1 INTRODUCTION 1

1.1 Historical Review 1

1.2 Elements of an Electrical Communication System 4

1.2.1 Digital Communication System, 7

1.2.2 Early Work in Digital Communications, 10

1.3 Communication Channels and Their Characteristics 12

1.4 Mathematical Models for Communication Channels 18

1.5 Summary and Further Reading 20

2 SIGNALS AND LINEAR SYSTEMS 21

2.1 Basic Concepts 21

2.1.1 Basic Operations on Signals, 21

2.1.2 Classification of Signals, 23

2.1.3 Some Important Signals and Their Properties, 31

2.1.4 Classification of Systems, 38

2.1.5 Analysis of LTI Systems in the Time Domain, 41

2.2 Fourier Series 43

2.2.1 Fourier Series and Its Properties, 44

2.2.2 Response of LTI Systems to Periodic Signals, 54

2.2.3 Parseval’s Relation, 56

2.3 Fourier Transform 58

2.3.1 From Fourier Series to Fourier Transforms, 58

2.3.2 Basic Properties of the Fourier Transform, 64

2.3.3 Fourier Transform for Periodic Signals, 78

2.3.4 Transmission over LTI Systems, 81

2.4 Filter Design 85

2.5 Power and Energy 89

2.5.1 Energy-Type Signals, 89

2.5.2 Power-Type Signals, 92

2.6 Hilbert Transform and Its Properties 95

2.7 Lowpass and Bandpass Signals 98

2.8 Summary and Further Reading 100

Problems 101

3 AMPLITUDE MODULATION 117

3.1 Introduction to Modulation 118

3.2 Amplitude Modulation 119

3.2.1 Double-Sideband Suppressed-Carrier AM, 119

3.2.2 Conventional Amplitude Modulation, 126

3.2.3 Single-Sideband AM, 132

3.2.4 Vestigial-Sideband AM, 134

3.3 Implementation of Amplitude Modulators and Demodulators 137

3.4 Signal Multiplexing 144

3.4.1 Frequency-Division Multiplexing, 144

3.4.2 Quadrature-Carrier Multiplexing, 145

3.5 AM Radio Broadcasting 146

3.6 Summary and Further Reading 149

Appendix 3A: Derivation of the Expression for SSB-AM Signals 149

Problems 151

4 ANGLE MODULATION 161

4.1 Representation of FM and PM Signals 161

4.2 Spectral Characteristics of Angle-Modulated Signals 166

4.2.1 Angle Modulation by a Sinusoidal Signal, 166

4.2.2 Angle Modulation by an Arbitrary Message Signal, 170

4.3 Implementation of Angle Modulators and Demodulators 171

4.4 FM Radio Broadcasting 179

4.5 Summary and Further Reading 181

Problems 182

5 PROBABILITY AND RANDOM PROCESSES 190

5.1 Review of Probability and Random Variables 190

5.1.1 Sample Space, Events, and Probability, 190

5.1.2 Conditional Probability, 191

5.1.3 Random Variables, 194

5.1.4 Functions of a Random Variable, 201

5.1.5 Multiple Random Variables, 203

5.1.6 Sums of Random Variables, 208

5.2 Random Processes: Basic Concepts 209

5.2.1 Statistical Averages, 212

5.2.2 Wide-Sense Stationary Processes, 215

5.2.3 Multiple Random Processes, 217

5.2.4 Random Processes and Linear Systems, 218

5.2.5 Power Spectral Density of Stationary Processes, 220

5.2.6 Power Spectral Density of a Sum Process, 225

5.3 Gaussian and White Processes 226

5.3.1 Gaussian Processes, 226

5.3.2 White Processes, 228

5.3.3 Filtered Noise Processes, 230

5.4 Summary and Further Reading 235

Problems 236

6 EFFECT OF NOISE ON ANALOG COMMUNICATION SYSTEMS 255

6.1 Effect of Noise on Amplitude Modulation Systems 255

6.1.1 Effect of Noise on a Baseband System, 256

6.1.2 Effect of Noise on DSB-SC AM, 256

6.1.3 Effect of Noise on SSB AM, 258

6.1.4 Effect of Noise on Conventional AM, 259

6.2 Effect of Noise on Angle Modulation 263

