数字通信

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Preface xvi
Chapter 1 Introduction 1
Chapter 2 Deterministic and Random Signal Analysis 17
Chapter 3 Digital Modulation Schemes 95
Chapter 4 Optimum Receivers for AWGN Channels 160
Chapter 5 Carrier and Symbol Synchronization 290
Chapter 6 An Introduction to Information Theory 330
Chapter 7 Linear Block Codes 400
Chapter 8 Trellis and Graph Based Codes 491
Chapter 9 Digital Communication Through Band-Limited
Channels 597
Chapter 10 Adaptive Equalization 689
Chapter 11 Multichannel and Multicarrier Systems 737
Chapter 12 Spread Spectrum Signals for Digital Communications 762
Chapter 13 Fading Channels I: Characterization and Signaling 830
Chapter 14 Fading Channels II: Capacity and Coding 899
Chapter 15 Multiple- Antenna Systems 966
Chapter 16 Multiuser Communications 1028
Appendices
Appendix A Matrices 1085
Appendix B Error Probability for Multichannel Binary Signals 1090
Appendix C Error Probabilities for Adaptive Reception of M -Phase
Signals 1096
Appendix D Square Root Factorization 1 107
References and Bibliography 1109
Index 1142
V
CONTENTS
Preface
xvi
Chapter 1 Introduction
1
1.1 Elements of a Digital Communication System
1
1.2 Communication Channels and Their Characteristics
3
1.3 Mathematical Models for Communication Channels
10
1.4 A Historical Perspective in the Development of
Digital Communications
12
1.5 Overview of the Book
15
1.6 Bibliographical Notes and References
15
Chapter 2 Deterministic and Random Signal Analysis
17
2.1 Bandpass and Lowpass Signal Representation
18
2.7-7 Bandpass and Lowpass Signals / 2.1-2 Lowpass
Equivalent of Bandpass Signals / 2. 1-3 Energy
Considerations / 2.1-4 Lowpass Equivalent of a
Bandpass System
2.2 Signal Space Representation of Waveforms
28
2.2—
1 Vector Space Concepts / 2.2—2 Signal Space
Concepts / 2.2-3 Orthogonal Expansions of Signals /
2.2-
4 Gram- Schmidt Procedure
2.3 Some Useful Random Variables
40
2.4 Bounds on Tail Probabilities
56
2.5 Limit Theorems for Sums of Random Variables
63
2.6 Complex Random Variables
63
2.6-
1 Complex Random Vectors
2.7 Random Processes
66
2.
7-
1 Wide-Sense Stationary Random Processes / 2. 7-2
Cyclostationary Random Processes / 2. 7-3 Proper and
Circular Random Processes / 2. 7-4 Markov Chains
2.8 Series Expansion of Random Processes
74
2.8-
1 Sampling Theorem for Band-Limited Random
Processes / 2.8—2 The Karhunen-Loeve Expansion
2.9 Bandpass and Lowpass Random Processes
78
vi
Contents
vii
2.10 Bibliographical Notes and References 82
Problems 82
Chapter 3 Digital Modulation Schemes 95
3.1 Representation of Digitally Modulated Signals 95
3.2 Memoryless Modulation Methods 97
3.2-
1 Pulse Amplitude Modulation (PAM) / 3.2-2 Phase
Modulation / 3.2-3 Quadrature Amplitude
Modulation / 3.2-4 Multidimensional Signaling
3.3 Signaling Schemes with Memory 114
3.3-
1 Continuous -Phase Frequency-Shift Keying
(CPFSK) / 3.3-2 Continuous-Phase Modulation (CPM)
3.4 Power Spectrum of Digitally Modulated Signals 131
3.4-
1 Power Spectral Density of a Digitally Modulated Signal
with Memory / 3.4-2 Power Spectral Density of Linearly
Modulated Signals / 3.4-3 Power Spectral Density of
Digitally Modulated Signals with Finite Memory / 3.4-4
Power Spectral Density of Modulation Schemes with a Markov
