1 Introduction 1
1-1 Elements of a Digital Communication System 1
1-2 Communication Channels and Their Characteristics 3
1-3 Mathematical Models for Communication Channels 11
1-4 A Historical Perspective in the Development of Digital Communications 13
1-5 Overview of the Book 16
1-6 Bibliographical Notes and References 16
2 Probability and Stochastic Processes 17
2-1 Probability 17
2-1-1 Random Variables, Probability Distributions, and Probability Densities 22
2-1-2 Functions of Random Variables 28
2-1-3 Statistical Averages of Random Variables 33
2-1-4 Some Useful Probability Distributions 37
2-1-5 Upper bounds on the Tail Probability 53
2-1-6 Sums of Random Variables and the Central Limit Theorem 58
2-2 Stochastic Processes 62
2-2-1 Statistical Averages 64
2-2-2 Power Density Spectrum 67
2-2-3 Response of a Linear Time-Invariant System to a Random Input Signal 68
2-2-4 Sampling Theorem for Band-Limited Stochastic Processes 72
2-2-5 Discrete-Time Stochastic Signals and Systems 74
2-2-6 Cyclostationary Processes 75
2-3 Bibliographical Notes and References 77
Problems 77
3 Source Coding 82
3-1 Mathematical Models for Information 82
3-2 A Logarithmic Measure of Information 84
3-2-1 Average Mutual Information and Entropy 87
3-2-2 Information Measures for Continuous Random Variables 91
3-3 Coding for Discrete Sources 93
3-3-1 Coding for Discrete Memoryless Sources 94
3-3-2 Discrete Stationary Sources 103
3-3-3 The Lemple-Ziv Algorithm 106
3-4-1 Rate-Distortion Function 108
3-4 Coding for Analog Sources-Optimum Quantization 108
3-4-2 Scalar Quantization 113
3-4-3 Vector Quantization 118
3-5 Coding Techniques for Analog Sources 125
3-5-1 Temporal Waveform Coding 125
3-5-2 Spectral Waveform Coding 136
3-5-3 Model-Based Source Coding 138
Problems 144
3-6 Bibliographical Notes and References 144
4 Characterization of Communication Signals and Systems 152
4-1 Representation of Bandpass Signals and Systems 152
4-1-1 Representation of Bandpass Signals 153
4-1-2 Representation of Linear Bandpass Systems 157
4-1-3 Response of a Bandpass System to a Bandpass Signal 157
4-1-4 Representation of Bandpass Stationary Stochastic Processes 159
4-2-1 Vector Space Concepts 163
4-2 Signal Space Representation 163
4-2-2 Signal Space Concepts 165
4-2-3 Orthogonal Expansions of Signals 165
4-3 Representation of Digitally Modulated Signals 173
4-3-1 Memoryless Modulation Methods 174
4-3-2 Linear Modulation with Memory 186
4-3-3 Nonlinear Modulation Methods with Memory 190
4-4 Spectral Characteristics of Digitally Modulated Signals 203
4-4-1 Power Spectra of Linearly Modulated Signals 204
4-4-2 Power Spectra of CPFSK and CPM Signals 209
4-4-3 Power Spectra of Modulated Signals with Memory 220
4-5 Bibliographical Notes and References 223
Problems 224
5 Optimum Receivers for the Additive White Gaussian Noise Channel 233
5-1 Optimum Receiver for Signals Corrupted by AWGN 233
5-1-1 Correlation Demodulator 234
5-1-2 Matched-Filter Demodulator 238
5-1-3 The Optimum Detector 244
5-1-4 The Maximum-Likelihood Sequence Detector 249
5-1-5 A Symbol-by-Symbol MAP Detector for Signals with Memory 254
5-2 Performance of the Optimum Receiver for Memoryless Modulation 257
5-2-1 Probability of Error for Binary Modulation 257
5-2-2 Probability of Error for M-ary Orthogonal Signals 260
5-2-3 Probability of Error for M-ary Biorthogonal Signals 264
5-2-4 Probability of Error for Simplex Signals 266
5-2-5 Probability of Error for M-ary Binary-Coded Signals 266
5-2-6 Probability of Error for M-ary PAM 267
5-2-7 Probability of Error for M-ary PSK 269
5-2-8 Differential PSK(DPSK)and its performance 274
5-2-9 Probability of Error for QAM 278
5-2-10 Comparison of Digital Modulation Methods 282
5-3 Optimum Receiver for CPM Signals 284
5-3-1 Optimum Demodulation and Detection of CPM 285
5-3-2 Performance of CPM Signals 290
5-3-3 Symbol-by Symbol Detection of CPM Signals 296
5-4 Optimum Receiver for Signals with Random Phase in AWGN Channel 301
5-4-1 Optimum Receiver for Binary Signals 302
5-4-2 Optimum Receiver for M-ary Orthogonal Signals 308
5-4-3 Probability of Error for Envelope Detection of M-ary Orthogonal Signals 308
5-4-4 Probability of Error for Envelope Detection of Correlated Binary Signals 312
5-5 Regenerative Repeaters and Link Budget Analysis 313
5-5-1 Regenerative Repeaters 314
