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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