V. Jungnickel, and K.-D. Langer, “Adaptive optical wireless OFDM system with controlled asymmetric clipping,” proc. ACSSC Conf., pp. 1896–1902, 2007. 156 [35] N. Hanik, A. Gladisch, C. Caspar, and B. Strebel,“Application of am- plitude histograms to monitor performance of optical channels,”Electronics Lett.,vol.35, no.5, pp.403-404, Mar 1999. [36] L. L. Hanzo, M. M¨ unster, B. J. Choi, and T. Keller, OFDM and MC-CDMA for Broadband Multi-User Communications, WLANs and Broadcasting,(John Wiely, England 2003). [37] K.-P. Ho,“Generation of Arbitrary Quadrature Signals Using One Dual-Drive Modulator,” J. Lightwave Technol.,vol. 23, no. 2, pp. 764–770, 2005. [38] J. A. Jargon, X. Wu, H. Y. Choi, Y. C. Chung, and A. E. Willner, “Optical performance monitoring of QPSK data channels by use of neural networks trained with parameters derived from asynchronous constellation diagrams,” Optics Express, vol. 18, pp. 4931-4938, 2010. [39] H.Ji,K.Park,J.Lee,H.Chung,E.Son,K.Han,S.Jun,andY.Chung, “Optical performance monitoring techniques based on pilot tones for WDM network applications,”Optics Letters,vol. 34, no. 7, pp. 1006–1008, April 2009. [40] S. L. Jansen, I. Morita, N. Takeda, and H. Tanaka,“20-Gb/s OFDM transmis- sion over 4160-km SSMF enabled by RF-pilot tone phase noise compensation,” proc.OFC Conf.,paper PDP15, Anaheim, CA, 2007. [41] S. L. Jansen, I. Morita, T. C. W. Schenk, N. Takeda, and H. Tanaka, “Co- herent optical 25.8-Gb/s OFDM transmission over 4160-km SSMF,”J. Lightw. Technol., vol. 26, pp. 6-15, 2008. [42] S. Johnson, “A new upper bound for error-correcting codes,” IEEE Trans. on Inf. Theory,vol. 8, pp. 203–207, 1962. [43] C. Jun-Jie and Y. Guu-Chang, “CDMA fiber-optic systems with optical hard limiters,” J. Lightwave Technol.,vol. 19, pp. 950–958, 2001. [44] W. Jyh-Horng and W. Jingshown, “Synchronous fiber-optic CDMA using hard-limiter and BCH codes,” J. Lightwave Technol.,vol. 13, pp. 1169–1176, 1995. [45] P. Kamath, J. D. Touch, and J. A. Bannister, “Algorithms for interference sensing in optical CDMA networks, ”proc. ICC Conf.,vol. 3, pp. 1720–1724, 2004. [46] P. Kamath, J. D. Touch, and J. A. Bannister, “The need for media access control in optical CDMA networks, ”proc. INFOCOM Conf., vol. 4, pp. 2208– 2219, 2004. [47] I. P. Kaminow, T. Li, and A. E. Willner, Optical Fiber Telecommunications V A: Components and Subsystems, (Academic, London, UK 2008). 157 [48] Y. K. Liz´ e, L. Christen, R. Gomma, S. Nuccio, N. Jayachandran, A. E. Will- ner, and R. Kashyap, “Multi-bit delay differential-phase-shift-keyed optical demodulation,”proc. SPIE Photonics North Conf.,vol. 6343, Sep 2006. [49] Y. K. Liz´ e, L. Christen, M. Nazarathy, S. Nuccio, X. Wu, A. E. Willner, and R. Kashyap, “Combination of optical and electronic logic gates for error correction in multipath differential demodulation,”Optics Express,vol. 15, no. 11, pp. 6831–6839, May. 2007. [50] Y. K. Liz´ e, L. Christen, M. Nazarathy, Y. Atzmon, S. Nuccio, P. Saghari, R. Gomma, J.