Structure / 3.4-5 Power Spectral Densities of CPFSK and
CPM Signals
3.5 Bibliographical Notes and References 148
Problems 148
Chapter 4 Optimum Receivers for AWGN Channels 160
4.1 Waveform and Vector Channel Models 160
4.1-
1 Optimal Detection for a General Vector Channel
4.2 Waveform and Vector AWGN Channels 167
4.2-
1 Optimal Detection for the Vector AWGN
Channel / 4.2-2 Implementation of the Optimal Receiver for
AWGN Channels / 4.2-3 A Union Bound on the Probability of
Error of Maximum Likelihood Detection
4.3 Optimal Detection and Error Probability for B and-Limited
Signaling 188
4.3-
1 Optimal Detection and Error Probability for ASK or
PAM Signaling / 4.3-2 Optimal Detection and Error
Probability for PSK Signaling / 4.3-3 Optimal Detection and
Error Probability for QAM Signaling / 4.3-4 Demodulation
and Detection
4.4 Optimal Detection and Error Probability for Power-Limited
Signaling 203
4.4-
1 Optimal Detection and Error Probability for Orthogonal
Signaling / 4.4-2 Optimal Detection and Error Probability
for Biortho gonal Signaling / 4.4-3 Optimal Detection and
Error Probability for Simplex Signaling
Contents
4.5
Optimal Detection in Presence of Uncertainty:
N oncoherent Detection 210
4.5-1 Noncoherent Detection of Carrier Modulated
Signals / 4.5-2 Optimal Noncoherent Detection of FSK
Modulated Signals / 4.5-3 Error Probability of Orthogonal
Signaling with Noncoherent Detection / 4.5-4 Probability of
Error for Envelope Detection of Correlated Binary
Signals / 4.5-5 Differential PS K (DPS K)
4.6 A Comparison of Digital Signaling Methods 226
4.6-
1 Bandwidth and Dimensionality
4.7 Lattices and Constellations Based on Lattices 230
4.
7-
1 An Introduction to Lattices / 4. 7-2 Signal
Constellations from Lattices
4.8 Detection of Signaling Schemes with Memory 242
4.8-
1 The Maximum Likelihood Sequence Detector
4.9 Optimum Receiver for CPM Signals 246
4.9-
1 Optimum Demodulation and Detection of CPM /
4.9-
2 Performance of CPM Signals / 4.9-3 Suboptimum
Demodulation and Detection of CPM Signals
4.10
Performance Analysis for Wireline and Radio
Communication Systems 259
4.10-1 Regenerative Repeaters / 4.10-2 Link Budget
Analysis in Radio Communication Systems
4.11 Bibliographical Notes and References 265
Problems 266
Chapter 5 Carrier and Symbol Synchronization 290
5.1 Signal Parameter Estimation
290
5.1-1 The Likelihood Function / 5.1-2 Carrier Recovery and
Symbol Synchronization in Signal Demodulation
5.2 Carrier Phase Estimation
295
5.2-
1 Maximum-Likelihood Carrier Phase Estimation /
5.2-
2 The Phase-Locked Loop / 5.2-3 Effect of Additive
Noise on the Phase Estimate / 5.2-4 Decision-Directed
Loops / 5.2-5 Non-Decision-Directed Loops
5.3 Symbol Timing Estimation
315
5.3-
1 Maximum-Likelihood Timing Estimation /
5.3-
2 Non-Decision-Directed Timing Estimation
5.4 Joint Estimation of Carrier Phase and Symbol Timing
321
5.5 Performance Characteristics of ML Estimators 323
5.6 Bibliographical Notes and References 326
Problems 327
Chapter 6 An Introduction to Information Theory
330
6.1 Mathematical Models for Information Sources
331
Contents IX
6.2 A Logarithmic Measure of Information 332
6.3 Lossless Coding of Information Sources 335
6.3-
1 The Lossless Source Coding Theorem / 6.3-2 Lossless
Coding Algorithms
