Table Of ContentSignal Processing Fundamentals
and Applications for Communications
and Sensing Systems
For a listing of recent titles in the Artech House Signal Processing Library,
turn to the back of this book.
Signal Processing Fundamentals
and Applications for Communications
and Sensing Systems
John Minkoff
Artech House
Boston • London
www.artechhouse.com
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Minkoff,John.
Signalprocessingfundamentalsandapplicationsforcommunicationsandsensing
systems/JohnMinkoff.
p.cm.—(ArtechHousesignalprocessinglibrary)
Includesbibliographicalreferencesandindex.
ISBN1-58053-360-4(alk.paper)
1.Signalprocessing. 2.Detectors. I.Title. II.Series.
TK5102.9.M56 2002
621.382’2—dc21 2002074493
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Minkoff,John
Signalprocessingfundamentalsandapplicationsforcommunicationsandsensing
systems.—Newed.—(ArtechHousesignalprocessinglibrary)
1.Signalprocessing I.Title II.Signals,noise,andactivesensors
621.3’822
ISBN1-58053-360-4
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InternationalStandardBookNumber:1-58053-360-4
LibraryofCongressCatalogCardNumber:2002074493
10987654321
Contents
Preface xi
Acknowledgments xiii
1 Introduction—Fundamentals of Receivers 1
1.1 Scope and Purpose of the Book 1
1.2 A Brief History of Sensing Systems, Their
Influence on Signal Processing Development and
Applications, and Receiver Fundamentals 4
2 Review of Probability 15
2.1 Bernoulli Trials—The Binomial Distribution 15
2.2 The Poisson Distribution 17
2.3 The Exponential Distribution 18
2.4 The Gaussian Distribution 19
2.5 The Rayleigh and Rice Distributions 19
2.6 Joint Distributions, Conditional Distributions,
and Bayes’ Theorem 19
v
vi SignalProcessingFundamentalsandApplications
2.7 Characteristic Functions 21
2.8 The Law of Large Numbers 24
2.9 The Central Limit Theorem 24
2.10 Approximations to the Gaussian Distribution 27
2.11 Functions of a Random Variable 29
Exercises for Chapter 2 30
3 Review of Noise and Random Processes 33
3.1 Introduction—Correlation Functions and Power
Spectral Densities 33
3.2 Types of Noise 37
3.3 Power Spectral Density of Thermal Noise—
Nyquist’s Theorem 39
3.4 Power Spectral Density of Shot Noise 41
3.5 Shot Noise and Optical Receivers—The
Quantum Limit 46
3.6 Noise Statistics—Shot Noise in RF and Optical
Systems 50
3.7 Noise Figure and Noise Temperature 56
3.8 Noise Figure of an Attenuator 59
3.9 Applications—Noise Power Measurements, SNR 60
3.10 Connections with Statistical Physics 65
Exercises for Chapter 3 68
4 Continuous and Discrete-Time Signals 75
4.1 The Sampling Theorem and Oversampling 75
4.1.1 Application of the Sampling Theorem to Delay
of Discrete-Time Signals 85
Contents vii
4.2 The Sampling Theorem for Bandpass Carrier
Signals 88
4.3 Signal Duration and Bandwidth 90
4.4 The Analytic Signal 92
4.5 Processing of Continuous and Discrete-Time
Signals 97
Exercises for Chapter 4 106
5 Detection of Signals in Noise 109
5.1 Statistical Decision Theory—The Likelihood
Ratio Test 109
5.2 Decision Criteria—Bayes, Maximum Likelihood,
and Neyman-Pearson 111
5.3 Implementation of Decision Criteria 115
5.3.1 Gaussian Noise 116
5.3.2 Shot Noise—Poisson Distribution 120
5.4 Correlation Detection: The Matched Filter—I 123
5.4.1 The Gaussian Channel 123
5.4.2 The Shot Noise Channel 131
5.5 The Matched Filter—II 133
Exercises for Chapter 5 136
6 Coherent and Noncoherent Detection and
Processing 145
6.1 Ideal Noncoherent Detection of a Single Pulse 146
6.2 Comparison of Coherent and Noncoherent
Detection of a Single Pulse 153
6.3 Improvement in SNR by Coherent and
Noncoherent Integration 159
6.3.1 Noncoherent Integration 160
6.3.2 Coherent Integration 167
viii SignalProcessingFundamentalsandApplications
6.4 Performance of Coherent and Noncoherent
Integration 173
6.4.1 Noncoherent Integration 173
6.4.2 Coherent Integration 175
6.5 Summary of Coherent and Noncoherent
Detection and Processing 178
Exercises for Chapter 6 180
7 Parameter Estimation and Applications 183
7.1 Estimation of Range to a Target 184
7.2 Generalized Parameter Estimation 195
7.2.1 The Cramer-Rao Lower Bound on the Variance
of an Estimator 196
7.2.2 Maximum-Likelihood Estimation 199
7.3 Applications of Maximum-Likelihood Estimation
to Sensor Measurements 200
7.3.1 Calculation of the Cramer-Rao Bound for
Coherent and Noncoherent Observations 202
7.4 Application of Parameter Estimation to Tracking
and Prediction 209
Exercises for Chapter 7 216
8 Waveform Analysis, Range-Doppler Resolution,
and Ambiguity 221
8.1 Waveform Analysis 222
8.2 Range-Doppler Resolution and Ambiguity—The
Generalized Ambiguity Function 227
Exercises for Chapter 8 235
9 Large Time Bandwidth Waveforms 237
9.1 Chirp Waveforms and Pulse Compression 239
Contents ix
9.2 Doppler-Invariant Properties of Chirp
Waveforms 246
9.3 Hyperbolic Frequency Modulation (HFM) 251
9.4 Ambiguity Functions for Large BT Waveforms 254
9.5 Coded Waveforms 257
Exercises for Chapter 9 260
10 Generalized Coherent and Noncoherent
Detection and Processing 263
10.1 Noncoherent Detection of a Single Pulse 264
10.2 Coherent and Noncoherent Integration 267
Exercises for Chapter 10 270
11 Systems Considerations 271
11.1 Beampatterns and Gain of Antennas and Arrays 271
11.2 The Radar and Sonar Equations 279
11.3 The Search Problem 282
11.4 Specification of the False-Alarm Probability, P 284
fa
Appendix A: Table of Values of the Error
Function 287
References 293
About the Author 297
Index 299
