CHAPTER 1 INTRODUCTION 1
1.1 The Block Diagram of a Communication System 4
1.2 Channel Characteristics 5
1.2.1 Noise Sources 5
1.2.2 Types of Transmission Channels 7
1.3 Summary of Systems-Analysis Techniques 13
1.3.1 Time and Frequency-Domain Analyses 13
1.3.2 Modulation and Communication Theories 13
1.4 Probabilistic Approaches to System Optimization 14
1.4.1 Statistical Signal Detection and EstimationTheory 14
1.4.2 Information Theory and Coding 15
1.4.3 Recent Advances 16
1.5 Preview of This Book 16
Further Reading 16
CHAPTER 2 SIGNAL AND LINEAR SYSTEM ANALYSIS 17
2.1 Signal Models 17
2.1.1 Deterministic and Random Signals 17
2.1.2 Periodic and Aperiodic Signals 18
2.1.3 Phasor Signals and Spectra 18
2.1.4 Singularity Functions 21
2.2 Signal Classifications 24
2.3 Fourier Series 26
2.3.1 Complex Exponential Fourier Series 26
2.3.2 Symmetry Properties of the Fourier Coefficients 27
2.3.3 Trigonometric Form of the Fourier Series 28
2.3.4 Parseval's Theorem 28
2.3.5 Examples of Fourier Series 29
2.3.6 Line Spectra 30
2.4 The Fourier Transform 34
2.4.1 Amplitude and Phase Spectra 35
2.4.2 Symmetry Properties 36
2.4.3 Energy Spectral Density 37
2.4.4 Convolution 38
2.4.5 Transform Theorems: Proofs and Applications 40
2.4.6 Fourier Transforms of Periodic Signals 48
2.4.7 Poisson Sum Formula 50
2.5 Power Spectral Density and Correlation 50
2.5.1 The Time-Average Autocorrelation Function 51
2.5.2 Properties of 𝑅(𝜏) 52
2.6 Signals and Linear Systems 55
2.6.1 Definition of a Linear Time-Invariant System 56
2.6.2 Impulse Response and the SuperpositionIntegral 56
2.6.3 Stability 58
2.6.4 Transfer (Frequency Response) Function 58
2.6.5 Causality 58
2.6.6 Symmetry Properties of 𝐻(𝑓) 59
2.6.7 Input-Output Relationships for Spectral Densities 62
2.6.8 Response to Periodic Inputs 62
2.6.9 Distortionless Transmission 64
2.6.10 Group and Phase Delay 64
2.6.11 Nonlinear Distortion 67
2.6.12 Ideal Filters 68
2.6.13 Approximation of Ideal Lowpass Filters by Realizable Filters 70
2.6.14 Relationship of Pulse Resolution and Risetime to Bandwidth 75
2.7 Sampling Theory 78
2.8 The Hilbert Transform 82
2.8.1 Definition 82
2.8.2 Properties 83
2.8.3 Analytic Signals 85
2.8.4 Complex Envelope Representation of Bandpass Signals 87
2.8.5 Complex Envelope Representation of Bandpass Systems 89
2.9 The Discrete Fourier Transform and Fast Fourier Transform 91
Further Reading 95
Summary 95
Drill Problems 98
Problems 100
Computer Exercises 111
CHAPTER 3 LINEAR MODULATION TECHNIQUES 112
3.1 Double-Sideband Modulation 113
3.2 Amplitude Modulation (AM) 116
3.2.1 Envelope Detection 118
3.2.2 The Modulation Trapezoid 122
3.3 Single-Sideband (SSB) Modulation 124
3.4 Vestigial-Sideband (VSB) Modulation 133
3.5 Frequency Translation and Mixing 136
3.6 Interference in Linear Modulation 139
3.7 Pulse Amplitude Modulation---PAM 142
3.8 Digital Pulse Modulation 144
3.8.1 Delta Modulation 144
3.8.2 Pulse-Code Modulation 146
3.8.3 Time-Division Multiplexing 147
3.8.4 An Example: The Digital Telephone System 149
Further Reading 150
Summary 150
Drill Problems 151
Problems 152
Computer Exercises 155
CHAPTER 4 ANGLE MODULATION ANDMULTIPLEXING 156
4.1 Phase and Frequency Modulation Defined 156
4.1.1 Narrowband Angle Modulation 157
4.1.2 Spectrum of an Angle-Modulated Signal 161