6.4 Lossy Data Compression 348
6.4-
1 Entropy and Mutual Information for Continuous
Random Variables / 6.4-2 The Rate Distortion Function
6.5 Channel Models and Channel Capacity 354
6.5-
1 Channel Models / 6.5-2 Channel Capacity
6.6 Achieving Channel Capacity with Orthogonal Signals 367
6.7 The Channel Reliability Function 369
6.8 The Channel Cutoff Rate 37
1
6.8-1 Bhattacharyya and Chernov Bounds / 6.8-2 Random
Coding
6.9 Bibliographical Notes and References 380
Problems 381
Chapter 7 Linear Block Codes 400
7.1 Basic Definitions 401
7.1-
1 The Structure of Finite Fields / 7.1-2 Vector Spaces
7.2 General Properties of Linear Block Codes 411
7.2-
1 Generator and Parity Check Matrices / 7.2-2 Weight
and Distance for Linear Block Codes / 7.2-3 The Weight
Distribution Polynomial / 7.2-4 Error Probability of Linear
Block Codes
7.3 Some Specific Linear Block Codes 420
7.3-
1 Repetition Codes / 7.3-2 Hamming Codes /
7.3-
3 Maximum-Length Codes / 7.3-4 Reed-Muller
Codes / 7.3-5 Hadamard Codes / 7.3-6 Golay Codes
7.4 Optimum Soft Decision Decoding of Linear
Block Codes 424
7.5 Hard Decision Decoding of Linear Block Codes 428
7.5-
1 Error Detection and Error Correction Capability of
Block Codes / 7.5-2 Block and Bit Error Probability for Hard
Decision Decoding
7.6 Comparison of Performance between Hard Decision and
Soft Decision Decoding 436
7.7 Bounds on Minimum Distance of Linear Block Codes 440
7.
7-
1 Singleton Bound / 7. 7-2 Hamming Bound /
7.
7-
3 Plotkin Bound / 7. 7-4 Elias Bound / 7. 7-5
McEliece-Rodemich-Rumsey-Welch (MRRW) Bound /
7.7-
6 Varshamov -Gilbert Bound
7.8 Modified Linear Block Codes 445
7.8-
1 Shortening and Lengthening / 7.8-2 Puncturing and
Extending / 7.8-3 Expurgation and Augmentation
X Contents
7.9
Cyclic Codes 447
7.9-
1 Cyclic Codes — Definition and Basic Properties /
7.9-
2 Systematic Cyclic Codes / 7.9-3 Encoders for Cyclic
Codes / 7.9-4 Decoding Cyclic Codes / 7.9-5 Examples of
Cyclic Codes
7.10 Bose-Chaudhuri-Hocquenghem (BCH) Codes 463
7.10-1 The Structure of BCH Codes / 7.10-2 Decoding
BCH Codes
7.11 Reed-Solomon Codes 471
7.12 Coding for Channels with Burst Errors 475
7.13 Combining Codes 477
7.13-1 Product Codes / 7.13-2 Concatenated Codes
7.14 Bibliographical Notes and References 482
Problems 482
Chapter 8 Trellis and Graph Based Codes 491
8.1 The Structure of Convolutional Codes 491
8.1-
1 Tree, Trellis, and State Diagrams / 8.1-2 The Transfer
Function of a Convolutional Code / 8.1-3 Systematic,
Nonrecursive, and Recursive Convolutional Codes /
8.1^1 The Inverse of a Convolutional Encoder and
Catastrophic Codes
8.2
Decoding of Convolutional Codes 510
8.2-
1 Maximum-Likelihood Decoding of Convolutional
Codes — The Viterbi Algorithm / 8.2-2 Probability of
Error for Maximum-Likelihood Decoding of Convolutional
Codes
8.3 Distance Properties of Binary Convolutional Codes 516
8.4 Punctured Convolutional Codes 516
8.4-1 Rate-Compatible Punctured Convolutional Codes
8.5 Other Decoding Algorithms for Convolutional Codes 525
8.6 Practical Considerations in the Application of
Convolutional Codes 532
8.7 Nonbinary Dual -k Codes and Concatenated Codes 537
8.8 Maximum a Posteriori Decoding of Convolutional
Codes — The B C JR Algorithm 54
1
8.9 Turbo Codes and Iterative Decoding 548
