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Main Sea Clutter: Scattering, the K Distribution and Radar Performance
Sea Clutter: Scattering, the K Distribution and Radar PerformanceKeith Ward, Robert Tough, Simon Watts
Sea Clutter: Scattering, the K Distribution and Radar Performance Second Edition gives an authoritative account of our current understanding of radar sea clutter. Topics covered include the characteristics of radar sea clutter, modelling radar scattering by the ocean surface, statistical models of sea clutter, the simulation of clutter and other random processes, detection of small targets in sea clutter, imaging ocean surface features, radar detection performance calculations, CFAR detection, and the specification and measurement of radar performance. The calculation of the performance of practical radar systems is presented in sufficient detail for the reader to be able to tackle related problems with confidence. For this fully revised and updated second edition new material has been added on the Doppler characteristics of sea clutter and associated detection processing methods, bistatic sea clutter measurements; electromagnetic scattering theory of littoral sea clutter and bistatic sea clutter; the use of models for predicting radar performance, including discussion of Lognormal and Weibull models; further results and extended discussion on the modelling of the K distribution shape parameter for different conditions; the simulation of Doppler spectra of sea clutter; high grazing angle scattering; and the use of the K distribution in other fields. The material has been reorganized into four parts: Sea Clutter Properties, Mathematics of the K distribution, Radar Detection and Physical Modelling. This reorganisation allows readers to access specific areas quickly, without the need for an extensive knowledge of the other parts.
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IET RADAR, SONAR AND NAVIGATION SERIES 25 Sea Clutter Other volumes in this series: Volume 1 Volume 3 Volume 7 Volume 8 Volume 10 Volume 11 Volume 13 Volume 14 Volume 15 Volume 16 Volume 17 Volume 18 Volume 19 Volume 20 Volume 21 Volume 22 Volume 23 Volume 101 Optimised radar processors A. Farina (Editor) Weibull radar clutter M. Sekine and Y. Mao Ultra-wideband radar measurements: analysis and processing L. Yu. Astanin and A.A. Kostylev Aviation weather surveillance systems: advanced radar and surface sensors for flight safety and air traffic management P.R. Mahapatra Radar techniques using array antennas W. Wirth Air and spaceborne radar systems: an introduction P. Lacomme (Editor) Introduction to RF stealth D. Lynch Applications of space-time adaptive processing R. Klemm (Editor) Ground penetrating radar, 2nd edition D. Daniels Target detection by marine radar J. Briggs Strapdown inertial navigation technology, 2nd edition D. Titterton and J. Weston Introduction to radar target recognition P. Tait Radar imaging and holography A. Pasmurov and S. Zinovjev Sea clutter: scattering, the K distribution and radar performance K. Ward, R. Tough and S. Watts Principles of space-time adaptive processing, 3rd edition R. Klemm Waveform design and diversity for advanced radar systems F. Gini, A. De Maio and L.K. Patton Tracking filter engineering: the Gauss-Newton and polynomial filters N. Morrison Introduction to airborne radar, 2nd edition G.W. Stimson Sea Clutter Scattering, the K Distribution and Radar Performance 2nd Edition Keith Ward, Robert Tough and Simon Watts The Institution of Engineering and Technology Published by The Institution of Engineering and Technology, London, United Kingdom The Institution of Engineering and Technology is registered as a Charity in England & Wales (no. 211014) and Scotland (no. SC038698). † 2013 The Institution of Engineering and Technology First published 2013 This publication is copyright under the Berne Convention and the Universal Copyright Convention. All rights reserved. Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may be reproduced, stored or transmitted, in any form or by any means, only with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms of licences issued by the Copyright Licensing Agency. Enquiries concerning reproduction outside those terms should be sent to the publisher at the undermentioned address: The Institution of Engineering and Technology Michael Faraday House Six Hills Way, Stevenage Herts, SG1 2AY, United Kingdom www.theiet.org While the author and publisher believe that the information and guidance given in this work are correct, all parties must rely upon their own skill and judgement when making use of them. Neither the author nor publisher assumes any liability to anyone for any loss or damage caused by any error or omission in the work, whether such an error or omission is the result of negligence or any other cause. Any and all such liability is disclaimed. The moral rights of the author to be identified as author of this work have been asserted by him in accordance with the Copyright, Designs and Patents Act 1988. British Library Cataloguing in Publication Data A catalogue record for this product is available from the British Library ISBN 978-1-84919-589-8 (hardback) ISBN 978-1-84919-590-4 (PDF) Typeset in India by MPS Limited Printed in the UK by CPI Group (UK) Ltd, Croydon Acknowledgements Much of the work described in this book was supported by research funding from the UK MOD in many programmes undertaken over the last 30 years. Work was also supported by funding from the authors' own organisations, Igence Radar and Thales UK. The authors gratefully acknowledge the support they have received and the work of many other workers in the United Kingdom and around the world who have contributed to the body of knowledge represented in this book. Contents List of symbols xv 1 Introduction 1.1 Prologue 1.2 Maritime radar 1.3 The modelling of radar returns from the sea 1.4 The use of clutter models in radar development 1.4.1 Requirement definition 1.4.2 Modelling of potential performance 1.4.3 System and algorithm development 1.4.4 Performance assessment and acceptance trials 1.4.5 In-service tactics and training 1.4.6 In-service upgrades 1.5 Outline of the book References 1 1 1 6 7 7 7 8 8 9 9 9 13 Part I 15 2 The 2.1 2.2 2.3 2.4 Sea clutter properties characteristics of radar sea clutter Overview The sea surface Sea clutter reflectivity Amplitude statistics 2.4.1 The compound nature of sea clutter amplitude statistics 2.5 Frequency agility and sea clutter 2.6 Observations of amplitude distributions 2.7 Polarisation characteristics 2.8 Clutter spikes and modulations 2.9 Coherent properties of radar sea clutter 2.10 Spatial characteristics 2.10.1 Range Autocorrelation Function (ACF) 2.10.2 Power spectrum analysis of range-time intensity plots 2.11 Bistatic clutter 2.11.1 Bistatic scattering geometry 2.11.2 Bistatic reflectivity NBRCS 2.11.3 Bistatic amplitude statistics 2.11.4 Bistatic Doppler spectra References 17 17 19 21 23 26 28 28 31 34 41 46 47 49 52 53 53 54 55 55 viii Sea clutter: scattering, the K distribution and radar performance 3 Empirical models for sea clutter 3.1 Overview 3.2 Low grazing angle normalised sea clutter RCS models 3.2.1 RRE model 3.2.2 GIT model 3.2.3 Sittrop's model 3.2.4 The TSC model 3.2.5 The hybrid model 3.2.6 Other results 3.3 Medium and high grazing angle normalised RCS models 3.4 Bistatic normalised RCS models 3.4.1 In-plane NBRCS models 3.4.2 Out-of-plane NBRCS 3.5 Low grazing angle statistics 3.5.1 Lognormal distribution 3.5.2 Weibull distribution 3.5.3 Compound K distribution 3.5.4 Compound K distribution plus noise 3.5.5 Shape parameter at low grazing angle 3.5.6 Discrete spike modelling 3.6 Medium grazing angle statistics 3.7 Bistatic amplitude statistics 3.8 Doppler spectra 3.8.1 Average Doppler spectra 3.8.2 Evolution of Doppler spectra with time 3.8.3 Bistatic Doppler spectra References 59 59 59 60 60 64 64 65 66 67 70 71 74 75 75 75 76 77 78 83 87 90 92 92 93 98 100 4 The simulation of clutter and other random processes 4.1 Introduction 4.2 Generating uncorrelated random numbers with a prescribed PDF 4.3 Generating correlated Gaussian random processes 4.4 Fourier synthesis of random processes 4.5 Approximate methods for the generation of correlated gamma distributed random numbers 4.6 The correlation properties of non-Gaussian processes generated by MNLT 4.7 Correlated exponential and Weibull processes 4.8 The generation of correlated gamma processes by MNLT 4.9 Simulating coherent clutter 4.9.1 Simulation of clutter spectra 4.9.2 Simulation of time series data 4.9.3 Discussion References 105 105 106 107 111 112 114 116 119 124 125 129 132 133 Contents ix Part II Mathematics of the K distribution 135 5 Elements of probability theory 5.1 Introduction 5.2 Finite numbers of discrete events 5.3 An infinite number of discrete events 5.4 Continuous random variables 5.5 Functions of random variables 5.6 The normal process 5.7 The time evolution of random processes 5.8 Power spectra and correlation functions 5.9 The complex Gaussian process 5.10 Spatially correlated processes 5.11 Stochastic differential equations and noise processes 5.12 Miscellaneous results 5.12.1 Correcting moments for the effect of noise 5.12.2 Correcting the moments for a limited number of samples 5.12.3 Order statistics 5.12.4 Sequential testing References 137 137 138 140 142 146 149 157 158 159 162 163 170 170 6 Gaussian and non-Gaussian clutter models 6.1 Introduction 6.2 Gaussian clutter models 6.3 Non-Gaussian clutter 6.3.1 Compound models of non-Gaussian clutter 6.3.2 The gamma distribution of local power and the K distribution 6.3.3 A coherent signal in K distributed clutter 6.3.4 K distributed clutter with added thermal noise 6.3.5 Phases of homodyned and generalised K processes 6.4 Modelling coherent clutter References 179 179 179 184 185 7 Random walk models 7.1 Introduction 7.2 A random walk model of non-Gaussian scattering 7.3 The Class A and breaking area models 7.4 A Fokker–Planck description of K distributed noise 7.5 Conclusions References 197 197 197 201 207 214 214 8 Some extensions of the K distribution 8.1 Introduction 8.2 The homodyned and generalised K models 217 217 218 171 173 174 177 186 187 188 189 190 196 x 9 Sea clutter: scattering, the K distribution and radar performance 8.3 Populations on coupled sites and their continuous limit 8.4 Some applications 8.5 Conclusions References 226 231 233 233 Special functions associated with the K distribution 9.1 Introduction 9.2 The gamma function and related topics 9.3 Some properties of the K distribution PDF 9.4 The Bessel functions In, Jn 9.5 Expansions in Hermite and Laguerre polynomials References 235 235 235 240 245 250 253 Part III Radar detection 255 10 Detection of small targets in sea clutter 10.1 Introduction 10.2 Statistical models for probabilities of detection and false alarm 10.3 Likelihood ratios and optimal detection 10.4 Some simple performance calculations 10.5 The generalised likelihood ratio method 10.6 A simple Gaussian example 10.6.1 A simple likelihood ratio–based approach 10.6.2 Generalised likelihood ratio–based approach 10.7 The detection of a steady signal in Rayleigh clutter 10.7.1 Generalised likelihood ratio–based approach 10.7.2 Peak within interval detection 10.8 Applications to coherent