Sea Clutter: Scattering, the K Distribution and Radar Performance

Sea Clutter: Scattering, the K Distribution and Radar Performance, 2nd Edition......Page 4
Acknowledgements......Page 6
Contents......Page 8
List of symbols......Page 16
1.2 Maritime radar......Page 24
1.3 The modelling of radar returns from the sea......Page 29
1.4.2 Modelling of potential performance......Page 30
1.4.4 Performance assessment and acceptance trials......Page 31
1.5 Outline of the book......Page 32
References......Page 36
Part I: Sea clutter properties......Page 38
2.1 Overview......Page 40
2.2 The sea surface......Page 42
2.3 Sea clutter reflectivity......Page 44
2.4 Amplitude statistics......Page 46
2.4.1 The compound nature of sea clutter amplitude statistics......Page 49
2.6 Observations of amplitude distributions......Page 51
2.7 Polarisation characteristics......Page 54
2.8 Clutter spikes and modulations......Page 57
2.9 Coherent properties of radar sea clutter......Page 64
2.10 Spatial characteristics......Page 69
2.10.1 Range Autocorrelation Function (ACF)......Page 70
2.10.2 Power spectrum analysis of range-time intensity plots......Page 72
2.11 Bistatic clutter......Page 75
2.11.2 Bistatic reflectivity NBRCS......Page 76
2.11.3 Bistatic amplitude statistics......Page 77
References......Page 78
3.2 Low grazing angle normalised sea clutter RCS models......Page 82
3.2.2 GIT model......Page 83
3.2.4 The TSC model......Page 87
3.2.5 The hybrid model......Page 88
3.2.6 Other results......Page 89
3.3 Medium and high grazing angle normalised RCS models......Page 90
3.4 Bistatic normalised RCS models......Page 93
3.4.1 In-plane NBRCS models......Page 94
3.4.2 Out-of-plane NBRCS......Page 97
3.5.2 Weibull distribution......Page 98
3.5.3 Compound K distribution......Page 99
3.5.4 Compound K distribution plus noise......Page 100
3.5.5 Shape parameter at low grazing angle......Page 101
3.5.6 Discrete spike modelling......Page 106
3.6 Medium grazing angle statistics......Page 110
3.7 Bistatic amplitude statistics......Page 113
3.8.1 Average Doppler spectra......Page 115
3.8.2 Evolution of Doppler spectra with time......Page 116
3.8.3 Bistatic Doppler spectra......Page 121
References......Page 123
4.1 Introduction......Page 128
4.2 Generating uncorrelated random numbers with a prescribed PDF......Page 129
4.3 Generating correlated Gaussian random processes......Page 130
4.4 Fourier synthesis of random processes......Page 134
4.5 Approximate methods for the generation of correlated gamma distributed random numbers......Page 135
4.6 The correlation properties of non-Gaussian processes generated by MNLT......Page 137
4.7 Correlated exponential and Weibull processes......Page 139
4.8 The generation of correlated gamma processes by MNLT......Page 142
4.9 Simulating coherent clutter......Page 147
4.9.1 Simulation of clutter spectra......Page 148
4.9.2 Simulation of time series data......Page 152
4.9.3 Discussion......Page 155
References......Page 156
Part II: Mathematics of the K distribution......Page 158
5.1 Introduction......Page 160
5.2 Finite numbers of discrete events......Page 161
5.3 An infinite number of discrete events......Page 163
5.4 Continuous random variables......Page 165
5.5 Functions of random variables......Page 169
5.6 The normal process......Page 172
5.7 The time evolution of random processes......Page 180
5.8 Power spectra and correlation functions......Page 181
5.9 The complex Gaussian process......Page 182
5.10 Spatially correlated processes......Page 185
5.11 Stochastic differential equations and noise processes......Page 186
5.12.1 Correcting moments for the effect of noise......Page 193
5.12.2 Correcting the moments for a limited number of samples......Page 194
5.12.3 Order statistics......Page 196
5.12.4 Sequential testing......Page 197
References......Page 200
