数字通信基础

1 Introduction 1

1.1 Components of a digital communication system 2

1.2 Text outline 5

1.3 Further reading 6

2 Modulation 7

2.1 Preliminaries 8

2.2 Complex baseband representation 18

2.3 Spectral description of random processes 31

2.3.1 Complex envelope for passband random processes 40

2.4 Modulation degrees of freedom 41

2.5 Linear modulation 43

2.5.1 Examples of linear modulation 44

2.5.2 Spectral occupancy of linearly modulated signals 46

2.5.3 The Nyquist criterion： relating bandwidth to symbol rate 49

2.5.4 Linear modulation as a building block 54

2.6 Orthogonal and biorthogonal modulation 55

2.7 Differential modulation 57

2.8 Further reading 60

2.9 Problems 60

2.9.1 Signals and systems 60

2.9.2 Complex baseband representation 62

2.9.3 Random processes 64

2.9.4 Modulation 66

3 Demodulation 74

3.1 Gaussian basics 75

3.2 Hypothesis testing basics 88

3.3 Signal space concepts 94

3.4 Optimal reception in AWGN 102

3.4.1 Geometry of the ML decision rule 106

3.4.2 Soft decisions 107

3.5 Performance analysis of ML reception 109

3.5.1 Performance with binary signaling 110

3.5.2 Performance with M-ary signaling 114

3.6 Bit-level demodulation 127

3.6.1 Bit-level soft decisions 131

3.7 Elements of link budget analysis 133

3.8 Further reading 136

3.9 Problems 136

3.9.1 Gaussian basics 136

3.9.2 Hypothesis testing basics 138

3.9.3 Receiver design and performance analysis for the AWGN channel 140

3.9.4 Link budget analysis 149

3.9.5 Some mathematical derivations 150

4 Synchronization and noncoherent communication 153

4.1 Receiver design requirements 155

4.2 Parameter estimation basics 159

4.2.1 Likelihood function of a signal in AWGN 162

4.3 Parameter estimation for synchronization 165

4.4 Noncoherent communication 170

4.4.1 Composite hypothesis testing 171

4.4.2 Optimal noncoherent demodulation 172

4.4.3 Differential modulation and demodulation 173

4.5 Performance of noncoherent communication 175

4.5.1 Proper complex Gaussianity 176

4.5.2 Performance of binary noncoherent communication 181

4.5.3 Performance of M-ary noncoherent orthogonal signaling 185

4.5.4 Performance of DPSK 187

4.5.5 Block noncoherent demodulation 188

4.6 Further reading 189

4.7 Problems 190

5 Channel equalization 199

5.1 The channel model 200

5.2 Receiver front end 201

5.3 Eye diagrams 203

5.4 Maximum likelihood sequence estimation 204

5.4.1 Alternative MLSE formulation 212

5.5 Geometric model for suboptimal equalizer design 213

5.6 Linear equalization 216

5.6.1 Adaptive implementations 223

5.6.2 Performance analysis 226

5.7 Decision feedback equalization 228

5.7.1 Performance analysis 230

5.8 Performance analysis of MLSE 231

5.8.1 Union bound 232

5.8.2 Transfer function bound 237

5.9 Numerical comparison of equalization techniques 240

5.10 Further reading 242

5.11 Problems 243

5.11.1 MLSE 243

6 Information-theoretic limits and their computation 252

6.1 Capacity of AWGN channel： modeling andgeometry 253

6.1.1 From continuous to discrete time 256

6.1.2 Capacity of the discrete-time AWGN channel 257

6.1.3 From discrete to continuous time 259

6.1.4 Summarizing the discrete-time AWGN model 261

6.2 Shannon theory basics 263

6.2.1 Entropy， mutual information， and divergence 265

