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Chapter 1 Introduction 1

1.1 A Brief History of Communications 1

1.2 Basics of Wireless Communications 10

1.3 Digital Communications 12

1.4 Why Discrete-Time Processing Is So Popular 14

1.5 Organization of the Text 19

1.6 Notes and References 22

Chapter 2 Signals and Systems 1:A Review of the Basics 23

2.1 Introduction 23

2.2 Signals 24

2.2.1 Continuous-Time Signals 24

2.2.2 Discrete-Time Signals 26

2.3 Systems 28

2.3.1 Continuous-Time Systems 28

2.3.2 Discrete-Time Systems 29

2.4 Frequency Domain Characterizations 30

2.4.1 Laplace Transform 32

2.4.2 Continuous-Time Fourier Transform 37

2.4.3 Z Transform 40

2.4.4 Discrete-Time Fourier Transform 46

2.5 The Discrete Fourier Transform 50

2.6 The Relationship Between Discrete-Time and Continuous-Time Systems 55

2.6.1 The Sampling Theorem 56

2.6.2 Discrete-Time Processing of Continuous-Time Signals 65

2.7 Discrete-Time Processing of Band-Pass Signals 67

2.8 Notes and References 70

2.9 Exercises 71

Chapter 3 Signals and Systems 2:Some Useful Discrete-Time Techniques for Digital Communications 114

