Digital Modulation Techniques

Second Edition

Fuqin Xiong

ARTECH HOUSE

BOSTON|LONDON artechhouse co"1 Contents

Preface XVu Chapter 1 Introduction 1 1.1 Digital Communication Systems 1 1.2 Communication Channels 4 1.2.1 Additive White Gaussian Noise Channel 4 1.2.2 Bandlimited Channel 6 1.2.3 Fading Channel 7 1.3 Basic Modulation Methods 7 1.4 Criteria of Choosing Modulation Schemes 9 1.4.1 Power Efficiency 10 1.4.2 Bandwidth Efficiency 10 1.4.3 System Complexity 1 ] 1.5 Overview of Digital Modulation Schemes and Comparison 12 References 17 Selected Bibliography ] 8

Chapter 2 Baseband Modulation (Line Codes) 19 2.1 Differential Coding 20 2.2 Description of Line Codes 24 2.2.1 Nonreturn-to-Zero Codes 26 2.2.2 Return-to-Zero Codes 27 2.2.3 Pseudoternary Codes (Including AMI) 28 2.2.4 Biphase Codes (Including Manchester) 29 2.2.5 Delay Modulation (Miller Code) 29 2.3 Power Spectral Density of Line Codes 30 2.3.1 PSD of Nonreturn-to-Zero Codes 32 2.3.2 PSD of Return-to-Zero Codes 36 2.3.3 PSD of Pseudoternary Codes 37 2.3.4 PSD of Biphase Codes 39 vi Digital Modulation Techniques

2.3.5 PSD of Delay Modulation 42 2.4 Bit Error Rate of Line Codes 45 2.4.1 BER of Binary Codes 46 2.4.2 BER of Pseudoternary Codes 51 2.4.3 BER of Biphase Codes 56 2.4.4 BER of Delay Modulation 59 2.5 Substitution Line Codes 59 2.5.1 Binary TV-Zero Substitution Codes 60 2.5.2 High Density Bipolar n Codes 62 2.6 Block Line Codes 64 2.6.1 Coded Mark Inversion Codes 65 2.6.2 Differential Mode Inversion Codes 71 2.6.3 mBnB Codes 73 2.6.4 mBIC Codes 76 2.6.5 DmBIM Codes 78 2.6.6 PFmB(m+l)B Codes 79 2.6.7 kBnT Codes 80 2.7 Pulse Time Modulation 83 2.7.1 Formats of Pulse Time Modulation 84 2.7.2 Spectra of Pulse Time Modulation 88 2.7.3 Performance of Pulse Time Modulation 91 2.8 Summary 93 References 95 Selected Bibliography 98

Chapter 3 Frequency Shift Keying 99 3.1 Binary FSK 99 3.1.1 Binary FSK Signal and Modulator 99 3.1.2 Power Spectral Density 104 3.2 Coherent Demodulation and Error Performance 107 3.3 Noncoherent Demodulation and Error Performance 110 3.4 M-aryFSK 114 3.4.1 MFSK Signal and Power Spectral Density 114 3.4.2 Modulator, Demodulator, and Error Performance 116 3.5 Demodulation Using Discriminator 127 3.6 Synchronization 133 3.7 Summary 133 References 134 Selected Bibliography 134 Contents vii

Chapter 4 Phase Shift Keying 135 4.1 Binary PSK 135 4.2 Differential BPSK 141 4.3 Af-aryPSK 148 4.4 PSDofMPSK 159 4.5 Differential MPSK 160 4.6 Quadrature PSK 166 4.7 Differential QPSK 173 4.8 Offset QPSK 180 4.9 7t/4-QPSK 183 4.10 Synchronization 191 4.10.1 Carrier Recovery 192 4.10.2 Clock Recovery 196 4.10.3 Effects of Phase and Timing Error 197 4.11 Summary 201 Appendix 4A Derivation of p(

Chapter 5 Minimum Shift Keying and MSK-Type Modulations 207 5.1 Description of MSK 208 5.1.1 MSK Viewed as a Sinusoidal Weighted OQPSK 208 5.1.2 MSK Viewed as a Special Case of CPFSK 213 5.2 Power Spectrum and Bandwidth 215 5.2.1 Power Spectral Density of MSK 215 5.2.2 Bandwidth of MSK and Comparison with PSK 216 5.3 Modulator 219 5.4 Demodulator 222 5.5 Synchronization 226 5.6 Error Probability 228 5.7 Serial MSK 231 5.7.1 SMSK Description 231 5.7.2 SMSK Modulator 233 5.7.3 SMSK Demodulator 235 5.7.4 Conversion and Matched Filter Implementation 239 5.7.5 Synchronization of SMSK 243 5.8 MSK-Type Modulation Schemes 243 5.9 Sinusoidal Frequency Shift Keying 248 5.10 Simon's Class of Symbol-Shaping Pulses 252 5.11 Rabzel and Pasupathy's Symbol-Shaping Pulses 259 viii Digital Modulation Techniques

