Impact of Nonlinearities on Fiber Optic Communications (eBook)

Preface 6
Contents 10
Contributors 12
Chapter 1:Coherent, Self-Coherent, and DifferentialDetection Systems 14
1.1 Introduction 14
1.2 Recent Advances in Fiberoptic Communication Systems 15
1.2.1 40-Gb s-1 Transmission 15
1.2.2 100-Gb s-1 Transmission 17
1.2.3 200-Gb s-1 Transmission and Beyond 18
1.2.4 From Research Demonstration to Commercial Reality 19
1.3 Self-Coherent and Differential Detection-Based Systems 20
1.3.1 Upgrading 10-Gb s-1-Based DWDM System to 40-Gb s-1 DBPSK and DQPSK 20
1.3.1.1 SE Consideration 21
1.3.1.2 Transmission Distance Consideration 22
1.3.1.3 CD and PMD Consideration 22
1.3.1.4 Nonlinear Tolerance Consideration 22
1.3.1.5 Overall Comparison 28
1.3.2 Self-Coherent Detection 28
1.3.2.1 Principle of Digital Self-Coherent Detection 30
1.3.2.2 Receiver Sensitivity Enhancement via Data-Aided MSPE 31
1.3.2.3 Unified Detection of m-ary DPSK 32
1.3.2.4 More Advanced DSCD Signal Processing 33
1.4 DCD-Based Systems 34
1.4.1 Digital Coherent Detection 34
1.4.2 State-of-the-Art DCD Demonstrations 38
1.4.2.1 100-Gb s-1 DCD-Based Field Trials 38
1.4.2.2 High-Capacity Transmission 39
1.4.2.3 High SE Transmission 39
1.4.2.4 448-Gb s-1 RGI-CO-OFDM Transmission 41
1.4.2.5 1-Tb s-1 NGI-CO-OFDM Transmission 44
1.5 Concluding Remarks 47
References 49
Chapter 2:Optical OFDM Basics 56
2.1 Introduction 56
2.2 Historical Perspective of OFDM 57
2.3 OFDM Fundamentals 58
2.3.1 Orthogonality Between OFDM Subcarriers and Subbands 59
2.3.2 Discrete Fourier Transform Implementation of OFDM 63
2.3.3 Cyclic Prefix for OFDM 64
2.3.4 Spectral Efficiency for Optical OFDM 66
2.3.5 Peak-to-Average Power Ratio for OFDM 68
2.3.6 Flavors of Optical OFDM 71
2.4 Coherent Optical OFDM Systems 72
2.4.1 Principle for CO-OFDM 73
2.4.2 OFDM Digital Signal Processing 75
2.4.2.1 Window Synchronization 75
2.4.2.2 Frequency Offset Synchronization 76
2.4.2.3 Channel Estimation 77
2.4.2.4 Phase Estimation 78
2.4.3 Polarization-Diversity Multiplexed OFDM 78
2.4.4 Real-Time Coherent Optical OFDM 79
2.4.4.1 Real-Time Window Synchronization 80
2.4.4.2 Real-Time Frequency Offset Synchronization 81
2.4.4.3 Real-Time Channel Estimation 83
2.4.4.4 Real-Time Phase Estimation 84
2.4.5 Experimental Demonstrations for CO-OFDM, from 100Gb s-1 to 1Tb s-1, from Offline to Real-Time 84
2.5 Promising Research Direction and Future Expectations 92
2.6 Conclusion 95
References 95
Chapter 3:Nonlinear Impairments in Coherent OpticalOFDM Systems and Their Mitigation 99
3.1 Introduction 99
3.2 Rigorous OFDM Transmission Model 102
3.2.1 Interpolation and Digital Frequency Up-Shifting 103
3.2.2 OFDM Analog-Like Tx Model 106
3.3 Fiber Channel Model: Third-Order Volterra Description of the FWM/XPM Impairment 107
3.3.1 Complex Representation 107
3.3.2 Fiber Channel Model 107
3.3.3 Linear + SPM/XPM Propagation of the Subcarriers 109
3.3.4 VTF for the FWM Among the Subcarriers 111
3.4 OFDM Receiver: Linear and Nonlinear Modeling 116
3.4.1 Rx Processing 116
3.4.2 Aliasing of NL Components in a Baud-Rate OFDM Receiver 118
3.4.3 Oversampling the NL Output 119
3.5 Derivation of the FWM VTF: OPI Model of Third-Order NL+CD Propagation 120
3.5.1 OPI Approach 120
3.5.2 Quasilinear Propagation Transfer Function 121
3.5.3 Virtual Backpropagated Fields 122
3.5.4 OPI Derivation of the VTF of a General Inhomogeneous Fiber Link 123
3.5.5 Homogeneous Fiber Link 126
3.5.6 Single Homogeneous Span 127
3.5.7 ``Regular' Multispan Link 128
3.5.8 Irregular Inhomogenenous Links 130