6.2 Gaussian clutter models......Page 202
6.3 Non-Gaussian clutter......Page 207
6.3.1 Compound models of non-Gaussian clutter......Page 208
6.3.2 The gamma distribution of local power and the K distribution......Page 209
6.3.3 A coherent signal in K distributed clutter......Page 210
6.3.4 K distributed clutter with added thermal noise......Page 211
6.3.5 Phases of homodyned and generalised K processes......Page 212
6.4 Modelling coherent clutter......Page 213
References......Page 219
7.2 A random walk model of non-Gaussian scattering......Page 220
7.3 The Class A and breaking area models......Page 224
7.4 A Fokker–Planck description of K distributed noise......Page 230
References......Page 237
8.1 Introduction......Page 240
8.2 The homodyned and generalised K models......Page 241
8.3 Populations on coupled sites and their continuous limit......Page 249
8.4 Some applications......Page 254
References......Page 256
9.2 The gamma function and related topics......Page 258
9.3 Some properties of the K distribution PDF......Page 263
9.4 The Bessel functions In; Jn......Page 268
9.5 Expansions in Hermite and Laguerre polynomials......Page 273
References......Page 276
Part III: Radar detection......Page 278
10.1 Introduction......Page 280
10.2 Statistical models for probabilities of detection and false alarm......Page 281
10.3 Likelihood ratios and optimal detection......Page 282
10.4 Some simple performance calculations......Page 284
10.5 The generalised likelihood ratio method......Page 288
10.6.1 A simple likelihood ratio–based approach......Page 290
10.6.2 Generalised likelihood ratio–based approach......Page 291
10.7.1 Generalised likelihood ratio–based approach......Page 295
10.7.2 Peak within interval detection......Page 299
10.8 Applications to coherent detection......Page 301
10.9.1 Maximum likelihood estimators for gamma and Weibull parameters......Page 303
10.9.2 Tractable, but sub-optimal, estimators for K and Weibull parameters......Page 305
10.10.1 Modified generalised likelihood ratio–based detection......Page 306
10.10.2 Modified peak within interval detection......Page 308
References......Page 309
11.2 The analysis of correlated Gaussian data......Page 312
11.2.2 χa processing and the whitening filter......Page 313
11.2.3 Optimal χo processing......Page 316
11.3 The Wishart distribution......Page 317
11.3.1 The real Wishart distribution......Page 318
11.3.2 The complex Wishart distribution......Page 319
11.4 Polarimetric and interferometric processing......Page 321
11.4.1 χ processing of interferometric and polarimetric data......Page 323
11.4.2 Phase increment processing of interferometric data......Page 325
11.4.3 Coherent summation and discrimination enhancement......Page 328
11.5 Feature detection by matched filtering......Page 331
11.6 False alarm rates for matched filter processing......Page 333
11.6.1 A simple model for the global maximum single point statistics......Page 334
11.6.2 The global maximum of a one-dimensional Gaussian process and the matched filter false alarm curve for a time series......Page 336
11.6.3 Extension to two-dimensional matched filters......Page 338
11.7 A compound model for correlated signals......Page 340
References......Page 342
12.1 Introduction......Page 344
12.2 Radar equation and geometry......Page 345
12.3 Sea clutter fluctuations and false alarms......Page 348
12.4 Target RCS models and detection probability......Page 355
12.5 Detection performance with a logarithmic detector......Page 368
12.6 Comparison of K distribution, Weibull and lognormal models......Page 371
12.7 Performance prediction of pulsed Doppler processing......Page 378
12.8 End-to-end radar detection performance......Page 380
12.8.1 Radar polarisation......Page 383
12.8.2 Target models......Page 385
12.8.3 Target exposure time......Page 386