5.12 Bazin's Class of Symbol-Shaping Pulses 262 5.13 MSK-Type Signal's Spectral Main Lobe 266 5.14 Summary 268 References 269 Selected Bibliography 270

Chapter 6 Continuous Phase Modulation 271 6.1 Description of CPM 272 6.1.1 Various Modulation Pulse Shapes 273 6.1.2 Phase and State of the CPM Signal 277 6.1.3 Phase Tree and Trellis and State Trellis 281 6.2 Power Spectral Density 284 6.2.1 Steps for Calculating PSDs for General CPM Signals 286 6.2.2 Effects of Pulse Shape, Modulation Index, and A Priori Distribution 288 6.2.3 PSDofCPFSK 289 6.3 MLSD for CPM and Error Probability 291 6.3.1 Error Probability and Euclidean Distance 293 6.3.2 Comparison of Minimum Distances 297 6.4 Modulator 298 6.4.1 Quadrature Modulator 298 6.4.2 Serial Modulator 304 6.4.3 All-Digital Modulator 307 6.5 Demodulator 309 6.5.1 Optimum ML Coherent Demodulator 309 6.5.2 Optimum ML Noncoherent Demodulator 313 6.5.3 Viterbi Demodulator 323 6.5.4 Reduced-Complexity Viterbi Demodulator 329 6.5.5 Reduction of the Number of Filters for LREC CPM 332 6.5.6 ML Block Detection of Noncoherent CPM 337 6.5.7 MSK-Type Demodulator 338 6.5.8 Differential and Discriminator Demodulator 342 6.5.9 Other Types of Demodulators 345 6.6 Synchronization 349 6.6.1 MSK-Type Synchronizer 349 6.6.2 Squaring Loop and Fourth-Power Loop Synchronizers 352 6.6.3 Other Types of Synchronizers 353 6.7 Gaussian Minimum Shift Keying (GMSK) 354 Contents

6.8 Summary 358 References 359

Chapter 7 Multi-/? Continuous Phase Modulation 363 7.1 MHPM Signal, Phase Tree, and Trellis 363 7.2 Power Spectral Density 373 7.3 Distance Properties and Error Probability 378 7.4 Modulator 394 7.5 Demodulator and Synchronization 394 7.5.1 A Simple ML Demodulator for Multi-/i Binary CPFSK 394 7.5.2 Joint Demodulation and Carrier Synchronization of Multi-/i CPFSK 400 7.5.3 Joint Carrier Phase Tracking and Data Detection of Multi-A CPFSK 404 7.5.4 Joint Demodulation, Carrier Synchronization, and Symbol Synchronization of M-ary M\x\n-h CPFSK 405 7.5.5 Synchronization of MHPM 410 7.6 Improved MHPM Schemes 411 7.6.1 MHPM with Asymmetrical Modulation Indexes 412 7.6.2 Multi-rRealization of Multi-/; Phase Codes 413 7.6.3 Correlatively Encoded Multi-A Signaling Technique 413 7.6.4 Nonlinear Multi-A CPFSK 415 7.7 Summary 415 Appendix 7A Orthonormal Base Functions 416 References 420 Selected Bibliography 422

Chapter 8 Amplitude Shift Keying 423 8.1 Pulse Amplitude Modulation 424 8.1.1 Power Spectral Density 424 8.1.2 Optimum Detection and Error Probability 425 8.2 Bipolar Symmetrical MASK 427 8.2.1 Power Spectral Density 427 8.2.2 Modulator and Demodulator 429 8.2.3 Error Probability 433 8.3 Unipolar M-ary ASK 434 8.3.1 Power Spectral Density 436 8.3.2 Modulator and Demodulator 436 8.3.3 Error Probability of Coherent Demodulation 437 8.3.4 Error Probability of Noncoherent Demodulation 439 Digital Modulation Techniques

8.4 Binary ASK (On-Off Keying) 442 8.5 Comparing MASK with MPSK 444 8.6 Summary 445 References 446 Selected Bibliography 446

