Principles of Communications

Cover
Title Page
Copyright
Preface
Contents
Chapter 1: Introduction
1.1 The Block Diagram of a Communication System
1.2 Channel Characteristics
1.2.1 Noise Sources
1.2.2 Types of Transmission Channels
1.3 Summary of Systems-Analysis Techniques
1.3.1 Time and Frequency-Domain Analyses
1.3.2 Modulation and Communication Theories
1.4 Probabilistic Approaches to System Optimization
1.4.1 Statistical Signal Detection and Estimation Theory
1.4.2 Information Theory and Coding
1.4.3 Recent Advances
1.5 Preview of This Book
Further Reading
Chapter 2: Signal and Linear System Analysis
2.1 Signal Models
2.1.1 Deterministic and Random Signals
2.1.2 Periodic and Aperiodic Signals
2.1.3 Phasor Signals and Spectra
2.1.4 Singularity Functions
2.2 Signal Classifications
2.3 Fourier Series
2.3.1 Complex Exponential Fourier Series
2.3.2 Symmetry Properties of the Fourier Coefficients
2.3.3 Trigonometric Form of the Fourier Series
2.3.4 Parseval’s Theorem
2.3.5 Examples of Fourier Series
2.3.6 Line Spectra
2.4 The Fourier Transform
2.4.1 Amplitude and Phase Spectra
2.4.2 Symmetry Properties
2.4.3 Energy Spectral Density
2.4.4 Convolution
2.4.5 Transform Theorems: Proofs and Applications
2.4.6 Fourier Transforms of Periodic Signals
2.4.7 Poisson Sum Formula
2.5 Power Spectral Density and Correlation
2.5.1 The Time-Average Autocorrelation Function
2.5.2 Properties of R (τ)
2.6 Signals and Linear Systems
2.6.1 Definition of a Linear Time-Invariant System
2.6.2 Impulse Response and the Superposition Integral
2.6.3 Stability
2.6.4 Transfer (Frequency Response) Function
2.6.5 Causality
2.6.6 Symmetry Properties of H (f)
2.6.7 Input-Output Relationships for Spectral Densities
2.6.8 Response to Periodic Inputs
2.6.9 Distortionless Transmission
2.6.10 Group and Phase Delay
2.6.11 Nonlinear Distortion
2.6.12 Ideal Filters
2.6.13 Approximation of Ideal Lowpass Filters by Realizable Filters
2.6.14 Relationship of Pulse Resolution and Risetime to Bandwidth
2.7 Sampling Theory
2.8 The Hilbert Transform
2.8.1 Definition
2.8.2 Properties
2.8.3 Analytic Signals
2.8.4 Complex Envelope Representation of Bandpass Signals
2.8.5 Complex Envelope Representation of Bandpass Systems
2.9 The Discrete Fourier Transform and Fast Fourier Transform
Further Reading
Summary
Drill Problems
Problems
Computer Exercises
Chapter 3: Linear Modulation Techniques
3.1 Double-Sideband Modulation
3.2 Amplitude Modulation (AM)
3.2.1 Envelope Detection
3.2.2 The Modulation Trapezoid
3.3 Single-Sideband (SSB) Modulation
3.4 Vestigial-Sideband (VSB) Modulation
3.5 Frequency Translation and Mixing
3.6 Interference in Linear Modulation
3.7 Pulse Amplitude Modulation---PAM
3.8 Digital Pulse Modulation
3.8.1 Delta Modulation
3.8.2 Pulse-Code Modulation
3.8.3 Time-Division Multiplexing
3.8.4 An Example: The Digital Telephone System
Further Reading
Summary
Drill Problems
Problems
Computer Exercises
Chapter 4: Angle Modulation and Multiplexing
4.1 Phase and Frequency Modulation Defined
4.1.1 Narrowband Angle Modulation
4.1.2 Spectrum of an Angle-Modulated Signal
4.1.3 Power in an Angle-Modulated Signal
4.1.4 Bandwidth of Angle-Modulated Signals
4.1.5 Narrowband-to-Wideband Conversion
4.2 Demodulation of Angle-Modulated Signals
4.3 Feedback Demodulators: The Phase-Locked Loop
4.3.1 Phase-Locked Loops for FM and PM Demodulation
4.3.2 Phase-Locked Loop Operation in the Tracking Mode: The Linear Model
4.3.3 Phase-Locked Loop Operation in the Acquisition Mode
4.3.4 Costas PLLs
4.3.5 Frequency Multiplication and Frequency Division
4.4 Interference in Angle Modulation
4.5 Analog Pulse Modulation
4.5.1 Pulse-Width Modulation (PWM)
4.5.2 Pulse-Position Modulation (PPM)