8.9-1 Performance Bounds for Turbo Codes / 8.9-2 Iterative
Decoding for Turbo Codes / 8.9-3 EXIT Chart Study of
Iterative Decoding
8.10 Factor Graphs and the Sum-Product Algorithm 558
8.10-1 Tanner Graphs / 8.10-2 Factor Graphs / 8.10-3 The
Sum-Product Algorithm / 8.10-4 MAP Decoding Using the
Sum-Product Algorithm
Contents
xi
8.11 Low Density Parity Check Codes 568
8.11-
1 Decoding LDPC Codes
8.12 Coding for Bandwidth-Constrained Channels — Trellis
Coded Modulation 571
8.12-
1 Lattices and Trellis Coded Modulation /
8.12-
2 Turbo-Coded Bandwidth Efficient Modulation
8.13 Bibliographical Notes and References 589
Problems 590
Chapter 9 Digital Communication Through Band-Limited
Channels 597
9.1 Characterization of Band-Limited Channels 598
9.2 Signal Design for Band-Limited Channels 602
9.2-
1 Design of Band-Limited Signals for No Intersymbol
Interference — The Nyquist Criterion / 9.2-2 Design of
Band-Limited Signals with Controlled ISI — Partial-Response
Signals / 9.2-3 Data Detection for Controlled ISI /
9.2-
4 Signal Design for Channels with Distortion
9.3 Optimum Receiver for Channels with ISI and AWGN
623
9.3-
1 Optimum Maximum-Likelihood Receiver /
9.3-
2 A Discrete-Time Model for a Channel with ISI /
9.3-
3 Maximum-Likelihood Sequence Estimation (MLSE) for
the Discrete-Time White Noise Filter Model /
9.3-
4 Performance of MLSE for Channels with ISI
9.4 Linear Equalization 640
9.4-
1 Peak Distortion Criterion / 9.4-2 Mean-Square-Error
(MSE) Criterion / 9.4-3 Performance Characteristics of the
MSE Equalizer / 9.4-4 Fractionally Spaced
Equalizers / 9.4-5 Baseband and Passband Linear Equalizers
9.5 Decision-Feedback Equalization
661
9.5-
1 Coefficient Optimization / 9.5-2 Performance
Characteristics of DEE / 9.5-3 Predictive Decision-Feedback
Equalizer / 9.5-4 Equalization at the
Transmitter — Tomlinson-Harashima Precoding
9.6 Reduced Complexity ML Detectors
669
9.7 Iterative Equalization and Decoding — Turbo
Equalization 67
1
9.8 Bibliographical Notes and References
673
Problems 674
Chapter 10 Adaptive Equalization
689
10.1 Adaptive Linear Equalizer
689
10.1-1 The Zero-Forcing Algorithm / 10.1-2 The LMS
Algorithm / 10.1-3 Convergence Properties of the LMS
Contents
xii
Algorithm / 10.1-4 Excess MSE due to Noisy Gradient
Estimates / 10.1-5 Accelerating the Initial Convergence Rate
in the LMS Algorithm / 10.1-6 Adaptive Fractionally Spaced
Equalizer — The Tap Leakage Algorithm / 10.1-7 An Adaptive
Channel Estimator for ML Sequence Detection
10.2 Adaptive Decision-Feedback Equalizer
705
10.3 Adaptive Equalization of Trellis-Coded Signals 706
10.4 Recursive Least-Squares Algorithms for Adaptive
Equalization 710
10.4-1 Recursive Least-Squares ( Kalman
)
Algorithm / 10.4-2 Linear Prediction and the Lattice Filter
10.5 Self-Recovering (Blind) Equalization 721
10.5-
1 Blind Equalization Based on the Maximum-Likelihood
Criterion / 10.5-2 Stochastic Gradient Algorithms /
10.5-
3 Blind Equalization Algorithms Based on Second- and
Higher-Order Signal Statistics
10.6 Bibliographical Notes and References
731
Problems 732
Chapter 11 Multichannel and Multicarrier Systems 737
11.1 Multichannel Digital Communications in AWGN
Channels
737
11.1-
1 Binary Signals / 11.1-2 M-ary Orthogonal Signals
11.2 Multicarrier Communications 743
11.2-