-Y. Yang, R. Kashyap, A. E. Willner and L. Paraschis,“Tolerances and receiver sensitivity penalties of multibit delay differential-phase shift- keying demodulation,” Photonics Tech. Letters,vol. 19, no. 23, pp. 1874–1876, Dec 2007. [51] A. Keshavarzian and J. A. Salehi, “Multiple-Shift CodeAcquisition ofOptical Orthogonal Codes in Optical CDMA Systems,”IEEE Trans. on Commun.,vol. 53, no. 4, pp. 687–697, Apr 2005. [52] K. Kiasaleh, “Multiple-symbol differential detection of DQPSK and DPSK mobilecommunicationsystemsimpairedbyoscillatorphasenoise,”proc.Globe- com Conf., pp. 1215–1219, Phoenix, AZ, Nov. 1997. [53] D. C. Kilper, R. Bach, D. J. Blumenthal, D. Einstein, T. Landolsi, L. Ostar, M. Preiss, and A. E. Willner, “Optical Performance Monitoring.” J. Lightwave Technol.,vol. 22, pp. 294–304, Jan. 2004. [54] K. S. Kim, D. M. Marom, L. B. Milstein, Y. Fainman,“Hybrid pulse posi- tion modulation/ultrashort light pulse code-division multiple-access systems .I. Fundamental analysis,” IEEE Trans. on Commun.,vol. 50, no. 12, pp. 90– 6778, 2002. [55] W.C.KwongandG.-C.Yang“Designofmultilengthopticalorthogonalcodes for optical CDMA multimedia networks,” IEEE Transactions on Communica- tions, vol. 50, no. 8, pp. 1256–1265, Aug 2002. [56] A.KumarandD.Patil,“StabilityandthroughputanalysisofCDMA-ALOHA with finite number of users and code sharing,”Telecommunication Systems (a Baltzer Science Journal), vol. 8, pp. 257–275, 1997. [57] 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” in Proc. OFC Conf.,2006. [58] S. C. J. Lee, F. Breyer, S. Randel, M. Schuster, J. Zeng, F. Huiskens, H. P. A. van den Boom, A. M. J. Koonen, and N. Hanik, “24-Gb/s transmission over 730 m of multimode fiber by direct modulation of 850-nm VCSEL using discrete multi-tone modulation,” proc. OFC Conf., paper PDP6, Anaheim, CA, 2007. 158 [59] S. C. J. Lee, F. Breyer, S. Randel, O. Ziemann, H. P. A. van den Boom, and A. M. J. Koonen, “Low-cost and robust 1-Gbit/s plastic optical fiber link based on light-emitting diode technology,” proc. OFC Conf.,paper OWB3, San Diego, CA, 2008. [60] Y.-M. Lin and P.-L. Tien, “Next-Generation OFDMA-Based Passive Optical Network Architecture Supporting Radio-Over-Fiber,”J. Sel. Areas in Com- mun., vol. 29, pp. 791–799, 2010. [61] R.A.LinkeandA.H.Gnauck,“High-CapacityCoherentLightwaveSystems,” J. Lightwave Technol.,vol. 6, no. 11, pp. 1750–1769, Nov. 1988. [62] A. J. Lowery and J. Armstrong, “10 Gbit/s multimode fiber link using power- efficient orthogonal-frequency-division multiplexing,” Optics Exp., vol. 13, pp. 1000310009, 2005. [63] H.LundqvistandG.Karlsson, “Onerror-correctioncodingfor CDMAPON,” J. Lightwave Technol.,vol. 23, pp. 2342–2351, 2005. [64] M. Mayrock and H. Haunstein, “Data Rate and Distance Scaling of CO- OFDM Systems,”Proc. ECOC Conf., paper. 4.2.3, 2007. [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 us- ing a three-dimensional (time-wavelength-polarization) codeset,” J. Lightwave Technol.,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 Tech. Letters,vol. 17, pp. 1112–1114, 2005. [67] T. Miyazawa, I. Sasase, “Multirate and multiquality transmission scheme us- ing adaptive overlapping pulse-position modulator and power controller in op- ticalCDMAnetworks,”proc. Int’l Conf. on Networks,vol.1, pp.127–131, 2004. [68] S. M. R. Motaghian Nezam, Y. W. Song, A. B. Sahin, Z. Pan, and A. E. Willner, “PMD monitoring in WDM systems for NRZ data using a chromatic- dispersion regenerated clock,” proc. OFC Conf.,, paper WE5, 2002. [69] S. M. R. Motaghian Nezam, Ting Luo, J.E. McGeehan, and A.E. Willner, “EnhancingthemonitoringrangeandsensitivityinCSRZchromaticdispersion monitors using a dispersion-biased RF clock tone,” IEEE Photon. Technol. Lett.,vol. 16, no. 5, pp. 1391–1393, 2004. [70] S. M. R. Motaghian Nezam, Y.