12.8.4 Radar resolution......Page 387
12.8.5 Scan rate......Page 388
References......Page 390
13.1 Introduction......Page 392
13.2 Adaptation to changing clutter amplitude......Page 393
13.2.1 Control of received signal dynamic range......Page 394
13.2.2 Log FTC receiver for Rayleigh clutter......Page 395
13.2.3 Cell-averaging CFAR detector......Page 396
13.2.3.1 CFAR variants......Page 398
13.2.3.2 CFAR loss in noise......Page 399
13.2.3.3 GO CFAR in noise......Page 401
13.2.3.4 OS CFAR in noise......Page 403
13.2.3.5 CFAR loss in K distributed clutter......Page 404
13.2.3.6 CFAR loss in K distributed clutter plus noise......Page 408
13.2.3.7 Ideal CFAR detection and CFAR gain in K distributed clutter......Page 409
13.2.3.8 CFAR gain with a cell-averaging CFAR......Page 412
13.2.4 Linear prediction techniques......Page 417
13.3 Adaptation to changing clutter PDF......Page 418
13.3.1 Fitting to a family of distributions......Page 419
13.3.2 Distribution-free detection......Page 421
13.3.3.1 Matching moments......Page 423
13.3.3.2 Matching to the tail of the distribution......Page 425
13.3.4 Estimation of a Weibull shape parameter......Page 428
13.4.2 Closed-loop systems......Page 429
13.4.3 Exploitation of transient coherence......Page 430
13.5 Practical CFAR detectors......Page 431
References......Page 432
14.1 Introduction......Page 434
14.2.1 Discussion......Page 435
14.2.2 Adaptive radars......Page 437
14.2.3 Specification of adaptive systems......Page 438
14.2.4.2 Spatial variation of PFA......Page 439
14.2.4.4 Spatial variation of PD......Page 443
14.3 Performance prediction......Page 444
14.3.2 Clutter speckle component......Page 447
14.3.3 False alarms......Page 448
14.4 Measuring performance......Page 449
14.4.1 Trials......Page 450
14.4.3 Modelling and simulation......Page 451
14.5 Measurement methods and accuracies......Page 452
14.5.1.1 Blip-to-scan ratio......Page 453
14.5.1.2 Estimation of SNR......Page 454
14.5.1.3 Detection in sea clutter......Page 456
14.5.3 Statistical analysis of trials......Page 458
14.5.3.1 Sequential testing......Page 459
References......Page 461
Part IV: Physical modelling......Page 462
15.1 Introduction......Page 464
15.2 The sea surface......Page 465
15.3 EM scattering from the sea at high grazing angles......Page 473
15.4 Imaging ocean currents at high grazing angles......Page 478
References......Page 489
16.2 The composite model for scattering at medium grazing angles......Page 492
16.3 Scattering at low grazing angles: beyond the composite model......Page 496
16.4 Scattering from breaking waves......Page 509
16.5 Average backscatter from the ocean at low grazing angles......Page 514
16.6 Imaging ocean currents at low grazing angles......Page 517
16.7 Sea clutter in littoral environments......Page 520
References......Page 521
17.1 The integral formulation of the scalar scattering problem......Page 524
17.2 Helmholtz equation Green’s functions in two and three dimensions......Page 527
17.3 Derivation of the Fresnel formulae......Page 530
17.4 Approximate decoupling of the integral equations: the impedance boundary condition......Page 533
17.5.1 The physical optics or Kirchoff approximation......Page 535
17.5.2 Small height perturbation theory: PC case......Page 537
17.5.3 The half-space and reciprocal field formalisms......Page 540
17.6 Scattering by an imperfectly conducting surface: small height perturbation theory......Page 545
17.7.1 Scattering from a perfect conductor......Page 549
17.7.2 Scattering from an imperfect conductor; modification of the F/B method......Page 558
17.8 Incorporation of the impedance boundary condition in F/B calculations......Page 561
17.9 Evaluation of adjunct plane contributions......Page 562
17.10 Summary......Page 565
References......Page 566
Index......Page 570