FUNDAMENTALS OF DIGITAL COMMUNICATION
CONTENTS 1 INTRODUCTION 1 1 COMPONENTS OF A DIGITAL COMMUNICATION SYSTEM 1 2 TEXT OUTLINE 1 3 FURTHER READING 2 MODULATION 2 1 PRELIMINARIES 2 2 COMPLEX BASEBAND REPRESENTATION 2 3 SPECTRAL DESCRIPTION OF RANDOM PROCESSES 2 3 1 COMPLEX ENVELOPE FOR PASSBAND RANDOM PROCESSES 2 4 MODULATION DEGREES OF FREEDOM 2 5 LINEAR MODULATION 2 5 1 EXAMPLES OF LINEAR MODULATION 2 5 2 SPECTRAL OCCUPANCY OF LINEARLY MODULATED SIGNALS 2 5 3 THE NYQUIST CRITERION: RELATING BANDWIDTH TO SYMBOL RATE 2 5 4 LINEAR MODULATION AS A BUILDING BLOCK 2 6 ORTHOGONAL AND BIORTHOGONAL MODULATION 2 7 DIFFERENTIAL MODULATION 2 8 FURTHER READING 2 9 PROBLEMS 2 9 1 SIGNALS AND SYSTEMS 2 9 2 COMPLEX BASEBAND REPRESENTATION 2 9 3 RANDOM PROCESSES 2 9 4 MODULATION 3 DEMODULATION 3 1 GAUSSIAN BASICS 3 2 HYPOTHESIS TESTING BASICS 3 3 SIGNAL SPACE CONCEPTS 3 4 OPTIMAL RECEPTION IN AWGN 3 4 1 GEOMETRY OF THE ML DECISION RULE 3 4 2 SOFT DECISIONS 3 5 PERFORMANCE ANALYSIS OF ML RECEPTION 3 5 1 PERFORMANCE WITH BINARY SIGNALING 3 5 2 PERFORMANCE WITH M-ARY SIGNALING 3 6 BIT-LEVEL DEMODULATION 3 6 1 BIT-LEVEL SOFT DECISIONS 3 7 ELEMENTS OF LINK BUDGET ANALYSIS 3 8 FURTHER READING 3 9 PROBLEMS 3 9 1 GAUSSIAN BASICS 3 9 2 HYPOTHESIS TESTING BASICS 3 9 3 RECEIVER DESIGN AND PERFORMANCE ANALYSIS FOR THE AWGN CHANNEL 3 9 4 LINK BUDGET ANALYSIS 3 9 5 SOME MATHEMATICAL DERIVATIONS 4 SYNCHRONIZATION AND NONCOHERENT COMMUNICATION 4 1 RECEIVER DESIGN REQUIREMENTS 4 2 PARAMETER ESTIMATION BASICS 4 2 1 LIKELIHOOD FUNCTION OF A SIGNAL IN AWGN 4 3 PARAMETER ESTIMATION FOR SYNCHRONIZATION 4 4 NONCOHERENT COMMUNICATION 4 4 1 COMPOSITE HYPOTHESIS TESTING 4 4 2 OPTIMAL NONCOHERENT DEMODULATION 4 4 3 DIFFERENTIAL MODULATION AND DEMODULATION 4 5 PERFORMANCE OF NONCOHERENT COMMUNICATION 4 5 1 PROPER COMPLEX GAUSSIANITY 4 5 2 PERFORMANCE OF BINARY NONCOHERENT COMMUNICATION 4 5 3 PERFORMANCE OF M-ARY NONCOHERENT ORTHOGONAL SIGNALING 4 5 4 PERFORMANCE OF DPSK 4 5 5 BLOCK NONCOHERENT DEMODULATION 4 6 FURTHER READING 4 7 PROBLEMS 5 CHANNEL EQUALIZATION 5 1 THE CHANNEL MODEL 5 2 RECEIVER FRONT END 5 3 EYE DIAGRAMS 5 4 MAXIMUM LIKELIHOOD SEQUENCE ESTIMATION 5 4 1 ALTERNATIVE MLSE FORMULATION 5 5 GEOMETRIC MODEL FOR SUBOPTIMAL EQUALIZER DESIGN 5 6 LINEAR EQUALIZATION 5 6 1 ADAPTIVE IMPLEMENTATIONS 5 6 2 PERFORMANCE ANALYSIS 5 7 DECISION FEEDBACK EQUALIZATION 5 7 1 PERFORMANCE ANALYSIS 5 8 PERFORMANCE ANALYSIS OF MLSE 5 8 1 UNION BOUND 5 8 2 TRANSFER FUNCTION BOUND 5 9 NUMERICAL