4.1.3 Power in an Angle-Modulated Signal 168
4.1.4 Bandwidth of Angle-Modulated Signals 168
4.1.5 Narrowband-to-Wideband Conversion 173
4.2 Demodulation of Angle-Modulated Signals 175
4.3 Feedback Demodulators: The Phase-Locked Loop 181
4.3.1 Phase-Locked Loops for FM and PM Demodulation 181
4.3.2 Phase-Locked Loop Operation in the Tracking Mode: The Linear Model 184
4.3.3 Phase-Locked Loop Operation in the Acquisition Mode 189
4.3.4 Costas PLLs 194
4.3.5 Frequency Multiplication and Frequency Division 195
4.4 Interference in Angle Modulation 196
4.5 Analog Pulse Modulation 201
4.5.1 Pulse-Width Modulation (PWM) 201
4.5.2 Pulse-Position Modulation (PPM) 203
4.6 Multiplexing 204
4.6.1 Frequency-Division Multiplexing 204
4.6.2 Example of FDM: Stereophonic FM Broadcasting 205
4.6.3 Quadrature Multiplexing 206
4.6.4 Comparison of Multiplexing Schemes 207
Further Reading 208
Summary 208
Drill Problems 209
Problems 210
Computer Exercises 213
CHAPTER 5 PRINCIPLES OF BASEBAND DIGITAL DATATRANSMISSION 215
5.1 Baseband Digital Data Transmission Systems 215
5.2 Line Codes and Their Power Spectra 216
5.2.1 Description of Line Codes 216
5.2.2 Power Spectra for Line-Coded Data 218
5.3 Effects of Filtering of Digital Data---ISI 225
5.4 Pulse Shaping: Nyquist's Criterion for Zero ISI 227
5.4.1 Pulses Having the Zero ISI Property 228
5.4.2 Nyquist's Pulse-Shaping Criterion 229
5.4.3 Transmitter and Receiver Filters for Zero ISI 231
5.5 Zero-Forcing Equalization 233
5.6 Eye Diagrams 237
5.7 Synchronization 239
5.8 Carrier Modulation of Baseband Digital Signals 243
Further Reading 244
Summary 244
Drill Problems 245
Problems 246
Computer Exercises 249
CHAPTER 6 OVERVIEW OF PROBABILITY AND RANDOMVARIABLES 250
6.1 What is Probability? 250
6.1.1 Equally Likely Outcomes 250
6.1.2 Relative Frequency 251
6.1.3 Sample Spaces and the Axioms of Probability 252
6.1.4 Venn Diagrams 253
6.1.5 Some Useful Probability Relationships 253
6.1.6 Tree Diagrams 257
6.1.7 Some More General Relationships 259
6.2 Random Variables and Related Functions 260
6.2.1 Random Variables 260
6.2.2 Probability (Cumulative) Distribution Functions 262
6.2.3 Probability-Density Function 263
6.2.4 Joint cdfs and pdfs 265
6.2.5 Transformation of Random Variables 270
6.3 Statistical Averages 274
6.3.1 Average of a Discrete Random Variable 274
6.3.2 Average of a Continuous Random Variable 275
6.3.3 Average of a Function of a Random Variable 275
6.3.4 Average of a Function of More Than One Random Variable 277
6.3.5 Variance of a Random Variable 279
6.3.6 Average of a Linear Combination of 𝑁Random Variables 280
6.3.7 Variance of a Linear Combination of Independent Random Variables 281
6.3.8 Another Special Average---The Characteristic Function 282
6.3.9 The pdf of the Sum of Two Independent Random Variables 283
6.3.10 Covariance and the Correlation Coefficient 285
6.4 Some Useful pdfs 286
6.4.1 Binomial Distribution 286
6.4.2 Laplace Approximation to the Binomial Distribution 288
6.4.3 Poisson Distribution and Poisson Approximation to the Binomial Distribution 289
6.4.4 Geometric Distribution 290
6.4.5 Gaussian Distribution 291
6.4.6 Gaussian 𝑄-Function 295
6.4.7 Chebyshev's Inequality 296
6.4.8 Collection of Probability Functions and Their Means and Variances 296
