DIGITAL SIGNAL PROCESSING

TECHNIQUES AND APPLICATIONS IN RADAR

IMAGE PROCESSING

Bu-Chin Wang

IWILEY

A JOHN WILEY & SONS, INC., PUBLICATION

CONTENTS

Preface xiii

List of Symbols xvii

List of Illustrations xxi

1 Signal Theory and Analysis 1

1.1 Special Functions Used in Signal Processing / 1 1.1.1 Delta or Impulse Function 8(f) / 1 1.1.2 Sampling or Interpolation Function sine (?) / 2

1.2 Linear System and Convolution / 3 1.2.1 Key Properties of Convolution / 5

1.2.1.1 Commutative I 5

1.2.1.2 Associative I 5

1.2.1.3 Distributive I 5

1.2.1.4 Timeshifi I 5

1.3 Fourier Series Representation of Periodic Signals / 6 1.3.1 Trigonometric Fourier Series / 6 1.3.2 Compact Trigonometric Fourier Series / 6 1.3.3 Exponential Fourier Series / 7

1.4 Nonperiodic Signal Representation by Fourier Transform / 1 1

1.5 Fourier Transform of a Periodic Signal / 16

1.6 Sampling Theory and Interpolation / 19

1.7 Advanced Sampling Techniques / 24

1.7.1 Sampling with Bandpass Signal / 24 1.7.2 Resampling by Evenly Spaced Decimation / 25 1.7.3 Resampling by Evenly Spaced Interpolation / 25 1.7.4 Resampling by Fractional Rate Interpolation / 26

vii

CONTENTS

1.7.5 Resampling from Unevenly Spaced Data / 28 1.7.5.1 Jacobian of Transformation I 28

Discrete Time and Frequency Transformation

2.1 Continuous and Discrete Fourier Transform / 35

2.2 Key Properties of Discrete Fourier Transform / 38

2.2.1 Shifting and Symmetry / 39 2.2.2 Linear and Circular Convolution / 39 2.2.3 Sectioned Convolution / 41

2.2.3.1 Overlap-and-AddMethod I 42

2.2.3.2 Overlap-and-Save Method I 42 2.2.4 Zero Stuffing and Discrete Fourier Transform (DFT)

Resolution / 43

2.3 Widows and Discrete Fourier Transform / 48

2.4 Fast Fourier Transform / 50 2.4.1 Radix-2 Fast Fourier Transform (FFT) Algorithms / 50

2.5 Discrete Cosine Transform (DCT) / 53 2.5.1 Two-Dimensional DCT / 57

2.6 Continuous and Discrete Signals in Time and Frequency Domains / 57 2.6.1 Graphical Representation of DFT / 57 2.6.2 Resampling with Fractional Interpolation Based on DFT / 60

Basics of Antenna Theory

3.1 Maxwell and Wave Equations / 63

3.1.1 Harmonic Time Dependence / 65

3.2 Radiation from an Infinitesimal Current Dipole / 67 3.2.1 Magnetic Vector Potential Due to a Small but Finite Current

Element / 68 3.2.2 Field Vectors Due to Small but Finite Current Radiation / 69 3.2.3 Far-Field Region / 70

3.2.4 Summary of Radiation Fields / 72

3.3 Radiation from a Half-Wavelength Dipole / 73

3.4 Radiation from a Linear Array / 74 3.4.1 Power Radiation Pattern from a Linear Array / 78

3.5 Power Radiation Pattern from a 2D Rectangular Array / 80

CONTENTS JX

3.6 Fundamentals of Antenna Parameters / 81 3.6.1 Radiation Beamwidth / 81 3.6.2 Solid Angle, Power Density, and Radiation Intensity / 82 3.6.3 Directivity and Gain / 84 3.6.4 Antenna Impedance / 84 3.6.5 Antenna Efficiency / 85 3.6.6 Effective Area and Antenna Gain / 85 3.6.7 Polarization / 89

3.7 Commonly Used Antenna Geometries / 89 3.7.1 Single-Element Radiators / 89 3.7.2 Microstrip Antennas and Antenna Array / 91

4 Fundamentals of Radar 93

4.1 Principles of Radar Operation / 93

4.2 Basic Configuration of Radar / 96

4.2.1 Waveform Generator / 96 4.2.2 Transmitter / 96 4.2.3 Antenna System / 96 4.2.4 Receiver / 97 4.2.5 Computer/Signal Processor / 97 4.2.6 Timing and Control / 97

4.3 The Radar Range Equation / 97

4.4 Cross Section and Clutter / 100 4.4.1 Target Cross Section / 100 4.4.2 Cross Section and the Equivalent Sphere / 101

4.4.3 Cross Section of Real Targets / 101 4.4.4 Radar Cross Section (RCS) / 101 4.4.5 Clutter / 102

4.5 Doppler Effect and Frequency Shift / 103 4.5.1 Doppler Frequency / 104

4.6 Radar Resolution and Ambiguity Function / 1 1 0

5 Radar Modulation and Target Detection Techniques 116

5.1 Amplitude Modulation (AM) Radar / 116

5.1.1 Continuous-Wave (CW) Radar / 117

5.1.2 Pulse Modulation Radar / 117

X CONTENTS

5.2 Target Detection Techniques of AM-Based Radar / 1 1 9 5.2.1 Doppler Frequency Extraction /119 5.2.2 Motion Direction Detection / 121

5.3 Frequency Modulation (FM)-Radar / 123 5.3.1 Pulsed Linear Frequency Modulation (LFM) Radar / 124 5.3.2 Continuous-Wave Linear Frequency Modulation Radar / 129 5.3.3 Stepped Frequency Modulation Radar / 130

5.4 Target Detection Techniques of FM-Based Radar / 133

5.4.1 In-Phase Quadrature-Phase Demodulator / 133 5.4.2 Matched Filter and Pulse Compression / 134 5.4.3 Target Detection Techniques of LFM Radar / 141 5.4.4 Target Detection Techniques of SFM Radar / 149

6 Basics of Radar Imaging 155

6.1 Background / 155

6.2 Geometry of Imaging Radar / 157

6.3 Doppler Frequency and Radar Image Processing / 159 6.3.1 Broadside SAR / 161 6.3.2 SAR with Squint Angle / 174

63.2.1 SAR with a Small Squint Angle I 176

6.3.2.2 SAR with a Low Squint Angle I 180

6.4 Range Migration and Curvature / 185

6.5 Geometric Distortions of the Radar Image / 188

6.5.1 Layover / 188 6.5.2 Foreshortening / 189

6.5.3 Shadowing / 189 6.5.4 Slant-to-Ground Range Distortion / 189

6.5.5 Speckle / 189

6.6 Radar Image Resolution / 189 6.6.1 Example of Real Aperture Radar (RAR) Resolution:

ERS-l/2-Imaging Radars / 191

7 System Model and Data Acquisition of SAR Image 194

7.1 System Model of Range Radar Imaging / 194 7.1.1 System Model / 194 7.1.2 Reconstruction of Range Target Function / 196

CONTENTS XI

7.2 System Model of Cross-Range Radar Imaging / 199 7.2.1 Broadside Radar Case / 199

7.2.1.1 System Model I 199

7.2.1.2 Principle of Stationary Phase I 203 7.2.1.3 Spatial Fourier Transform of Cross-Range Target

Response I 207

7.2.1.4 Reconstruction of Cross-Range Target Function I 210

7.2.2 Squint Radar Case / 213 7.2.2.1 System Model I 213

7.2.2.2 Spatial Fourier Transform of Cross-Range Target Response I 216

7.2.2.3 Reconstruction of Cross-Range Target Function I 219

7.3 Data Acquisition, Sampling, and Power Spectrum of Radar Image /221 7.3.1 Digitized Doppler Frequency Power Spectrum / 223

7.3.1.1 Broadside SAR I 223

7.3.1.2 Squint SAR I 223

8 Range-Doppler Processing on SAR Images 226

8.1 SAR Image Data Generation / 227

8.2 Synthesis of a Broadside SAR Image Data Array / 2 3 1 8.2.1 Single-Target Case / 231

8.2.2 Multiple-Target Case / 235

8.3 Synthesis of a Squint SAR Image Data Array / 240 8.3.1 Single-Target Case / 240 8.3.2 Multiple-Target Case / 242

8.4 Range-Doppler Processing of SAR Data / 246 8.4.1 Range Compression / 248 8.4.2 Corner Turn / 249 8.4.3 Range Cell Migration Correction / 249

8.4.3.1 Computation of Range Migration Amount I 249

8.4.3.2 Fractional Range Sample Interpolation I 252

8.4.3.3 Range Sample Shift I 252

8.4.4 Azimuth Compression / 254

8.4.4.1 Doppler Frequency Centroid I 254

8.4.4.2 Doppler Frequency Change Rate ß / 254

8.4.4.3 Pulse Duration Time Ta I 254

XII CONTENTS

8.5 Simulation Results / 255 8.5.1 Broadside SAR with Single Target / 255 8.5.2 Broadside SAR with Multiple Targets / 261 8.5.3 Squint SAR with Single Target / 267

8.5.4 Squint SAR with Multiple Targets / 275

9 Stolt Interpolation Processing on SAR Images 285

9.1 Wavenumber Domain Processing of SAR Data / 285

9.2 Direct Interpolation from Unevenly Spaced Samples / 288

9.3 Stolt Interpolation Processing of SAR Data / 290

9.3.1 System Model of Broadside SAR with Six Targets / 294 9.3.2 Synthesis of Broadside SAR Data Array / 296 9.3.3 Simulation Results / 298 9.3.4 System Model of Squint SAR with Six Targets / 305 9.3.5 Synthesis of Squint SAR Data Array / 307 9.3.6 Simulation Results / 309

9.4 Reconstruction of Satellite Radar Image Data / 320

9.5 Comparison Between Range-Doppler and Stolt Interpolation on SAR Data Processing / 328

Further Reading

Index

333

335