Chapter 9 Quadrature Amplitude Modulation 447 9.1 QAM Signal Description 447 9.2 QAM Constellations 452 9.2.1 Square QAM 454 9.3 Power Spectral Density 457 9.4 Modulator 459 9.5 Demodulator 461 9.6 Error Probability 462 9.7 Synchronization 467 9.8 Differential Coding in QAM 473 9.9 Summary 480 Appendix 9A Proof of (9.39) 481 References 482 Selected Bibliography 483

Chapter 10 Nonconstant-Envelope Bandwidth-Efficient Modulations 485 10.1 Two-Symbol-Period Schemes and Optimum Demodulator 486 10.2 Quasi-Bandlimited Modulation 491 10.3 QORC, SQORC, and QOSRC 497 10.4 IJF-OQPSK and TSI-OQPSK 504 10.5 Superposed-QAM 516 10.6 Quadrature Quadrature PSK 524 10.7 Summary 541 References 541

Chapter 11 Modulations in Fading Channels, Equalization, and Diversity 543 11.1 Fading Channel Characteristics 544 11.1.1 Channel Characteristics 544 11.1.2 Channel Classification 547 11.1.3 Fading Envelope Distributions 550 11.2 Digital Modulation in Slow, Flat Fading Channels 552 11.2.1 Rayleigh Fading Channel 554 11.2.2 Rician Fading Channel 558 Contents

11.3 Digital Modulation in Frequency Selective Channels 560 11.4 Tt/4-DQPSK in Fading Channels 571 11.5 MHPM in Fading Channels 575 11.6 QAM in Fading Channels 580 11.6.1 Square QAM 581 11.6.2 Star QAM 582 11.7 Overview of Remedial Measures Against Channel Impairment 587 11.8 Channel Estimation and Correction 589 11.8.1 Pilot Tone Methods 589 11.8.2 Pilot Symbol Assisted Modulation (PSAM) 589 11.8.3 Decision Feedback Channel Estimation (DFCE) 597 11.9 Equalization 601 11.9.1 Linear Equalizers (LE) 602 11.9.2 Decision-Feedback Equalizers (DFE) 607 11.10 Diversity Reception 612 11.10.1 Diversity Techniques 612 11.10.2 Combining Techniques 613 11.11 MIMO Wireless Link 616 11.11.1 Capacity of MIMO Channel 618 11.11.2 MIMO Signaling: Space-Time Coding and Spatial Multiplexing 621 11.12 Summary 627 Appendix 11A Derivation of (11.80) 628 References 631 Selected Bibliography 634

Chapter 12 Orthogonal Frequency Division Multiplexing 635 12.1 OFDM Signal and Spectrum 637 12.1.1 Baseband OFDM Signal 638 12.1.2 Bandpass OFDM Signal 641 12.2 OFDM Modulator and Demodulator 646 12.2.1 Analog OFDM Modem 649 12.2.2 DFT-Based Digital OFDM Modem 651 12.3 Real-Output DFT 658 12.4 FFT Algorithms 661 12.5 Partial FFT Algorithms 666 12.5.1 The Pruned Partial FFT 668 12.5.2 Transform Decomposition 668 xii Digital Modulation Techniques

12.6 Cyclic Extension 672 12.6.1 Continuous-Time OFDM 672 12.6.2 Discrete-Time OFDM 674 12.7 Spectrum Shaping 676 12.8 Summary 681 Appendix 12A Derivation of (12.23), (12.24), and (12.25) 682 Appendix 12B Derivation of DFT-Based OFDM Modem 684 Appendix 12C Recovering Data from Real OFDM Signal 687 Appendix 12D Method of Generating Real OFDM Signal 689 References 690 Selected Bibliography 692

Chapter 13 Peak-to-Average Power Ratio Reduction 693 13.1 Maximum Peak-to-Average Power Ratio 694 13.2 Envelope Power and PAPR Distribution 696 13.3 Introduction to PAPR Reduction Techniques 702 13.4 Clipping and Clipping Noise Mitigation 703 13.4.1 Decision-Aided Reconstruction 703 13.4.2 Oversampling and Frequency-Domain Filtering 705 13.4.3 Iterative Estimation and Canceling 713 13.5 Amplitude Alteration Other Than Clipping 716 13.5.1 Companding 716 13-5.2 Complementary Clipping Transform 717 13.6 Pre-IFFT Data Alteration 718 13.6.1 Selective Mapping . 719 13.6.2 Repeated Random Phasor Transform 720 13.6.3 Selective Scrambling 721 13.6.4 Partial Transmit Sequences 723 13.6.5 Dummy Sequence Insertion 726 13.7 Coding 729 13.7.1 Parity-Check Coding 729 13.7.2 Rudin-Shapiro Coding 731 13.7.3 Golay Complementary Sequences and Reed-Muller Codes 733 13.8 Summary 740 References 741 Selected Bibliography 743