5-5-2 Communication Link Budget Analysis 316
5-6 Bibliographical Notes and References 319
Problems 320
6 Carrier and Symbol Synchronization 333
6-1 Signal Parameter Estimation 333
6-1-1 The Likelihood Function 335
6-1-2 Carrier Recovery and Symbol Synchronization in Signal Demodulation 336
6-2 Carrier Phase Estimation 337
6-2-1 Maximum-Likelihood Carrier Phase Estimation 339
6-2-2 The Phase-locked Loop 341
6-2-3 Effect of Additive Noise on the Phase Estimate 343
6-2-4 Decision-Directed Loops 347
6-2-5 Non-Decision-Directed Loops 350
6-3 Symbol Timing Estimation 358
6-3-1 Maximum-Likelihod Timing Estimation 359
6-3-1 Non-Decision-Directed Timing Estimation 361
6-4 Joint Estimation of Carrier Phase and Symbol Timing 365
6-5 Performance Characteristics of ML Estimators 367
6-6 Bibliographical Notes and References 370
Problems 371
7 Channel Capacity and Coding 374
7-1 Channel Models and Channel Capacity 375
7-1-1 Channel Models 375
7-1-2 Channel Capacity 380
7-1-3 Achieving Channel Capacity with Orthogonal Signals 387
7-1-4 Channel Reliability Functions 389
7-2 Random Selection of Codes 390
7-2-1 Random Coding Based on M-ary Binary-Coded Signals 390
7-2-2 Random Coding Based on M-ary Multiamplitude Signals 397
7-2-3 Comparison of ? with the Capacity of the A WGN Channle 399
7-3 Communication System Design Based on the Cutoff Rate 400
7-4 Bibliographical Notes and References 406
Problems 406
8 Block and Convolutional Channel Codes 413
8-1 Linear Block Codes 413
8-1-1 The Generator Matrix and the Parity Check Matrix 417
8-1-2 Some Specific Linear Block Codes 421
8-1-3 Cyclic Codes 423
8-1-4 Optimum Soft-Decision Decoding of Linear Block Codes 436
8-1-5 Hard-Decision Decoding 445
8-1-6 Comparison of Performance between Hard-Decision and Soft-Decision Decoding 456
8-1-7 Bounds on Minimum Distance of Linear Block Codes 461
8-1-8 Nonbinary Block Codes and Concatenated Block Codes 464
8-1-9 Interleaving of Coded Data for Channels with Burst Errors 468
8-2 Convolutional Codes 470
8-2-1 The Transfer Function of a Convolutional Code 477
8-2-2 Optimum Decoding of Convolutional Codes—The Viterbi Algorithm 483
8-2-3 Probability of Error for Soft-Decision Decoding 486
8-2-4 Probability of Error for Hard-Decision Decoding 489
8-2-5 Distance Properties of Binary Convolutional Codes 492
8-2-6 Nonbinary Dual-k Codes and Concatenated Codes 492
8-2-7 Other Decoding Algorithms for Convolutional Codes 500
8-2-8 Practical Considerations in the Application of Convolutional Codes 506
8-3 Coded Modulation for Bandwidth-Constrained Channels 511
8-4 Bibliographical Notes and References 526
Problems 528
9-1 Characterization of Band-Limited Channels 534
9 Signal Design for Band-Limited Channels 534
9-2 Signal Design for Band-Limited Channels 540
9-2-1 Design of Band-Limited Signals for No Intersymbol Interference-The Nyquist Criterion 542
9-2-2 Design of Band-Limited Sygnals with Controlled ISI-Partial-Response Signals 548
9-2-3 Data Detection for Controlled ISI 551
9-2-4 Signal Design for Channels with Distortion 557
9-3 Probability of Error in Detection of PAM 561
9-3-1 Probability of Error for Detection of PAM with Zero ISI 561
9-3-2 Probability of Error for Detection of Partial-Response Signals 562
9-3-3 Probability of Error for Optimum Signals in Channel with Distortion 565
9-4 Modulation Codes for Spectrum Shaping 566
9-5 Bibliographical Notes and References 576
Problems 576
10 Communication through Band-Limited Linear Filter Channels 583
10-1 Optimum Receiver for Channels with ISI and AWGN 584
10-1-1 Optimum Maximum-Likelihood Receiver 584
10-1-2 A Discrete-Time Model for a Channel with ISI 586
10-1-3 The Viterbi Algorithm for the Discrete-Time White Noise Filter Model 589
10-1-4 Performance of MLSE for Channels with ISI 593
10-2 Linear Equalization 601
10-2-1 Peak Distortion Criterion 602
10-2-2 Mean Square Error (MSE) Criterion 607
10-2-3 Performance Characteristics of the MSE Equalizer 612
10-2-4 Fractionally Spaced Equalizer 617
10-3 Decision-Feedback Equalization 621
10-3-1 Coefficient Optimization 621
10-3-2 Performance Characteristics of DFE 622
10-3-3 Predictive Decision-Feedback Equalizer 626
10-4 Bibliographical Notes and References 628
Problems 628
11 Adaptive Equalization 636
11-1 Adaptive Linear Equalizer 636
11-1-1 The Zero-Forcing Algorithm 637