Further Reading 298
Summary 298
Drill Problems 300
Problems 301
Computer Exercises 307
CHAPTER 7 RANDOM SIGNALS AND NOISE 308
7.1 A Relative-Frequency Description of Random Processes 308
7.2 Some Terminology of Random Processes 310
7.2.1 Sample Functions and Ensembles 310
7.2.2 Description of Random Processes in Terms of Joint pdfs 311
7.2.3 Stationarity 311
7.2.4 Partial Description of Random Processes: Ergodicity 312
7.2.5 Meanings of Various Averages for Ergodic Processes 315
7.3 Correlation and Power Spectral Density 316
7.3.1 Power Spectral Density 316
7.3.2 The Wiener--Khinchine Theorem 318
7.3.3 Properties of the Autocorrelation Function 320
7.3.4 Autocorrelation Functions for Random Pulse Trains 321
7.3.5 Cross-Correlation Function and Cross-Power Spectral Density 324
7.4 Linear Systems and Random Processes 325
7.4.1 Input-Output Relationships 325
7.4.2 Filtered Gaussian Processes 327
7.4.3 Noise-Equivalent Bandwidth 329
7.5 Narrowband Noise 333
7.5.1 Quadrature-Component and Envelope-Phase Representation 333
7.5.2 The Power Spectral Density Function of 𝑛𝑐(𝑡) and𝑛𝑠(𝑡) 335
7.5.3 Ricean Probability Density Function 338
Further Reading 340
Summary 340
Drill Problems 341
Problems 342
Computer Exercises 348
CHAPTER 8 NOISE IN MODULATION SYSTEMS 349
8.1 Signal-to-Noise Ratios 350
8.1.1 Baseband Systems 350
8.1.2 Double-Sideband Systems 351
8.1.3 Single-Sideband Systems 353
8.1.4 Amplitude Modulation Systems 355
8.1.5 An Estimator for Signal-to-Noise Ratios 361
8.2 Noise and Phase Errors in Coherent Systems 366
8.3 Noise in Angle Modulation 370
8.3.1 The Effect of Noise on the Receiver Input 370
8.3.2 Demodulation of PM 371
8.3.3 Demodulation of FM: Above Threshold Operation 372
8.3.4 Performance Enhancement through the Use ofDe-emphasis 374
8.4 Threshold Effect in FM Demodulation 376
8.4.1 Threshold Effects in FM Demodulators 376
8.5 Noise in Pulse-Code Modulation 384
8.5.1 Postdetection SNR 384
8.5.2 Companding 387
Further Reading 389
Summary 389
Drill Problems 391
Problems 391
Computer Exercises 394
CHAPTER 9 PRINCIPLES OF DIGITAL DATA TRANSMISSIONIN NOISE 396
9.1 Baseband Data Transmission in White Gaussian Noise 398
9.2 Binary Synchronous Data Transmission with Arbitrary Signal Shapes 404
9.2.1 Receiver Structure and Error Probability 404
9.2.2 The Matched Filter 407
9.2.3 Error Probability for the Matched-Filter Receiver 410
9.2.4 Correlator Implementation of the Matched-Filter Receiver 413
9.2.5 Optimum Threshold 414
9.2.6 Nonwhite (Colored) Noise Backgrounds 414
9.2.7 Receiver Implementation Imperfections 415
9.2.8 Error Probabilities for Coherent Binary Signaling 415
9.3 Modulation Schemes not Requiring Coherent References 421
9.3.1 Differential Phase-Shift Keying (DPSK) 422
9.3.2 Differential Encoding and Decoding of Data 427
9.3.3 Noncoherent FSK 429
9.4 M-ary Pulse-Amplitude Modulation (PAM) 431
9.5 Comparison of Digital Modulation Systems 435
9.6 Noise Performance of Zero-ISI Digital Data Transmission Systems 438
9.7 Multipath Interference 443
9.8 Fading Channels 449
9.8.1 Basic Channel Models 449
9.8.2 Flat-Fading Channel Statistics and Error Probabilities 450
9.9 Equalization 455
9.9.1 Equalization by Zero-Forcing 455
9.9.2 Equalization by MMSE 459
9.9.3 Tap Weight Adjustment 463
