Principles of Digital Transmission

by Benedetto, Sergio; Biglieri, Ezio

• ISBN13: 9780306457531
• ISBN10: 0306457539
• Format: Hardcover
• Copyright: 1998-12-01
• Publisher: Plenum Pub Corp

Summary

Principles of Digital Transmission is designed for advanced undergraduate and graduate level students and professions in telecommunications. Teachers and learners can mix and match chapters to create four distinct courses: (1) a one-term basic course in digital communications; (2) a one-term course in advanced digital communications; (3) a one-term course in information theory and coding; (4) a two-term course sequence in digital communications and coding. The book provides rigorous mathematical tools for the analysis and design of digital transmission systems. The authors emphasize methodology in their aim to teach the reader how to do it rather than how it is done. They apply the fundamental tools of the discipline onto a number of systems, such as wireless data transmission systems.

Table of Contents

Introduction and motivation	1	(8)
A mathematical introduction	9	(94)
Signals and systems	9	(10)
Discrete signals and systems	10	(4)
Continuous signals and systems	14	(5)
Random processes	19	(10)
Discrete-time processes	19	(7)
Continuous-time processes	26	(3)
Spectral analysis of deterministic and random signals	29	(25)
Spectral analysis of random digital signals	36	(18)
Narrowband signals and bandpass systems	54	(15)
Narrowband signals: Complex envelopes	56	(7)
Bandpass systems	63	(6)
Discrete representation of continuous signals	69	(14)
Orthonormal expansions of finite-energy signals	70	(12)
Orthonormal expansions of random signals	82	(1)
Elements of detection theory	83	(13)
Optimum detector: One real signal in noise	84	(6)
Optimum detector: M real signals in noise	90	(3)
Detection problem for complex signals	93	(2)
Summarizing the detection procedure	95	(1)
Bibliographical notes	96	(1)
Problems	97	(6)
Basic results from information theory	103	(56)
Introduction	104	(2)
Discrete stationary sources	106	(16)
A measure of information: entropy of the source alphabet	106	(3)
Coding of the source alphabet	109	(6)
Entropy of stationary sources	115	(7)
Communication channels	122	(28)
Discrete memoryless channel	122	(6)
Capacity of the discrete memoryless channel	128	(6)
Equivocation and error probability	134	(7)
Additive Gaussian channel	141	(9)
Bibliographical notes	150	(1)
Problems	151	(8)
Waveform transmission over the Gaussian channel	159	(56)
Introduction	160	(6)
A simple modulation scheme with memory	163	(1)
Coherent vs. incoherent demodulation	164	(2)
Symbol error probability	166	(1)
Memoryless modulation and coherent demodulation	166	(21)
Geometric interpretation of the optimum demodulator	172	(4)
Error probability evaluation	176	(2)
Exact calculation of error probability	178	(9)
Approximations and bounds to P(e)	187	(9)
An ad hoc technique: Bounding P(e) for M-PSK	188	(2)
The union bound	190	(1)
The union-Bhattacharyya bound	191	(2)
A looser upper bound	193	(1)
A lower bound	193	(1)
Significance of dmin	194	(1)
An approximation to error probability	195	(1)
Incoherent demodulation of bandpass signals	196	(10)
Equal-energy signals	198	(1)
On-off signaling	199	(3)
Equal-energy binary signals	202	(2)
Equal-energy M-ary orthogonal signals	204	(2)
Bibliographical notes	206	(1)
Problems	206	(9)
Digital modulation schemes	215	(57)
Bandwidth, power, error probability	215	(6)
Bandwidth	216	(2)
Signal-to-noise ratio	218	(2)
Error probability	220	(1)
Trade-offs in the selection of a modulation scheme	221	(1)
Pulse-amplitude modulation (PAM)	221	(3)
Error probability	222	(2)
Power spectrum and bandwidth efficiency	224	(1)
Phase-shift keying (PSK)	224	(3)
Error probability	225	(2)
Power spectrum and bandwidth efficiency	227	(1)
Quadrature amplitude modulation (QAM)	227	(11)
Error probability	230	(4)
Asymptotic power efficiency	234	(2)
Power spectrum and bandwidth efficiency	236	(1)
QAM and the capacity of the two-dimensional channel	236	(2)
Orthogonal frequency-shift keying (FSK)	238	(4)
Error probability	239	(1)
Asymptotic power efficiency	240	(1)
Power spectrum and bandwidth efficiency	240	(2)
Multidimensional signal constellations: Lattices	242	(7)
Lattice constellations	245	(2)
Examples of lattices	247	(2)
Carving a signal constellation out of a lattice	249	(3)