detection 10.9 The estimation of clutter parameters 10.9.1 Maximum likelihood estimators for gamma and Weibull parameters 10.9.2 Tractable, but sub-optimal, estimators for K and Weibull parameters 10.10 Implications of the compound form of non-Gaussian clutter 10.10.1 Modified generalised likelihood ratio–based detection 10.10.2 Modified peak within interval detection 10.11 Concluding remarks References 257 257 Imaging ocean surface features 11.1 Introduction 11.2 The analysis of correlated Gaussian data 11.2.1 c processing 11.2.2 ca processing and the whitening filter 11.2.3 Optimal co processing 289 289 289 290 290 293 11 258 259 261 265 267 267 268 272 272 276 278 280 280 282 283 283 285 286 286 Contents 11.3 12 13 xi The Wishart distribution 11.3.1 The real Wishart distribution 11.3.2 The complex Wishart distribution 11.4 Polarimetric and interferometric processing 11.4.1 c processing of interferometric and polarimetric data 11.4.2 Phase increment processing of interferometric data 11.4.3 Coherent summation and discrimination enhancement 11.5 Feature detection by matched filtering 11.6 False alarm rates for matched filter processing 11.6.1 A simple model for the global maximum single point statistics 11.6.2 The global maximum of a one-dimensional Gaussian process and the matched filter false alarm curve for a time series 11.6.3 Extension to two-dimensional matched filters 11.7 A compound model for correlated signals References 294 295 296 298 300 302 305 308 310 Radar detection performance calculations 12.1 Introduction 12.2 Radar equation and geometry 12.3 Sea clutter fluctuations and false alarms 12.4 Target RCS models and detection probability 12.5 Detection performance with a logarithmic detector 12.6 Comparison of K distribution, Weibull and lognormal models 12.7 Performance prediction of pulsed Doppler processing 12.8 End-to-end radar detection performance 12.8.1 Radar polarisation 12.8.2 Target models 12.8.3 Target exposure time 12.8.4 Radar resolution 12.8.5 Scan rate 12.9 Modelling other types of radar References 321 321 322 325 332 345 348 355 357 360 362 363 364 365 367 367 CFAR detection 13.1 Introduction 13.2 Adaptation to changing clutter amplitude 13.2.1 Control of received signal dynamic range 13.2.2 Log FTC receiver for Rayleigh clutter 13.2.3 Cell-averaging CFAR detector 369 369 370 371 372 373 22.214.171.124 CFAR variants 126.96.36.199 CFAR loss in noise 126.96.36.199 GO CFAR in noise 311 313 315 317 319 375 376 378 xii Sea clutter: scattering, the K distribution and radar performance 220.127.116.11 OS CFAR in noise 18.104.22.168 CFAR loss in K distributed clutter 184.108.40.206 CFAR loss in K distributed clutter plus noise 188.8.131.52 Ideal CFAR detection and CFAR gain in K distributed clutter 220.127.116.11 CFAR gain with a cell-averaging CFAR 13.2.4 Linear prediction techniques 13.2.5 Non-linear predictors 13.3 Adaptation to changing clutter PDF 13.3.1 Fitting to a family of distributions 13.3.2 Distribution-free detection 13.3.3 Estimation of the K distribution shape parameter 18.104.22.168 Matching moments 126.96.36.199 Matching to the tail of the distribution 385 386 389 394 395 395 396 398 400 400 402 13.3.4 Estimation of a Weibull shape parameter Other CFAR detection techniques 13.4.1 Site-specific CFAR 13.4.2 Closed-loop systems 13.4.3 Exploitation of transient coherence 13.4.4 Scan-to-scan integration 13.5 Practical CFAR detectors References 405 406 406 406 407 408 408 409 The specification and measurement of radar performance 14.1 Introduction 14.2 Performance specification issues 14.2.1 Discussion 14.2.2 Adaptive radars 14.2.3 Specification of adaptive systems 14.2.4 Practical performance specification 411 411 412 412 414 415 416 13.4 14 380 381 184.108.40.206 22.214.171.124 184.108.40.206 184.108.40.206 14.3 Probability of false alarm, PFA Spatial variation of PFA Probability of detection, PD Spatial variation of PD Performance prediction 14.3.1 Clutter amplitude statistics 14.3.2 Clutter speckle component 14.3.3 False alarms 14.4 Measuring performance 14.4.1 Trials 14.4.2 Factory measurements 14.4.3 Modelling and simulation 416 416 420 420 421 424 424 425 426 427 428 428 Contents 14.5 Measurement methods and accuracies 14.5.1 Probability of detection 14.5.2 14.5.3 xiii 429 430 220.127.116.11 Blip-to-scan ratio 184.108.40.206 Estimation of SNR 18.104.22.168 Detection in sea clutter 430 431 433 Probability of false alarm PFA Statistical analysis of trials 435 435 22.214.171.124 Sequential testing References 436 438 Part IV Physical modelling 439 15 High grazing angle radar scattering 15.1 Introduction 15.2 The sea surface 15.3 EM scattering from the sea at high grazing angles 15.4 Imaging ocean currents at high grazing angles References 441 441 442 450 455 466 16 Low grazing angle scattering by the ocean surface 16.1 Introduction 16.2 The composite model for scattering at medium grazing angles 16.3 Scattering at low grazing angles: beyond the composite model 16.4 Scattering from breaking waves 16.5 Average backscatter from the ocean at low grazing angles 16.6 Imaging ocean currents at low grazing angles 16.7 Sea clutter in littoral environments References 469 469 17 Scattering from a corrugated surface 17.1 The integral formulation of the scalar scattering problem 17.2 Helmholtz equation Green's functions in two and three dimensions 17.3 Derivation of the Fresnel formulae 17.4 Approximate decoupling of the integral equations: the impedance boundary condition 17.5 Scattering by a perfectly conducting surface 17.5.1 The physical optics or Kirchoff approximation 17.5.2 Small height perturbation theory: PC case 17.5.3 The half-space and reciprocal field formalisms 17.6 Scattering by an imperfectly conducting surface: small height perturbation theory 469 473 486 491 494 497 498 501 501 504 507 510 512 512 514 517 522 Sea clutter: scattering, the K distribution and radar performance xiv 17.7 Numerical solutions of the scattering problem 17.7.1 Scattering from a perfect conductor 17.7.2 Scattering from an imperfect conductor; modification of the F/B method 17.8 Incorporation of the impedance boundary condition in F/B calculations 17.9 Evaluation of adjunct plane contributions 17.10 Summary References Index 526 526 535 538 539 542 543 547 List of symbols Symbols Meaning Page1 Section h iN hi r a a a average over N trials expectation gradient operator negative binomial bunching parameter threshold multiplier (relative to mean) probability of Type 1 error (Seller's risk) in sequential testing estimate of threshold multiplier, a shape parameter of Weibull distribution probability of Type 2 error (Buyer's risk) in sequential testing Bistatic angle relaxation rate of wave growth Gamma function incomplete gamma function Measure of the curvature of the correlation function of az Euler's constant Half power width of Doppler spectrum frequency step size (frequency agility) dielectric constant or relative permittivity permittivity of free space amplitude of the Hermitian product x normal component of the field gradient at a surface sea surface height sea surface heights of long and short wave components signal phase Incident and scattering angles, bistatic geometry antenna azimuth beamwidth azimuth look direction 139 24 450 141 86 5.2 2.4 15.3 5.3 3.5.6 437 404 75 14.5 13.3 3.5.2 437 53 459 24 327 14.5 2.11 15.4 2.4 12.3 204 373 93 28 450 450 232 7.3 13.2 3.8 2.5 15.3 15.3 8.4 478 443 16.3 15.2 471 183 16.2 6.2 53 323 324 2.11 12.2 12.2 ^ a b b b b(t) G(.) G(v, t) g g D Df e e0 z z(x) h hL, hs q q1, q2 qaz q xvi Sea clutter: scattering, the K distribution and radar performance Symbols Meaning Page1 Section qsw qgr qi qloc qw l l L L2 direction of sea swell grazing angle angle of incidence local incidence angle wind direction discrimination ratio in sequential testing radar wavelength likelihood ratio matrix of derivatives of the correlation function of a random field relative permeability permeability of free space K-distribution intensity after pulse-to-pulse integration vector of mean values of image pixels effective K-distribution shape parameter shape parameter of gamma and K distribution estimate of K-distribution shape parameter Hermitian product of two complex signals charge density surface roughness parameter range resolved length (range resolution) PDF fluctuation index Normalised mean spike intensity, ssp/sBW, for KA distribution Normalised mean spike intensity, ssp/s, for KK distribution correlation function of long wave component range correlation coefficient for lag j water density radar cross section (RCS) and scattered power Lognormal PDF shape parameter area reflectivity (normalised clutter RCS), VV and HH mean Bragg and whitecap intensity in K plus spike model root mean square wave height Standard deviation of spectrum width, s mean spike intensity in K plus spike model Normalised bistatic clutter RCS Normalised clutter RCS; upwind, downwind and crosswind 79 491 470 472 443 436 62 260 3.5 16.5 16.2 16.2 15.2 14.5 3.2.2 10.3 316 450 450 11.6 15.3 15.3 326 289 205 76 404 232 450 491 323 76 12.3 11.2 7.3 3.5.3 13.3 8.4 15.3 16.5 12.2 3.5 m m0 m m veff v ^ v x r r r r r r rL rj rw s s s0, s0HH ; s0V V sBW sh ss ssp s0B s0u ; s0d ; s0c 84 3.5 89 472 48 445 480 75 3.7 16.2 2.10 15.2 16.3 3.5 17 2.1 84 443 97 84 72 68 3.5.6 15.2 3.8 3.5.6 3.4 3.3 List of symbols xvii Symbols Meaning Page1 Section ^1 s t f f f f fel fgr j(t) c estimate of parameter s1 pulse length look direction in elevation, long wave surface lateral tilt phase of individual scatterer Bistatic azimuth angle antenna elevation beamwidth grazing angle wave action spectral density discriminant used as detection test statistic, or to enhance imagery scalar fields satisfying the Helmholtz equation antenna depression angle digamma function temporal frequency wave age area of scattering surface Radar resolved area scale parameter of Weibull distribution coherent signal with in phase and quadrature components parameters of logarithmic amplifier autocorrelation function automatic gain control cell-averager weights contribution of individual scatterer to field E Anti-Surface Warfare Anti-Submarine Warfare vertical acceleration of water surface wave height saturation spectrum magnetic induction pulse bandwidth and receiver noise bandwidth Phillips constant scale parameter of gamma and K distributions breaking area model sea wave phase velocity characteristic function 269 432 324 472 480 53 323 323 459 10.6 14.5 12.2 16.2 6.2 2.11 12.2 12.2 15.4 279 475 323 282 50 446 454 79 75 10.8 16.3 12.2 10.9 2.10 15.2 15.3 3.5 3.5.2 182 372 47 414 392 180 3 3 204 444 454 28 443 6.2 13.2 2.10 14.2 13.2 6.2 1.2 1.2 7.3 15.2 15.3 2.5 15.2 76 492 445 180 3.5.3 16.5 15.2 6.2 cell-averaging constant false alarm rate Constant false alarm rate clutter-to-noise ratio 373 12 339 13.2 1.5 12.4 y y y(z) w W A Ac a A, AI, AQ a, b ACF AGC aj an ASuW ASW az Bh(q) B B b b BAM c C(U) or C(k) CA CFAR CFAR CNR xviii Sea clutter: scattering, the K distribution and radar performance Symbols Meaning Page1 Section D E E EI, EQ EM hEniRice erf() erfc() ERS1 ESA ET ez 2F1, 1F1 electric field displacement amplitude electric field vector in phase and quadrature components of E Electromagnetic nth moment of a Rice distribution error function, defined in equation (5.31) complementary error function Remote sensing SAR satellite