1 Single-Carrier Versus Multicarrier
Modulation / 11.2-2 Capacity of a Nonideal Linear Filter
Channel / 11.2-3 Orthogonal Frequency Division
Multiplexing (OFDM) / 11.2-4 Modulation and
Demodulation in an OFDM System / 11.2-5 An FFT
Algorithm Implementation of an OFDM System / 11.2-6
Spectral Characteristics of Multicarrier Signals / 11.2-7 Bit
and Power Allocation in Multicarrier Modulation / 11.2-8
Peak-to-Average Ratio in Multicarrier Modulation / 11.2-9
Channel Coding Considerations in Multicarrier Modulation
11.3 Bibliographical Notes and References
759
Problems
760
Chapter 12 Spread Spectrum Signals for Digital
Communications 762
12.1 Model of Spread Spectrum Digital Communication
System
763
12.2 Direct Sequence Spread Spectrum Signals
765
12.2-
1 Error Rate Performance of the Decoder /
12.2-
2 Some Applications of DS Spread Spectrum
Signals / 12.2-3 Effect of Pulsed Interference on DS Spread
Contents xiii
Spectrum Systems / 12.2^1 Excision of Narrowband
Interference in DS Spread Spectrum Systems /
12.2-
5 Generation of PN Sequences
12.3
Frequency-Hopped Spread Spectrum Signals 802
12.3-
1 Performance of FH Spread Spectrum Signals in an
AWGN Channel / 12.3-2 Performance of FH Spread
Spectrum Signals in Partial-Band Interference / 12.3-3 A
CDMA System Based on FH Spread Spectrum Signals
12.4 Other Types of Spread Spectrum Signals 814
12.5 Synchronization of Spread Spectrum Systems 815
12.6 Bibliographical Notes and References 823
Problems 823
Chapter 13 Fading Channels I: Characterization
and Signaling 830
13.1 Characterization of Fading Multipath Channels 831
13.1-1 Channel Correlation Functions and Power
Spectra / 13.1-2 Statistical Models for Fading Channels
13.2 The Effect of Signal Characteristics on the Choice of a
Channel Model 844
13.3 Frequency-Nonselective, Slowly Fading Channel 846
13.4 Diversity Techniques for Fading Multipath Channels 850
13.4-1 Binary Signals / 13.4-2 Multiphase Signals / 13.4-3
M-ary Orthogonal Signals
13.5 Signaling over a Frequency-Selective, Slowly Fading
Channel: The RAKE Demodulator 869
13.5-1 A Tapped-Delay-Line Channel Model / 13.5-2 The
RAKE Demodulator / 13.5-3 Performance of RAKE
Demodulator / 13.5^1 Receiver Structures for Channels with
Intersymbol Interference
13.6 Multicarrier Modulation (OFDM) 884
13.6-1 Performance Degradation of an OFDM System due to
Doppler Spreading / 13.6-2 Suppression ofICI in OFDM
Systems
13.7 Bibliographical Notes and References 890
Problems 891
Chapter 14 Fading Channels II: Capacity and Coding 899
14.1 Capacity of Fading Channels 900
14.1-
1 Capacity of Finite-State Channels
14.2 Ergodic and Outage Capacity 905
14.2-
1 The Ergodic Capacity of the Rayleigh Fading
Channel / 14.2-2 The Outage Capacity of Rayleigh Fading
Channels
14.3 Coding for Fading Channels 918
XIV Contents
14.4 Performance of Coded Systems In Fading Channels 919
14.4-
1 Coding for Fully Interleaved Channel Model
14.5 Trellis-Coded Modulation for Fading Channels 929
14.5-
1 TCM Systems for Fading Channels / 14.5-2 Multiple
Trellis-Coded Modulation (MTCM)
14.6 Bit-Interleaved Coded Modulation 936
14.7 Coding in the Frequency Domain 942
14.7-1 Probability of Error for Soft Decision Decoding of
Linear Binary Block Codes / 14. 7-2 Probability of Error for
Hard-Decision Decoding of Linear Block Codes / 14. 7-3