-W. Song, C. Yu, J. E. McGeehan, A. B. Sahin, and A. E. Willner, “First-Order PMD Monitoring for NRZ Data Using RF Clock Regeneration Techniques,”J. Lightwave Technol.,vol. 22, pp. 1086– 1093, 2004. 159 [71] M.NazarathyandE.Simony,“Multi-ChipDifferentialPhaseEncodedOptical Transmission,” IEEE Photonics Tech. Letters,vol. 17, no. 5, pp. 1133–1135, May 2005. [72] S. Nobilet, J.-F. Helard, and D. Mottier, “Spreading sequences for uplink and downlink MC-CDMA systems: PAPR and MAI minimization,”European Trans. Telecommun., vol.13, pp. 465–473, 2002. [73] T. Ohtsuki, K. Sato, I. Sasase, and S. Mori, “Direct-detection optical syn- chronous CDMA systems with double optical hard-limiters using modified prime sequence codes,” IEEE J. Sel. Areas in Commun.,vol. 14, pp. 1879– 1887, 1996. [74] R. Omrani, E. Elia, and P. V. Kumar,“New Constructions and Bounds for 2- D Optical Orthogonal Codes Sequences, and Their Applications,”proc. SETA Conf.,Korea, 2004. [75] R. Omrani , O. Moreno and P. V. Kumar, “Improved Johnson bounds for optical orthogonal codes with,” proc. ISIT Symp., p.259, 2005. [76] J. H. Park, “On Binary DPSK Detection,” IEEE Trans. Commun.,vol. COM- 26, no. 4, pp. 484–486, Apr 1978. [77] W.-R. Peng, X. Wu, V. R. Arbab, B. Shamee, J. Yang, L. C. Christen, K. Feng, A. E. Willner, and S. Chi, “Theoretical and Experimental Investigations of a Direct-Detected RF-Tone Assisted Optical OFDM System,”J. Lightwave Tech., vol. 27, pp. 1332–1339, 2009. [78] W.-R. Peng, X. Wu, K. M. Feng, V. R. Arbab , B. Shamee, J. Y. Yang, L. C. Christen, A. E. Willner, and S. Chi, “Spectrally efficient direct-detected OFDM transmission employing an iterative estimation and cancellation tech- nique,”Opt. Express, vol. 17, pp. 9099–9111, 2009. [79] W.-R. Peng “Analysis of Laser Phase Noise Effect in Direct-Detection Optical OFDM Transmission,”J. Lightwave Tech., vol. 28, pp. 2526–2536, 2010. [80] D. Qian, N. Cvijetic, J. Hu, and T. Wang, “108 Gb/s OFDMA-PON With Polarization Multiplexing and Direct Detection,”J. Lightwave Tech., vol. 28, pp. 484–493, 2010. [81] D. Raychaudhuri, “Traffic traces from an OC48 link,”2005, www.nlanr.net [82] D. Raychaudhuri, “Performance analysis of random access packet-switched code division multiple access systems,”IEEE Trans. on Communications, vol. 29, no. 6, pp. 895- 901, Jun 1981. [83] P. R. Prucnal, M. A. Santoro, and T. R. Fan, “Spread spectrum fiber-optic local area network using optical processing,” J. Lightwave Technology,vol. 4, pp. 547–554, 1986. 160 [84] P. Saghari, P. Kamath, V. R. Arbab, M. Haghi, A. E. Willner, J. Bannister, and J. D. Touch,“Experimental demonstration of Interference Avoidance Pro- tocol (Transmission Scheduling) in OCDMA Networks,” OSA Optics Express, vol. 15, no. 25, pp.16442-16447, Nov. 2007. [85] P. Saghari, P. Kamath, V. R. Arbab, M. Haghi, A. E. Willner, J. Bannister, and J. D. Touch, “Experimental demonstration of an Interference Avoidance based protocol for O-CDMA networks,” proc.OFC Conf., Anaheim, CA, 2006. [86] P. Saghari, M. Haghi, V. R. Arbab, S. Kumar, R. Golizadeh, A. E. Willner, P. V. Kumar, and J. D. Touch,“Experimental Demonstration of Code Position Modulation in an O-CDMA System to Increase the Number of Users,”proc. CLEO Conf.,paper CWH3, 