Spherical constellations	250	(1)
Shell mapping	251	(1)
Error probability	252	(1)
No perfect carrier-phase recovery	252	(10)
Coherent demodulation of differentially-encoded PSK (DCPSK)	255	(3)
Differentially-coherent demodulation of differentially encoded PSK	258	(4)
Incoherent demodulation of orthogonal FSK	262	(1)
Digital modulation trade-offs	262	(2)
Bibliographical notes	264	(1)
Problems	264	(8)
Modulations for the wireless channel	272	(40)
Variations on the QPSK theme	274	(7)
Offset QPSK	274	(2)
Minimum-shift keying (MSK)	276	(3)
Pseudo-octonary QPSK (π/4-QPSK)	279	(2)
Continuous-phase modulation	281	(18)
Time-varying vs. time-invariant trellises	284	(2)
General CPM	286	(3)
Power spectrum of full-response CPM	289	(5)
Modulators for CPM	294	(1)
Demodulating CPM	295	(4)
MSK and its multiple avatars	299	(8)
MSK as CPFSK	299	(3)
Massey's implementation	302	(2)
Rimoldi's implementation	304	(1)
De Buda's implementation	305	(1)
Amoroso and Kivett's implementation	306	(1)
GMSK	307	(2)
Bibliographical notes	309	(1)
Problems	310	(2)
Intersymbol interference channels	312	(68)
Analysis of coherent digital systems	313	(10)
Evaluation of the error probability	323	(14)
PAM modulation	324	(5)
Two-dimensional modulation schemes	329	(8)
Eliminating intersymbol interference: the Nyquist criterion	337	(11)
The raised-cosine spectrum	343	(4)
Optimum design of the shaping and receiving filters	347	(1)
Mean-square error optimization	348	(10)
Optimizing the receiving filter	350	(3)
Performance of the optimum receiving filter	353	(1)
Optimizing the shaping filter	354	(2)
Information-theoretic optimization	356	(2)
Maximum-likelihood sequence receiver	358	(15)
Maximum-likelihood sequence detection using the Viterbi algorithm	359	(6)
Error probability for the maximum-likelihood sequence receiver	365	(5)
Significance of dmin and its computation	370	(1)
Implementation of maximum-likelihood sequence detectors	371	(2)
Bibliographical notes	373	(2)
Problems	375	(5)
Adaptive receivers and channel equalization	380	(49)
Channel model	381	(1)
Channel identification	382	(8)
Using a channel-sounding sequence	383	(1)
Mean-square error channel identification	383	(6)
Blind channel identification	389	(1)
Channel equalization	390	(12)
Performance of the infinitely long equalizer	392	(4)
Gradient algorithm for equalization	396	(6)
Fractionally-spaced equalizers	402	(1)
Training the equalizer: Cyclic equalization	403	(3)
Non-MSE criteria for equalization	406	(3)
Zero-forcing equalization	406	(1)
Least-squares algorithms	407	(2)
Non-TDL equalizer structures	409	(1)
Decision-feedback equalization	409	(5)
Blind equalization	414	(4)
Constant-modulus algorithm	415	(2)
Shalvi-Weinstein algorithm	417	(1)
Stop-and-go algorithm	418	(1)
More on complex equalizers	418	(3)
Tomlinson-Harashima precoding	421	(3)
Bibliographical notes	424	(2)
Problems	426	(3)
Carrier and clock synchronization	429	(23)
Introduction	429	(1)
Acquisition and training	430	(4)
The phase-locked loop	434	(6)
Order of the phase-locked loop	436	(4)
Carrier synchronization	440	(5)
Clock synchronizers	445	(2)
Effect of phase and timing jitter	447	(1)
Bibliographical notes	448	(2)
Problems	450	(2)
Improving the transmission reliability: Block codes	452	(80)
A taxonomy of channel codes	453	(6)
Block codes	459	(44)
Error-detecting and error-correcting capabilities of a block code	465	(4)
Decoding table and standard array of a linear block code	469	(3)
Hamming codes	472	(2)
Dual codes	474	(1)
Maximal-length codes	474	(1)
Reed-Muller codes	475	(1)
Cyclic codes	476	(15)
Special classes of cyclic codes	491	(5)
Maximal-length (pseudonoise) sequences	496	(3)
Codes for burst-error detection and correction	499	(4)
Performance evaluation of block codes	503	(16)
Performance of error detection systems	506	(1)
Performance of error correction systems: word error probability	507	(5)
Performance of error correction systems: bit error probability	512	(7)
Coding bounds	519	(7)
Bounds on the code minimum distance	520	(1)
Bounds on code performance	521	(5)
Bibliographical notes	526	(1)
Problems	527	(5)
Convolutional and concatenated codes	532	(96)
Convolutional codes	533	(45)
State diagram representation of convolutional codes	539	(7)
Best known short-constraint-length convolutional codes	546	(8)
