Digital Communications and Signal Processing

1 Digital Communicationsand Signal ProcessingK. VasudevanDepartment of Electrical EngineeringIndian Institute of TechnologyKanpur - 208 016 INDIA version 16, 2022iiK. Vasudevan Faculty of EE IIT Kanpur India email: Communications and Signal Processing 2001-present K. Vasudevan. All rights reserved. No part of thisbook may be reproduced without prior permission from the book is set in LATEXTo my familyAcknowledgementsDuring the course of my master s degree and PhD at IIT Madras, I had theopportunity to learn the fundamental concepts of Digital Communications frommy instructors, Dr. V. G. K. Murthy, Dr. V. V. Rao, Dr. K. RadhakrishnaRao, Dr. Bhaskar Ramamurthi and Dr.

2 Ashok Jhunjhunwalla. It is apleasureto acknowledge their teaching. I also gratefully acknowledge the guidance ofDr. K. Giridhar and Dr. Bhaskar Ramamurthi who were jointly my Doctoralsupervisors. I also wish to thank Dr. Devendra Jalihal for introducing me tothe LATEX document Processing system without which this book would not havebeen complete. I would like to express my gratitude to my instructors at IITK haragpur (where I had completed my undergraduate) Dr. S. ,Dr. T. S. Lamba, Dr. R. V. Rajkumar and Dr. S. Shanmugavel (nowwithAnna University, Chennai). I thank Dr. Surendra Prasad of IIT Delhi and Y. Kam of the National University of Singapore for encouraging me to writethis the early stages of my career (1991-1992), I was associated with theCAD-VLSI Group, Indian Telephone Industries Ltd.

3 , at would liketo express my gratitude to Mr. K. S. Raghunathan (formerly a Deputy ChiefEngineer at the CAD-VLSI Group), for his supervision of the implementationof a statistical fault analyzer for Digital circuits. It was from him that I learntthe concepts of good programming, which I cherish and use to this mention is also due to Dr. Bixio Rimoldi of the Mobile Communi-cations Lab, EPFL Switzerland and Dr. Raymond Knopp, now with InstituteEurecom, Sophia Antipolis France, for providing me the opportunityto imple-ment the Signal Processing algorithms discussed in Chapter 4, in real-time, fortheir software radio would like to thank many of my students for their valuable feedbackonthe first edition of this book.

4 Finally, I thank my colleagues at IIT Kanpur,in particular Dr. S. C. Srivastava, Dr. V. Sinha (now retired from IITK), Sharma, Dr. Pradip Sircar, Dr. R. K. Bansal, Dr K. S. Venkatesh andDr. A. K. Chaturvedi, for their support and encouragement. Thanks are alsodue to the Open Source community for providing operating systemslike Linuxand software like Scilab, LATEX, Xfig and Gnuplot, without which this bookwould not have been complete. I also wish to thank the publisher, and the editor Ms. Sreelatha Menon for their skill and dedication inbringing out the third edition of this spite of my best efforts, some errors might have gone unnoticed. Sugges-tions for improving the book are VasudevanAugust 2012 Notation{A}\{B}Elements of setAminus {A}ais an element of / {A}ais not an element of bLogical AND bLogical OR or may not be equal tob.

5 There exists. !There exists uniquely. Does not exist. For all. x Largest integer less than or equal tox. x Smallest integer greater than or equal 1 =Equal to by definition. Convolution. D( )Dirac delta function. K( )Kronecker delta function. xA complex quantity. xEstimate vector or Midentity symbol (note the absence of tilde). { }Real part. { }Imaginary or in-phase part of or quadrature part of [ ] ( )Complementary error function.[x1, x2]Closed interval, inclusive ofx1andx2.[x1, x2)Open interval, inclusive ofx1and exclusive ofx2.(x1, x2)Open interval, exclusive ( ) ( )Probability density in respect LettersAABBCCDDEEFFGGHHIIJJKKLLMMNNOOPPQ QRRSSTTUUVVWWXXYYZZC ontentsPreface to the Second EditionxiPreface to the Third EditionxiiList of Programsxiii1 Overview of the Book.]

6 Bibliography.. 72 Communicating with Coherent Detectors for 2D Constellations.. Performance Analysis.. Optimizing the Constellation.. Union Bound on the Probability of Error.. Signalling Schemes.. Constellations with Minimum Average Power.. Analysis for Non-Equiprobable Symbols.. Coherent Detectors for Multi-D Orthogonal Constellations.. Performance Analysis.. Union Bound on the Probability of Error.. Minimum SNR Required for Error-free Transmission.. Binary Antipodal and Orthogonal Constellations.. Bi-Orthogonal Constellations.. Simplex Constellations.. Noncoherent Detectors for Multi-D Orthogonal Constellations.

7 Performance Analysis.. Exact Expression for Probability of Error.. Noncoherent Detectors forM-ary PSK.. Approximate Performance Analysis.. Coherent Detectors in Coloured Noise.. Performance Analysis.. Predictive VA for Channel Coded Symbols.. Coherent Detectors for Flat Fading Channels.. 63viiiK. Vasudevan Faculty of EE IIT Kanpur India email: Performance Analysis.. Performance Analysis for BPSK.. Approximate Performance Analysis.. Multiple Input Multiple Output (MIMO) Systems.. Differential Detectors for Flat Fading Channels.. Summary.. 933 Channel The Convolutional Encoder.. Are the Encoded Symbols Correlated?

8 Hard Decision Decoding of CC.. The Viterbi Algorithm (VA).. Performance Analysis of Hard Decision Decoding.. Soft Decision Decoding of CC.. Performance Analysis of Soft Decision Decoding.. Trellis Coded Modulation (TCM).. Mapping by Set Partitioning.. Performance of TCM Schemes.. Analysis of a QPSK TCM Scheme.. Analysis of a 16-QAM TCM Scheme.. Maximization of the Shape Gain.. Constellation Shaping by Shell Mapping.. The Shell Mapping Algorithm.. Turbo Codes.. The Turbo Decoder.. The BCJR Algorithm.. Performance of ML Decoding of Turbo Codes.. Summary.. 1734 Transmission of Signals through Distortionless Linear Modulation.

9 Transmitter.. Power Spectral Density of the Transmitted Signal .. Proof of Proposition .. Receiver.. Pulse Shapes with Zero ISI.. Application of Matched Filtering in CDMA.. Discrete-Time Receiver Implementation.. Carrier and Timing Synchronization.. Data-Aided Carrier Phase Estimation.. Non-Data-Aided Carrier Phase Estimation.. Error-Rate Analysis.. Data-Aided Timing Synchronization.. Results for Synchronization.. Non-Linear Modulation.. CPFM with Full response Rectangular Filters.. 231K. Vasudevan Faculty of EE IIT Kanpur India email: Summary.. 2465 Transmission of Signals through Distorting Receivers Based on Equalization.

10 Linear Equalization Symbol-Spaced Equalizers.. Finite Length Equalizer.. The Steepest Descent Algorithm.. The Least Mean Square (LMS) Algorithm.. Linear Equalization Fractionally-Spaced Equalizers.. Non-Linear Equalization The Predictive DFE.. Implementation of the Predictive DFE.. The Conventional DFE.. Receivers Based on MLSE.. Symbol-Spaced MLSE.. Fractionally-Spaced MLSE.. andT /2-spaced ML Detectors.. Multicarrier Communication.. Channel Loading.. The Discrete Multitone (DMT).. Summary.. 307A Complex Differentiation309B The Chernoff Bound311C On Groups and Finite Groups.. Fields.. TheD-Transform.