2006. [87] P. Saghari, R. Gholizadeh, P. Kamath, R. Omrani, A. E. Willner, J. A. Ban- nister, J. D. Touch, and P. V. Kumar, “Analytical model of variable quality of service to increase the number of users in an O-CDMA network,” proc. ECOC Conf., paper Th1.4.7, 2005. [88] P. Saghari, R. Omrani, A. E. Willner, and P. V. Kumar, “Analytical Inter- ference model for 2-Dimensional (Time-Wavelength) Asynchronous O-CDMA Systems Using various Receiver Structure,” J. Lightwave Technol.,vol. 23, pp. 3260–3269, Oct 2005. [89] 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 Deci- sion Threshold for Varying Numbers of Active Users in a 2-D time-wavelength Asynchronous O-CDMA System,”proc. CLEO Conf.,2005. [90] P. Saghari, R. Omrani, V. R. Arbab, A. E. Willner, and P. V. Kumar, “In- creasing the Number of Users in an Optical CDMA System by Pulse-Position Modulation,”proc. OFC Conf.,paper JThA73, 2007. [91] J. Sakaguchi, Y. Awaji, N. Wada, A. Kanno, T. Kawanishi, T. Hayashi, T. Taru, T. Kobayashi, M. Watanabe,“109-Tb/s (7x97x172-Gb/s SDM/WDM/PDM) QPSK transmission through 16.8-km homogeneous multi- core fiber,”proc. OFC Conf.,paper PDPB6, Los Angeles, CA, 1011. [92] J. A. Salehi, “Emerging OCDMA communication systems and data net- works,”OSA Journal Optical Netw., vol. 6, pp. 1138–1178, 2007. [93] J. A. Salehi, “Code division multiple-access techniques in optical fiber net- works. I. Fundamental principles,” IEEE Trans. on Communications, vol. 37, no. 8, pp. 824–833, 1989. [94] A.Sano, H.Masuda, T.Kobayashi, M.Fujiwara, K.Horikoshi, E.Yoshida, Y. Miyamoto, M. Matsui, M. Mizoguchi, H. Yamazaki, Y. Sakamaki, and H. Ishii, “69.1-Tb/s (432 x 171-Gb/s) C- and Extended L-Band Transmission over 240 Km Using PDM-16-QAM Modulation and Digital Coherent Detection,”proc. OFC Conf.,paper PDPB7, San Diego, CA, 1010. 161 [95] S. J. Savory, “Digital signal processing options in long haul transmission,” proc.OFC Conf.,paper O.Tu.O3, San Diego, CA, 2008. [96] B. J. C. Schmidt, A. J. Lowery, and J. Armstrong, “Experimental demonstra- tions of electronic dispersion compensation for long haul transmission using direct-detection optical OFDM,” J. Lightw. Technol.,vol. 26, no. 1, pp. 196- 203, 2008. [97] H. M. H. Shalaby, “Performance analysis of optical synchronous CDMA com- munication systems with PPM signaling,” J. Lightwave Technol.,vol. 43, no.2, pp. 624–634, 1995. [98] H. M. H. Shalaby, “A Performance Analysis of Optical Overlapping PPM- CDMA Communication Systems,” J. Lightwave Technol.,vol. 17, no. 3, pp. 426–433, 1999. [99] W. Shieh and C. Athaudage, “Coherent optical orthogonal frequency division multiplexing,”Electron. Letters, vol. 42, pp. 587-588, 2006. [100] X.Yi,W.Shieh,andY.Ma,“PhaseNoiseEffectsonHighSpectralEfficiency Coherent Optical OFDM Transmission,”J. Lightwave Tech., vol. 26, pp. 1309- 1316, 2008. [101] D. Shiu and J. M. Kahn,“Differential pulse-position modulation for power- efficient optical communication,” IEEE Trans. on Commun.,vol. 47, pp. 1201- 1210, 1999. [102] B. Spinnler, “Recent advances on polarization multiplexing,” proc. IEEE Summer Topicals,, paper Tu.D.2.3, 2008. [103] S. N. Srihari, “Reliability Analysis of Majority Vote Systems,” Elsevier In- formation Sciences,vol. 26, no. 3, pp. 243–256, Apr. 1982. [104] A. Stok and E. H. Sargent, “The role of optical CDMA in access net- works,”IEEE