Digital Communication Systems

Cover......Page 1
Title Page......Page 3
Copyright
......Page 4
Preface......Page 7
Contents......Page 15
1.1 Historical Background......Page 21
1.2 The Communication Process......Page 22
1.3 Multiple-Access Techniques......Page 24
1.4 Networks......Page 26
1.5 Digital Communications......Page 29
1.6 Organization of the Book......Page 31
Notes......Page 32
2.2 The Fourier Series......Page 33
2.3 The Fourier Transform......Page 36
2.4 The Inverse Relationship between Time-Domain and Frequency-Domain Representations......Page 44
2.5 The Dirac Delta Function......Page 48
2.6 Fourier Transforms of Periodic Signals......Page 54
2.7 Transmission of Signals through Linear Time-Invariant Systems......Page 57
2.8 Hilbert Transform......Page 62
2.9 Pre-envelopes......Page 65
2.10 Complex Envelopes of Band-Pass Signals......Page 67
2.11 Canonical Representation of Band-Pass Signals......Page 69
2.12 Complex Low-Pass Representations of Band-Pass Systems......Page 72
2.13 Putting the Complex Representations of Band-Pass Signals and Systems All Together......Page 74
2.14 Linear Modulation Theory......Page 78
2.15 Phase and Group Delays......Page 86
2.16 Numerical Computation of the Fourier Transform......Page 89
2.17 Summary and Discussion......Page 98
Problems......Page 99
Notes......Page 105
3.1 Introduction......Page 107
3.2 Set Theory......Page 108
3.3 Probability Theory......Page 110
3.4 Random Variables......Page 117
3.5 Distribution Functions......Page 118
3.6 The Concept of Expectation......Page 125
3.7 Second-Order Statistical Averages......Page 128
3.8 Characteristic Function......Page 131
3.9 The Gaussian Distribution......Page 133
3.10 The Central Limit Theorem......Page 138
3.11 Bayesian Inference......Page 139
3.12 Parameter Estimation......Page 142
3.13 Hypothesis Testing......Page 146
3.14 Composite Hypothesis Testing......Page 152
3.15 Summary and Discussion......Page 153
Problems......Page 156
Notes......Page 164
4.2 Mathematical Definition of a Stochastic Process......Page 165
4.3 Two Classes of Stochastic Processes: Strictly Stationary and Weakly Stationary......Page 167
4.4 Mean, Correlation, and Covariance Functions of Weakly Stationary Processes......Page 169
4.5 Ergodic Processes......Page 177
4.6 Transmission of a Weakly Stationary Process through a Linear Time-invariant Filter......Page 178
4.7 Power Spectral Density of a Weakly Stationary Process......Page 180
4.8 Another Definition of the Power Spectral Density......Page 190
4.9 Cross-spectral Densities......Page 192
4.10 The Poisson Process......Page 194
4.11 The Gaussian Process......Page 196
4.12 Noise......Page 199
4.13 Narrowband Noise......Page 203
4.14 Sine Wave Plus Narrowband Noise......Page 213
4.15 Summary and Discussion......Page 215
Problems......Page 218
Notes......Page 225
5.2 Entropy......Page 227
5.3 Source-coding Theorem......Page 234
5.4 Lossless Data Compression Algorithms......Page 235
5.5 Discrete Memoryless Channels......Page 243
5.6 Mutual Information......Page 246
5.7 Channel Capacity......Page 250
5.8 Channel-coding Theorem......Page 252
5.9 Differential Entropy and Mutual Information for ContinuousRandom Ensembles......Page 257
5.10 Information Capacity Law......Page 260
5.11 Implications of the Information Capacity Law......Page 264
5.12 Information Capacity of Colored Noisy Channel......Page 268
5.13 Rate Distortion Theory......Page 273
5.14 Summary and Discussion......Page 276
Problems......Page 277
Notes......Page 284
6.1 Introduction......Page 287
6.2 Sampling Theory......Page 288
6.3 Pulse-Amplitude Modulation......Page 294
6.4 Quantization and its Statistical Characterization......Page 298
6.5 Pulse-Code Modulation......Page 305
6.6 Noise Considerations in PCM Systems......Page 310
6.7 Prediction-Error Filtering for Redundancy Reduction......Page 314
6.8 Differential Pulse-Code Modulation......Page 321
6.9 Delta Modulation......Page 325
6.10 Line Codes......Page 329
6.11 Summary and Discussion......Page 332
Problems......Page 333
Notes......Page 342
7.1 Introduction......Page 343
7.2 Geometric Representation of Signals......Page 344
7.3 Conversion of the Continuous AWGN Channel into a Vector Channel......Page 352
7.4 Optimum Receivers Using Coherent Detection......Page 357
7.5 Probability of Error......Page 364
7.6 Phase-Shift Keying Techniques Using Coherent Detection......Page 372
7.7 M-ary Quadrature Amplitude Modulation......Page 390
7.8 Frequency-Shift Keying Techniques Using Coherent Detection......Page 395
7.9 Comparison of M-ary PSK and M-ary FSK from an Information-Theoretic Viewpoint......Page 418
7.10 Detection of Signals with Unknown Phase......Page 420
