List of Contributors xv
Preface xvii
1 Introduction 1
Xiang Zhou and Chongjin Xie
1.1 High-Capacity Fiber Transmission Technology Evolution, 1
1.2 Fundamentals of Coherent Transmission Technology, 4
1.2.1 Concept of Coherent Detection, 4
1.2.2 Digital Signal Processing, 5
1.2.3 Key Devices, 7
1.3 Outline of this Book, 8
References, 9
2 Multidimensional Optimized Optical Modulation Formats 13
Magnus Karlsson and Erik Agrell
2.1 Introduction, 13
2.2 Fundamentals of Digital Modulation, 15
2.2.1 System Models, 15
2.2.2 Channel Models, 17
2.2.3 Constellations and Their Performance Metrics, 18
2.3 Modulation Formats and Their Ideal Performance, 20
2.3.1 Format Optimizations and Comparisons, 21
2.3.2 Optimized Formats in Nonlinear Channels, 30
2.4 Combinations of Coding and Modulation, 31
2.4.1 Soft-Decision Decoding, 31
2.4.2 Hard-Decision Decoding, 37
2.4.3 Iterative Decoding, 39
2.5 Experimental Work, 40
2.5.1 Transmitter Realizations and Transmission Experiments, 40
2.5.2 Receiver Realizations and Digital Signal Processing, 45
2.5.3 Formats Overview, 49
2.5.4 Symbol Detection, 50
2.5.5 Realizing Dimensions, 51
2.6 Summary and Conclusions, 54
References, 56
3 Advances in Detection and Error Correction for Coherent Optical Communications: Regular, Irregular, and Spatially Coupled LDPC Code Designs 65
Laurent Schmalen, Stephan ten Brink, and Andreas Leven
3.1 Introduction, 65
3.2 Differential Coding for Optical Communications, 67
3.2.1 Higher-Order Modulation Formats, 67
3.2.2 The Phase-Slip Channel Model, 69
3.2.3 Differential Coding and Decoding, 71
3.2.4 Maximum a Posteriori Differential Decoding, 78
3.2.5 Achievable Rates of the Differentially Coded Phase-Slip
Channel, 81
3.3 LDPC-Coded Differential Modulation, 83
3.3.1 Low-Density Parity-Check (LDPC) Codes, 85
3.3.2 Code Design for Iterative Differential Decoding, 91
3.3.3 Higher-Order Modulation Formats with V < Q, 100
3.4 Coded Differential Modulation with Spatially Coupled LDPC Codes, 101
3.4.1 Protograph-Based Spatially Coupled LDPC Codes, 102
3.4.2 Spatially Coupled LDPC Codes with Iterative Demodulation, 105
3.4.3 Windowed Differential Decoding of SC-LDPC Codes, 108
3.4.4 Design of Protograph-Based SC-LDPC Codes for
Differential-Coded Modulation, 108
3.5 Conclusions, 112
Appendix: LDPC-Coded Differential Modulation—Decoding Algorithms, 112
Differential Decoding, 114
LDPC Decoding, 115
References, 117
4 Spectrally Efficient Multiplexing: Nyquist-WDM 123
Gabriella Bosco
4.1 Introduction, 123
4.2 Nyquist Signaling Schemes, 125
4.2.1 Ideal Nyquist-WDM (Δf = Rs), 126
4.2.2 Quasi-Nyquist-WDM (Δf > Rs), 128
4.2.3 Super-Nyquist-WDM (Δf < Rs), 130
4.3 Detection of a Nyquist-WDM Signal, 134
4.4 Practical Nyquist-WDM Transmitter Implementations, 137
4.4.1 Optical Nyquist-WDM, 139
4.4.2 Digital Nyquist-WDM, 141
4.5 Nyquist-WDM Transmission, 146
4.5.1 Optical Nyquist-WDM Transmission Experiments, 148
4.5.2 Digital Nyquist-WDM Transmission Experiments, 148
4.6 Conclusions, 149
References, 150
5 Spectrally Efficient Multiplexing – OFDM 157
An Li, Di Che, Qian Hu, Xi Chen, and William Shieh 5.1 OFDM Basics, 158
5.2 Coherent Optical OFDM (CO-OFDM), 161
5.2.1 Principle of CO-OFDM, 161
5.3 Direct-Detection Optical OFDM (DDO-OFDM), 169
5.3.1 Linearly Mapped DDO-OFDM, 169
5.3.2 Nonlinearly Mapped DDO-OFDM (NLM-DDO-OFDM), 173
5.4 Self-Coherent Optical OFDM, 174
5.4.1 Single-Ended Photodetector-Based SCOH, 175
5.4.2 Balanced Receiver-Based SCOH, 177
5.4.3 Stokes Vector Direct Detection, 177
5.5 Discrete Fourier Transform Spread OFDM System (DFT-S OFDM), 180
5.5.1 Principle of DFT-S OFDM, 180