European Space Agency threshold field amplitude unit vector in vertical direction hypergeometric and confluent hypergeometric functions, defined in equations (9.15) and (9.16) Radar frequency cumulative distribution function or probability distribution Fast Fourier transform receiver noise figure Pulse repetition frequency one-way antenna gain gravitational acceleration number of gap cells either side of cell under test in CA CFAR Green's function Power spectral density normal component of gradient of Green's function Term in Rice and composite model scattering RCS Gaussian uncorrelated random variate Horizontal polarisation magnetic field vector height of radar above the Earth surface Average wave height zeroth order Hankel function null hypothesis in sequential testing alternative hypothesis in sequential testing significant wave height of the sea Hermite polynomial integrand in scattering formula Bessel functions (modified) of the first kind and order n 450 24 31 181 12 275 184 115 2 2 181 472 15.3 2.4 2.7 6.2 1.5 10.7 6.2 4.6 1.2 1.2 6.2 16.2 237 28 9.2 2.5 312 40 323 93 325 50 11.6 2.8 12.2 3.8 12.2 2.10 373 452 97 13.2 15.3 3.8 529 17.7 470 107 22 31 324 62 477 437 437 20 115 482 16.2 4.3 2.3 2.7 12.2 3.2 16.3 14.5 14.5 2.2 4.6 16.3 182 6.2 f F(x) FFT Fn fr G(q, f) g G G() G() G gHH, gVV gn H, HH H h hav ð1Þ H 0 ðzÞ H0 H1 h1=3 Hn =(.) In List of symbols xix Symbols Meaning Page1 Section in(z), kn(z) j modified spherical Bessel functions electric current vector 302 450 11.4 15.3 Jn Bessel functions (unmodified) of the first kind and order n target fluctuation parameter Boltzman's constant wave vector spatial frequency or wavenumber degree of coherence of complex Gaussian process rank of ordered statistic KK distribution parameter covariance matrix of SAR image pixels horizontal component of backscattered wavevector wavenumber of slowest waves modified Bessel function of the second kind (Hankel function of imaginary argument) Polarisation parameter vertical component of backscattered wavevector surface length in scattering calculations FFT length associated Laguerre polynomial radar microwave loss left-hand polarisation atmospheric and propagation loss low grazing angle Laguerre polynomial Pierson Moskowitz saturation spectrum lateral extent of scattering surface estimate of mean intensity MTF value number of averaging cells in CA CFAR maximum value in Greater-of CFAR (GO CFAR) Lognormal PDF scale parameter Mean of spectrum width, s Mean Doppler frequency of spectrum ideal value in sequential testing maximum acceptable value in sequential testing Multi-function radar 245 334 323 453 50 9.4 12.4 12.2 15.3 2.10 300 380 89 290 11.4 13.2 3.6 11.2 470 445 16.2 15.2 76 79 3.5.3 3.5 470 479 94 118 432 32 322 469 118 446 488 47 494 373 16.2 16.3 3.8.2 4.7 14.5 2.7 12.2 16.1 4.7 15.2 16.4 2.10 16.6 13.2 379 75 77 77 437 13.2 3.5 3.8 3.8 14.5 437 5 14.5 1.2 k k k k k k k K kH km Kv kpol kz L L Lan Lm L, LL La LGA Ln LPM 'x ^ m M M m m ms mf () m0 m1 MFR xx Sea clutter: scattering, the K distribution and radar performance Symbols mn MTF n n n N N N N Neff Norm(K) NBRCS p p P(E1jE2) P(njN) P(x) p^ pc Pc(x) PD PFA pn PPI pr ps pt q Q qcut Qdist R R r, r0 R, RR RAF RCS re RG(t) Meaning th n moment modulation transfer function vector normal to a surface number of scans Number of pulses number of pulses integrated number of discrete events (trials) mean populations supported by Poisson and negative binomial processes Mean number of spikes effective number of independent samples normalisation integral of matrix K Normalised bistatic RCS number of random variables in set modelled by Wishart distribution probability of an event conditional PDF probability of throwing n heads in N trials probability density function (pdf) estimate of probability of an event mean clutter power clutter local power pdf probability of detection probability of false alarm noise power plan position indicator power received by a radar mean signal power peak transmit power wavenumber (variable) upper triangular matrix from Cholesky decomposition of K wavenumber separating long and short waves complementary quantile function Fresnel reflection coefficient range to the target points above a scattering surface Right-hand polarisation Royal Air Force radar cross section radar Earth radius (4/3 times actual radius) correlation coefficient of Gaussian random variable Page1 Section 203 494 451 430 84 376 138 7.3 16.6 15.3 14.5 3.5 13.2 5.2 202 84 425 152 53 7.3 3.5 14.3 5.6 2.11 295 404 182 141 181 404 323 76 182 183 77 419 322 323 322 443 11.3 13.3 6.2 5.3 6.2 13.3 12.2 3.5.3 6.2 6.2 3.5.4 14.2 12.2 12.2 12.2 15.2 289 471 114 508 324 451 32 3 18 324 11.2 16.2 4.6 17.3 12.2 15.3 2.7 1.2 2.1 12.2 115 4.6 List of symbols xxi Symbols Meaning Page1 Section Rj or R(j) RN s s s Sh SAR SCR SIR SNR S(w) Ss, SL STC T0 t T T ta td Tr(A) U U U u* U10 V, VV v range ACF, lag j Royal Navy area of a breaking wave in the BAM model Spike intensity Spectrum width sea surface height power spectrum Synthetic Aperture Radar signal-to-clutter ratio signal-to-interference ratio signal-to-noise ratio sea clutter Doppler power spectrum Wave spectrum of short and long waves sensitivity-time control standard noise temperature (290 K) detection threshold test statistic surface tension mean time between alarms mean alarm duration trace of matrix A water current log estimator of Weibull shape parameter Wind speed wind friction velocity wind speed (at 10 m above the sea surface) Vertical polarisation a point on the mean x, y plane of a scattering surface Variance Cross-polarisations 46 4 204 84 97 443 2 337 336 374 191 471 416 323 373 398 445 425 425 295 455 405 60 447 443 22 2.10 1.2 7.3 3.5 3.8 15.2 1.2 12.4 12.4 13.2 6.4 16.2 14.2 12.2 13.2 13.3 15.2 14.3 14.3 11.3 15.4 13.3 3.2 15.2 15.2 2.3 453 403 31 15.3 13.3 2.7 Mean local clutter intensity non-dimensional fetch points on a scattering surface set of values of variable or parameters x correlated random variate Threshold Log transformed intensity Bessel function of the second kind and order n clutter intensity 24 446 451 265 107 327 372 506 24 2.4 15.2 15.3 10.5 4.3 12.3 13.2 17.2 2.4 var(.) VH, HV, RL, LR x X x, x0 {x} xn Y y Yn z 1 The page and section denote the first occurrence of the symbol with the defined meaning. Chapter 1 Introduction 1.1 Prologue The largest part of the Earth's surface lies beneath the sea (see Figure 1.1); events taking place in, on and directly above the oceans have an enormous impact on our lives. Consequently, maritime remote sensing and surveillance are of great importance. Since its discovery during the 1930s, radar has played a central role in these activities. Much of their military development was driven by the circumstances of the Cold War; now this era is past and a different set of imperatives holds sway. Military surveillance does, however, remain a key requirement. Great progress has been made recently on non-military applications, particularly the remote sensing of the environment, of which the sea is the most important component. These newly emerging concerns, whether they are ecological or geopolitical, currently define the requirements imposed on maritime radar systems. Nonetheless, the underlying principles of the systems' operation, and the interpretation of their output, remain the same; the body of knowledge developed in the twentieth century provides us with the tools with which to address the problems facing the radar engineer of the twenty-first century. This book attempts to bring together those aspects of maritime radar relating to scattering from the sea surface, and their exploitation in radar systems. The presentation aims to emphasise the unity and simplicity of the underlying principles and so should facilitate their application in these changing circumstances. 1.2 Maritime radar A wide variety of radars can be deployed to sense or interrogate a maritime environment. Space-based radars are used for Earth remote sensing and, particularly, for oceanography. The earliest example of this application was SEASAT [1]. The SEASAT-A satellite was launched on 26 June 1978, and continued until 19 October 1978. Its mission was to demonstrate that measurements of the ocean dynamics are feasible. It carried a synthetic aperture radar (SAR), which was intended to obtain radar imagery of ocean wave patterns in deep oceans and coastal regions, sea and fresh water ice, land surfaces and a number of other remote sensing objectives. It also carried a radar altimeter and a wind scatterometer. More recent 2 Sea clutter: scattering, the K distribution and radar performance Figure 1.1 A view of the Earth from space (http://images.jsc.nasa.gov/) examples of remote sensing radars have been the ESA ERS-1 and ERS-2 [2] satellites, which had similar missions to SEASAT and a similar range of radar instruments. The most recent example at the time of writing this book is ENVISAT [3]. Each of the radar instruments carried by these satellites exploits different aspects of scattering from the sea surface. The radar altimeter is used to make very accurate measurements of the sea height. The SEASAT-A satellite carried an altimeter having a measurement accuracy of better than 10 cm, which allowed the measurement of oceanographic features such as currents, tides and wave heights. A wind scatterometer measures the average backscatter power over large areas of the sea surface. The measurement of backscatter scattering coefficients at three different directions relative to the satellite track allows the surface wind direction to be calculated. Finally, an SAR images the surface at much finer resolution (typically about 25 m 25 m) over grazing angles typically in the range of 20 –60 . Figure 1.2 shows an example of an ERS-1 SAR image of the sea surface, showing wave, current and weather patterns on the sea off the eastern tip of Kent in the south of England. Data such as these allow scientists to better understand air–sea interactions, which have a major effect on the world's weather patterns and overall climate. They are therefore an important component of modelling for climate change, and in particular global warming. Introduction 3 Figure 1.2 ERS-1 radar image of North East Kent and the surrounding sea (data copyright ESA – image processed by DERA UK) The backscatter from the sea observed by remote sensing radars is the intended radar signal. Airborne radar may also be used for ocean imaging in this way. However, for most airborne and surface radars operating in a maritime environment, the backscatter from the sea is unwanted and is called sea clutter. A prime example of a military application that encounters problems of this kind is maritime surveillance. Typical examples include the Searchwater radar [4], which was in service with the UK RAF Nimrod MR2 aircraft (Figure 1.3), the AN/APS-137 radar fitted in the US Navy P3-C aircraft, and the Blue Kestrel radar in the Royal Navy Marlin helicopter. These radars have many operating modes, but in particular are used for long-range surveillance of surface ships (known as ASuW, anti-surface warfare) and detection of small surface targets, including submarine masts (ASW, anti-submarine warfare). For ASuW operation, the radar must detect, track and classify surface ships at ranges in excess of 100 nautical miles. For ASW operation, the radar must detect submarine masts just above the surface in high sea states, at ranges of many miles. In both of these modes, the radar operator and the automatic detection processing must be able to distinguish between returns from wanted targets and those from the sea surface. Unlike satellite radars, the grazing angle at the sea surface for such radars is typically less than 10 and often the area of interest extends out to the radar horizon (i.e. zero grazing angle). Under these conditions, returns from the sea can often have target-like characteristics and may be very difficult to distinguish from real targets. In order to aid discrimination between targets and clutter and, in extreme cases, prevent overload of the radar operator or signal processor, the radar detection processing must attempt to achieve an acceptable and constant false alarm rate (CFAR) from the sea clutter. 