Further Reading 466
Summary 466
Drill Problems 468
Problems 469
Computer Exercises 476
CHAPTER 10 ADVANCED DATA COMMUNICATIONSTOPICS 477
10.1 M-ary Data Communications Systems 477
10.1.1 M-ary Schemes Based on Quadrature Multiplexing 477
10.1.2 OQPSK Systems 481
10.1.3 MSK Systems 482
10.1.4 M-ary Data Transmission in Terms of Signal Space 489
10.1.5 QPSK in Terms of Signal Space 491
10.1.6 M-ary Phase-Shift Keying 493
10.1.7 Quadrature-Amplitude Modulation (QAM) 495
10.1.8 Coherent FSK 497
10.1.9 Noncoherent FSK 498
10.1.10 Differentially Coherent Phase-Shift Keying 502
10.1.11 Bit Error Probability from Symbol Error Probability 503
10.1.12 Comparison of M-ary Communications Systems on the Basis of Bit Error Probability 505
10.1.13 Comparison of M-ary Communications Systems on the Basis of Bandwidth Efficiency 508
10.2 Power Spectra for Digital Modulation 510
10.2.1 Quadrature Modulation Techniques 510
10.2.2 FSK Modulation 514
10.2.3 Summary 516
10.3 Synchronization 516
10.3.1 Carrier Synchronization 517
10.3.2 Symbol Synchronization 520
10.3.3 Word Synchronization 521
10.3.4 Pseudo-Noise (PN) Sequences 524
10.4 Spread-Spectrum Communication Systems 528
10.4.1 Direct-Sequence Spread Spectrum 530
10.4.2 Performance of DSSS in CW Interference Environments 532
10.4.3 Performance of Spread Spectrum in Multiple User Environments 533
10.4.4 Frequency-Hop Spread Spectrum 536
10.4.5 Code Synchronization 537
10.4.6 Conclusion 539
10.5 Multicarrier Modulation and Orthogonal Frequency-Division Multiplexing 540
10.6 Cellular Radio Communication Systems 545
10.6.1 Basic Principles of Cellular Radio 546
10.6.2 Channel Perturbations in Cellular Radio 550
10.6.3 Multiple-Input Multiple-Output (MIMO) Systems---Protection Against Fading 551
10.6.4 Characteristics of 1G and 2G Cellular Systems 553
10.6.5 Characteristics of cdma2000 and W-CDMA 553
10.6.6 Migration to 4G 555
Further Reading 556
Summary 556
Drill Problems 557
Problems 558
Computer Exercises 563
CHAPTER 11 OPTIMUM RECEIVERS AND SIGNAL-SPACECONCEPTS 564
11.1 Bayes Optimization 564
11.1.1 Signal Detection versus Estimation 564
11.1.2 Optimization Criteria 565
11.1.3 Bayes Detectors 565
11.1.4 Performance of Bayes Detectors 569
11.1.5 The Neyman-Pearson Detector 572
11.1.6 Minimum Probability of Error Detectors 573
11.1.7 The Maximum a Posteriori (MAP) Detector 573
11.1.8 Minimax Detectors 573
11.1.9 The M-ary Hypothesis Case 573
11.1.10 Decisions Based on Vector Observations 574
11.2 Vector Space Representation of Signals 574
11.2.1 Structure of Signal Space 575
11.2.2 Scalar Product 575
11.2.3 Norm 576
11.2.4 Schwarz's Inequality 576
11.2.5 Scalar Product of Two Signals in Terms of Fourier Coefficients 578
11.2.6 Choice of Basis Function Sets---The Gram--Schmidt Procedure 579
11.2.7 Signal Dimensionality as a Function of Signal Duration 581
11.3 Map Receiver for Digital Data Transmission 583
11.3.1 Decision Criteria for Coherent Systems in Terms of Signal Space 583
11.3.2 Sufficient Statistics 589
11.3.3 Detection of𝑀-ary Orthogonal Signals 590
11.3.4 A Noncoherent Case 592
11.4 Estimation Theory 596
11.4.1 Bayes Estimation 596
11.4.2 Maximum-Likelihood Estimation 598
11.4.3 Estimates Based onMultiple Observations 599
11.4.4 Other Properties of ML Estimates 601