11-1-2 The LMS algorithm 639
11-1-3 Convergence Properties of the LMS Algorithm 642
11-1-4 Excess MSE Due to Noisy Gradient Estimates 644
11-1-5 Baseband and Passband Linear Equalizers 648
11-2 Adaptive Decision-Feedback Equalizer 649
11-2-1 Adaptive Equalization of Trellis-Coded Signals 650
11-3 An Adaptive Channel Estimator for ML Sequence Detection 652
11-4 Recursive Least-Squares Algorithms for Adaptive Equalization 654
11-4-1 Recursive Least-Squares (Kalman) Algorithm 656
11-4-2 Linear Prediction and the Lattice Filter 660
11-5 Self-Recovering (Blind) Equalization 664
11-5-1 Blind Equalization Based on Maximum-Likelihood Criterion 664
11-5-2 Stochastic Gradient Algorithms 668
11-5-3 Blind Equalization Algorithms Based on Second-and Higher-Order Signal Statistics 673
11-6 Bibliographical Notes and References 675
Problems 676
12 Multichannel and Multicarrier Systems 680
12-1 Multichannel Digital Communication in AWGN Channels 680
12-1-1 Binary Signals 682
12-1-2 M-ary Orthogonal Signals 684
12-2 Multicarrier Communications 686
12-2-1 Capacity of a Non-Ideal Linear Filter Channel 687
12-2-2 An FFT-Based Multicarrier System 689
12-3 Bibiliographical Notes and References 692
Problems 693
13 Spread Spectrum Signals for Digital Communications 695
13-1 Model of Spread Spectrum Digital Communication System 697
13-2 Direct Sequence Spread Spectrum Signals 698
13-2-1 Error Rate Performance of the Decoder 702
13-2-2 Some Applications of DS Spread Spectrum Signals 712
13-2-3 Effect of Pulsed Interference on DS Spread Spectrum Systems 717
13-2-4 Generation of PN Sequences 724
13-3 Frequency-Hopped Spread Spectrum Signals 729
13-3-1 Performance of FH Spread Spectrum Signals in AWGN Channel 732
13-3-2 Performance of FH Spread Spectrum Signals in Partial-Band Interference 734
13-3-3 A CDMA System Based on FH Spread Spectrum Signals 741
13-4 Other Types of Spread Spectrum Signals 743
13-5 Synchronization of Spread Spectrum Signals 744
13-6 Bibliographical Notes and References 752
Problems 753
14 Digital Communication through Fading Multipath Channds 758
14-1 Characterization of Fading Multipath Channels 759
14-1-1 Channel Correlation Functions and Power Spectra 762
14-1-2 Statistical Models for Fading Channels 767
14-2 The Effect of Characteristics on the Choice of a Channel Model 770
14-3 Frequency-Nonselective, Slowly Fading Channel 772
14-4 Diversity Techniques for Fading Multipath Channels 777
14-4-1 Binary Signals 778
14-4-2 Multiphase Signals 785
14-4-3 M-ary Orthogonal Signals 787
14-5 Digital Signaling over a Frequency-Selective, Slowly Fading Channel 795
14-5-1 A Tapped-Delay-Line Channel Model 795
14-5-2 The RAKE Demodulator 797
14-5-3 Performance of RAKE Receiver 798
14-6 Coded Waveforms for Fading Channels 806
14-6-1 Probability of Error for Soft-Decision Decoding of Linear Binary Block Codes 808
14-6-2 Probability of Error for Hard-Decision Decoding of Linear Binary Block Codes 811
14-6-3 Upper Bounds on the Performance of Convolutional Codes for a Raleigh Fading Channel 811
14-6-4 Usc of Constant-Weight Codes and Concatenated Codes for a Fading Channel 814
14-6-5 System Design Based on the Cutoff Rate 825
14-6-6 Trellis-Coded Modulation 830
14-7 Bibliographical Notes and References 832
Problems 833
15 Multiuser Communications 840
15-1 Introduction to Multiple Access Techniques 840
15-2 Capacity of Multiple Access Methods 843
15-3 Code-Division Multiple Access 849
15-3-1 CDMA Signal and Channel Models 849
15-3-2 The Optimum Receiver 851
15-3-3 Suboptimum Detectors 854
15-3-4 Performance Characteristics of Detectors 859
15-4 Random Access Methods 862
15-4-1 ALOHA System and Protocols 863
15-4-2 Carrier Sense Systems and Protocols 867
15-5 Bibliographical Notes and References 872
Problems 873
Appendix A The Levinson-Durbin Algorithm 879
Appendix B Error Probability for Multichannel Binary Signals 882
Appendix C Error Probabilities for Adaptive Reception of M-phase Signals 887
C-1 Mathematical Model for an M-phase Signaling Communications System 887
C-2 Characteristic Function and Probability Denstiy Function of the Phase? 889
C-3 Error Probabilities for Slowly Rayleigh Fading Channels 891
C-4 Error Probabilities for Time-Invariant and Ricean Fading Channels 893
Appendix D Square-Root Factorization 897
References and Bibliography 899
Index 917