4 Sea clutter: scattering, the K distribution and radar performance Figure 1.3 Nimrod MR2 with Searchwater radar (copyright Crown Copyright/MOD, image from www.photos.mod.uk) Figure 1.4 RN Mk2 Sea King helicopter with Searchwater AEW radar (copyright Crown Copyright/MOD, image from www.photos.mod.uk) Air-to-air detection modes are also important for airborne radars. Obvious examples are airborne interceptor (AI) radars for fast jets, such as the Blue Vixen radar on the RN Sea Harriers [5], and Airborne Early Warning Radars such as the AWACS or the Searchwater 2000AEW radar fitted to the RN Mk7 Sea King helicopters (see Figure 1.4, which shows the earlier Mk2 Sea King with the Introduction 5 Searchwater radar). In order to detect targets that are much smaller than the sea backscatter, these radars use pulsed Doppler processing to distinguish moving targets from the sea clutter. Targets with a high radial velocity are easily distinguished from the clutter, but slower targets or those on a crossing trajectory may have Doppler shifts that are not much separated from the Doppler spectrum of the sea clutter. Once again, the challenge for the radar processing is to maintain an acceptable false alarm rate from the clutter, especially in the edges of its Doppler spectrum. Surface radars, especially ship-borne radars, must also cope with sea clutter. Ship radars are used, among other applications, for navigation, surface surveillance and air defence. Naval warships are increasingly being fitted with multi-function radars (MFRs), such as the Sampson radar, fitted to the RN Type 45 Destroyers. These MFRs must undertake all these modes and many others in an interleaved manner. Once again, the radar processing must distinguish between clutter returns and targets. Figure 1.5 shows the MESAR MFR which was the experimental precursor to Sampson. Figure 1.5 MESAR 2 MFR (reproduced with the kind permission of BAESystems Integrated Systems Technology) 6 Sea clutter: scattering, the K distribution and radar performance 1.3 The modelling of radar returns from the sea The accurate and physically motivated modelling of radar returns from the sea surface should provide a firm foundation for the analysis of their impact on maritime radar performance. Simple models, of limited application, formed the basis of earlier work: thus the physical optics or Kirchoff approximation could be made in an EM scattering approach, while a Gaussian model might form the basis of a tractable statistical description. These models can be applied quite effectively to the analysis of sea clutter in low resolution radar systems, deployed well away from grazing incidence. In the past four decades modelling techniques able to capture the salient features of low grazing angle, high resolution, radar sea clutter have been developed. Ad hoc non-Gaussian statistical models had been proposed, chosen in the main for their analytic convenience; since the 1970s these have been supplanted by the K distribution and related models. This class of models was first introduced, in the context of radar sea clutter, by Jakeman and Pusey [6]; these authors drew on analogies between scattering at microwave and optical wavelengths to motivate their discussion. The K distribution was shown to emerge directly from a detailed analysis of sea clutter in the work of Ward [7]. This approach highlighted the usefulness of the compound representation of the clutter process, which, in the hands of Ward, Watts and others, made possible the systematic analysis of effects of thermal noise and the spatial and temporal correlation properties displayed by the clutter and their impact on maritime surveillance radar [8]. Oliver developed similar ideas, in the context of SAR, which have contributed significantly to interpretation of two-dimensional radar imagery [9]. These developments in the application of the K distribution in the microwave regime have been complemented by work at optical wavelengths [10]; a further interchange of ideas between these two areas occurred when the generalised K model, developed by Jakeman and Tough for weak forward scattering in the visible regime, proved invaluable in the analysis of polarimetric and interferometric SAR performance [11, 12]. This brief review of the development of the K distribution would be incomplete if it did not mention the careful statistical analysis that has ensured that the estimation of the parameters defining the K distribution has been carried out accurately and meaningfully; Oliver and co-workers contributed significantly in this area. The electromagnetic scattering by the sea surface at close to grazing incidence presents many problems. Perhaps the simplest model that makes direct contact with both EM theory and a reasonable statistical description of the sea surface is Rice's perturbation theory analysis of scattering by a slightly rough surface, from which a picture of resonant or Bragg scattering from small-scale structure emerges [13]. The composite model [14] incorporated the imperfect electrical conductivity of sea water and allowed for the modulation of local grazing angle by the large-scale structure of the sea surface. Subsequent attempts to incorporate shadowing and multipath effects, which become important at low grazing angles, have been in the main essentially uncontrolled, or ad hoc. More recently, however, the problems Introduction 7 inherent in the direct numerical calculation of scattering by a surface wave profile have been addressed; the past decade or so has seen the development of methods able to cope with low grazing angle geometries and realistic conductivities [15]. These can now be used in the careful analysis of grazing angle and polarisation dependence of the fluctuations and dynamics of scattering in this regime; detailed numerical results of this type have led to significant insights into the observed properties of sea clutter. 1.4 The use of clutter models in radar development Modelling and simulation are essential elements of almost all aspects of engineering design and development of complex systems. A modern radar is no exception to this. In this book, we examine a particular component of the design, development and testing processes of radar systems, namely the use of modelling and simulation of radar sea clutter. The principal reason for modelling radar clutter is to inform the development of improved radar systems that meet the operational needs of their users. Models of the interaction of radar with its environment are needed in almost every phase of radar development. The requirements of different design phases will dictate the types of models to be used. These will vary from simple analytic models for rudimentary performance prediction to extremely detailed models able to represent the dynamic interaction of an adaptive radar in a rapidly changing scenario. Models of clutter are used in many different ways throughout the life cycle of a radar design, development and usage. A diagram of various phases where this occurs is shown in Figure 1.6. These phases are discussed further in this section. 1.4.1 Requirement definition Modern radars, especially those using adaptive processing, are extremely complex and their performance is very difficult to specify. A customer needs to ensure that those characteristics that will affect his ability to achieve his operational mission are effectively specified. The ability to do this is dependent on a detailed understanding of the likely behaviour of the radar in many different operational conditions. However, a supplier needs a simple set of performance parameters upon which to base the system design. One way to bridge this gap is to use a model that relates the basic performance of the radar to its behaviour in complex operational environments. For maritime radars an important component of such a model is the behaviour of sea clutter. 1.4.2 Modelling of potential performance Basic performance estimates are usually developed from a version of the radar range equation. In addition to the standard radar parameters, detection performance in clutter is likely to need estimates of clutter characteristics and the operation of the detection signal processing. 8 Sea clutter: scattering, the K distribution and radar performance Customer Requirement definition Performance assessment and acceptance trials Customer & supplier Customer & supplier Supplier Modelling of potential performance System and algorithm design In-service tactics and training User In-service upgrades User, customer & supplier Figure 1.6 Use of models during a radar life cycle Reliable prediction of radar performance over the sea depends on accurate models of both the radar processing and of the sea clutter. At early stages of a radar design, the basic radar parameters (waveform design, antenna gain, transmitter power, receiver noise figure, signal and data processing algorithms) are defined. As the radar design develops and is refined, the radar performance needs to be continuously assessed in the context of this initial modelling. 1.4.3 System and algorithm development As the radar design is refined, each design decision is assessed in terms of its impact on radar performance. Initial estimates of parameters and system losses are thus continuously reassessed. The performance of signal and data processing is typically compared with idealised models of performance. As well as contributing to ideal performance models, good clutter models often provide insight into likely performance of different signal processing schemes and help to inform design decisions and monitor the expected performance of an emerging design. 1.4.4 Performance assessment and acceptance trials Once a radar has been built and integrated into a working system, its overall performance needs to be quantified to the customer and user. This process is discussed in detail in Chapter 12, where it is noted that measurement of radar performance directly from trials may often be impossible, especially when quantifying dynamic adaptive performance. The measurement of detection performance of small targets in sea clutter is particularly difficult from trials alone. A practical solution is to Introduction 9 instrument the radar used in the trial and measure the actual target and clutter characteristics. These measured parameters can then be used in the analytic model to predict performance for the actual target in the conditions observed. This predicted performance can then be compared with the actual performance observed in the trial. 