6.2.2 The channel coding theorem 270

6.3 Some capacity computations 272

6.3.1 Capacity for standard constellations 272

6.3.2 Parallel Gaussian channels and waterfilling 277

6.4 Optimizing the input distribution 280

6.4.1 Convex optimization 281

6.4.2 Characterizing optimal input distributions 282

6.4.3 Computing optimal input distributions 284

6.5 Further reading 287

6.6 Problems 287

7 Channel coding 293

7.1 Binary convolutional codes 294

7.1.1 Nonrecursive nonsystematic encoding 295

7.1.2 Recursive systematic encoding 297

7.1.3 Maximum likelihood decoding 298

7.1.4 Performance analysis of ML decoding 303

7.1.5 Performance analysis for quantized observations 309

7.2 Turbo codes and iterative decoding 311

7.2.1 The BCJR algorithm： soft-in， soft-out decoding 311

7.2.2 Logarithmic BCJR algorithm 320

7.2.3 Turbo constructions from convolutional codes 325

7.2.4 The BER performance of turbo codes 328

7.2.5 Extrinsic information transfer charts 329

7.2.6 Turbo weight enumeration 336

7.3 Low density parity check codes 342

7.3.1 Some terminology from coding theory 343

7.3.2 Regular LDPC codes 345

7.3.3 Irregular LDPC codes 347

7.3.4 Message passing and density evolution 349

7.3.5 Belief propagation 352

7.3.6 Gaussian approximation 354

7.4 Bandwidth-efficient coded modulation 357

7.4.1 Bit interleaved coded modulation 358

7.4.2 Trellis coded modulation 360

7.5 Algebraic codes 364

7.6 Further reading 367

7.7 Problems 369

8 Wireless communication 379

8.1 Channel modeling 380

8.2 Fading and diversity 387

8.2.1 The problem with Rayleigh fading 387

8.2.2 Diversity through coding and interleaving 390

8.2.3 Receive diversity 393

8.3 Orthogonal frequency division multiplexing 397

8.4 Direct sequence spread spectrum 406

8.4.1 The rake receiver 409

8.4.2 Choice of spreading sequences 413

8.4.3 Performance of conventional reception in CDMA systems 415

8.4.4 Multiuser detection for DS-CDMA systems 417

8.5 Frequency hop spread spectrum 426

8.6 Continuous phase modulation 428

8.6.1 Gaussian MSK 432

8.6.2 Receiver design and Laurents expansion 433

8.7 Space–time communication 439

8.7.1 Space–time channel modeling 440

8.7.2 Information-theoretic limits 443

8.7.3 Spatial multiplexing 447

8.7.4 Space–time coding 448

8.7.5 Transmit beamforming 451

8.8 Further reading 451

8.9 Problems 453

Appendix A Probability， random variables， and random processes 474

A.1 Basic probability 474

A.2 Random variables 475

A.3 Random processes 478

A.3.1 Wide sense stationary random processes through LTI systems 478

A.3.2 Discrete-time random processes 479

A.4 Further reading 481

Appendix B The Chernoff bound 482

Appendix C Jensens inequality 485

References 488

Index 495

《数字通信基础（英文版）》阐述了现代数字通信系统设计的基本知识，主要内容有：信号和噪声的复基带表述，调制和调解，分散信道通信，用信息理论计算性能基准点，现代解码方法基础知识，无线通信简介。书中实例丰富，每章还配有练习题，帮助读者深刻理解重要通信原理。
《数字通信基础（英文版）》是通信专业高年级本科生和研究生教材，也可供工程技术人员参考。

近十年来，数字通信技术发展迅猛，已经深入人们日常生活的每个角落，如宽带上网、手机、数字电视等。受这些应用的驱使，大量人才投身数字通信行业，但他们常常被通信理论所需的数学知识吓倒。
Madtlow博士拥有多年科研和教学工作经验.深知如何通过讲解实例来减轻这种恐惧。《数字通信基础（英文版）》旨在保持知识严谨性的同时，通过各种方式让读者轻松掌握通信理论。书中首先建立了调制和解调的经典基础概念，接着介绍了同步、非相干通信、信道均衡、信息论、信道编码、无线通信等高级概念；此外，还涵盖了Turbo马和LDPC码的相关内容，读者既可以据此实现并进行性能评估，也可以仅仅以它们为性能基准进行性能对比。《数字通信基础（英文版）》特色使用复基带表示作为收发机设计和实现的统一框架包括空时通信等不同调制样式的无线链路设计非相干通信和均衡的几何内涵。