4.6 Multiplexing
4.6.1 Frequency-Division Multiplexing
4.6.2 Example of FDM: Stereophonic FM Broadcasting
4.6.3 Quadrature Multiplexing
4.6.4 Comparison of Multiplexing Schemes
Further Reading
Summary
Drill Problems
Problems
Computer Exercises
Chapter 5: Principles of Baseband Digital Data Transmission
5.1 Baseband Digital Data Transmission Systems
5.2 Line Codes and Their Power Spectra
5.2.1 Description of Line Codes
5.2.2 Power Spectra for Line-Coded Data
5.3 Effects of Filtering of Digital Data---ISI
5.4 Pulse Shaping: Nyquist’s Criterion for Zero ISI
5.4.1 Pulses Having the Zero ISI Property
5.4.2 Nyquist’s Pulse-Shaping Criterion
5.4.3 Transmitter and Receiver Filters for Zero ISI
5.5 Zero-Forcing Equalization
5.6 Eye Diagrams
5.7 Synchronization
5.8 Carrier Modulation of Baseband Digital Signals
Further Reading
Summary
Drill Problems
Problems
Computer Exercises
Chapter 6: Overview of Probability and Random Variables
6.1 What is Probability?
6.1.1 Equally Likely Outcomes
6.1.2 Relative Frequency
6.1.3 Sample Spaces and the Axioms of Probability
6.1.4 Venn Diagrams
6.1.5 Some Useful Probability Relationships
6.1.6 Tree Diagrams
6.1.7 Some More General Relationships
6.2 Random Variables and Related Functions
6.2.1 Random Variables
6.2.2 Probability (Cumulative) Distribution Functions
6.2.3 Probability-Density Function
6.2.4 Joint cdfs and pdfs
6.2.5 Transformation of Random Variables
6.3 Statistical Averages
6.3.1 Average of a Discrete Random Variable
6.3.2 Average of a Continuous Random Variable
6.3.3 Average of a Function of a Random Variable
6.3.4 Average of a Function of More Than One Random Variable
6.3.5 Variance of a Random Variable
6.3.6 Average of a Linear Combination of N Random Variables
6.3.7 Variance of a Linear Combination of Independent Random Variables
6.3.8 Another Special Average---The Characteristic Function
6.3.9 The pdf of the Sum of Two Independent Random Variables
6.3.10 Covariance and the Correlation Coefficient
6.4 Some Useful pdfs
6.4.1 Binomial Distribution
6.4.2 Laplace Approximation to the Binomial Distribution
6.4.3 Poisson Distribution and Poisson Approximation to the Binomial Distribution
6.4.4 Geometric Distribution
6.4.5 Gaussian Distribution
6.4.6 Gaussian Q-Function
6.4.7 Chebyshev’s Inequality
6.4.8 Collection of Probability Functions and Their Means and Variances
Further Reading
Summary
Drill Problems
Problems
Computer Exercises
Chapter 7: Random Signals and Noise
7.1 A Relative-Frequency Description of Random Processes
7.2 Some Terminology of Random Processes
7.2.1 Sample Functions and Ensembles
7.2.2 Description of Random Processes in Terms of Joint pdfs
7.2.3 Stationarity
7.2.4 Partial Description of Random Processes: Ergodicity
7.2.5 Meanings of Various Averages for Ergodic Processes
7.3 Correlation and Power Spectral Density
7.3.1 Power Spectral Density
7.3.2 The Wiener--Khinchine Theorem
7.3.3 Properties of the Autocorrelation Function
7.3.4 Autocorrelation Functions for Random Pulse Trains
7.3.5 Cross-Correlation Function and Cross-Power Spectral Density
7.4 Linear Systems and Random Processes
7.4.1 Input-Output Relationships
7.4.2 Filtered Gaussian Processes
7.4.3 Noise-Equivalent Bandwidth
7.5 Narrowband Noise
7.5.1 Quadrature-Component and Envelope-Phase Representation
7.5.2 The Power Spectral Density Function of nc (t) and ns (t)
7.5.3 Ricean Probability Density Function
Further Reading
Summary
Drill Problems
Problems
Computer Exercises
Chapter 8: Noise in Modulation Systems
8.1 Signal-to-Noise Ratios
8.1.1 Baseband Systems
8.1.2 Double-Sideband Systems
8.1.3 Single-Sideband Systems
8.1.4 Amplitude Modulation Systems