6.2.1 Threshold Effect in Angle Modulation, 271

6.2.2 Preemphasis and Deemphasis Filtering for FM, 274

6.3 Comparison of Analog-Modulation Systems 277

6.4 Effects of Transmission Losses and Noise in Analog Communication

Systems 278

6.4.1 Characterization of Thermal Noise Sources, 279

6.4.2 Effective Noise Temperature and Noise Figure, 280

6.4.3 Transmission Losses, 283

6.4.4 Repeaters for Signal Transmission, 284

6.5 Summary and Further Reading 287

Problems 288

7 ANALOG-TO-DIGITAL CONVERSION 296

7.1 Sampling of Signals and Signal Reconstruction from Samples 297

7.1.1 The Sampling Theorem, 297

7.2 Quantization 301

7.2.1 Scalar Quantization, 302

7.2.2 Vector Quantization, 309

7.3 Encoding 311

7.4 Waveform Coding 312

7.4.1 Pulse Code Modulation, 313

7.4.2 Differential Pulse Code Modulation, 317

7.4.3 Delta Modulation, 318

7.5 Analysis—Synthesis Techniques 321

7.6 Digital Audio Transmission and Digital Audio Recording 325

7.6.1 Digital Audio in Telephone Transmission Systems, 325

7.6.2 Digital Audio Recording, 327

7.7 The JPEG Image-Coding Standard 332

7.8 Summary and Further Reading 335

Problems 336

8 DIGITAL MODULATION METHODS IN AN ADDITIVE WHITE GAUSSIAN NOISE CHANNEL 347

8.1 Geometric Representation of Signal Waveforms 348

8.2 Binary Modulation Schemes 352

8.2.1 Binary Antipodal Signaling, 352

8.2.2 Binary Orthogonal Signaling, 356

8.3 Optimum Receiver for Binary Modulated Signals in Additive White Gaussian Noise 361

8.3.1 Correlation-Type Demodulator, 362

8.3.2 Matched-Filter-Type Demodulator, 371

8.3.3 The Performance of the Optimum Detector for Binary Signals, 379

8.4M-ary Digital Modulation 384

8.4.1 The Optimum Receiver for M-ary Signals in AWGN, 384

8.4.2 A Union Bound on the Probability of Error, 396

8.5M-ary Pulse Amplitude Modulation 398

8.5.1 Carrier-Modulated PAM for Bandpass Channels (M-ary ASK), 400

8.5.2 Demodulation and Detection of Amplitude-Modulated PAM Signals, 403

8.5.3 Probability of Error for M-ary PAM, 403

8.6 Phase-Shift Keying 406

8.6.1 Geometric Representation of PSK Signals, 408

8.6.2 Demodulation and Detection of PSK Signals, 410

8.6.3 Probability of Error for Phase-Coherent PSK Modulation, 411

8.6.4 Differential Phase Encoding and Differential Phase Modulation

and Demodulation, 416

8.6.5 Probability of Error for DPSK, 418

8.7 Quadrature Amplitude-Modulated Digital Signals 419

8.7.1 Geometric Representation of QAM Signals, 421

8.7.2 Demodulation and Detection of QAM Signals, 423

8.7.3 Probability of Error for QAM, 424

8.8 Carrier-Phase Estimation 429

8.8.1 The Phase-Locked Loop, 429

8.8.2 The Costas Loop, 437

8.8.3 Carrier-Phase Estimation for PAM, 439

8.8.4 Carrier-Phase Estimation for PSK, 440

8.8.5 Carrier-Phase Estimation for QAM, 444

8.9 Symbol Synchronization 446

8.9.1 Early—Late Gate Synchronizers, 447

8.9.2 Minimum Mean Square Error Method, 450

8.9.3 Maximum-Likelihood Method, 451

8.9.4 Spectral-Line Method, 452

8.9.5 Symbol Synchronization for Carrier-Modulated Signals, 455

8.10 Regenerative Repeaters 456

8.11 Summary and Further Reading 457

Problems 459

9 MULTIDIMENSIONAL DIGITAL MODULATION 485

9.1M-ary Orthogonal Signals 485

9.1.1 Probability of Error for M-ary Orthogonal Signals, 488

9.1.2 A Union Bound on the Error Probability of M-ary Orthogonal Signals, 491

