Radar System Analysis, Design, and Simulation

Eyung W. Kang

к; A R T E C H H O U S E BOSTON|LONDON a r techhouse .com

Contents

Preface

Acknowledyi i ici m

Introduction CHAPTER 1 1

Matrix, Vector, and Linear Equations

1.1 1.2

1.3

1.4

1.5 1.6 1.7

Introduction Simultaneous Linear Equation 1.2.1 1.2.2

Gaussian Elimination with Backsubstitution Gaussian Elimination with Forward Substitution

Matrix Factorization 1.3.1 1.3.2 1.3.3 1.3.4 1.3.5

LU Factorization LLT Factorization (Cholesky)

LDLT Factorization (Modified Cholesky) UDLF Factorization QR Factorization

Matrix Inversion 1.4.1 1.4.2 1.4.3 1.4.4 1.4.5 1.4.6 Vectoi

LI Li u-i u-i D 1

Q 1

' Operations Matrix Operations Conclusion Selected Bibliography

XI

xiii

xv

1

1 1 2 4 5 5 7 8

10 11 15 16 17 19 20 21 21 21 22 23 24

CHAPTER 2

Pseudorandom Number, Noise, and Clutter Generation 25

2.1 Introduction 25 2.2 Pseudorandom Numbers and Unit Uniform Variables 25

2.2.1 PRN Generation of an Arbirary Population 27 2.3 White Gaussian Noise 28 2.4 Rayleigh Noise 30 2.5 Rician Random Variables, Signal-to-Noise Ratio 31 2.6 Chi-Squared Noise 35

2.7 Square-Law Detector 36 2.8 Exponential Noise 38 2.9 Lognormal Clutter 40

2.10 Weibull Clutter 42 2.11 Postulate of Probability Density Function from Sampled Data 44 2.12 Construction of Gaussian (Normal) Probability Paper 49 2.13 Conclusion 51

References 52

CHAPTER 3

Filters, FIR, and IIR 53

3.1 Introduction 53 3.2 Finite Impulse Response Filter (FIR) 56

3.2.1 FIR Filters: Lowpass, Highpass, Bandpass, and Bandstop 56 3.2.2 Window Functions: Rectangle, von Hann, Hamming, and

Blackman 59 3.2.3 Kaiser Filter: Lowpass, Highpass, Bandpass, and Bandstop 65

3.3 Infinite Impulse Response Filter (IIR) 68 3.3.1 Bilinear Transform 69 3.3.2 Review of Analog Filters 71 3.3.3 IIR Filter, Butterworth Lowpass 83 3.3.4 IIR Filter, Chebyshev Lowpass 84 3.3.5 IIR Filter, Elliptic Lowpass 85 3.3.6 IIR Filter, Elliptic Bandpass 87 3.3.7 Issue of Nonlinearity 89 3.3.8 Comparison Between FIR and IIR Filters 90 3.3.9 Quantized Noise and Dynamic Range of A/D Converter 90 References 94

CHAPTER 4

Fast Fourier Transform (FFT) and IFFT 95

4.1 Introduction 95 4.2 Fast Fourier Transform Decimation-in-Time and Decimation-

in-Frequency 96 4.3 Demonstration of FFT_DIT and FFT_DIF 101 4.4 Spectral Leakage and Window Function 104 4.5 Inverse Fast Fourier Transform Decimation-in-Time, and Decimation-

in-Frequency 106 4.6 Applications of FFT and IFFT 107

4.6.1 Filtering in the Frequency Domain 109 4.6.2 Detection of Signal Buried in Noise 110 4.6.3 Interpolation of Data 110 4.6.4 Pulse Compression 110 4.6.5 Amplitude Unbalance and Phase Mismatch 118 Appendix 4A 122 References 124

Contents VII

CHAPTER 5

Ambiguity Function 125

5.1 Introduction 125 5.2 Rectangle Pulse with a Single Constant Frequency 126 5.3 Linear Frequency Modulation (LFM) 128 5.4 Costas-Coded Frequency Hopping Modulation 131

References 140 Selected Bibliography 141 Appendix 5A 141

CHAPTER 6

Array Antennas 143

6.1 Introduction 143 6.2 Linear Array 143 6.3 Circular Aperture Array 149 6.4 Elliptical Aperture Array 153 6.5 Monopulse Aperture Array 154 6.6 Conclusion 159

References 161 Appendix 6A 162 Closing Remarks 163

CHAPTER 7

Target Detection 165

7.1 Introduction 165 7.2 The Probability of Detection and the False Alarm

Probability for Marcum's Target Model 169 7.3 The Probability of Detection, Swerling Target Models 180

7.3.1 Swerling Target Model 1 183 7.3.2 Swerling Target Model 2 186 7.3.3 Swerling Target Model 3 187 7.3.4 Swerling Target Model 4 190

7.4 Conclusion 192 References 196 Selected Bibliography 197

CHAPTER 8

Kaiman Filter 199

8.1 Introduction 199 8.2 Derivation of Kaiman Filter Equations 202 8.3 Passenger Airliner 211 8.4 Air Traffic Control Radar 214 8.5 Air Defense Radar, Cartesian Coordinate System 223

via Contents

8.6 Air Defense Radar, LOS Coordinates 233 8.7 Kaiman Filter without Matrix Inversion 238

References 245 Selected Bibliography 246

CHAPTER 9

Monte Carlo Method and Function Integration 247

9.1 Introduction 247 9.2 Hit-or-Miss Method 247 9.3 Ordered Sample Method 251 9.4 Sample Mean Method 252 9.5 Importance Sampling Method 253 9.6 Observations and Remarks 255 9.7 Probability of False Alarm, Exponential Probability Density Function 256 9.8 Probability of False Alarm, Gaussian Density Function 260 9.9 Integration of Functions 265

9.9.1 Trapezoidal Rule 265 9.9.2 Simpson's Rule and Extended Simpson's Rule 266 9.9.3 Gaussian Quadrature 267

9.10 Quadrature in Two Dimensions 275 9.11 Quadrature in Three Dimensions 278 9.12 Concluding Remarks 279

References 280 Appendix 9A 280

CHAPTER 10

Constant False Alarm Rate (CFAR) Processing 281

10.1 Introduction 281 10.2 Cell Average CFAR (CA-CFAR) 281 10.3 Order-Statistics CFAR (OS-CFAR) 289 10.4 Weibull Clutter 295

10.4.1 Weibull Probability Density Function 295 10.4.2 Weibull Clutter After a Square-Law Detector 297

10.5 Weber-Haykin CFAR (WH-CFAR) 299 10.6 Maximum Likelihood CFAR (ML-CFAR) 305 10.7 Minimum Mean Square Error CFAR (MMSE-CFAR) 313 10.8 Conclusion 319

References 320 Selected Bibliography 321

Contents IX

CHAPTER 11

Moving Target Indicator 323

11.1 Introduction 323 11.2 Nonrecursive Delay-Line Canceller 323 11.3 Recursive Delay-Line Canceller 327 11.4 Blind Speed and Staggered PRFs 331 11.5 Clutter Attenuation and Improvement Factor 334 11.6 Limitation Due to System Instability 346 11.7 A/D Converter Quantization Noise 348 11.8 Clutter Map 349 11.9 Conclusion 349

References 350

CHAPTER 12

Miscellaneous Program Routines 351

Index 355