8.1.5 An Estimator for Signal-to-Noise Ratios
8.2 Noise and Phase Errors in Coherent Systems
8.3 Noise in Angle Modulation
8.3.1 The Effect of Noise on the Receiver Input
8.3.2 Demodulation of PM
8.3.3 Demodulation of FM: Above Threshold Operation
8.3.4 Performance Enhancement through the Use of De-emphasis
8.4 Threshold Effect in FM Demodulation
8.4.1 Threshold Effects in FM Demodulators
8.5 Noise in Pulse-Code Modulation
8.5.1 Postdetection SNR
8.5.2 Companding
Further Reading
Summary
Drill Problems
Problems
Computer Exercises
Chapter 9: Principles of Digital Data Transmission in Noise
9.1 Baseband Data Transmission in White Gaussian Noise
9.2 Binary Synchronous Data Transmission with Arbitrary Signal Shapes
9.2.1 Receiver Structure and Error Probability
9.2.2 The Matched Filter
9.2.3 Error Probability for the Matched-Filter Receiver
9.2.4 Correlator Implementation of the Matched-Filter Receiver
9.2.5 Optimum Threshold
9.2.6 Nonwhite (Colored) Noise Backgrounds
9.2.7 Receiver Implementation Imperfections
9.2.8 Error Probabilities for Coherent Binary Signaling
9.3 Modulation Schemes not Requiring Coherent References
9.3.1 Differential Phase-Shift Keying (DPSK)
9.3.2 Differential Encoding and Decoding of Data
9.3.3 Noncoherent FSK
9.4 M-ary Pulse-Amplitude Modulation (PAM)
9.5 Comparison of Digital Modulation Systems
9.6 Noise Performance of Zero-ISI Digital Data Transmission Systems
9.7 Multipath Interference
9.8 Fading Channels
9.8.1 Basic Channel Models
9.8.2 Flat-Fading Channel Statistics and Error Probabilities
9.9 Equalization
9.9.1 Equalization by Zero-Forcing
9.9.2 Equalization by MMSE
9.9.3 Tap Weight Adjustment
Further Reading
Summary
Drill Problems
Problems
Computer Exercises
Chapter 10: Advanced Data Communications Topics
10.1 M-ary Data Communications Systems
10.1.1 M-ary Schemes Based on Quadrature Multiplexing
10.1.2 OQPSK Systems
10.1.3 MSK Systems
10.1.4 M-ary Data Transmission in Terms of Signal Space
10.1.5 QPSK in Terms of Signal Space
10.1.6 M-ary Phase-Shift Keying
10.1.7 Quadrature-Amplitude Modulation (QAM)
10.1.8 Coherent FSK
10.1.9 Noncoherent FSK
10.1.10 Differentially Coherent Phase-Shift Keying
10.1.11 Bit Error Probability from Symbol Error Probability
10.1.12 Comparison of M-ary Communications Systems on the Basis of Bit Error Probability
10.1.13 Comparison of M-ary Communications Systems on the Basis of Bandwidth Efficiency
10.2 Power Spectra for Digital Modulation
10.2.1 Quadrature Modulation Techniques
10.2.2 FSK Modulation
10.2.3 Summary
10.3 Synchronization
10.3.1 Carrier Synchronization
10.3.2 Symbol Synchronization
10.3.3 Word Synchronization
10.3.4 Pseudo-Noise (PN) Sequences
10.4 Spread-Spectrum Communication Systems
10.4.1 Direct-Sequence Spread Spectrum
10.4.2 Performance of DSSS in CW Interference Environments
10.4.3 Performance of Spread Spectrum in Multiple User Environments
10.4.4 Frequency-Hop Spread Spectrum
10.4.5 Code Synchronization
10.4.6 Conclusion
10.5 Multicarrier Modulation and Orthogonal Frequency-Division Multiplexing
10.6 Cellular Radio Communication Systems
10.6.1 Basic Principles of Cellular Radio
10.6.2 Channel Perturbations in Cellular Radio
10.6.3 Multiple-Input Multiple-Output (MIMO) Systems---Protection Against Fading
10.6.4 Characteristics of 1G and 2G Cellular Systems
10.6.5 Characteristics of cdma2000 and W-CDMA
10.6.6 Migration to 4G
Further Reading
Summary
Drill Problems
Problems
Computer Exercises
Chapter 11: Optimum Receivers and Signal-Space Concepts
11.1 Bayes Optimization
11.1.1 Signal Detection versus Estimation
11.1.2 Optimization Criteria
11.1.3 Bayes Detectors
11.1.4 Performance of Bayes Detectors
11.1.5 The Neyman-Pearson Detector