COMPARISON OF EQUALIZATION TECHNIQUES 5 10 FURTHER READING 5 11 PROBLEMS 5 11 1 MLSE 6 INFORMATION-THEORETIC LIMITS AND THEIR COMPUTATION 6 1 CAPACITY OF AWGN CHANNEL: MODELING AND GEOMETRY 6 1 1 FROM CONTINUOUS TO DISCRETE TIME 6 1 2 CAPACITY OF THE DISCRETE TIME AWGN CHANNEL 6 1 3 FROM DISCRETE TO CONTINUOUS TIME 6 1 4 SUMMARIZING THE DISCRETE-TIME AWGN MODEL 6 2 SHANNON THEORY BASICS 6 2 1 ENTROPY, MUTUAL INFORMATION AND DIVERGENCE 6 2 2 THE CHANNEL CODING THEOREM 6 3 SOME CAPACITY COMPUTATIONS 6 3 1 CAPACITY FOR STANDARD CONSTELLATIONS 6 3 2 PARALLEL GAUSSIAN CHANNELS AND WATERFILLING 6 4 OPTIMIZING THE INPUT DISTRIBUTION 6 4 1 CONVEX OPTIMIZATION 6 4 2 CHARACTERIZING OPTIMAL INPUT DISTRIBUTIONS 6 4 3 COMPUTING OPTIMAL INPUT DISTRIBUTIONS 6 5 FURTHER READING 6 6 PROBLEMS 7 CHANNEL CODING 7 1 BINARY CONVOLUTIONAL CODES 7 1 1 NONRECURSIVE NONSYSTEMATIC ENCODING 7 1 2 RECURSIVE SYSTEMATIC ENCODING 7 1 3 MAXIMUM LIKELIHOOD DECODING 7 1 4 PERFORMANCE ANALYSIS OF ML DECODING 7 1 5 PERFORMANCE ANALYSIS FOR QUANTIZED OBSERVATIONS 7 2 TURBO CODES AND ITERATIVE DECODING 7 2 1 THE BCJR ALGORITHM: SOFT-IN, SOFT-OUT DECODING 7 2 2 LOGARITHMIC BCJR ALGORITHM 7 2 3 TURBO CONSTRUCTIONS FROM CONVOLUTIONAL CODES 7 2 4 THE BER PERFORMANCE OF TURBO CODES 7 2 5 EXTRINSIC INFORMATION TRANSFER CHARTS 7 2 6 TURBO WEIGHT ENUMERATION 7 3 LOW DENSITY PARITY CHECK CODES 7 3 1 SOME TERMINOLOGY FROM CODING THEORY 7 3 2 REGULAR LDPC CODES 7 3 3 IRREGULAR LDPC CODES 7 3 4 MESSAGE PASSING AND DENSITY EVOLUTION 7 3 5 BELIEF PROPAGATION 7 3 6 GAUSSIAN APPROXIMATION 7 4 BANDWIDTH-EFFICIENT CODED MODULATION 7 4 1 BIT INTERLEAVED CODED MODULATION 7 4 2 TRELLIS CODED MODULATION 7 5 ALGEBRAIC CODES 7 6 FURTHER READING 7 7 PROBLEMS 8 WIRELESS COMMUNICATION 8 1 CHANNEL MODELING 8 2 FADING AND DIVERSITY 8 2 1 THE PROBLEM WITH RAYLEIGH FADING 8 2 2 DIVERSITY THROUGH CODING AND INTERLEAVING 8 2 3 RECEIVE DIVERSITY 8 3 ORTHOGONAL FREQUENCY DIVISION MULTIPLEXING 8 4 DIRECT SEQUENCE SPREAD SPECTRUM 8 4 1 THE RAKE RECEIVER 8 4 2 CHOICE OF SPREADING SEQUENCES 8 4 3 PERFORMANCE OF CONVENTIONAL RECEPTION IN CDMA SYSTEMS 8 4 4 MULTIUSER DETECTION FOR DS-CDMA SYSTEMS 8 5 FREQUENCY HOP SPREAD SPECTRUM 8 6 CONTINUOUS PHASE MODULATION 8 6 1 GAUSSIAN MSK 8 6 2 RECEIVER DESIGN AND LAURENT’S EXPANSION 8 7 SPACE–TIME COMMUNICATION 8 7 1 SPACE–TIME CHANNEL MODELING 8 7 2 INFORMATION-THEORETIC LIMITS 8 7 3 SPATIAL MULTIPLEXING 8 7 4 SPACE–TIME CODING 8 7 5 TRANSMIT BEAMFORMING 8 8 FURTHER READING 8 9 PROBLEMS