1.4.5 In-service tactics and training Some radar systems have a large array of operator controls and settings. These may be essential to achieve optimum performance of the radar under different conditions. The operator may also need to intervene when confronted by jamming or interference. One application of clutter models aimed at assisting the radar operator is the probability of detection display. This system predicts the detectability of targets over the radar display by analysing the system's gains and threshold settings required to achieve a CFAR. In a radar system with an automatic detection system, these change dynamically over the radar display, adapting to different conditions. These settings can be interpreted in relation to a clutter model to predict the minimum target radar cross-section (RCS) that could be detected at any point on the display. Adjustment of the radar parameters, either by the operator or by the automatic detection system, or changes of other factors, such as the radar height, can then be assessed in terms of their effect on the radar performance. Complex modern radars require well-trained operators to achieve the best performance. A radar simulator used for training needs to replicate the effects of adjusting operator controls on the radar performance. One way of achieving this is by generating synthetic returns from targets and clutter and using them as inputs to the simulator. Again, this requires good models of clutter to achieve realistic performance. 1.4.6 In-service upgrades Upgrades and improvements may be needed through the life of a radar in response to changing user requirements and improvements in technology. In support of these aims, it is particularly important to monitor the operational performance of a radar system and to identify limitations in performance compared with those predicted by modelling. This helps the user to better specify any improvements that may be required, as well as identifying shortcomings in any modelling. This knowledge is also essential for better specification and development of the next generation of radars. 1.5 Outline of the book Many types of radar, with both civil and military applications, will encounter backscatter from the sea, either as wanted signal or as clutter. In all cases the radar designer must understand the characteristics of the backscatter from the sea in order either to relate the signal to the ocean characteristics or to achieve the performance required by the radar users. These characteristics are found to vary very widely, 10 Sea clutter: scattering, the K distribution and radar performance according to the radar parameters, viewing geometry and weather conditions. This book describes the very many different aspects that must be studied in order to design and develop new radars and to predict and understand the performance of operational systems. As a result it is addressed to a wide and varied audience, not all of whom may wish, at least initially, to read it in its entirety. The investigation of the mechanisms that give rise to radar sea clutter and the ways in which its impact on performance is modelled and calculated will be of great use to radar engineers, be they graduate students, academics or professional research and development workers. The discussion of the physical principles that underpin this work may be of wider interest: our presentation of low grazing angle scattering from rough surfaces can be adapted to other wavelengths and might well, for example, be of relevance to workers in optics and sonar. The use of non-Gaussian statistical models has become increasingly important in many areas; in several of these, the K distributed process has proved to have wide applicability. Our discussion of the K distribution is motivated by its relevance to radar clutter; nonetheless we feel that it contains insights that should be of more general interest and so will complement that published recently by Jakeman and Ridley [16]. The numerical simulation of non-Gaussian noise processes also has widespread application; our discussion of this topic may again attract the interest of those outside the immediate radar community. Some prior knowledge is expected of a reader who intends to work through the whole book. A reasonable acquaintance with the fundamentals of radar operation, a knowledge of EM theory and probability, and sufficient 'mathematical maturity' to look an unfamiliar equation in the eye without flinching are all required. The specialist reader, whose interest is confined to the contents of individual chapters, can happily 'jump straight in', as each chapter is reasonably self-contained and, it is hoped, achieves a logical and consistent presentation of its subject matter. The authors also hope that some readers will, once they have worked through a topic of immediate interest, wish to venture further afield in the book. The scene is set by the qualitative description, empirical modelling and simulation of the phenomena observed in radar sea clutter; these relate many of the modelling tools used by radar engineers to experimental observations. The mathematics behind one of the principal statistical models, the K distribution, are developed and related to applications in other fields. Once these essential preliminaries have been covered, they are applied to radar design, optimisation and calculation of radar system performance; the methods we present here are chosen for their efficiency, versatility and accuracy, rather than a summary of everything described in the literature. From this we lead to application of the knowledge to the specification and measurement of radar performance, which are parts of the process of radar system procurement. Finally, the mechanisms that give rise to sea clutter effects are elucidated in a review of the physics that governs the scattering of microwaves by the sea surface and other objects. The book is split into four parts covering Sea Clutter Properties, the Mathematics of the K Distribution, Radar Detection and Physical Modelling. Summaries of the topics covered in each part and chapter are given below. Introduction 11 Part I, on Sea Clutter Properties, consists of Chapters 2–4. Chapter 2 describes the experimental evidence of sea clutter characteristics that has been collected over many years of observation, mainly based on data collected from high-resolution airborne and ship-borne radars operating in G/H-band (5.3 GHz) and I-band (9 GHz). The features used to characterise sea clutter, such as reflectivity, amplitude statistics, temporal statistics (Doppler spectra) and spatial features, are defined and illustrated. In Chapter 3, empirical models derived from these types of data are described and illustrated. Details are given on the dependencies of these models on radar parameters (such as radar frequency, spatial resolution, frequency agility, polarisation and so on), and on the environment (sea state, sea swell, wind speed, viewing geometry and so on). A key model described here is the compound K distribution, which allows an important separation of the coherent interference properties (speckle) from the slower and larger spatial modulations. The realistic simulation of clutter plays a vital role in the development of new detection algorithms and the testing of systems with controlled and well-understood data. Chapter 4 describes how this can be done. Gaussian processes are considered first; their single-point statistics are preserved under linear operations while their correlation properties can be controlled through simple recurrence relations and by Fourier synthesis. In the compound model, clutter is represented as a Gaussian process of constant power that is, in turn, multiplied by a non-Gaussian process. The latter can be generated by the non-linear transformation of an input Gaussian process, whose controlled correlation properties are related unambiguously to those of its output. Much of the development and application of clutter models is mathematical, and Part II (which consists of Chapters 5–8) is therefore devoted to the Mathematics of the K distribution. Chapter 5 provides an introduction to probability theory, followed by Chapter 6 on Gaussian and compound models, which are used extensively for target and clutter radar returns form the basis of the performance calculations presented in this book. We develop these models, starting with a simple, physically motivated analysis of the Rayleigh clutter encountered in lowresolution radar systems. The effects of target returns and increasingly higher radar resolution can be accommodated within this framework, which leads us to the compound representation of the K distribution. Some properties of coherent clutter are considered, again within the compound model. Chapter 7 introduces the concept of random walks for clutter modelling and shows how this approach provides insights into many of the properties of the K distribution and how it may be extended to include discrete sea spikes. Chapter 8 looks beyond the K distribution to such things as the generalised K distribution and its use in applications other than radar. Finally, Chapter 9 provides a 'mathematical toolbox' of special functions that are used in association with the K distribution. Part III, which consists of Chapters 10–14, covers the topic of Radar Detection and considers the application of sea clutter models. Chapter 10 addresses several issues relevant to the detection of small targets in clutter. The pertinent elements of statistical theory underlying the problems of detection and estimation are reviewed, 12 Sea clutter: scattering, the K distribution and radar performance with particular attention being paid to likelihood-based methods. As well as being optimal, in a well-defined sense, these are quite tractable when applied to Gaussian processes. Consequently, they provide a useful guide to the construction of localised small target detection strategies. Some problems that arise in the imaging and detection of ocean surface features are considered in Chapter 11. The detection theory concepts developed in Chapter 10 find further application here, suggesting ways in which anomalous features can be enhanced by local processing. Particular attention is paid to interferometric and polarimetric processing of pairs of SAR images; rather intriguingly, K distribution–related concepts play an important role in this analysis. Once a feature in an image has been enhanced, the matched filter technique allows us to exploit our prior knowledge of its structure in its detection. When applied to features that are barely discernible, this technique can easily produce false alarms. Using the background mathematical techniques developed in the earlier chapters, Chapter 12 develops the practical procedures for radar performance prediction. These techniques provide for the estimation of the probability of target detection and the probability of false alarms from clutter and thermal noise, taking into account their dependency on radar parameters, signal processing strategies and environmental conditions. The results show the extent to which optimal radar design is affected by clutter statistics. Chapter 