11.4.5 Asymptotic Qualities of ML Estimates 602
11.5 Applications of Estimation Theory to Communications 602
11.5.1 Pulse-Amplitude Modulation (PAM) 603
11.5.2 Estimation of Signal Phase: The PLL Revisited 604
Further Reading 606
Summary 607
Drill Problems 607
Problems 608
Computer Exercises 614
CHAPTER 12 INFORMATION THEORY AND CODING 615
12.1 Basic Concepts 616
12.1.1 Information 616
12.1.2 Entropy 617
12.1.3 Discrete Channel Models 618
12.1.4 Joint and Conditional Entropy 621
12.1.5 Channel Capacity 622
12.2 Source Coding 626
12.2.1 An Example of Source Coding 627
12.2.2 Several Definitions 630
12.2.3 Entropy of an Extended Binary Source 631
12.2.4 Shannon--Fano Source Coding 632
12.2.5 Huffman Source Coding 632
12.3 Communication in Noisy Environments: Basic Ideas 634
12.4 Communication in Noisy Channels: Block Codes 636
12.4.1 Hamming Distances and Error Correction 637
12.4.2 Single-Parity-Check Codes 638
12.4.3 Repetition Codes 639
12.4.4 Parity-Check Codes for Single Error Correction 640
12.4.5 Hamming Codes 644
12.4.6 Cyclic Codes 645
12.4.7 The Golay Code 647
12.4.8 Bose--Chaudhuri--Hocquenghem (BCH) Codes and Reed Solomon Codes 648
12.4.9 Performance Comparison Techniques 648
12.4.10 Block Code Examples 650
12.5 Communication in Noisy Channels: Convolutional Codes 657
12.5.1 Tree and Trellis Diagrams 659
12.5.2 The Viterbi Algorithm 661
12.5.3 Performance Comparisons for Convolutional Codes 664
12.6 Bandwidth and Power Efficient Modulation (TCM) 668
12.7 Feedback Channels 672
12.8 Modulation and Bandwidth Efficiency 676
12.8.1 Bandwidth and SNR 677
12.8.2 Comparison of Modulation Systems 678
12.9 Quick Overviews 679
12.9.1 Interleaving and Burst-Error Correction 679
12.9.2 Turbo Coding 681
12.9.3 Source Coding Examples 683
12.9.4 Digital Television 685
Further Reading 686
Summary 686
Drill Problems 688
Problems 688
Computer Exercises 692
APPENDIX A PHYSICAL NOISE SOURCES 693
A.1 Physical Noise Sources 693
A.1.1 Thermal Noise 693
A.1.2 Nyquist's Formula 695
A.1.3 Shot Noise 695
A.1.4 Other Noise Sources 696
A.1.5 Available Power 696
A.1.6 Frequency Dependence 697
A.1.7 Quantum Noise 697
A.2 Characterization of Noise in Systems 698
A.2.1 Noise Figure of a System 699
A.2.2 Measurement of Noise Figure 700
A.2.3 Noise Temperature 701
A.2.4 Effective Noise Temperature 702
A.2.5 Cascade of Subsystems 702
A.2.6 Attenuator Noise Temperature and Noise Figure 704
A.3 Free-Space Propagation Example 705
Further Reading 708
Problems 708
APPENDIX B JOINTLY GAUSSIAN RANDOM VARIABLES 710
B.1 The pdf 710
B.2 The Characteristic Function 711
B.3 Linear Transformations 711
APPENDIX C PROOF OF THE NARROWBAND NOISEMODEL 712
APPENDIX D ZERO-CROSSING AND ORIGIN ENCIRCLEMENTSTATISTICS 714
D.1 The Zero-Crossing Problem 714
D.2 Average Rate of Zero Crossings 716
Problems 719
APPENDIX E CHI-SQUARE STATISTICS 720
APPENDIX F MATHEMATICAL AND NUMERICAL TABLES 722
F.1 The Gaussian Q-Function 722
F.2 Trigonometric Identities 724
F.3 Series Expansions 724
F.4 Integrals 725
F.4.1 Indefinite 725
F.4.2 Definite 726
F.5 Fourier-Transform Pairs 727
F.6 Fourier-Transform Theorems 727
APPENDIX G ANSWERS TO DRILL PROBLEMS
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BIBLIOGRAPHY
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INDEX 728