Commu. Mag., vol. 40, no. 9, pp. 83–87, 2002. [105] H. Tagami, T. Kobayashi, Y. Miyata, K. Ouchi, K. Sawada, K. Kubo, K. Kuno, H. Yoshida, K. Shimizu, T. Mizuochi, and K. Motoshima, “A 3-bit soft- decision IC for powerful forward error correction in 10-Gb/s optical commu- nication systems,” IEEE J. Solid-State Circuits,vol. 40, no. 8, pp. 1695–1705, Aug 2006. [106] Z. Taghavi, N. Alic, and G. Papen, “Maximum-Likelihood Detection and Constrained Coding on Optical Channels,”J. Lightwave Technol., vol. 27, pp. 1469-1479, 2009. [107] F. A. Tobagi and V. B. Hunt,“Performance analysis of carrier sense multiple access with collision detection,”Computer Networks, vol. 4, pp. 245–259, 1980. 162 [108] E. Vanin, “Performance evaluation of intensity modulated optical OFDM system with digital baseband distortion,”Opt. Express, vol. 19, pp. 4280-4293, 2011. [109] J. Wang and J. M. Kahn, “Impact of Chromatic and Polarization-Mode Dispersions on DPSK Systems Using Interferometric Demodulation and Direct Detection,” J. Lightwave Technol.,vol. 22, no. 2, pp. 362–371, Feb 2004. [110] A. E. Willner, P. Saghari, and V. R. Arbab “Advanced Techniques to In- crease the Number of Users and Bit Rate in OCDMA Networks,”J. Sel. Topics Quantum Elec., vol. 13, pp. 1403-1414, 2007. [111] T. J. Xia, G. A. Wellbrock, Y.-K. Huang, E. Ip, M.-F. Huang, Y. Shao, T. Wang, Y. Aono, T. Tajima, S. Murakami, and M. Cvijetic,“Field Experiment with Mixed Line-Rate Transmission (112-Gb/s, 450-Gb/s, and 1.15-Tb/s) over 3,560 km of Installed Fiber Using Filterless Coherent Receiver and EDFAs Only,”proc. OFC Conf.,paper PDPA3, Los Angeles, CA, 2011. [112] Y. Yadin, M. Nazarathy, A. Bilenca, and M. Orenstein “Multichip Differen- tial Phase-Shift-Keyed Transmission Over (Non)Linear Optical Channels,”J. Lightwave Technol.,vol. 25, no. 6, pp. 1431–1440, Jun 2007. [113] J.-Y. Yang, L. Zhang, Y. Yue, V. R. Arbab, A. Agrawal, L. Paraschis, and A. E. Willner, “Optical signal-to-noise ratio monitoring of an 80 Gbits/s polarization-multiplexed return-to-zero differential phase-shift keying chan- nel,”Optics Letters,vol. 34, no. 7, pp. 1006–1008, April 2009. [114] R. You and J. M. Kahn,“Average Power Reduction Techniques for Multiple- Subcarrier Intensity-Modulated Optical Signals,”IEEE Trans. on Commun., vol. 49, pp. 2164–2171, 2001. [115] C. Yu, Y. Wang, T. Luo, Z. Pan, S.M.R. Motaghian Nezam, A.B. Sahin, and A.E.Willner, “Opticalperformancemonitoringtechniquesbasedonpilottones for WDM network applications,” proc.ECOC Conf., , vol. 2, paper TU4.2.3, pp. 290–291, 2003. [116] Q. Yu, Z. Pan, L.-S. Yan, and A. E. Willner, “Chromatic Dispersion Mon- itoring TechniqueUsing Sideband Optical Filtering andClock Phase-Shift De- tection,”J. Lightwave Technol.,vol. 20, no. 12, pp. 2267–2271, Dec 2002. [117] S. Zahedi and J. A. Salehi, “Analytical comparison of various fiber-optic CDMA receiver structures,” J. Lightwave Technol.,vol. 18, pp. 1718-1727, 2000. [118] S. Zahedi, J. A. Salehi, M. Nasiri-Kenari,“M-ary infrared CDMA for indoors wirelesscommunications,”proc. Int’lPersonal, IndoorandMobileRadioCom- mun. Conf.,vol. 2, pp. E.6-E.10, 2001. [119] L. Zhang, J.-Y. Yang, M. Song, Y. Li, B. Zhang, R. G. Beausoleil, and A. E. Willner, “Microring-based modulation and demodulation of DPSK signal,” OSA Optics Express,vol. 15, no. 18, pp. 11564–11569, Aug. 2007. 163