13 describes and analyses some of the techniques used to achieve CFAR detection. The radar must continuously adapt its detection thresholds to both the local clutter power and its amplitude statistics. The performance of CFAR detectors is analysed for both thermal noise and sea clutter, including the effects of spatial correlation of the sea clutter. Chapter 14 looks at some of the issues facing manufacturers and procurers of radar. For them, the ultimate aim of all the works presented in this book must be to support the design of radar systems that meet the requirements of their users. The very complex nature of radar performance in sea clutter, combined with the advanced adaptive radar signal processing techniques that may be employed, means that the specification and measurement of radar performance for procurement processes are very difficult. The need to understand the empirical observations of sea clutter has led to an extensive study of the theory of electromagnetic scattering from the sea surface. Much progress has been made on this subject, as described in Part IV on Physical Modelling. Chapter 15 introduces a description of the sea surface and the EM techniques employed to calculate scattering from the sea at high grazing angles. A worked example is given of application of the techniques to the radar imaging of tidal current flows over submerged sandbanks. Chapter 16 considers the more difficult problem of low-grazing-angle sea clutter, where the effects of multiple scattering become important. Much of the detail of the techniques used is glossed over in Chapters 15 and 16 to allow the broader issues to be addressed. This is put right in Chapter 17, where the mathematical background to the theory of electromagnetic scattering from corrugated surfaces is derived in much more detail in order to allow readers to get 'hands-on' experience. Introduction 13 References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. L. J. Cantafio, Space-based radar handbook, Artech House, Boston, 1989 S. J. Austin, D. J. Q. Carter, J. D. McCaughey, 'ERS-1 spacecraft – active microwave instrumentation: a major achievement', GEC J. Res., 9(1), 1991 ESA Earthnet Online website, https://earth.esa.int/web/guest/missions/esaoperational-eo-missions/envisat S. Watts, A. J. Gordon, 'The Searchwater family of radars', IEE International Conference Radar 97, 14–16 October 1997, IEE Publication No. 449, pp. 334–338, 1997 A. M. Kinghorn, P. E. Holbourn, M. J. Smith, J. F. Roulston, 'The blue vixen radar for Sea Harrier FRS.2', GEC REV., 9(3), 131–145, 1994 E. Jakeman, P. N. Pusey, 'A model for non-Rayleigh sea echo', IEEE Trans. Antennas Propag., AP-24, 808, 1976 K. D. Ward, 'Compound representation of high resolution sea clutter', Electronics Letters, 17, 561, 1981 K. D. Ward, C. J. Baker, S. Watts, 'Maritime surveillance radar, Part 1: Radar scattering from the ocean surface', Proc. IEE, 137F(2), 51–62, April 1990; S. Watts, C. J. Baker, K. D. Ward, 'Maritime surveillance radar, Part 2: Detection performance prediction in sea clutter', Proc. IEE, 137F(2), 1990, 63–72 C. J. Oliver, S. Quegan, Understanding synthetic aperture radar images, Artech House, Boston, MA, 1998 E. Jakeman, R. J. A. Tough, 'Non-Gaussian models for the statistics of scattered waves', Adv. Phys., 37, 471, 1988 E. Jakeman, R. J. A. Tough, 'The generalized K distribution: A statistical model for weak scattering', J. Opt. Soc. Am., A4, 1764, 1987 R. J. A. Tough, D. Blacknell, S. Quegan, 'A statistical description of polarimetric and interferometric synthetic aperture data', Proc. Roy. Soc. Series A, 449, 567, 1995 S. O. Rice, 'Reflection of electromagnetic waves from slightly rough surfaces', Comm. Pure Appl. Math., 4, 351–478, 1951 G. R. Valenzuela, 'Theories for the interaction of electromagnetic waves and oceanic waves – a review', Boundary-Layer Meteor., 13, 61–85, 1978 IEEE Trans. Antennas Propag., Special Issue on LGA scattering of the sea surface AP-46(1), 1998 E. Jakeman, K. Ridley, Modelling fluctuations in scattered waves, Taylor and Francis London, 2006 Part I Sea clutter properties Chapter 2 The characteristics of radar sea clutter 2.1 Overview In this chapter, sea clutter is described in terms of its observed characteristics. These observations will provide the foundations upon which the themes of subsequent chapters are developed. Radars operating in a maritime environment inevitably encounter backscattered radar signals from the sea surface, usually referred to as sea clutter. For some applications, such as remote sensing systems, the reception of this backscattered signal may be the main purpose of the radar. Space-borne synthetic aperture radars, with spatial resolutions of a few metres, are used for oceanographic studies, gathering data on waves and currents, sea ice and so on. Scatterometers measure average backscatter over hundreds of square kilometres to measure wind speed and direction over the sea surface. For most other applications, the backscatter from the sea is unwanted and may interfere with the radar's operation. For example, almost all airborne radar operation over the sea encounters sea clutter, whether the radar is used for long-range surveillance of shipping, detection of other aircraft or detecting very small targets such as submarine periscopes. Similarly, ship-borne radars, whether used for navigation or surveillance of the air and sea, must contend with unwanted sea clutter. The characteristics of sea clutter over this range of applications may vary extremely widely. The radar system designer needs to understand these characteristics in order to develop suitable signal processing strategies and to predict performance under different conditions. An important step in achieving these goals is the development of accurate statistical models of the clutter return. These models must be able to incorporate the spatial and temporal properties of the backscatter, under a wide range of environmental conditions and for different radar waveforms and viewing geometries. A number of features are used to characterise the clutter returns. These are ● ● ● The area reflectivity, s0. The amplitude distribution of the clutter amplitudes or power. The spectrum of the clutter returns. 18 ● ● ● Sea clutter: scattering, the K distribution and radar performance The spatial variation of the clutter return. The polarisation scattering matrix. Discrete clutter spikes. The average radar cross-section (RCS) of the returns per unit area is defined by the area reflectivity s0. For a surface area A illuminated by the radar resolution cell (e.g. for a pulsed radar, the area defined by the compressed pulse length and the antenna azimuth beamwidth), the RCS of the clutter is given by s0A. The constantly changing and complex nature of the sea surface means that the instantaneous RCS of the returns fluctuates widely around the mean value determined by s0. The statistics of these fluctuations are an important characteristic of sea clutter. The single-point amplitude statistics are described using families of probability density functions (PDFs), with a specific PDF being appropriate for a given set of observations. The manner in which these amplitude fluctuations vary with time is characterised by the spectrum of the returns. It is apparent from casual observation of the sea surface (as shown in Figures 2.1 and 2.2) that it is not a random rough surface but contains significant structure. When the wind blows it generates small ripples, which grow and transfer Figure 2.1 The sea surface before the onset of significant wave breaking (courtesy of Charlotte Pagendam) Figure 2.2 Wave breaking on the sea surface (courtesy of Charlotte Pagendam) The characteristics of radar sea clutter 19 their energy to longer waves. At some point the waves become large enough to break (as shown in Figure 2.2) and this redistributes the wave energy further. When the wind has been blowing for some time, an equilibrium is established between the input of energy and its dissipation. There is then a wide spectrum of waves propagating on the sea, which can be added to by swell travelling into the area from remote rough weather. All of these waves and the breaking events are reflected in the spatial variation of clutter returns and the nature of such variation needs to be characterised. As will be described, each of these characteristics is dependent in complex ways on the prevailing environment, radar waveforms and viewing geometry. One aspect of the radar waveform that requires particular attention is its polarisation and the dependence on polarisation of the back-scattered radar signals; this can be represented by the polarisation scattering matrix. While sea clutter can generally be described in terms of the statistical behaviour of the returns from multiple distributed scatterers, individual discrete scatterers or isolated clutter spikes are sometimes observed. These spikes can also be characterised and incorporated into the standard distributed clutter models. 2.2 The sea surface As might be expected, observations of radar sea clutter are usually associated with particular characteristics of the sea surface and the environment, such as sea waves, sea swell or wind speed. Before discussing these observations in more detail, some of the basic terms used to describe the sea surface are presented here. Further detail, can be found in classic texts such as References 1–3. The following definitions are given in Reference 3: Wind wave: a wave resulting from the action of the wind on a water surface. While the wind is acting upon it, it is a sea; thereafter, it is a swell. Gravity wave: a wave whose velocity of propagation is controlled primarily by gravity. Water waves of a length greater than 5 cm are considered gravity waves. Capillary wave (also called ripple or capillary ripple): a wave whose velocity of propagation is controlled primarily by the surface tension of the liquid in which the wave is travelling. Water waves of a length of less than 2.5 cm are considered capillary waves. Fetch: (1) (also called generating area) an area of the sea surface over which seas are generated by a wind having a constant direction and speed; (2) the length of the fetch area, measured in the direction of the wind in which the seas are generated. Duration: the length of time the wind blows in essentially the same direction over the fetch. Fully developed sea (also called a fully arisen sea): the maximum height to which ocean waves can be generated by a given wind force blowing over sufficient fetch, regardless of duration, as a result of all possible wave 20 Sea clutter: scattering, the K distribution and radar performance components in the spectrum being present with their maximum amount of spectral energy. Sea state: the numerical or written description of ocean-surface roughness. Ocean sea state may be defined more precisely as the average height of the highest one-third of the waves (the significant wave height) observed in a wave train (see Tables 2.1 and 2.2). Clutter reflectivity is often characterised in terms of sea state and the description of sea state is a common source of confusion in the specification of radar performance. Often the Beaufort wind scale is used, but this wind speed only gives a reliable estimate of wave height if the duration (length