11.1.6 Minimum Probability of Error Detectors
11.1.7 The Maximum a Posteriori (MAP) Detector
11.1.8 Minimax Detectors
11.1.9 The M-ary Hypothesis Case
11.1.10 Decisions Based on Vector Observations
11.2 Vector Space Representation of Signals
11.2.1 Structure of Signal Space
11.2.2 Scalar Product
11.2.3 Norm
11.2.4 Schwarz’s Inequality
11.2.5 Scalar Product of Two Signals in Terms of Fourier Coefficients
11.2.6 Choice of Basis Function Sets---The Gram--Schmidt Procedure
11.2.7 Signal Dimensionality as a Function of Signal Duration
11.3 Map Receiver for Digital Data Transmission
11.3.1 Decision Criteria for Coherent Systems in Terms of Signal Space
11.3.2 Sufficient Statistics
11.3.3 Detection of..-ary Orthogonal Signals
11.3.4 A Noncoherent Case
11.4 Estimation Theory
11.4.1 Bayes Estimation
11.4.2 Maximum-Likelihood Estimation
11.4.3 Estimates Based on Multiple Observations
11.4.4 Other Properties of ML Estimates
11.4.5 Asymptotic Qualities of ML Estimates
11.5 Applications of Estimation Theory to Communications
11.5.1 Pulse-Amplitude Modulation (PAM)
11.5.2 Estimation of Signal Phase: The PLL Revisited
Further Reading
Summary
Drill Problems
Problems
Computer Exercises
Chapter 12: Information Theory and Coding
12.1 Basic Concepts
12.1.1 Information
12.1.2 Entropy
12.1.3 Discrete Channel Models
12.1.4 Joint and Conditional Entropy
12.1.5 Channel Capacity
12.2 Source Coding
12.2.1 An Example of Source Coding
12.2.2 Several Definitions
12.2.3 Entropy of an Extended Binary Source
12.2.4 Shannon--Fano Source Coding
12.2.5 Huffman Source Coding
12.3 Communication in Noisy Environments: Basic Ideas
12.4 Communication in Noisy Channels: Block Codes
12.4.1 Hamming Distances and Error Correction
12.4.2 Single-Parity-Check Codes
12.4.3 Repetition Codes
12.4.4 Parity-Check Codes for Single Error Correction
12.4.5 Hamming Codes
12.4.6 Cyclic Codes
12.4.7 The Golay Code
12.4.8 Bose--Chaudhuri--Hocquenghem (BCH) Codes and Reed Solomon Codes
12.4.9 Performance Comparison Techniques
12.4.10 Block Code Examples
12.5 Communication in Noisy Channels: Convolutional Codes
12.5.1 Tree and Trellis Diagrams
12.5.2 The Viterbi Algorithm
12.5.3 Performance Comparisons for Convolutional Codes
12.6 Bandwidth and Power Efficient Modulation (TCM)
12.7 Feedback Channels
12.8 Modulation and Bandwidth Efficiency
12.8.1 Bandwidth and SNR
12.8.2 Comparison of Modulation Systems
12.9 Quick Overviews
12.9.1 Interleaving and Burst-Error Correction
12.9.2 Turbo Coding
12.9.3 Source Coding Examples
12.9.4 Digital Television
Further Reading
Summary
Drill Problems
Problems
Computer Exercises
Appendix A: Physical Noise Sources
A.1 Physical Noise Sources
A.1.1 Thermal Noise
A.1.2 Nyquist’s Formula
A.1.3 Shot Noise
A.1.4 Other Noise Sources
A.1.5 Available Power
A.1.6 Frequency Dependence
A.1.7 Quantum Noise
A.2 Characterization of Noise in Systems
A.2.1 Noise Figure of a System
A.2.2 Measurement of Noise Figure
A.2.3 Noise Temperature
A.2.4 Effective Noise Temperature
A.2.5 Cascade of Subsystems
A.2.6 Attenuator Noise Temperature and Noise Figure
A.3 Free-Space Propagation Example
Further Reading
Problems
Appendix B: Jointly Gaussian Random Variables
B.1 The pdf
B.2 The Characteristic Function
B.3 Linear Transformations
Appendix C: Proof of The Narrowband Noise Model
Appendix D: Zero-Crossing and Origin Encirclement Statistics
D.1 The Zero-Crossing Problem
D.2 Average Rate of Zero Crossings
Problems
Appendix E: Chi-Square Statistics
Appendix F: Mathematical and Numerical Tables
F.1 The Gaussian Q-Function
F.2 Trigonometric Identities
F.3 Series Expansions
F.4 Integrals
F.4.1 Indefinite
F.4.2 Definite
F.5 Fourier-Transform Pairs
F.6 Fourier-Transform Theorems
Index