Space Based Radar: Theory & Applications

Contents......Page 7
Preface......Page 11
List of Abbreviations......Page 15
1 Introduction......Page 17
1.1 Overview......Page 19
1.2 The Radar Equation......Page 23
1.3 Notations and Matrix Identities......Page 25
1.3.1 Eigenvalues and Eigenvectors......Page 26
1.3.2 Hermitian Matrices......Page 28
1.3.3 Singular Value Decomposition (SVD)......Page 32
1.3.4 Schur, Kronecker, and Khatri-Rao Products......Page 33
1.3.5 Matrix Inversion Lemmas......Page 41
Appendix 1-A: Line Spectra and Singular Covariance Matrices......Page 42
References......Page 44
2.1 What Is a Conic?......Page 47
2.1.1 Ellipse......Page 49
2.1.2 Parabola......Page 55
2.1.3 Hyperbola......Page 56
2.2 The Solar System......Page 60
Appendix 2-A: Spherical Triangles......Page 62
References......Page 66
3.1 Orbital Mechanics......Page 67
3.1.1 The Motion of the Center of Mass......Page 68
3.1.2 Equations of Relative Motion......Page 70
3.2 Kepler’s Laws......Page 73
3.3 Synchronous and Polar Orbits......Page 76
3.4 Satellite Velocity......Page 77
Appendix 3-A: Kepler’s Equation......Page 83
Appendix 3-B: Euler’s Equation and the Identification of Comets......Page 87
Appendix 3-C: Lambert’s Equation for Elliptic Orbits......Page 90
References......Page 92
4.1 Radar-Earth Geometry......Page 93
4.2 Maximum Range on Earth......Page 97
4.3 Mainbeam Footprint Size......Page 99
4.4 Packing of Mainbeam Footprints......Page 102
4.5.1 Mainbeam Foldover......Page 106
4.5.2 Total Range Foldover......Page 110
4.6 Doppler Shift......Page 113
4.7 Crab Angle and Crab Magnitude: Modeling Earth’s Rotation for SBR......Page 117
4.7.1 Range Foldover and Crab Phenomenon......Page 134
Appendix 4-A: Ground Range from Latitude and Longitude Coordinates......Page 137
Appendix 4-B: Nonsphericity of Earth and the Grazing Angle Correction Factor......Page 139
Appendix 4-C: Doppler Effect......Page 146
Appendix 4-D: Oblate Spheroidal Earth and Crab Angle Correction......Page 150
References......Page 153
5.1 Spatial Array Processing......Page 155
5.1.1 Why Use an Array?......Page 156
5.1.2 Maximization of Output SNR......Page 164
5.2 Space-Time Adaptive Processing......Page 169
5.3 Side-Looking Airborne Radar......Page 171
5.3.2 Sample Matrix Inversion (SMI)......Page 178
5.4 Eigen-Structure Based STAP......Page 181
5.4.1 Brennan’s Rule......Page 182
5.4.2 Eigencanceler Methods......Page 183
5.4.3 Hung-Turner Projection (HTP)......Page 187
5.5 Subaperture Smoothing Methods......Page 189
5.5.1 Subarray Smoothing......Page 193
5.6.1 Subarray Method......Page 199
5.6.3 Subarry-Subpluse Method......Page 200
5.7 Array Tapering and Covariance Matrix Tapering......Page 204
5.7.1 Diagonal Loading as Tapering......Page 208
5.8 Convex Projection Techniques......Page 210
5.8.1 Convex Sets......Page 211
5.8.2 Toeplitz Property......Page 212
5.8.3 Positive-Definite Property......Page 213
5.8.4 Methods of Alternating Projections......Page 214
5.8.5 Relaxed Projection Operators......Page 216
5.9 Factor Time-Space Approach......Page 217
5.10 Joint-Domain Localized Approach......Page 221
Appendix 5-A: Uniform Array Sidelobe Levels......Page 224
References......Page 229
6 STAP for SBR......Page 231
6.1 SBR Data Modeling......Page 232
6.1.1 Mainbeam and Sidelobe Clutter......Page 234
6.1.2 Ideal Clutter Spectrum......Page 239
6.2 Minimum Detectable Velocity (MDV)......Page 248
6.3 MDV with Earth’s Rotation and Range Foldover......Page 250
6.4 Range Foldover Minimization Using Orthogonal Pulsing......Page 262
6.5 Scatter Return Modeling......Page 271
6.5.1 Terrain Modeling......Page 272
6.5.2 ICM Modeling......Page 277
6.6 MDV with Terrain Modeling and Wind Effect......Page 284
6.6.1 Effect of Wind on Doppler......Page 286
6.6.2 General Theory of Wind Damping Effect on Doppler......Page 291
6.7 Joint Effect of Terrain, Wind, Range Foldover, and Earth’s Rotation on Performance......Page 296
6.8 STAP Algorithms for SBR......Page 299
Appendix 6-A: Matrix Inversion Identity......Page 312
Appendix 6-B: Output SINR Derivation......Page 313
Appendix 6-C: Spectral Factorization......Page 314
Appendix 6-D: Rational System Representation......Page 319
References......Page 323
7.1 Cramer-Rao Bounds for Multiparameter Case......Page 325
7.2 Cramer-Rao Bounds for Target Doppler and Power in Airborne and SBR Cases......Page 336
7.3 Simulation Results......Page 347
References......Page 354
8 Waveform Diversity......Page 357
8.1 Matched Filter Receivers......Page 360
8.1.1 Matched Filter Receivers in White Noise......Page 362
8.1.2 Matched Filter Receivers in Colored Noise......Page 369
8.2 Chirp and Pulse Compression......Page 374
8.3 Joint Transmitter–Receiver Design in Noise......Page 380
8.4 Joint Time Bandwidth Optimization......Page 392
Appendix 8-A: Transform of a Chirp Signal......Page 401
References......Page 407
9 Advanced Topics......Page 409
9.1 An Infinitesimal Body Around Two Finite Bodies......Page 410
9.1.1 Particular Solutions of the Three-Body Problem......Page 417
9.1.2 Stability of the Particular Solutions......Page 421
9.1.3 Stability of Linear Solutions......Page 425
9.1.4 Stability of Equilateral Solutions......Page 428
Appendix 9-A: Hill Sphere......Page 433
References......Page 436
A......Page 437
C......Page 438
D......Page 439
E......Page 440
H......Page 441
K......Page 442
M......Page 443
O......Page 444
R......Page 445
S......Page 446
T......Page 448
W......Page 449