3.5.9 Dispersion-Unmanaged ``Regular' Spans Revisited 132
3.5.10 Phased-Array Effect Tends to Reduce FWM Build-up 133
3.5.11 The Effect of Dispersion-Compensation Fiber: Dispersion-Managed Links 135
3.5.12 Intermod Statistics: Power Propagation Over a ``Regular' Spans Link 136
3.5.13 The FWM Power for Dispersion-Managed Links 138
3.6 OFDM Link Performance 139
3.6.1 Angular Variance 140
3.6.2 Q-Factor, Symbol Error Rate, BER 142
3.7 PA Effect for Dispersion-Unmanaged Regular Multispan Links 143
3.7.1 Compounding Multiple PAs 144
3.7.2 The NLT is set by Bandwidth2xLengthxGVD 144
3.7.3 A Simple Q-Factor Performance Lower Bound for Dispersion Unmanaged Links 145
3.8 Overview of NLC Methods 148
3.9 Baud-Rate Sampled Version of the B-NLPR NLC 150
3.10 Volterra DF-Based NLC: Principle of Operation 152
3.11 Volterra DF NLC: Complete Block Diagram, Overall Characteristics and Performance 156
3.12 Baud-Rate Sampling Principles for the Volterra DF NLC 158
3.13 Low Error Propagation for the Volterra DF NLC 160
3.14 The Role of Higher-Order (5th, 7th, …) Nonlinearities 162
3.15 ``XPM Undo and Derotate' Decoupling XPM and FWM Mitigation in the Volterra DF NLC 163
3.16 Volterra DF NLC Performance Simulations (Q-Factor and BER) 165
3.17 Computational Complexity vs. NL Tolerance Performance Trade-Offs 166
3.18 Discussion: Volterra DF NLC vs. BP – Suggested Roadmap for Future NLC 168
3.19 Conclusions 170
3.20 Appendix A: Derivation of the Analog-Like OFDM Transmitter Model 172
3.21 Appendix B: Volterra NL Systems Formalism Extending to Third-Order 174
3.22 Appendix C: Sampling and Nonlinearity Effects in the OFDM Receiver 178
3.22.1 Nyquist Sampling the Linear Component Under Samples the NL Component 178
3.22.2 AA Filtering 180
References 185
Chapter 4:Systems with Higher-Order Modulation 188
4.1 Introduction 188
4.2 Higher-Order Modulation Formats 189
4.3 Signal Generation 192
4.3.1 External Optical Modulators 192
4.3.2 Higher-Order PSK/DPSK and QAM Transmitters 194
4.3.2.1 Transmitters Based on Multi-Level Driving Signals 194
4.3.2.2 Transmitters Based on Binary Driving Signals 196
4.4 Signal Detection 199
4.4.1 Direct Detection Receivers 199
4.4.2 Homodyne Receivers 201
4.4.2.1 Receivers with Homodyne Synchronous Detection 202
4.4.2.2 Receivers with Homodyne Differential Detection 205
4.4.2.3 2×4 90 Hybrid Optical Front-end 206
4.5 Trends in System Performance 208
4.6 Long-Haul Transmission 211
4.6.1 System Experiments with Optical Inline CD Compensation 212
4.6.2 System Experiments with Electrical CD Compensation 216
4.6.3 System Simulations with Nonlinear Phase Shift Compensation 220
4.7 Issues of Future Research 224
References 226
Chapter 5:Power-Efficient Modulation Schemes 229
5.1 Introduction 229
5.1.1 Optical Coherent Modulation: Background 230
5.2 Definitions and System Model 232
5.2.1 The Four-Dimensional Optical Signal 232
5.2.2 Digital Transmission Over a Noisy Channel 233
5.2.3 Symbol Error Rates and Sphere Packing 235
5.3 N-Dimensional Sphere Packing Results 237
5.3.1 Sphere Packings: Background 237
5.3.2 Results: Sensitivity vs. Spectral Efficiency 239
5.3.3 Specific Formats 241
5.3.3.1 Two-Dimensional Constellations, N=2 242
5.3.3.2 Four-Dimensional Constellations, N=4 245
5.4 Symbol- and Bit-Error Rates 251
5.5 Sensitivities and Nonlinearities 254
5.5.1 Fundamental Sensitivity Limits 255
5.5.2 Nonlinear Effects 256
5.5.2.1 Power Efficiency 257
5.5.2.2 Nonlinear Robustness 258
5.5.2.3 XPM-Induced Crosstalk 258
5.5.2.4 Relevance of Maximum Energy Optimization 258
5.6 Summary and Outlook 260
References 261
