Digital Modulation Techniques

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Table Of Contents

Contents

Preface xvii
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 11
1.5 Overview of Digital Modulation Schemes and Comparison 12
References 17
Selected Bibliography 17
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

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

N-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 mB1C Codes 76
2.6.5 DmB1M Codes 78
2.6.6 PFmB(m+1)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-ary FSK 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

Chapter 4 Phase Shift Keying 135
4.1 Binary PSK 135
4.2 Differential BPSK 141
4.3

M-ary PSK 148
4.4 PSD of MPSK 159
4.5 Differential MPSK 160
4.6 Quadrature PSK 166
4.7 Differential QPSK 173
4.8 Offset QPSK 180
4.9 p/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(j / Hi ) 203
References 205
Selected Bibliography 205
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 PSD of CPFSK 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

6.8 Summary 358
References 359
Chapter 7 Multi-

h 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-h Binary
CPFSK 394
7.5.2 Joint Demodulation and Carrier Synchronization of
Multi-h CPFSK 400
7.5.3 Joint Carrier Phase Tracking and Data Detection of
Multi-h CPFSK 404
7.5.4 Joint Demodulation, Carrier Synchronization, and
Symbol Synchronization of M-ary Multi-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-T Realization of Multi-h Phase Codes 413
7.6.3 Correlatively Encoded Multi-h Signaling Technique 413
7.6.4 Nonlinear Multi-h 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

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

11.3 Digital Modulation in Frequency Selective Channels 560
11.4

p/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
11.9Equalization 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

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

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 802.11a 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 Channel s 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

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.1 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.1 Detection of Discrete Signals 933
B.1.1 Binary Hypothesis Test 933
B.1.2 Decision Criteria 934
B.1.3

M Hypotheses 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

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


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[hexium]

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