9.2 Biorthogonal Signals 492

9.2.1 Probability of Error for M-ary Biorthogonal Signals, 495

9.3 Simplex Signals 497

9.3.1 Probability of Error for M-ary Simplex Signals, 498

9.4 Binary-Coded Signals 499

9.4.1 Probability of Error for Binary-Coded Signals, 501

9.5 Frequency-Shift Keying 501

9.5.1 Demodulation of M-ary FSK, 503

9.5.2 Optimum Detector for Noncoherent Binary FSK, 507

9.5.3 Probability of Error for Noncoherent Detection of M-ary FSK, 510

9.6 Modulation Systems with Memory 513

9.6.1 Continuous-Phase FSK, 513

9.6.2 Spectral Characteristics of CPFSK Signals, 524

9.7 Comparison of Modulation Methods 525

9.8 Summary and Further Reading 532

Problems 533

10 DIGITAL TRANSMISSION THROUGH BANDLIMITED AWGN CHANNELS 543

10.1 Characterization of Bandlimited Channels and Signal Distortion 543

10.1.1 Intersymbol Interference in Signal Transmission, 547

10.1.2 Digital Transmission through Bandlimited Bandpass Channels, 549

10.2 The Power Spectrum of Digitally Modulated Signals 552

10.3 Signal Design for Bandlimited Channels 556

10.3.1 Design of Bandlimited Signals for Zero ISI–The Nyquist

Criterion, 558

10.3.2 Design of Bandlimited Signals with Controlled ISI–Partial Response Signals, 564

10.4 Detection of Partial-Response Signals 566

10.4.1 Symbol-by-Symbol Detection, 567

10.4.2 Probability of Error for Symbol-by-Symbol Detection, 570

10.4.3 Maximum-Likelihood Sequence Detection of Partial-Response

Signals, 573

10.4.4 Error Probability of the Maximum-Likelihood Sequence

Detector, 576

10.5 System Design in the Presence of Channel Distortion 577

10.5.1 Design of Transmitting and Receiving Filters for a Known

Channel, 578

10.5.2 Channel Equalization, 582

10.6 Summary and Further Reading 599

Appendix 10A: Power Spectrum of Modulated Signals 601

10A.1 The Power Spectrum of the Baseband Signal, 601

10A.2 The Power Spectrum of the Carrier Modulated Signals, 603

Problems 604

11 MULTICARRIER MODULATION AND OFDM 621

11.1 Orthogonal Frequency-Division Multiplexing 621

11.2 Modulation and Demodulation in an OFDM System 622

11.3 An OFDM System Implemented via the FFT Algorithm 626

11.4 Spectral Characteristics of OFDM Signals 629

11.5 Peak-to-Average Power Ratio in OFDM Systems 631

11.6 Applications of OFDM 633

11.6.1 Digital Subscriber Lines, 633

11.6.2 Wireless LANs, 635

11.6.3 Digital Audio Broadcasting, 636

11.7 Summary and Further Reading 636

Problems 637

12 AN INTRODUCTION TO INFORMATION THEORY 641

12.1 Modeling Information Sources 642

12.1.1 Measure of Information, 644

12.1.2 Joint and Conditional Entropy, 647

12.1.3 Mutual Information, 650

12.1.4 Differential Entropy, 650

12.2 The Source Coding Theorem 652

12.3 Source Coding Algorithms 655

12.3.1 The Huffman Source Coding Algorithm, 655

12.3.2 The Lempel—Ziv Source Coding Algorithm, 659

12.4 Modeling of Communication Channels 661

12.5 Channel Capacity 664

12.5.1 Gaussian Channel Capacity, 669

12.6 Bounds on Communication 671

12.7 Summary and Further Reading 674

Problems 675

13 CODING FOR RELIABLE COMMUNICATIONS 689

13.1 The Promise of Coding 689

13.2 Linear Block Codes 694

13.2.1 Decoding and Performance of Linear Block Codes, 700

13.2.2 Some Important Linear Block Codes, 707

13.2.3 Error Detection versus Error Correction, 708

13.2.4 Burst-Error-Correcting Codes, 709

