Preface
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
2.1–1 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-Loève Expansion
2.9 Bandpass and Lowpass Random Processes 78
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 Band-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 Biorthogonal Signaling / 4.4–3 Optimal Detection and Error Probability for Simplex Signaling
4.5 Optimal Detection in Presence of Uncertainty: Noncoherent 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 PSK (DPSK)
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
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