Chapter 6:A Unified Theory of Intrachannel Nonlinearityin Pseudolinear Transmission 263
6.1 Introduction 263
6.2 Basic Formalism 264
6.3 First-Order Perturbation Theory 265
6.4 Sequence of Gaussian Pulses 268
6.5 Coherent and Direct Detection 269
6.6 Effect of the Symmetry of the Dispersion Profile 273
6.7 Pseudo-Random Sequence in DPSK and DQPSK 274
6.7.1 FWM Terms Afwm and Bfwm, and Correlation Terms Acorr,fwm and Bcorr,fwm 277
6.7.2 Cross-Phase Modulation Term Axpm and Correlation Term Bcorr,xpm 277
6.8 Pseudo-Random Sequence in IMDD 278
6.9 Continuous Approximation 279
6.10 Numerical Examples 281
6.11 Total Receiver Noise 286
6.12 Discussion 289
6.13 Information Rate for DPSK and DQPSK Transmission 290
6.14 Timing Jitter Between Two Pulses 292
6.15 Timing Jitter in a Pseudo-Random Sequence 295
6.16 Conclusions 300
References 300
Chapter 7:Analysis of Nonlinear Phase Noisein Single-Carrier and OFDM Systems 302
7.1 Introduction 302
7.2 Linear Phase Noise 304
7.3 Gordon–Mollenauer Phase Noise 307
7.4 Phase Noise in Dispersive Nonlinear Fiberoptic Single Carrier System 311
7.4.1 Results and Discussion 316
7.5 Phase Noise in OFDM Systems 320
7.5.1 SPM and XPM Induced Nonlinear Phase Noise 321
7.5.2 FWM-Induced Nonlinear Phase Noise 323
7.5.3 Total Phase Noise 326
7.5.4 Results and Discussions 326
7.6 Conclusions 331
References 332
Chapter 8:Cross-Phase Modulation-Induced NonlinearPhase Noise for Quadriphase-Shift-KeyingSignals 334
8.1 Introduction 334
8.2 Gaussian-Distributed Phase Error 335
8.2.1 DQPSK Signals 336
8.2.2 QPSK Signals 336
8.3 XPM-Induced Nonlinear Phase Noise 338
8.3.1 Pump-Probe Model 338
8.3.2 XPM from Phase-Modulated Channels 340
8.3.3 XPM from On-Off Keying Channels 341
8.4 XPM-Induced Nonlinear Phase Noise to DQPSK Signals 341
8.5 XPM-Induced Nonlinear Phase Noise for QPSK Signals 343
8.5.1 Feedforward Carrier Recovery 343
8.5.2 Performance of QPSK Signals 345
8.6 Conclusion 348
References 349
Chapter 9:Nonlinear Polarization Scatteringin Polarization-Division-Multiplexed CoherentCommunication Systems 351
9.1 Introduction 351
9.2 Analytical Theory 352
9.3 Nonlinear Polarization Scattering in PDM-QPSK Coherent Transmission Systems 356
9.3.1 System Model 357
9.3.2 42.8-Gb/s PDM-QPSK Systems 359
9.3.3 112-Gb/s PDM-QPSK Systems 362
9.3.4 Hybrid OOK and PDM-QPSK Systems 365
9.4 Nonlinear Polarization Scattering Mitigation Techniques 366
9.4.1 Time Interleaved RZ-PDM Modulation Format 367
9.4.1.1 Coherent ILRZ-PDM-QPSK Systems 368
9.4.1.2 Direct-Detection ILRZ-PDM Systems 369
9.4.2 PGD Dispersion Compensators 373
9.4.3 Adding PMD into the System 375
9.5 Conclusion 376
References 377
Chapter 10:Multicanonical Monte Carlofor Simulation of Optical Links 380
10.1 Introduction 380
10.2 Monte Carlo Techniques 381
10.2.1 Conventional Monte Carlo Estimation 382
10.2.2 Importance Sampling 383
10.2.3 Uniform Weight Importance Sampling 385
10.3 Multicanonical Monte Carlo 387
10.3.1 MMC Adaptation 387
10.3.2 Smoothed MMC 389
10.3.3 Example: Chi-Square Distribution 392
10.3.4 Drawing Warped Samples: Markov Chain Monte Carlo 394
10.4 Implementation Issues 396
10.4.1 Minimizing Rejections 396
10.4.1.1 Discretization of the Output Space 396
10.4.1.2 Exploration of the Input Space 396
10.4.2 Input Vector Correlations 396
10.4.3 Choice of Number of Cycles vs. Samples per Cycle 397
10.4.4 Dealing with System Memory 398
10.5 Examples 399
10.5.1 Example: Bit Patterning in SOAs 399
10.5.1.1 SOA Memory 399
10.5.1.2 SOA Modeling 399
10.5.1.3 MMC Platform 402
10.5.1.4 Results 403
