Digital Communications and Signal Processing

by Vasudevan; K.

• ISBN13: 9781420068115
• ISBN10: 1420068113
• Edition: CD
• Format: Hardcover
• Copyright: 2008-01-24
• Publisher: CRC Press

Summary

Examining the topic from both a theoretical and practical perspective, this book covers a wide variety of topics in digital communications. Notable features include expression of the probability of error in terms of the Euclidean distance instead of the usual EbIN0 adoption of a new approach to the Viterbi algorithm that does not assume any knowledge of the encoder starting and ending states, discussions on constellation shaping, shell mapping algorithm and root-raised cosine pulse shaping, and a unified approach to continuous phase frequency modulation where M-ary FSK and MSK are special cases. The book is well suited for a senior undergraduate to a graduate level course in communications theory. The accompanying CD-ROM containing C programs on Viterbi algorithm, shell mapping and turbo codes will aid the student in understanding these topics better.

Table of Contents

Notations	p. ix
Calligraphic Letters	p. x
Preface	p. xi
Acknowledgements	p. xiii
Introduction	p. 1
Overview of the Book	p. 3
Bibliography	p. 4
Communicating with Points	p. 6
Coherent Detectors for Two-Dimensional Constellations	p. 6
Performance analysis	p. 8
Optimizing the constellation	p. 9
Union bound on the probability of error for 2-D constellations	p. 10
M-ary signalling schemes	p. 10
Constellations with minimum average power	p. 18
Coherent Detectors for Multidimensional Orthogonal Constellations	p. 19
Performance analysis	p. 20
Union bound on the probability of error for multi-D constellations	p. 23
Minimum SNR required for error-free transmission	p. 23
Binary antipodal and orthogonal constellations	p. 29
Bi-Orthogonal Constellations	p. 30
Simplex Constellations	p. 31
Noncoherent Detectors for Multidimensional Orthogonal Constellations	p. 31
Performance analysis	p. 33
Exact expression for probability of error	p. 35
Noncoherent Detectors for M-ary PSK	p. 37
Approximate performance analysis of differential M-ary PSK	p. 38
Coherent Detectors in Coloured Noise	p. 41
Performance analysis	p. 45
Coherent Detectors for Frequency Nonselective (Flat) Fading Channels	p. 49
Performance analysis	p. 51
Performance analysis for BPSK	p. 55
Approximate performance analysis	p. 56
Summary	p. 58
Channel Coding	p. 59
Introduction	p. 59
The Convolutional Encoder	p. 61
Are the Encoded Symbols Correlated?	p. 69
Hard-Decision Decoding of Convolutional Codes	p. 70
The Viterbi algorithm (VA)	p. 74
Performance analysis of hard-decision decoding	p. 77
Soft-Decision Decoding of Convolutional Codes	p. 85
Performance analysis of soft-decision decoding	p. 87
Trellis Coded Modulation (TCM)	p. 90
Mapping by set partitioning	p. 92
Performance of TCM schemes	p. 96
Analysis of a QPSK TCM scheme	p. 100
Analysis of a 16-QAM TCM scheme	p. 101
Maximization of the Shape Gain	p. 104
Constellation Shaping by Shell Mapping	p. 107
The shell mapping algorithm	p. 111
Turbo Codes	p. 118
The turbo decoder	p. 120
The BCJR algorithm	p. 124
Performance of ML decoding of turbo codes	p. 127
Summary	p. 129
Transmission of Signals Through Distortionless Channels	p. 130
Linear Modulation	p. 131
Transmitter	p. 131
Power spectral density of the transmitted signal	p. 135
Proof of Proposition 3.1.1	p. 140
Receiver	p. 141
Pulse shapes with zero ISI	p. 144
Application of matched filtering in CDMA	p. 146
Discrete-time receiver implementation	p. 152
Nonlinear Modulation	p. 158
CPFM with full response rectangular filters	p. 158
Summary	p. 169
Transmission of Signals Through Distorting Channels	p. 170
Receivers Based on Equalization	p. 171
Linear equalization - symbol-spaced equalizers	p. 171
Finite length equalizer	p. 179
The steepest descent algorithm	p. 181
The least mean square (LMS) algorithm	p. 184
Linear equalization - fractionally-spaced equalizers	p. 184
Nonlinear equalization - the predictive DFE	p. 188
Implementation of the predictive DFE	p. 190
The conventional DFE	p. 191
Receivers Based on Maximum Likelihood Sequence Estimation (MLSE)	p. 194
Symbol-spaced MLSE	p. 194
Fractionally-spaced MLSE	p. 203
Equivalence between T-spaced and T/2-spaced ML detectors	p. 206
Multicarrier Communication	p. 212
Channel loading	p. 218
The discrete multitone (DMT)	p. 221
Summary	p. 225
Complex Differentiation	p. 226
The Chernoff Bound	p. 229
On Groups and Finite Fields	p. 231
Groups	p. 231
Fields	p. 235
The D-transform	p. 237
Polynomials over GF(2)	p. 239
Properties of the Correlation Matrix	p. 241
Some Aspects of Discrete-Time Signal Processing	p. 245
The Sampling Theorem	p. 245
Discrete-Time Matched Filtering of Signals Having an Arbitrary Time Delay	p. 248
Time Domain Response for the Root-Raised Cosine Spectrum	p. 252
Parseval's Energy Theorem	p. 255
Transmission of a Random Process Through a Filter	p. 257
Lowpass Equivalent Representation of Passband Systems	p. 259
Linear Prediction	p. 263
Forward Prediction	p. 263
Backward Prediction	p. 265
The Levinson-Durbin Algorithm	p. 267
Minimum Phase Property of the Forward Prediction Filter	p. 271
Cholesky Decomposition of the Autocovariance Matrix	p. 276
Eigendecomposition of a Circulant Matrix	p. 278
References	p. 281
Index	p. 289
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