3.1 Introduction 114

3.2 Multirate Signal Processing 115

3.2.1 Impulse-Train Sampling 115

3.2.2 Downsampling 118

3.2.3 Upsampling 120

3.2.4 The Noble Identities 122

3.2.5 Polyphase Filterbanks 122

3.3 Discrete-Time Filter Design Methods 127

3.3.1 IIR Filter Designs 129

3.3.2 FIR Filter Designs 134

3.3.3 Two Important Filters:The Differentiator and the Integrator 149

3.4 Notes and References 159

3.5 Exercises 159

Chapter 4 A Review of Probability Theory 178

4.1 Basic Definitions 178

4.2 Gaussian Random Variables 188

4.2.1 Density and Distribution Functions 188

4.2.2 Product Moments 192

4.2.3 Functions of Random Variables 193

4.3 Multivariate Gaussian Random Variables 195

4.3.1 Bivariate Gaussian Distribution 196

4.3.2 Linear Operators and Multivariate Gaussian Random Variables 197

4.4 Random Sequences 198

4.4.1 Power Spectral Density 199

4.4.2 Random Sequences and Discrete-Time LTI Systems 200

4.5 Additive White Gaussian Noise 202

4.5.1 Continuous-Time Random Processes 202

4.5.2 The White Gaussian Random Process:A Good Model for Noise？ 204

4.5.3 White Gaussian Noise in a Sampled Data System 206

4.6 Notes and References 208

4.7 Exercises 208

Chapter 5 Linear Modulation 1:Modulation,Demodulation,and Detection 214

5.1 Signal Spaces 215

5.1.1 Definitions 215

5.1.2 The Synthesis Equation and Linear Modulation 222

5.1.3 The Analysis Equation and Detection 223

5.1.4 The Matched Filter 226

5.2 M-ary Baseband Pulse Amplitude Modulation 227

5.2.1 Continuous-Time Realization 229

5.2.2 Discrete-Time Realization 233

5.3 M-ary Quadrature Amplitude Modulation 238

5.3.1 Continuous-Time Realization 246

5.3.2 Discrete-Time Realization 256

5.4 Offset QPSK 260

5.5 Multicarrier Modulation 265

5.6 Maximum Likelihood Detection 273

5.6.1 Introduction 273

5.6.2 Preliminaries 274

5.6.3 Maximum Likelihood Decision Rule 276

5.7 Notes and References 279

5.7.1 Topics Covered 279

5.7.2 Topics Not Covered 280

5.8 Exercises 280

Chapter 6 Linear Modulation 2:Performance 305

6.1 Performance of PAM 306

6.1.1 Bandwidth 306

6.1.2 Probability of Error 307

6.2 Performance of QAM 313

6.2.1 Bandwidth 313

6.2.2 Probability of Error 314

6.3 Comparisons 325

6.4 Link Budgets 331

6.4.1 Received Power and the Friis Equation 331

6.4.2 Equivalent Noise Temperature and Noise Figure 334

6.4.3 The Link Budget Equation 339

6.5 Projecting White Noise onto an Orthonormal Basis Set 345

6.6 Notes and References 347

6.6.1 Topics Covered 347

6.6.2 Topics Not Covered 347

6.7 Exercises 348

Chapter 7 Carrier Phase Synchronization 359

7.1 Basic Problem Formulation 360

7.1.1 Approach 1 360

7.1.2 Approach 2 362

7.2 Carrier Phase Synchronization for QPSK 365

7.2.1 A Heuristic Phase Error Detector 365

7.2.2 The Maximum Likelihood Phase Error Detector 370

7.2.3 Examples 374

7.3 Carrier Phase Synchronization for BPSK 375

7.4 Carrier Phase Synchronization for MQAM 381

7.5 Carrier Phase Synchronization for Offset QPSK 382

7.6 Carrier Phase Synchronization for BPSK and QPSK Using Continuous-Time Techniques 391

7.7 Phase Ambiguity Resolution 394

7.7.1 Unique Word 396

7.7.2 Differential Encoding 398

7.8 Maximum Likelihood Phase Estimation 409

7.8.1 Preliminaries 409

7.8.2 Carrier Phase Estimation 414

7.9 Notes and References 421

7.9.1 Topics Covered 421

7.9.2 Topics Not Covered 423

7.10 Exercises 423

Chapter 8 Symbol Timing Synchronization 434

8.1 Basic Problem Formulation 436

8.2 Continuous-Time Techniques for M-ary PAM 438

8.3 Continuous-Time Techniques for MQAM 443

8.4 Discrete-Time Techniques for M-ary PAM 445

8.4.1 Timing Error Detectors 449

8.4.2 Interpolation 462

8.4.3 Interpolation Control 475

8.4.4 Examples 478

8.5 Discrete-Time Techniques for MQAM 494

8.6 Discrete-Time Techniques for Offset QPSK 497

8.7 Dealing with Transition Density:A Practical Consideration 501

8.8 Maximum Likelihood Estimation 503

8.8.1 Preliminaries 503

8.8.2 Symbol Timing Estimation 510

8.9 Notes and References 514

8.9.1 Topics Covered 514

8.9.2 Topics Not Covered 515

8.10 Exercises 515

Chapter 9 System Components 519

9.1 The Continuous-Time Discrete-Time Interface 519

9.1.1 Analog-to-Digital Converter 520

9.1.2 Digital-to-Analog Converter 529

9.2 Discrete-Time Oscillators 537

9.2.1 Discrete Oscillators Based on LTI Systems 538

9.2.2 Direct Digital Synthesizer 542

9.3 Resampling Filters 555

9.3.1 CIC and Hogenauer Filters 557

9.3.2 Half-Band Filters 562

9.3.3 Arbitrary Resampling Using Polyphase Filterbanks 565

9.4 CoRDiC:Coordinate Rotation Digital Computer 578

9.4.1 Rotations:Moving on a Circle 578

9.4.2 Moving Along Other Shapes 585

9.5 Automatic Gain Control 588

9.6 Notes and References 593

9.6.1 Topics Covered 593

9.6.2 Topics Not Covered 597

9.7 Exercises 597

Chapter 10 System Design 604

10.1 Advanced Discrete-Time Architectures 604

10.1.1 Discrete-Time Architectures for QAM Modulators 605

10.1.2 Discrete-Time Architectures for QAM Demodulators 611

10.1.3 Putting It All Together 632

10.2 Channelization 637

10.2.1 Continuous-Time Techniques:The Superheterodyne Receiver 637

10.2.2 Discrete-Time Techniques Using Multirate Processing 650

10.3 Notes and References 658

10.3.1 Topics Covered 658

10.3.2 Topics Not Covered 660

10.4 Exercises 662

Appendix A Pulse Shapes 673

Appendix B The Complex-Valued Representation for QAM 700

Appendix C Phase Locked Loops 718

Bibliography 751