Chapter 14 Synchronization for OFDM 745 14.1 Effect of Carrier Frequency Offset and Phase Noise 745 Contents

14.2 Effect of Timing Errors 750 14.3 Architecture of Synchronization System 754 14.4 Synchronization Methods Overview 754 14.5 Synchronization Using Cyclic Extension 756 14.6 Synchronization Using Pilot Symbols 763 14.7 The Schmidl-Cox Synchronizer 764 14.7.1 Frame/Symbol Timing Estimator 765 14.7.2 Performance of Timing Estimator 767 14.7.3 Frequency Offset Estimator 773 14.7.4 Performance of Frequency Offset Estimator 774 14.8 The Coulson Synchronizer 775 14.9 The Minn-Zeng-Bhargava Synchronizer 780 14.10 The Shi-Serpedin Synchronizer 783 14.11 More Training Symbol Patterns 791 14.12 Synchronization for the IEEE 802.1 la Standard 793 14.13 Summary 796 References 797 Selected Bibliography 799

Chapter 15 OFDM in Multipath Fading Channels 801 15.1 Performance of OFDM in Fading Channels 801 15.1.1 Frequency Flat Slow Fading Channel 803 15.1.2 Frequency Selective Slow Fading Channel 804 15.1.3 Frequency Flat Fast Fading Channel 813 15.1.4 Frequency Selective Fast Fading Channel 818 15.1.5 Summary of Expressions of Fading Factors and ICI Terms 823 15.2 Channel Estimation and Equalization 823 15.2.1 Pilot-Assisted Channel Estimation 825 15.2.2 Slow Fading Channel Estimation and Equalization 827 15.2.3 Reduction of Complexity of the LMMSE Estimator 836 15.2.4 Estimator for Fast Fading Channels 843 15.2.5 Decision-Directed Channel Estimation 848 15.3 Other Remedial Measures Against Fading 849 15.3.1 Differential Detection 849 15.3.2 Diversity Reception 850 15.3.3 Coded OFDM (COFDM) 851 15.3.4 MIMO-OFDM 852 15.4 Summary 853 xiv Digital Modulation Techniques

Appendix 15A Derivation of (15.39) and (15.47) 856 Appendix 15B Proof of (15.58), (15.65), (15.66), and (15.67) 860 Appendix 15C Proof of (15.105) 862 References 862 Selected Bibliography 866

Chapter 16 Wavelet OFDM and MASK-OFDM 869 16.1 Wavelet Fundamentals 869 16.2 Multiscale Wavelet Modulation (MSM) 876 16.3 Fractal Modulation 880 16.4 Wavelet Packet Modulation (WPM) 882 16.5 Wavelet PAM 884 16.6 M-Band Wavelet Modulation (MWM) 891 16.7 Overlapped Discrete Wavelet Multitone (DWMT) Modulation 892 16.8 DCT-Based OFDM: MASK-OFDM 897 16.9 Summary 903 Appendix 16A Power Spectrum of MSM 906 References 909 Selected Bibliography 910

Appendix A Power Spectral Densities of Signals 911 A.I Bandpass Signals and Spectra 911 A.2 Bandpass Stationary Random Process and PSD 913 A.3 Power Spectral Densities of Digital Signals 916 A.3.1 Case 1: Data Symbols Are Uncorrelated 918 A.3.2 Case 2: Data Symbols Are Correlated 920 A.4 Power Spectral Densities of Digital Bandpass Signals 921 A.5 Power Spectral Densities of CPM Signals 924 References 930

Appendix B Detection of Signals 933 B.I Detection of Discrete Signals 933 B.I.I Binary Hypothesis Test 933 B.1.2 Decision Criteria 934 B.I.3 MHypotheses 938 B.2 Detection of Continuous Signals with Known Phases 940 B.2.1 Detection of Binary Signals 940 B.2.2 Decision of M-ary Signals 952 B.3 Detection of Continuous Signals with Unknown Phases 959 B.3.1 Receiver Structure 959 Contents

B.3.2 Receiver Error Performance 965 References 969

Appendix C Mathematical Tables 971 C. 1 Trigonometry Identities 971 C.2 Fourier Transform Pairs 972 C.3 Fourier Transform Theorems 973 C.4 Discrete Fourier Transform Theorems 974 C.5 Q-Function and Error Functions 975 C.6 Relations Between Q-Function and Error Functions 977 C.7 Approximation of Q-Function 978 References 979

Acronyms 981 About the Author 987 Index 989