5.5.2 Unique-Word-Assisted DFT-S OFDM (UW-DFT-S OFDM), 182
5.6 OFDM-Based Superchannel Transmissions, 183
5.6.1 No-Guard-Interval CO-OFDM (NGI-CO-OFDM) Superchannel, 184
5.6.2 Reduced-Guard-Interval CO-OFDM (RGI-CO-OFDM) Superchannel, 186
5.6.3 DFT-S OFDM Superchannel, 188
5.7 Summary, 193
References, 194
6 Polarization and Nonlinear Impairments in Fiber Communication Systems 201
Chongjin Xie
6.1 Introduction, 201
6.2 Polarization of Light, 202
6.3 PMD and PDL in Optical Communication Systems, 206
6.3.1 PMD, 206
6.3.2 PDL, 208
6.4 Modeling of Nonlinear Effects in Optical Fibers, 209
6.5 Coherent Optical Communication Systems and Signal Equalization, 211
6.5.1 Coherent Optical Communication Systems, 211
6.5.2 Signal Equalization, 213
6.6 PMD and PDL Impairments in Coherent Systems, 215
6.6.1 PMD Impairment, 216
6.6.2 PDL Impairment, 222
6.7 Nonlinear Impairments in Coherent Systems, 228
6.7.1 System Model, 229
6.7.2 Homogeneous PDM-QPSK System, 230
6.7.3 Hybrid PDM-QPSK and 10-Gb/s OOK System, 233
6.7.4 Homogeneous PDM-16QAM System, 234
6.8 Summary, 240
References, 241
7 Analytical Modeling of the Impact of Fiber Non-Linear Propagation on Coherent Systems and Networks 247
Pierluigi Poggiolini, Yanchao Jiang, Andrea Carena, and Fabrizio Forghieri
7.1 Why are Analytical Models Important?, 247
7.1.1 What Do Professionals Need?, 247
7.2 Background, 248
7.2.1 Modeling Approximations, 249
7.3 Introducing the GN–EGN Model Class, 260
7.3.1 Getting to the GN Model, 260
7.3.2 Towards the EGN Model, 265
7.4 Model Selection Guide, 269
7.4.1 From Model to System Performance, 269
7.4.2 Point-to-Point Links, 270
7.4.3 The Complete EGN Model, 272
7.4.4 Case Study: Determining the Optimum System Symbol Rate, 286
7.4.5 NLI Modeling for Dynamically Reconfigurable Networks, 289
7.5 Conclusion, 294
Acknowledgements, 295
Appendix, 295
A.1 The White-Noise Approximation, 295
A.1 BER Formulas for the Most Common QAM Systems, 295
A.2 The Link Function ?, 296
A.3 The EGN Model Formulas for the X2-X4 and M1-M3 Islands, 297
A.4 Outline of GN–EGN Model Derivation, 299
A.5 List of Acronyms, 303
References, 305
8 Digital Equalization in Coherent Optical Transmission Systems 311
Seb Savory
8.1 Introduction, 311
8.2 Primer on the Mathematics of Least Squares FIR Filters, 312
8.2.1 Finite Impulse Response Filters, 313
8.2.2 Differentiation with Respect to a Complex Vector, 314
8.2.3 Least Squares Tap Weights, 314
8.2.4 Application to Stochastic Gradient Algorithms, 316
8.2.5 Application to Wiener Filter, 317
8.2.6 Other Filtering Techniques and Design Methodologies, 318
8.3 Equalization of Chromatic Dispersion, 318
8.3.1 Nature of Chromatic Dispersion, 318
8.3.2 Modeling of Chromatic Dispersion in an Optical Fiber, 318
8.3.3 Truncated Impulse Response, 319
8.3.4 Band-Limited Impulse Response, 320
8.3.5 Least Squares FIR Filter Design, 321
8.3.6 Example Performance of the Chromatic Dispersion Compensating Filter, 321
8.4 Equalization of Polarization-Mode Dispersion, 323
8.4.1 Modeling of PMD, 324
8.4.2 Obtaining the Inverse Jones Matrix of the Channel, 325
8.4.3 Constant Modulus Update Algorithm, 325
8.4.4 Decision-Directed Equalizer Update Algorithm, 326
8.4.5 Radially Directed Equalizer Update Algorithm, 327
8.4.6 Parallel Realization of the FIR Filter, 327
8.4.7 Generalized 4 × 4 Equalizer for Mitigation of Frequency or Polarization-Dependent Loss and Receiver Skew, 328
8.4.8 Example Application to Fast Blind Equalization of PMD, 328
8.5 Concluding Remarks and Future Research Directions, 329
Acknowledgments, 330
References, 330
