# Digital Communications: A Discrete-Time Approach, 1st edition

• Michael Rice

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## Overview

This text uses the principles of discrete-time signal processing to introduce and analyze digital communications – connecting continuous-time and discrete-time ideas. KEY TOPICS: The text brings under one cover the theoretical and practical issues from discrete-time signal processing, discrete-time filter design, multi-rate discrete-time processing, estimation theory, signal space analysis, numerical algorithms – all focused on digital communications. MARKET: A useful reference for programmers.

Contents

1 Introduction

1.1 A brief History of Communications

1.2 Basics of Wireless Communications

1.3 Digital Communications

1.4 Why Discrete-Time Processing is so Popular

1.5 Organization of the Text

1.6 Notes and References

2 Signals and Systems 1: A Review of the Basics

2.1 Introduction

2.2 Signals

2.2.1 Continuous-Time Signals

2.2.2 Discrete-Time Signals

2.3 Systems

2.3.1 Continuous-Time Systems

2.3.2 Discrete- Time Systems

2.4 Frequency Domain Characterization

2.4.1 Laplace Transform

2.4.2 Continuous-Time Fourier Transform

2.4.3 Z Transform

2.4.4 Discrete-Time Fourier Transform

2.5 The Discrete Fourier Transform

2.6 The Relationship Between Discrete-Time and Continuous-

Time Systems

2.6.1 The Sampling Theorem

2.6.2 Discrete-Time Processing of Continuous-Time Signals

2.7 Discrete-Time Processing of Bandpass Signals

2.8 Notes and References

2.9 Exercises

3 Signals and Systems 2: Some Useful Discrete-Time Techniques for Digital Communications

3.1 Introduction

3.2 Multirate

3.2.1 Impulse Train Sampling

3.2.2 Downsampling

3.2.3 Upsampling

3.2.4 The Noble Identities

3.2.5 Polyphase Filterbanks

3.3 Discrete-Time Filters Design Methods

3.3.1 IIR Filter Design

3.3.2 FIR Filter Design

3.3.3 Two Important Filters: The Differentiator and the

Intergrator

3.4 Notes and References

3.5 Exercises

4 A Review of Probability Theory

4.1 Basic Definitions

4.2 Gaussian Random Variables

4.2.1 Density and Distribution Functions

4.2.2 Product Moments

4.2.3 BivariateGaussian Distribution

4.2.4 Functions of Random Variables

4.3 Multivariate Gaussian Random Variables

4.4 Random Sequences

4.4.1 Power Spectral Density

4.4.2 Random Sequences and Discrete-Time LTI Systems

4.5.1 Continuous Time Random Processes

4.5.2 The White Gaussian Random Process: A Good Model

For Noise

4.5.3 White Gaussian Noise in a sampled data System

4.6 Notes and References

4.7 Exercises

5 Linear Modulation 1: Demodulation, and Detection

5.1 Signal Spaces

5.1.1 Definitions

5.1.2 The Synthesis Equation and Linear Modulation

5.1.3 The Analysis Equation and Detection

5.1.4 The matched Filter

5.2 M-ary Baseband Pulse Amplitude Modulation (PAM)

5.2.1 Continuous-Time Realization

5.2.2 Discrete-Time Realization

5.3 M-ary Quadrature Amplitude Modulation (MQAM)

5.3.1 Continuous-Time Realization

5.3.2 Discrete-Time Realization

5.4 Offset QPSK

5.5 Multicarrier

5.6 Maximum Likelihood detection

5.6.1 Introduction

5.6.2 Preliminaries

5.6.3 Maximum Likelihood Decision Rule

5.7 Notes and References

5.8 Exercises

6 Linear Modulation 2: Performance

6.1 Performance of PAM

6.1.1 Bandwidth

6.1.2 Probability of Error

6.2 Performance of QAM

6.2.1 Bandwidth

6.2.2 Probability of Error

6.3 Comparisons

6.4.1 Received Power and The Friis equation

6.4.2 Equivalent Noise Temperature and Noise Figure

6.5 Projection White Noise Onto An Orthonormal Basis Set

6.6 Notes and References

6.7 Exercises

7 Carrier Phase Synchronization

7.1 Basics Problem Formulation

7.2 Carrier Phase Synchronization for QPSK

7.2.1 A Heuristic Phase Error Detector

7.2.2 The Maximum Likelihood Phase Error Detector

7.2.3 Examples

7.3 Carrier Phase Synchronization for BPSK

7.4 Carrier Phase Synchronization for MQAM

7.5 Carrier Phase Synchronization for Offset QPSK

7.6 Carrier Phase Synchronization for BPSK and QPSK Using

Continuous-Time-Techniques

7.7 Phase Ambiguity Resolution

7.7.1 Unique Word

7.7.2 Differential Encoding

7.8 Maximum Likelihood Phase Estimation

7.8.1 Preliminaries

7.8.2 Carrier Phase Estimation

7.9 Notes and References

7.10 Exercises

8 Symbol Timing Synchronization

8.1 Basic Problem Formulation

8.2 Continuous-Time Techniques for M-ary PAM

8.3 Continuous-Time Techniques for MQAM

8.4 Discrete-Time Techniques for M-ary PAM

8.4.1 Timing Error Detectors

8.4.2 Interpolation

8.4.3 Interpolation Control

8.4.4 Examples

8.5 Discrete-Time Techniques for MQAM

8.6 Discrete-Time Techniques for Offset QPSK

8.7 Dealing with Transition Density: A Parctical Consideration

8.8 Maximum Likelihood Estimation

8.8.1 Preliminaries

8.2.2 Symbol Timing Estimation

8.9 Notes and References

8.10 Exercises

9 System Components

9.1 The Continuous-Time Discrete-Time Interface

9.1.1 Analog-to-Digital Converter

9.2.2 Digital-to-Analog Converter

9.2 Discrete-Time Oscillators

9.2.1 Discrete Oscillators Based on LTI Systems

9.2.2 Direct Digital Synthesizer

9.3 Resampling Filters

9.3.1 CIC and Hogenauer Filters

9.3.2 Half-Band Filters

9.3.3 Arbitrary Resampling Using Polyphase Filterbanks

9.4 CoRDiC: Coordinate Rotation Digital Computer

9.4.1 Rotations: Moving on a Circle

9.4.2 Moving Along Other Shapes

9.5 Automatic gain Control

9.6 Notes and References

9.7 Exercise

10 System Design

10.1.1 Discrete-Time Architectures for QAM Modulators

10.1.2 Discrete-Time Architectures for QAM

Demodulators

10.1.3 Putting It all Together

10.2 Channelization

10.2.1 Continuous-Time Techniques: The