10.5.2 Example: Spectral Efficiency in SS-WDM 404
10.5.2.1 Use of Forward Error Correction 404
10.5.2.2 Modeling SOA Noise Suppression 405
10.5.2.3 Multi-Channel MMC Platform 406
10.5.2.4 Parallelization of MMC 407
10.5.2.5 Simulation Results 409
10.5.3 Example: Nonlinear Interaction Between Signal and Noise in Very-Long-Haul Dispersion-Managed Amplified Optical Links 410
10.5.3.1 Received ASE Statistics 411
10.5.3.2 Transmission Test 413
10.5.4 Further Examples in the Literature 415
10.6 Conclusions 416
10.7 Appendix: MCMC Fundamentals 417
References 419
Chapter 11:Optical Regenerators for NovelModulation Schemes 421
11.1 Introduction 421
11.2 Regeneration of Binary Phase-Shift Keying Signals 423
11.2.1 DPSK Signal Regeneration Using Amplitude Regenerators 423
11.2.1.1 DPSK Regenerator Using a Straight-Line Phase Modulator 423
11.2.1.2 DPSK Regenerator Using MZI Phase Modulator 424
11.2.1.3 Experiment Using Fiber-Based Amplitude Regenerator 427
11.2.1.4 Logic Alteration by the Regenerator and Its Compensation 432
11.2.2 Noise Reduction of BPSK Signals Based on Noise Averaging 433
11.2.3 Phase-Preserving Amplitude Regeneration 435
11.2.3.1 Nonlinear Phase Noise and Its Suppression 435
11.2.3.2 Phase-Preserving Amplitude Regenerator 438
11.2.3.3 Transmission Experiment Using a Phase-Preserving Amplitude Limiter 440
11.2.4 BPSK Signal Regeneration Using Phase-Sensitive Amplifiers 442
11.2.4.1 BPSK Regenerator Using Nonlinear Sagnac Interferometer 442
11.2.4.2 BPSK Regenerator Using Two-Pump Degenerate FWM in Fiber 444
11.3 Regeneration of Quadrature Phase-Shift Keying Signals 446
11.3.1 DQPSK Signal Regeneration Using Differential Demodulation 447
11.3.2 QPSK Signal Regeneration Using Coherent Demodulation 451
11.4 Discussion and Summary 452
References 453
Chapter 12:Codes on Graphs, Coded Modulationand Compensation of Nonlinear Impairmentsby Turbo Equalization 456
12.1 Introduction 456
12.2 Channel Coding Preliminaries 458
12.2.1 Linear Block Codes 464
12.2.1.1 Generator Matrix for Linear Block Code 465
12.2.1.2 Parity-Check Matrix 466
12.2.1.3 Coding Gain 467
12.3 Codes on Graphs 469
12.3.1 Quasi-cyclic (QC) Binary LDPC Codes 471
12.3.1.1 Design of Large Girth Quasi-cyclic LDPC Codes 471
12.3.1.2 Decoding of LDPC Codes 472
12.3.1.3 BER Performance of LDPC Codes 475
12.4 Coded Modulation 476
12.4.1 Multilevel Coding and Bit-Interleaved Coded Modulation 477
12.4.2 Polarization-Multiplexed Coded-OFDM 480
12.4.3 Multidimensional Coded Modulation 482
12.5 LDPC-Coded Turbo Equalization 487
12.5.1 Optimum Detection 487
12.5.2 Multilevel Turbo Equalizer Description 488
12.5.3 Performance of LDPC-Coded Turbo Equalizer 492
12.5.4 Multilevel Turbo Equalizer with Digital Backpropagation 497
12.6 Information Capacity of Fiber-Optics Systems 499
12.6.1 Channel Capacity of Channels with Memory 500
12.6.2 Calculation of Information Capacity of Multilevel Modulation Schemes by Forward Recursion of BCJR Algorithm 502
12.6.3 Information Capacity of Coherent detection Systems 503
References 507
Chapter 13:Channel Capacity of Non-Linear TransmissionSystems 511
13.1 Introduction 511
13.2 Linear Capacity Limits 514
13.2.1 The Shannon Limit 514
13.2.2 Constellation Analysis 515
13.3 Non-linear Limits 524
13.3.1 Theoretical Information Capacity Limits 524
13.3.2 Comparison of Reported Results with Theoretical Limit 531
13.4 Increasing the Information Capacity Limit 532
13.4.1 Optical Regeneration 532
13.4.2 Fibre Design 534
13.4.3 Channel Bandwidth 535
13.4.4 Amplifier Noise Figure 536
13.5 Conclusions 538
References 538
Index 543