7.11 Noncoherent Orthogonal Modulation Techniques......Page 424
7.12 Binary Frequency-Shift Keying Using Noncoherent Detection......Page 430
7.13 Differential Phase-Shift Keying......Page 431
7.14 BER Comparison of Signaling Schemes over AWGN Channels......Page 435
7.15 Synchronization......Page 438
7.16 Recursive Maximum Likelihood Estimation for Synchronization......Page 439
7.17 Summary and Discussion......Page 451
Problems......Page 452
Notes......Page 464
8.1 Introduction......Page 465
8.2 Error Rate Due to Channel Noise in a Matched-Filter Receiver......Page 466
8.3 Intersymbol Interference......Page 467
8.5 Ideal Nyquist Pulse for Distortionless BasebandData Transmission......Page 470
8.6 Raised-Cosine Spectrum......Page 474
8.7 Square-Root Raised-Cosine Spectrum......Page 478
8.8 Post-Processing Techniques: The Eye Pattern......Page 483
8.9 Adaptive Equalization......Page 489
8.10 Broadband Backbone Data Network: Signaling over Multiple Baseband Channels......Page 494
8.11 Digital Subscriber Lines......Page 495
8.12 Capacity of AWGN Channel Revisited......Page 497
8.13 Partitioning Continuous-Time Channel into a Set of Subchannels......Page 498
8.14 Water-Filling Interpretation of the Constrained Optimization Problem......Page 504
8.15 DMT System using Discrete Fourier Transform......Page 507
8.16 Summary and Discussion......Page 514
Problems......Page 515
Notes......Page 519
9.1 Introduction......Page 521
9.2 Propagation Effects......Page 522
9.4 Statistical Characterization of Wideband Wireless Channels......Page 531
9.5 FIR Modeling of Doubly Spread Channels......Page 540
9.6 Comparison of Modulation Schemes: Effects of Flat Fading......Page 545
9.7 Diversity Techniques......Page 547
9.8 “Space Diversity-on-Receive” Systems......Page 548
9.9 “Space Diversity-on-Transmit” Systems......Page 558
9.10 “Multiple-Input, Multiple-Output” Systems: Basic Considerations......Page 566
9.11 MIMO Capacity for Channel Known at the Receiver......Page 571
9.12 Orthogonal Frequency Division Multiplexing......Page 576
9.13 Spread Spectrum Signals......Page 577
9.14 Code-Division Multiple Access......Page 580
9.15 The RAKE Receiver and Multipath Diversity......Page 584
9.16 Summary and Discussion......Page 586
Problems......Page 588
Notes......Page 595
10.1 Introduction......Page 597
10.2 Error Control Using Forward Error Correction......Page 598
10.3 Discrete Memoryless Channels......Page 599
10.4 Linear Block Codes......Page 602
10.5 Cyclic Codes......Page 613
10.6 Convolutional Codes......Page 625
10.7 Optimum Decoding of Convolutional Codes......Page 633
10.8 Maximum Likelihood Decoding of Convolutional Codes......Page 634
10.9 Maximum a Posteriori Probability Decoding ofConvolutional Codes......Page 643
10.10 Illustrative Procedure for Map Decoding in the Log-Domain......Page 658
10.11 New Generation of Probabilistic Compound Codes......Page 664
10.12 Turbo Codes......Page 665
10.13 EXIT Charts......Page 677
10.14 Low-Density Parity-Check Codes......Page 686
10.15 Trellis-Coded Modulation......Page 695
10.16 Turbo Decoding of Serial Concatenated Codes......Page 701
10.17 Summary and Discussion......Page 708
Problems......Page 709
Notes......Page 718
A.1 The Chi-Square Distribution......Page 721
A.2 The Log-Normal Distribution......Page 723
A.3 The Nakagami Distribution......Page 726
Notes......Page 729
Appendix B: Bounds on the Q-Function......Page 731
C.1 Series Solution of Bessel’s Equation......Page 733
C.2 Properties of the Bessel Function......Page 734
C.3 Modified Bessel Function......Page 736
Notes......Page 738
D.1 Optimization Involving a Single Equality Constraint......Page 739
E.1 Log-Det Capacity Formula of MIMO Channels......Page 741
E.2 MIMO Capacity for Channel Known at the Transmitter......Page 744
Notes......Page 748
Appendix F: Interleaving......Page 749
F.1 Block Interleaving......Page 750
F.2 Convolutional Interleaving......Page 752
F.3 Random Interleaving......Page 753
Notes......Page 754
G.1 PAPR Properties of OFDM Signals......Page 755
G.2 Maximum PAPR in OFDM Using M-ary PSK......Page 756
G.3 Clipping-Filtering: A Technique for PAPR Reduction......Page 757
Notes......Page 758
H.1 Power Amplifier Nonlinearities......Page 759
H.2 Nonlinear Modeling of Band-Pass Power Amplifiers......Page 762
Notes......Page 763
Appendix I: Monte Carlo Integration......Page 765
Notes......Page 766
J.1 Properties of Maximal-Length Sequences......Page 767
J.2 Choosing a Maximal-Length Sequence......Page 770
Notes......Page 774
Appendix K: Mathematical Tables......Page 775
Conventions and Notations......Page 779
Abbreviations......Page 782
References......Page 785
Further Reading......Page 790
Index......Page 791
Credits......Page 801