9 Nonlinear Compensation for Digital Coherent Transmission 333
Guifang Li
9.1 Introduction, 333
9.2 Digital Backward Propagation (DBP), 334
9.2.1 How DBP Works, 334
9.2.2 Experimental Demonstration of DBP, 335
9.2.3 Computational Complexity of DBP, 336
9.3 Reducing DBP Complexity for Dispersion-Unmanaged WDM Transmission, 339
9.4 DBP for Dispersion-Managed WDM Transmission, 342
9.5 DBP for Polarization-Multiplexed Transmission, 349
9.6 Future Research, 350
References, 351
10 Timing Synchronization in Coherent Optical Transmission Systems 355
Han Sun and Kuang-Tsan Wu
10.1 Introduction, 355
10.2 Overall System Environment, 357
10.3 Jitter Penalty and Jitter Sources in a Coherent System, 359
10.3.1 VCO Jitter, 359
10.3.2 Detector Jitter Definitions and Method of Numerical Evaluation, 361
10.3.3 Laser FM Noise- and Dispersion-Induced Jitter, 363
10.3.4 Coherent System Tolerance to Untracked Jitter, 366
10.4 Digital Phase Detectors, 368
10.4.1 Frequency-Domain Phase Detector, 369
10.4.2 Equivalence to the Squaring Phase Detector, 371
10.4.3 Equivalence to Godard’s Maximum Sampled Power Criterion, 373
10.4.4 Equivalence to Gardner’s Phase Detector, 374
10.4.5 Second Class of Phase Detectors, 377
10.4.6 Jitter Performance of the Phase Detectors, 378
10.4.7 Phase Detectors for Nyquist Signals, 380
10.5 The Chromatic Dispersion Problem, 383
10.6 The Polarization-Mode Dispersion Problem, 386
10.7 Timing Synchronization for Coherent Optical OFDM, 390
10.8 Future Research, 391
References, 392
11 Carrier Recovery in Coherent Optical Communication Systems 395
Xiang Zhou
11.1 Introduction, 395
11.2 Optimal Carrier Recovery, 397
11.2.1 MAP-Based Frequency and Phase Estimator, 397
11.2.2 Cramer–Rao Lower Bound, 398
11.3 Hardware-Efficient Phase Recovery Algorithms, 399
11.3.1 Decision-Directed Phase-Locked Loop (PLL), 399
11.3.2 Mth-Power-Based Feedforward Algorithms, 401
11.3.3 Blind Phase Search (BPS) Feedforward Algorithms, 405
11.3.4 Multistage Carrier Phase Recovery Algorithms, 408
11.4 Hardware-Efficient Frequency Recovery Algorithms, 416
11.4.1 Coarse Auto-Frequency Control (ACF), 416
11.4.2 Mth-Power-Based Fine FO Estimation Algorithms, 418
11.4.3 Blind Frequency Search (BFS)-Based Fine FO Estimation Algorithm, 421
11.4.4 Training-Initiated Fine FO Estimation Algorithm, 423
11.5 Equalizer-Phase Noise Interaction and its Mitigation, 424
11.6 Carrier Recovery in Coherent OFDM Systems, 429
11.7 Conclusions and Future Research Directions, 430
References, 431
12 Real-Time Implementation of High-Speed Digital Coherent Transceivers 435
Timo Pfau
12.1 Algorithm Constraints, 435
12.1.1 Power Constraint and Hardware Optimization, 436
12.1.2 Parallel Processing Constraint, 438
12.1.3 Feedback Latency Constraint, 440
12.2 Hardware Implementation of Digital Coherent Receivers, 442
References, 446
13 Photonic Integration 447
Po Dong and Sethumadhavan Chandrasekhar
13.1 Introduction, 447
13.2 Overview of Photonic Integration Technologies, 449
13.3 Transmitters, 451
13.3.1 Dual-Polarization Transmitter Circuits, 451
13.3.2 High-Speed Modulators, 452
13.3.3 PLC Hybrid I/Q Modulator, 455
13.3.4 InP Monolithic I/Q Modulator, 455
13.3.5 Silicon Monolithic I/Q Modulator, 457
13.4 Receivers, 459
13.4.1 Polarization Diversity Receiver Circuits, 459
13.4.2 PLC Hybrid Receivers, 461
13.4.3 InP Monolithic Receivers, 462
13.4.4 Silicon Monolithic Receivers, 462
13.4.5 Coherent Receiver with 120? Optical Hybrids, 465
13.5 Conclusions, 467
Acknowledgments, 467
References, 467
14 Optical Performance Monitoring for Fiber-Optic Communication Networks 473
Faisal N. Khan, Zhenhua Dong, Chao Lu, and Alan Pak Tao Lau