Upper Bounds on the Performance of Convolutional Codes for
a Rayleigh Fading Channel / 14.7^1 Use of Constant-Weight
Codes and Concatenated Codes for a Fading Channel
14.8 The Channel Cutoff Rate for Fading Channels 957
14.8-1 Channel Cutoff Rate for Fully Interleaved Fading
Channels with CSI at Receiver
14.9 Bibliographical Notes and References 960
Problems 961
Chapter 15 Multiple-Antenna Systems 966
15.1 Channel Models for Multiple- Antenna Systems 966
15.1-1 Signal Transmission Through a Slow Fading
Frequency -N onselective MIMO Channel / 15.1-2 Detection
of Data Symbols in a MIMO System / 15.1-3 Signal
Transmission Through a Slow Fading Frequency-Selective
MIMO Channel
15.2 Capacity of MIMO Channels 981
15.2-
1 Mathematical Preliminaries / 15.2-2 Capacity of a
Frequency-Nonselective Deterministic MIMO
Channel / 15.2-3 Capacity of a Frequency-Nonselective
Ergodic Random MIMO Channel / 15.2-4 Outage
Capacity / 15.2-5 Capacity of MIMO Channel When the
Channel Is Known at the Transmitter
15.3 Spread Spectrum Signals and Multicode Transmission 992
15.3-
1 Orthogonal Spreading Sequences / 15.3-2
Multiplexing Gain Versus Diversity Gain / 15.3-3 Multicode
MIMO Systems
15.4 Coding for MIMO Channels 1001
15.4-
1 Performance of Temporally Coded SISO Systems in
Rayleigh Fading Channels / 15.4-2 Bit-Interleaved Temporal
Coding for MIMO Channels / 15.4-3 Space-Time Block
Codes for MIMO Channels / 15. 4-^4 Pairwise Error
Probability for a Space-Time Code / 15.4-5 Space-Time
Trellis Codes for MIMO Channels / 15.4-6 Concatenated
Space-Time Codes and Turbo Codes
Contents
xv
15.5 Bibliographical Notes and References
1021
Problems
1021
Chapter 16 Multiuser Communications
1028
16.1 Introduction to Multiple Access Techniques
1028
16.2 Capacity of Multiple Access Methods
1031
16.3 Multiuser Detection in CDMA Systems
1036
16.3-
1 CDMA Signal and Channel Models / 16.3-2 The
Optimum Multiuser Receiver / 16.3-3 Suboptimum
Detectors / 16.3-4 Successive Interference
Cancellation / 16.3-5 Other Types of Multiuser
Detectors / 16.3-6 Performance Characteristics of Detectors
16.4 Multiuser MIMO Systems for Broadcast Channels
1053
16.4-
1 Linear Precoding of the Transmitted Signals / 16.4-2
Nonlinear Precoding of the Transmitted Signals — The QR
Decomposition / 16.4-3 Nonlinear Vector
Precoding / 16.4-4 Lattice Reduction Technique for
Precoding
16.5 Random Access Methods
1068
16.5-1 ALOHA Systems and Protocols / 16.5-2 Carrier
Sense Systems and Protocols
16.6 Bibliographical Notes and References
1077
Problems
1078
Appendix A Matrices
1085
A.l Eigenvalues and Eigenvectors of a Matrix
1086
A.2 Singular- Value Decomposition
1087
A.3 Matrix Norm and Condition Number
1088
A.4 The Moore-Penrose Pseudoinverse
1088
Appendix B Error Probability for Multichannel Binary Signals
1090
Appendix C Error Probabilities for Adaptive Reception
of M-Phase Signals
1096
C.l Mathematical Model for an M-Phase Signaling Communi-
cation System
1096
C.2 Characteristic Function and Probability Density Function of
the Phase 6 1098
C.3 Error Probabilities for Slowly Fading Rayleigh Channels
1100
C.4 Error Probabilities for Time-Invariant and Ricean Fading
Channels
1104
Appendix D Square Root Factorization
1107
References and Bibliography
1 109
Index
1142