of time the wind has been blowing) and the fetch (the range extent of the sea over which the wind has been blowing) are known. A standard estimate of wave height is the Douglas sea state (this is the scale used by Nathanson [1] in his tables of reflectivity), which is shown in Table 2.1. The wave height, h1=3 , is the 'significant wave height', defined as the average peakto-trough height of the highest one-third of the waves. In Table 2.1, the stated wind speed produces the stated wave height with the fetch and duration shown. Other descriptions of sea state are also used, such as the World Meteorological Organisation sea state; this is listed in Table 2.2. When modelling or predicting Table 2.1 Douglas sea state Douglas sea state Description Wave height, h1=3 (ft) Wind speed (kn) Fetch (nmi) Duration (h) 1 2 3 4 5 6 7 Smooth Slight Moderate Rough Very rough High Very high 0–1 1–3 3–5 5–8 8–12 12–20 20–40 0–6 6–12 12–15 15–20 20–25 25–30 30–50 50 120 150 200 300 500 5 20 23 25 27 30 Table 2.2 World Meteorological Organisation sea state Sea state Wave height, h1=3 (ft) Description 0 1 2 3 4 5 6 7 8 9 0 0–1/3 1/3–2 2–4 4–8 8–13 13–20 20–30 30–45 > 45 Calm, glassy Calm, rippled Smooth, wavelets Slight Moderate Rough Very rough High Very high Phenomenal The characteristics of radar sea clutter 21 radar performance, it is very important to agree what scale of measurement is being used. Assessing the environment in an actual radar trial is notoriously difficult and the sea state estimated by observers often shows a wide variation. Wave-rider buoys are used to estimate local wave height but these only give a rough guide to the likely clutter characteristics, which also depend on such things as 'wind friction velocity', 'wave age' and other factors discussed in Chapter 15. 2.3 Sea clutter reflectivity Radar backscatter from the sea is derived from a complex interaction between incident electromagnetic waves and the sea surface. There are many theoretical models for backscatter based on different descriptions of the rough surface and approximations to the scattering mechanism. Attempts have been made to represent the sea surface in terms of many small segments, called facets, with orientations modulated by the sea waves and swell. Scattering from local wind-derived ripples may be approximated by Bragg (or resonant) scattering. The tilting of the ripples by longer waves on the sea changes the scattered power, and this is incorporated in the so-called composite model. These models, which are discussed further in Chapter 15, tend to give satisfactory results at high and medium grazing angles. At low grazing angles the scattering mechanisms are much more complex and the observed values of reflectivity deviate from the models. Here scattering is complicated by factors such as shadowing from up-range surface features, diffraction over edges and interference between scattered signals travelling over different paths. Some progress has recently been made in our understanding of scattering at low grazing angles; this is described in Chapter 16. Generally speaking, however, the practical development of models for sea clutter still relies mainly on empirical measurements and observations. Clutter reflectivity is usually represented by s0, the normalised sea clutter RCS (i.e. the average RCS divided by the illuminated area, as illustrated in Figure 12.1), with units of m2/m2. Figure 2.3 illustrates the form of the variation in sea clutter reflectivity with grazing angle that is observed in practice for microwave radars. This example is typical of backscatter for a wind speed of around 15 kn (sea state 3 in a fully developed sea) for an I-band (9 GHz) radar. At near-vertical incidence, backscatter is quasi-specular. In this region, the backscatter varies inversely with surface roughness, with maximum backscatter at vertical incidence from a perfectly flat surface. At medium grazing angles, in this example below about 50 from grazing, the reflectivity shows a lower dependence on grazing angle; this is often called the plateau region. Below a critical angle (typically around 10 from grazing, but dependent on the sea roughness) it is found that the reflectivity reduces much more rapidly with smaller grazing angles; this region is shown in Figure 2.3 as the interference region. Also shown in Figure 2.3 is the dependence of the reflectivity on radar polarisation. In the plateau and interference regions the backscatter from horizontal (H) 22 Sea clutter: scattering, the K distribution and radar performance 10 Plateau region (diffuse scatter) Reflectivity (dB•m2/m2) 0 –10 V pol –20 Quasi-specular region (near-vertical incidence) –30 H pol –40 Interference region (near-grazing incidence) 20 40 60 80 Grazing angle (deg) Figure 2.3 Typical variation with grazing angle and polarisation of sea clutter reflectivity at I-band (for a wind speed of about 15 kn) polarisation is significantly less than that for vertical (V) polarisation. As will be seen in Section 2.7, many other clutter characteristics are dependent on radar polarisation and often quite different scattering mechanisms are present for different polarisations. In addition to the variation with grazing angle and polarisation discussed above, it is found that the average reflectivity of sea clutter is dependent on many other factors. Empirical models often present reflectivity as a function of sea state. However, as discussed earlier, this is not always a reliable indicator as it is dominated by the wave height of long waves and sea swell. Local wind causes smallscale surface roughening, which responds quickly to changes in wind speed and changes the backscatter. A strong swell with no local wind gives a low reflectivity, while a local strong wind gives a high backscatter from a comparatively flat sea. Further deviation from a simple sea state trend may be caused by propagation effects such as ducting, which can affect the illumination grazing angle. Figure 2.4 is an illustration of the variability of reflectivity that can occur within a simple sea state description. It shows an example of an image from the ERS-1 satellite [4]. This was a synthetic aperture radar operating in G/H-band (5.3 GHz), achieving a spatial resolution of about 30 m 30 m. The image is of the ocean surface, over which a very large variation of reflectivity is apparent. This variation is due to many causes, including local wind speed variations, rain and cloud, currents and internal waves. The ocean currents are influenced by the topology of the sea bottom and cause a roughening on the sea surface, and hence a variation in radar reflectivity, which appears to replicate the sea bottom features below. (This effect is discussed and modelled in Chapter 15.) The lower right-hand corner of the image shows returns from land, actually part of Belgium. The characteristics of radar sea clutter 23 Figure 2.4 ERS-1 image of the sea surface (data copyright ESA – image processed by DERA UK) Specific empirical models for the reflectivity of sea clutter are discussed in Chapter 3. It is important to realise that the spread in values of s0 observed between the various models for a given set of conditions is not dissimilar to that which might be encountered in practice, especially given the difficulty in characterising the actual sea conditions. The value of these models lies in their use for radar design. They allow the radar systems engineer to determine the range of values to be expected. The models of s0 discussed in Chapter 3 provide good estimates of the range of values of s0 likely to be encountered in different conditions and the expected variation with radar parameters and viewing geometry. Some models are defined in terms of the median reflectivity, rather than the mean. For a uniform scattering surface, characterised by a Rayleigh amplitude distribution, the mean reflectivity is about 1.6 dB greater than the median. This is negligible in practice in view of the uncertainties of measuring the average reflectivity. However, as will be discussed later, the ratio of mean to median reflectivity in very spiky clutter can be much larger and it is then important to establish which value is presented by the model. 2.4 Amplitude statistics Many radars use only the envelope of the received signal in their signal processing. Since they do not use the signal phase, these systems need not be coherent from pulse to pulse. Non-coherent statistics may be described in terms of either the 24 Sea clutter: scattering, the K distribution and radar performance envelope (i.e. following a linear detector) or the power (i.e. following a square law detector) of the return. For coherent processing, where the phase of the returns is retained, the statistics are described in terms of the temporal variation of the complex amplitude and its associated Fourier transform, or spectrum; this is discussed in Section 2.9. As discussed earlier, the area reflectivity s0 represents the mean clutter power. The instantaneous power received from a single radar resolution cell varies about this mean value. This variation is characterised by the PDF of the returns. There are two main contributions to the fluctuations. First, the variation of local surface shape, grazing angle, ripple density, and other factors associated with the passage of long waves and swell cause the backscatter from local small areas to vary widely about the mean reflectivity. Second, within a radar resolution patch, scattering occurs from many small structures (often called scatterers), which move relative to each other and create interference in the scattered signal (often referred to as speckle). Speckle is often described as resulting from a uniform field of many random scatterers, which exhibits Gaussian scattering statistics (as discussed in Chapters 3 and 6). The PDF of the amplitude, E, of these returns, as observed by a linear detection, is given by the Rayleigh distribution: PðEÞ ¼ 2 2E E exp ; x x 0E1 ð2:1Þ pffiffiffiffi where the average value of E, hEi ¼ 2px ; the mean square, hE2 i ¼ x; and the higher moments, hEn i ¼ xn=2 Gð1 þ n=2Þ: The PDF of the power of the returns (i.e. as observed by a square-law detector) is given by z 1 PðzÞ ¼ exp ; x x 0z1 ð2:2Þ where z ¼ E2, hzi ¼ x and hzni ¼ n!xn. For radars that have a low spatial resolution, where the resolution cell dimensions are much greater than the sea swell wavelength, and for grazing angles greater than about 10 , clutter is usually modelled simply as speckle and the amplitude is Rayleigh distributed. The clutter returns have fairly short temporal decorrelation times, typically in the range 5–10 ms, and are fairly well decorrelated from pulse to pulse by a radar employing frequency agility (provided that the radar frequency is changed from pulse to pulse by at least the transmitted pulse bandwidth – see Section 2.5). There is no inherent correlation of returns in range, beyond that imposed by the transmitted pulse length. As the radar resolution is increased, and for smaller grazing angles, the clutter amplitude distribution is observed to develop a longer 'tail' and the returns are often The characteristics of radar sea clutter 25 described as becoming spiky. In other words, there is a higher probability of large amplitude values (relative to its mean) being observed, compared