14.1 Introduction, 473
14.1.1 OPM and Their Roles in Optical Networks, 474
14.1.2 Network Functionalities Enabled by OPM, 475
14.1.3 Network Parameters Requiring OPM, 477
14.1.4 Desirable Features of OPM Techniques, 480
14.2 OPM Techniques For Direct Detection Systems, 482
14.2.1 OPM Requirements for Direct Detection Optical Networks, 482
14.2.2 Overview of OPM Techniques for Existing Direct Detection Systems, 483
14.2.3 Electronic DSP-Based Multi-Impairment Monitoring Techniques for Direct Detection Systems, 485
14.2.4 Bit Rate and Modulation Format Identification Techniques for Direct Detection Systems, 488
14.2.5 Commercially Available OPM Devices for Direct Detection Systems, 489
14.2.6 Applications of OPM in Deployed Fiber-Optic Networks, 489
14.3 OPM For Coherent Detection Systems, 490
14.3.1 Non-Data-Aided OSNR Monitoring for Digital Coherent Receivers, 491
14.3.2 Data-Aided (Pilot Symbols Based) OSNR Monitoring for Digital Coherent Receivers, 494
14.3.3 OPM at the Intermediate Network Nodes Using Low-Cost Structures, 495
14.3.4 OSNR Monitoring in the Presence of Fiber Nonlinearity, 496
14.4 Integrating OPM Functionalities in Networking, 499
14.5 Conclusions and Outlook, 499
Acknowledgments, 500
References, 500
15 Rate-Adaptable Optical Transmission and Elastic Optical Networks 507
Patricia Layec, Annalisa Morea, Yvan Pointurier, and Jean-Christophe Antona
15.1 Introduction, 507
15.1.1 History of Elastic Optical Networks, 509
15.2 Key Building Blocks, 511
15.2.1 Optical Cross-Connect, 512
15.2.2 Elastic Transponder, 513
15.2.3 Elastic Aggregation, 515
15.2.4 Performance Prediction, 516
15.2.5 Resource Allocation Tools, 520
15.2.6 Control Plane for Flexible Optical Networks, 524
15.3 Practical Considerations for Elastic WDM Transmission, 527
15.3.1 Flexible Transponder Architecture, 527
15.3.2 Example of a Real-Time Energy-Proportional Prototype, 529
15.4 Opportunities for Elastic Technologies in Core Networks, 530
15.4.1 More Cost-Efficient Networks, 531
15.4.2 More Energy Efficient Network, 532
15.4.3 Filtering Issues and Superchannel Solution, 532
15.5 Long Term Opportunities, 534
15.5.1 Burst Mode Elasticity, 534
15.5.2 Elastic Passive Optical Networks, 536
15.5.3 Metro and Datacenter Networks, 537
15.6 Conclusions, 539
Acknowledgments, 539
References, 539
16 Space-Division Multiplexing and MIMO Processing 547
Roland Ryf and Nicolas K. Fontaine
16.1 Space-Division Multiplexing in Optical Fibers, 547
16.2 Optical Fibers for SDM Transmission, 548
16.3 Optical Transmission in SDM Fibers with Low Crosstalk, 551
16.3.1 Digital Signal Processing Techniques for SDM Fibers with Low Crosstalk, 552
16.4 MIMO-Based Optical Transmission in SDM Fibers, 553
16.5 Impulse Response in SDM Fibers with Mode Coupling, 558
16.5.1 Multimode Fibers with no Mode Coupling, 561
16.5.2 Multimode Fibers with Weak Coupling, 561
16.5.3 Multimode Fibers with Strong Mode Coupling, 565
16.5.4 Multimode Fibers: Scaling to Large Number of Modes, 566
16.6 MIMO-Based SDM Transmission Results, 566
16.6.1 Digital Signal Processing for MIMO Transmission, 567
16.7 Optical Components for SDM Transmission, 568
16.7.1 Characterization of SDM Systems and Components, 570
16.7.2 Swept Wavelength Interferometry for Fibers with Multiple Spatial Paths, 571
16.7.3 Spatial Multiplexers, 576
16.7.4 Photonic Lanterns, 578
16.7.5 Spatial Diversity for SDM Components and Component sharing, 582
16.7.6 Wavelength-Selective Switches for SDM, 583
16.7.7 SDM Fiber Amplifiers, 590
16.8 Conclusion, 593
Acknowledgments, 593
References, 594
Index 609