Maximum-likelihood decoding of convolutional codes and the Viterbi algorithm	554	(7)
Other decoding techniques for convolutional codes	561	(3)
Performance evaluation of convolutional codes with ML decoding	564	(7)
Systematic recursive convolutional encoders	571	(5)
Coding bounds	576	(2)
Concatenated codes	578	(4)
Reed-Solomon codes and orthogonal modulation	579	(1)
Reed-Solomon and convolutional codes	580	(2)
Concatenated codes with interleaver	582	(41)
Performance analysis	583	(13)
Design of concatenated codes with interleaver	596	(9)
Iterative decoding of concatenated codes with interleavers	605	(18)
Bibliographical notes	623	(1)
Problems	624	(4)
Coded modulation	628	(58)
The cutoff rate and its role	628	(6)
Computing the cutoff rate: AWGN channel with coherent detection	629	(5)
Introducing TCM	634	(6)
Fundamentals of TCM	636	(2)
Trellis representation	638	(1)
Decoding TCM	638	(2)
Free distance of TCM	640	(1)
Some examples of TCM schemes	640	(11)
Coding gains achieved by TCM schemes	645	(1)
Set partitioning	645	(2)
Representation of TCM	647	(2)
TCM with multidimensional constellations	649	(2)
Error probability of TCM	651	(19)
Upper bound to error event probability	652	(11)
Examples	663	(3)
Computation of δfree	666	(4)
Power density spectrum	670	(2)
Rotationally-invariant TCM	672	(6)
Multilevel coded modulation and BCM	678	(3)
Staged decoding of multilevel constructions	681	(1)
Bibliographical notes	681	(2)
Problems	683	(3)
Digital transmission over fading channels	686	(39)
Impulse response and transfer function of a fading channel	688	(3)
Examples of radio channels	691	(8)
Two-path propagation	691	(2)
Single-path propagation: Effect of movement	693	(1)
Two-path propagation: Effect of movement	694	(1)
Multipath propagation: Effect of movement	695	(2)
Multipath propagation with a fixed path	697	(2)
Frequency-flat, slowly fading channels	699	(11)
Coherent detection of binary signals with perfect CSI	700	(2)
A general technique for computing error probabilities	702	(7)
No channel-state information	709	(1)
Differential and noncoherent detection	710	(1)
Introducing diversity	710	(6)
Diversity combining techniques	711	(5)
Coding for the Rayleigh fading channel	716	(5)
Guidelines of code design for the Rayleigh fading channel	719	(1)
Cutoff rate of the fading channel	720	(1)
Bibliographical notes	721	(2)
Problems	723	(2)
Digital transmission over nonlinear channels	725	(48)
A model for the nonlinear channel	726	(2)
Spectral analysis of nonlinear signals	728	(2)
Volterra model for bandpass nonlinear channels	730	(16)
Error probability evaluation for M-ary CPSK	738	(4)
Including uplink noise in the analysis	742	(4)
Optimum linear receiving filter	746	(6)
Maximum-likelihood sequence receiver	752	(6)
Error performance	756	(2)
Identification and equalization of nonlinear channels	758	(7)
Compensation of nonlinear channels	765	(5)
pth-order compensation	766	(4)
Bibliographical notes	770	(1)
Problems	770	(3)
A Useful formulas and approximations	773	(5)
A.1. Error function and complementary error function	773	(2)
A.2. The modified Bessel function I0	775	(1)
A.3. Marcum Q-function and related integrals	775	(1)
A.4. Probability that one Rice-distributed RV exceeds another one	776	(2)
B Some facts from matrix theory	778	(10)
B.1. Basic matrix operations	778	(2)
B.2. Numbers associated with a matrix	780	(3)
B.3. Some classes of matrices	783	(2)
B.4. Convergence of matrix sequences	785	(1)
B.5. The gradient vector	786	(1)
B.6. The diagonal decomposition	786	(1)
B.7. Bibliographical notes	787	(1)
C Variational techniques and constrained optimization	788	(3)
D Transfer functions of directed graphs	791	(3)
E Approximate computation of averages	794	(13)
E.1. Computation of the moments of a RV	794	(2)
E.2. Series expansion technique	796	(3)
E.3. Quadrature approximations	799	(4)
E.3.1. Computation of Gauss quadrature rules	801	(1)
E.3.2. Round-off errors in Gauss quadrature rules	802	(1)
E.4. Moment bounds	803	(2)
E.4.1. Computation of moment bounds	804	(1)
E.5. Approximating the averages depending on two random variables	805	(2)
F Viterbi algorithm	807	(9)
F.1. Introduction	807	(4)
F.1.1. The truncated Viterbi algorithm	810	(1)
F.1.2. An example of application	810	(1)
F.2. Maximum a posteriori detection. The BCJR algorithm	811	(2)
F.3. Bibliographical notes	813	(3)
References	816	(29)
Index	845