13.3 Convolutional Codes 711

13.3.1 Basic Properties of Convolutional Codes, 712

13.3.2 Maximum Likelihood Decoding of Convolutional Codes–The Viterbi

Algorithm, 717

13.3.3 Other Decoding Algorithms for Convolutional Codes, 722

13.3.4 Bounds on the Error Probability of Convolutional Codes, 722

13.4 Good Codes Based on Combination of Simple Codes 725

13.4.1 Product Codes, 727

13.4.2 Concatenated Codes, 728

13.5 Turbo Codes and Iterative Decoding 728

13.5.1 MAP Decoding of Convolutional Codes–The BCJR Algorithm, 731

13.5.2 Iterative Decoding for Turbo Codes, 737

13.5.3 Performance of Turbo Codes, 739

13.6 Low-Density Parity-Check Codes 741

13.6.1 Decoding LDPC Codes, 745

13.7 Coding for Bandwidth-Constrained Channels 747

13.7.1 Combined Coding and Modulation, 748

13.7.2 Trellis-Coded Modulation, 749

13.8 Practical Applications of Coding 756

13.8.1 Coding for Deep-Space Communications, 756

13.8.2 Coding for Telephone-Line Modems, 758

13.9 Summay and Further Reading 759

Problems 760

14 DATA TRANSMISSION IN FADING MULTIPATH CHANNELS 769

14.1 Characterization of Physical Wireless Channels 769

14.2 Channel Models for Time-Variant Multipath Channels 771

14.2.1 Frequency Nonselective Fading Channel, 774

14.2.2 Frequency Selective Fading Channel, 777

14.2.3 Models for the Doppler Power Spectrum, 778

14.2.4 Propagation Models for Mobile Radio Channels, 781

14.3 Performance of BinaryModulation in Rayleigh Fading Channels 783

14.3.1 Probability of Error in Frequency Nonselective Channels, 783

14.3.2 Performance Improvement through Signal Diversity, 786

14.3.3 The RAKE Demodulator and Its Performance in Frequency Selective

Channels, 792

14.3.4 OFDM Signals in Frequency Selective Channels, 794

14.4 Multiple Antenna Systems 795

14.4.1 Channel Models for Multiple Antenna Systems, 796

14.4.2 Signal Transmission in a Slow Fading Frequency NonselectiveMIMO

Channel, 797

14.4.3 Detection of Data Symbols in a MIMO System, 799

14.4.4 Error Rate Performance of the Detectors, 800

14.4.5 Space—Time Codes for MIMO Systems, 802

14.5 Link Budget Analysis for Radio Channels 810

14.6 Summary and Further Reading 813

Problems 815

15 SPREAD-SPECTRUM COMMUNICATION SYSTEMS 825

15.1 Model of a Spread-Spectrum Digital Communication System 826

15.2 Direct Sequence Spread-Spectrum Systems 827

15.2.1 Effect of Despreading on a Narrowband Interference, 830

15.2.2 Probability of Error at the Detector, 831

15.2.3 Performance of Coded Spread-Spectrum Signals, 836

15.3 Some Applications of DS Spread-Spectrum Signals 836

15.3.1 Low-Detectability Signal Transmission, 836

15.3.2 Code Division Multiple Access, 837

15.3.3 Communication over Channels with Multipath, 838

15.3.4 Wireless LANs, 839

15.4 Generation of PN Sequences 840

15.5 Frequency-Hopped Spread Spectrum 843

15.5.1 Slow Frequency-Hopping Systems and Partial-Band Interference, 844

15.5.2 Fast Frequency Hopping, 847

15.5.3 Applications of FH Spread Spectrum, 848

15.6 Synchronization of Spread-Spectrum Systems 849

15.6.1 Acquisition Phase, 849

15.6.2 Tracking, 852

15.7 Digital Cellular Communication Systems 856

15.7.1 The GSM System, 858

15.7.2 CDMA System Based on IS-95, 862

15.7.3 Third Generation Cellular Communication Systems and Beyond, 866

15.8 Summary and Further Reading 868

Problems 869

REFERENCES 877

INDEX 886