Abstract (if available)

Abstract Optical code division multiple access (OCDMA) systems have recently become a topic of interest for their potential application in access points and optical local area networks (LAN). In this thesis, we review OCDMA systems and their limitations, as well as various experimental techniques to increase the number of users and/or bit rate in a system or a network. These techniques include incorporating M-ary modulation formats, such as pulse position modulation (PPM), code position modulation (CPM), double-PPM (2-PPM), differential-PPM (DPPM), and multiple-PPM (MPPM). We also discuss and experimentally demonstrate variable quality of service (QoS) in OCDMA networks. Congestion collapse problems in OCDMA networks are reviewed, and we experimentally demonstrate the interference avoidance (IA) algorithm to overcome it. ❧ Advanced data modulation formats are playing an ever-increasing role within the optical communications community. For example, phase-shift-keying (PSK) provides better receiver sensitivity and tolerance to nonlinear effects, and quadrature-PSK (QPS) and quadrature-amplitude-modulation (QAM) provide increased spectral efficiency and tolerance to chromatic dispersion (CD).We investigate multiple-bit delay detection (MBDD) as an advanced technique for incoherent detection of optical differential-PSK (DPSK) signals in fiber-optic systems. We show that with a large number of delay segments and employing the optimum decision rule or the majority vote decision rule, the power efficiency asymptotically approaches the power efficiency of the coherent detection. Monitoring constellation diagrams of phase-modulated signals is also presented as a new tool to visualize different effects of fiber impairments. ❧ A new research topic in optical communications community is optical frequency division multiplexing (OFDM). We describe a multiple-access technique based on optical OFDM called optical multicarrier CDMA (OMC-CDMA) that has the advantages of both CDMA and OFDM. These advantages include high flexibility in serving multiple users and changing the transmitted baseband symbols without modification of the hardware, tolerance to dispersion, and simplified equalization. Analytical and experimental evaluations of OMC-CDMA are presented as well. ❧ We expect that the modulation, detection, and monitoring techniques presented in this thesis may potentially play key roles in future optical communication systems and networks.

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Asset Metadata

Creator Arbab, Vahidreza (author)

Core Title Advanced modulation, detection, and monitoring techniques for optical communication systems

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Electrical Engineering

Publication Date 05/07/2013

Defense Date 05/07/2012

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

Tag dpsk,multicarrier cdma,OAI-PMH Harvest,ocdma,OFDM,optical cdma,optical communications,optical performance monitoring

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Sawchuk, Alexander A. (Sandy) (committee chair), Khoshnevis, Behrokh (committee member), Saghari, Poorya (committee member), Steier, William Henry (committee member)

Creator Email v.arbab@gmail.com,varbab@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c3-33907

Unique identifier UC11289502

Identifier usctheses-c3-33907 (legacy record id)

Legacy Identifier etd-ArbabVahid-797.pdf

Dmrecord 33907

Document Type Dissertation

Rights Arbab, Vahidreza

Type texts

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

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA