Table of Contents |
| List of Figures | xi |
| List of Tables | xviii |
| Preface | xix |
| Acknowledgments | xxiii |
1. | Applications of RF Interferometry | 1 |
1.1. | Military Applications | 1 |
1.2. | Sports Applications | 3 |
1.3. | Synthetic Aperture Radar | 6 |
1.4. | Radio Astronomy | 7 |
1.4.1. | Stellar Imaging Using Radio Astronomy | 10 |
1.5. | Near-Geostationary Interferometric Tracking | 11 |
| References | 15 |
2. | Probability Theory | 17 |
2.1. | Random Variable | 17 |
2.2. | Probability Density | 18 |
2.3. | Mean and Covariance | 19 |
2.4. | Maximum Likelihood | 20 |
2.5. | Cramer-Rao Lower Bound | 20 |
2.6. | Lower Bounds for Biased Estimators | 22 |
2.6.1. | Bhattacharyya Bound | 24 |
2.6.2. | Bobrovsky-Zakai Bound | 24 |
2.6.3. | Weiss-Weinstein Bound | 24 |
2.6.4. | Ziv-Zakai Bound | 25 |
| References | 25 |
3. | Radar Fundamentals | 27 |
3.1. | Signal Propagation and Representation | 27 |
3.2. | Continuous Wave Doppler Waveforms | 29 |
3.3. | Pulse Doppler Waveforms | 29 |
3.3.1. | Basic Pulse-Doppler Parameters | 30 |
3.3.2. | Pulse Modulation and the Time-Bandwidth Product | 31 |
3.3.3. | Pulse Doppler Waveform Processing and Pulse Compression | 32 |
3.4. | Radar Range Equation | 34 |
3.5. | Phase Error | 37 |
3.5.1. | Thermal Noise | 37 |
3.5.2. | Clutter | 38 |
3.5.3. | Multipath and Interference | 39 |
| References | 42 |
4. | Radar Angle-of-Arrival Estimation | 43 |
4.1. | The Angle-of-Arrival Problem | 43 |
4.2. | Monopulse Angle Estimation | 44 |
4.3. | Phased Array Beam Pointing Error | 48 |
4.3.1. | Effect of Correlated Phase Errors on Phased Array Beam Pointing | 49 |
4.3.2. | Interferometer Accuracy and Beam Pointing Error | 50 |
4.4. | Resolution Versus Accuracy | 51 |
4.5. | Enhanced Angle Estimation Using the Array Covariance | 52 |
4.5.1. | Angle-of-Arrival Resolution Performance | 52 |
4.5.2. | Signal Versus Noise Eigenvalue Classification | 58 |
4.6. | Enhanced Angle Resolution Algorithms | 61 |
| References | 62 |
5. | Radar Waveforms | 65 |
5.1. | Frequency Coding | 66 |
5.1.1. | Costas Codes | 67 |
5.1.2. | Linear Frequency Modulation | 68 |
5.1.3. | Frequency-Modulated Continuous Wave (FMCW) | 73 |
5.1.4. | Nonlinear Frequency Modulation | 75 |
5.2. | Phase Coding | 80 |
5.2.1. | Pseudorandom Noise Codes (Kasami Codes) | 80 |
5.2.2. | Group Modulation of PRN Codes | 82 |
5.2.3. | Essentially Orthogonal Waveforms | 88 |
5.2.4. | Optimized Multiphase Waveforms | 90 |
5.3. | Bounds on Autocorrelation and Cross-Correlation Performance | 92 |
5.3.1. | Correlation and Cross-Correlation of Random Binary Phase Sequences | 93 |
5.3.2. | Derivation of the Welch Bound for k = 1 | 94 |
5.4. | Chaotic Waveforms | 97 |
| References | 99 |
6. | The Radar Interferometer | 101 |
6.1. | Monopulse Interferometry | 101 |
6.1.1. | Monopulse Interferometer Phase Sensitivity | 102 |
6.1.2. | Monopulse Beamwidth | 103 |
6.1.3. | Monopulse Interferometer Angle Error | 104 |
6.1.4. | Off-Axis Monopulse Error | 105 |
6.2. | Digital Interferometer Angle Error | 107 |
6.2.1. | Correlated and Nonidentically Distributed Error Effects | 108 |
6.2.2. | Impact of Baseline Errors | 110 |
6.3. | Transmit Interferometry | 111 |
6.3.1. | Correlated and Nonidentically Distributed Error Effects | 113 |
6.4. | Cramer-Rao Lower Bound Analysis | 114 |
6.5. | Amplitude Interferometer | 116 |
6.6. | Bistatic Interferometer | 117 |
6.7. | Differential Interferometry | 117 |
6.8. | Synthetic Aperture Radar Interferometry | 119 |
6.8.1. | SAR Interferometry Using Differentials | 120 |
6.8.2. | SAR Interferometry Using Angle-of-Arrival | 121 |
6.8.3. | SAR Interferometry Height Error | 122 |
6.9. | Cramer Rao Lower Bound for Time-of-Arrival | 123 |
6.10. | Coherent Phase Trilateration | 127 |
6.10.1. | Geometric Dilution of Precision | 130 |
6.11. | Summary of Interferometer Angle Precision | 132 |
| References | 133 |
7. | Interferometer Signal Processing | 135 |
7.1. | Basic Interferometer Processing | 135 |
7.2. | Orthogonal Interferometer Processing | 137 |
7.3. | Angle Ambiguity Resolution | 137 |
7.3.1. | Nyquist Sampling for a Spatial Array | 139 |
7.3.2. | Number of Angle Ambiguities | 141 |
7.3.3. | Angle Ambiguity Resolution Using Frequency and Spatial Diversity | 142 |
7.3.4. | Probability of Correct Ambiguity Resolution | 145 |
7.3.5. | Angle Ambiguity Resolution Using Doppler | 148 |
7.4. | Angle-of-Arrival Determination | 151 |
7.4.1. | First-Order Angle Estimation | 153 |
7.4.2. | Second-Order Angle Estimation | 154 |
7.4.3. | Interferometer Angle Measurements for Distributed Transmit/Receive Antennas | 155 |
7.5. | LFM Stretch Processing | 161 |
7.5.1. | Angle-of-Arrival and Stretch Processing | 162 |
7.5.2. | CW/FMCW Homodyne Processing | 165 |
7.6. | Transmit Interferometry Calibration | 166 |
7.7. | Synthetic Aperture Radar Interferometry | 171 |
7.7.1. | Reference Phase Determination | 173 |
7.7.2. | Phase Unwrapping | 173 |
7.8. | Near-Geostationary Interferometry Tracking | 175 |
7.9. | Adaptive Array Processing | 181 |
7.9.1. | The Multiple Sidelobe Canceller | 181 |
7.9.2. | The Generalized Sidelobe Canceller (GSC) | 182 |
7.9.3. | The Orthogonal Space Projection Canceler | 185 |
| References | 187 |
8. | Sparsely Populated Antenna Arrays | 189 |
8.1. | Sparse Linear Arrays | 190 |
8.2. | Interval Partitions | 190 |
8.3. | Cyclic Coprime Partitions | 194 |
8.3.1. | Application to Spatial Sampling | 195 |
8.4. | Nested Cyclic Partitions | 198 |
8.5. | Numerical Sieve Methods for Optimized Sparse Array Generation | 199 |
8.5.1. | Summary of Numerical Sieve Method | 202 |
8.6. | Sparse Array Antenna Performance | 203 |
8.7. | Antenna Pattern Methods | 206 |
8.7.1. | Unequally Spaced Arrays | 207 |
8.7.2. | Polynomial Factorization Method | 210 |
8.8. | Sparse Array Angle-of-Arrival | 214 |
8.8.1. | Sparse Array Monopulse | 215 |
8.8.2. | Sparse Array Interferometry | 216 |
8.8.3. | Sparse Array Angle Estimation Using the Array Covariance | 224 |
8.9. | Two-Dimensional Sparse Arrays | 225 |
8.10. | Multiple-Input and Multiple-Output (MIMO) Sparse Arrays | 229 |
| References | 232 |
9. | Interferometer Angle-of-Arrival Error Effects | 235 |
9.1. | Specular Multipath | 236 |
9.1.1. | Multipath Mitigation Using the Orthogonal Interferometer | 237 |
9.1.2. | Multipath Mitigation Using Sparse Arrays | 240 |
9.1.3. | Quantification of Multipath Using Interferometry | 245 |
9.2. | Angle Glint | 250 |
9.3. | ADC Timing Jitter | 255 |
9.4. | I and Q Imbalances | 256 |
9.5. | Quantization Effects | 258 |
9.5.1. | Phase Shifter Quantization Error | 258 |
9.5.2. | ADC Phase Quantization Error | 259 |
9.6. | Wideband Effects | 262 |
9.6.1. | Antenna Dispersion Loss | 264 |
9.6.2. | Channel Transfer Function Mismatch | 266 |
9.7. | Error Summary | 269 |
| References | 269 |
10. | Tropospheric Effects on Angle-of-Arrival | 271 |
10.1. | Tropospheric Refraction Effects | 272 |
10.1.1. | Geometric Optics (Ray Tracing) | 272 |
10.1.2. | Ray Tracing Adjoint Operator | 280 |
10.2. | Tropospheric Turbulence Effects | 281 |
10.2.1. | Basic Theory for RF Turbulence | 281 |
10.2.2. | Turbulence-Induced Radar Effects | 282 |
10.2.3. | Turbulence-Induced Radar Scintillation | 283 |
10.2.4. | Radar Beam Fluctuation at the Target | 283 |
10.2.5. | Space-to-Ground Turbulence Analysis | 284 |
| References | 287 |
Appendix A | Discrete Fourier Transform | 289 |
Appendix B | The Matched Filter | 291 |
Appendix C | The Principle of Stationary Phase | 295 |
Appendix D | The Fundamental Theory of Binary Code | 299 |
Appendix E | Theoretical Development of Kasami Codes | 303 |
Appendix F | Relationship of the Continuous Power Spectrum and Discrete Variance | 307 |
Appendix G | Time-of-Arrival CRLB (Alternative Approach) | 309 |
Appendix H | Two-Dimensional Trilateration Using CPT and RGS Ranging Methods--MATLAB® Code | 313 |
Appendix I | Angle-of-Arrival Determination Using a Rotated Antenna Configuration | 317 |
Appendix J | First- and Second-Order Interferometer Angle Measurements---MATLAB® Code | 321 |
Appendix K | Interferometer Angle Measurements for Distributed Transmit/Receive Antennas---MATLAB® Code | 323 |
| Index | 325 |