to that expected for a Rayleigh distribution. This is a result of the first effect described above, which in essence is the radar resolving the 'structure' of the sea surface. The causes of this spikiness are quite complex and a number of different mechanisms contribute to the effects that are observed; descriptions of data are given in Section 2.6 and the mechanisms giving rise to these features are discussed in more detail in Chapter 16. Figure 2.5 illustrates the essential difference between the amplitude variation of Gaussian clutter and spiky clutter. The data in each plot have the same mean level of 1 unit but the different ranges of variation about the mean are quite apparent. In this case, the spiky clutter has been modelled as having a K distribution PDF, which is discussed in detail in Chapter 3 and Part II (Chapters 5–9). In addition to the deviations of high-resolution clutter amplitude from the Rayleigh distribution, the temporal and spatial correlation properties also change from those of speckle. In particular, frequency agility no longer decorrelates clutter and the longest correlation times stretch to seconds rather than milliseconds. Also, there is range correlation beyond the radar resolution patch that is not evident in speckle. In the literature, much work on understanding the non-Gaussian nature of sea clutter concentrates on the amplitude distribution of the envelope (or intensity) of the returns and on the average temporal power spectrum. These features are sufficient to describe Gaussian processes but in general provide an incomplete description of non-Gaussian processes. Therefore, they may result in modelling that omits features of importance concerning the effects of the nonGaussian nature. This is the case for sea clutter, where correlation properties not evident in the average power spectrum (nor in the complex autocorrelation function, which is equivalent) severely affect radar performance and signal processing optimisation. Amplitude 7 Rayleigh noise 0 Range K distribution, 0.5 7 0 Range Figure 2.5 Gaussian clutter contrasted with spiky clutter 26 Sea clutter: scattering, the K distribution and radar performance The evidence for these complex properties of sea clutter is presented in the next section, using experimental observations of sea clutter from airborne and clifftop radars. Nearly all the results presented in this chapter were collected from radars operating at I-band, with a range of pulse bandwidths and polarisations. These observations form the basis of the compound K distribution mathematical model for sea clutter, which is described in Chapter 3. 2.4.1 The compound nature of sea clutter amplitude statistics Measurements of high-resolution, low grazing angle sea clutter returns have identified two components of the amplitude fluctuations [5, 6]. The first component is a spatially varying mean level that results from a bunching of scatterers associated with the long sea waves and swell structure. This component has a long correlation time and is unaffected by frequency agility. A second 'speckle' component occurs due to the multiple scatterer nature of the clutter in any range cell. This decorrelates through relative motion of the scatterers or through the use of frequency agility. These properties can be appreciated with the aid of Figures 2.6 and 2.7, which show radar sea echo data, collected from a clifftop radar at I-band (8–10 GHz) incorporating frequency agility, with a 1.2 beamwidth and 28 ns pulse length. Figure 2.7 shows range-time intensity plots of pulse-to-pulse clutter from a range window of 800 m at a range of 5 km and grazing angle of 1.5 . The upper plot of Figure 2.6 is for fixed frequency and shows that at any range the return fluctuates with a characteristic time of approximately 10 ms as the scatterers within the patch Time (ms) 125 0 0 Range 800 m Time (ms) 125 0 Figure 2.6 Range-time intensity plots of sea clutter; upper plot shows returns from a fixed frequency radar and lower plot shows returns with pulse-to-pulse frequency agility The characteristics of radar sea clutter Time (s) 0 27 V pol 60 H pol 120 0 Range (m) 600 Figure 2.7 Range-time intensity plot of sea clutter averaged over 250 successive pulses to remove the speckle component, revealing the underlying mean level. After 60 s, the radar was switched from vertical to horizontal polarisation move with the internal motion of the sea and change their phase relationships. This varying speckle pattern is decorrelated from pulse to pulse by frequency agility as shown in the lower plot of Figure 2.6. Both of the figures show that the local mean level varies with range due to the bunching of scatterers. This is unaffected by frequency agility. The total time (1/8 s) of Figure 2.6 is not sufficient for the bunching to change at any given range. In Figure 2.7, averaging has been used to remove the speckle component, and the plot therefore shows the 'bunching' term over a longer time period of about 120 s. Over the first 60 s, the radar was transmitting and receiving with vertical polarisation. The plot demonstrates the wavelike nature of this component. It can be deduced that the dominant long waves were moving towards the radar at a speed of about 10 m/s. After 60 s, the radar polarisation was switched to horizontal. Some vestiges of the long wave pattern can still be detected, but now the clutter appears much more patchy, with isolated clutter spikes having a lifetime of about 1 s or so. In both polarisations the spikes and modulations shown in Figure 2.7 appear to be associated with long waves and associated breaking events. The mechanisms for producing spiky backscatter may be different for the two polarisations (as discussed in Chapter 16). The horizontally polarised spikes illustrated in Figure 2.7 are seen in this data to have a much higher amplitude relative to the mean level, compared to those for vertical polarisation. Also, the overall mean level for horizontal polarisation is lower than for vertical polarisation. Both these trends are regularly observed in sea clutter, as discussed in Chapter 3. The compound K distribution model allows the separate characterisation of these two components of the clutter envelope fluctuations, as shown in Chapter 3. The returns from a given patch of sea (a radar resolution cell) have an amplitude distribution corresponding to that of the speckle component of the clutter with a mean given by the local value of the spatially varying mean level component of the clutter. 28 Sea clutter: scattering, the K distribution and radar performance 2.5 Frequency agility and sea clutter As discussed in Section 2.4, Gaussian clutter can be characterised as comprising multiple scatterers distributed in range over the clutter patch. If the radar frequency changes, the vector sum of the scatterer returns also changes. For a patch of Gaussian clutter illuminated by a radar pulse of bandwidth B, returns on two different frequencies are decorrelated if the change in frequency, Df , causes the change of phase from the leading edge of the clutter patch to the trailing edge to be at least 2p. For a radar frequency f, the phase change over the two-way path across the clutter patch is 2pf/B and so a frequency step Df ¼ B causes successive pulse returns to be decorrelated. Consequently, in uniform clutter with Rayleigh amplitude statistics, pulse-topulse frequency agility with frequency steps of at least the pulse bandwidth should ensure that returns are decorrelated from pulse to pulse. This ability to decorrelate the returns is very important in the design of radar processing for detecting small targets in sea clutter. This is discussed in detail in Chapters 12 and 13. As discussed in Section 2.4.1, the speckle component of the compound representation of sea clutter is observed to be decorrelated by frequency agility, implying many scatterers evenly distributed in range along the clutter resolution cell. Equally, it can be understood that the large-scale spatial variation of the underlying mean level, associated with the changing area reflectivity induced by long waves the sea swell, cannot be decorrelated by frequency agility. Again, the exploitation of this effect in the design of radar detection algorithms is described in Chapters 12 and 13. To be more precise, the presence of the underlying spatial correlation means that the scatterers cannot be completely uniformly distributed along the clutter cell. For this reason, pulse-to-pulse frequency steps equal to the pulse bandwidth cannot fully decorrelate the clutter speckle component. This is described further in Reference 7. However, in practice this effect is often small and it is usually quite accurate to assume pulse-to-pulse decorrelation with frequency agility steps of the pulse bandwidth. This is especially true for radar with an antenna scanning in azimuth across the sea surface. Here, additional decorrelation is introduced due to the changing composition of the scatterers in the clutter cell [8]. This is discussed further in Chapter 12. 2.6 Observations of amplitude distributions As mentioned previously, the non-Gaussian amplitude statistics of sea clutter vary considerably, dependent on the prevailing sea and weather conditions, the viewing geometry and the radar parameters. Some insight into the causes of these variations is given in Chapter 16, while Chapter 3 shows how empirical models have been developed based on practical measurements. An initial appreciation of the range of these variations may be obtained from observation of range-time intensity plots of the underlying modulation of clutter, The characteristics of radar sea clutter 29 as shown in Figure 2.8(a–f), using the same type of I-band radar as for Figures 2.6 and 2.7. These indicate how the clutter structure is dependent on radar polarisation, sea state and grazing angle. Figure 2.8(a) is taken looking at 30 to the dominant wave direction, with a sea condition of medium roughness (sea state 3, significant wave height 1.2 m). The grazing angle is 1 . If this is compared with Figure 2.8(b), where the sea condition is rougher (sea state 4, significant wave height 2 m) and the radar is looking upwind, we find that in the latter the wave pattern is more pronounced and the polarisation change has less effect on the clutter. The calm sea plot, Figure 2.8(c), shows both vertical and horizontal polarisation with large spikes 60 80 40 60 80 0 100 200 300 400 500 600 700 Range (m) 40 60 80 (d) 0 20 Time (s) 20 Time (s) 0 100 200 300 400 500 600 700 Range (m) Horizontal Vertical polarisation polarisation (c) 0 40 60 80 0 100 200 300 400 500 600 700 Range (m) (e) 0 0 100 200 300 400 500 600 700 Range (m) (f ) 0 5 5 Time (s) Time (s) Horizontal Vertical polarisation polarisation 40 20 Horizontal Vertical polarisation polarisation Time (s) 20 (b) 0 Time (s) Vertical Horizontal polarisation polarisation (a) 0 10 15 20 10 15 20 25 25 0 100 200 300 400 500 600 Range (m) 0 100 200 300 400 500 600 Range (m) Figure 2.8 Range-time intensity plots of averaged clutter showing the dependence of the structure on radar and environmental parameters. (a) Sea state 3, 30 to upwind, 1 grazing, (b) sea state 4, upwind, 1 grazing, (c) sea state 1, upwind, 1 grazing, (d) sea state 5, upwind, 0.1 grazing, (e) sea state 3, up-swell, 1 grazing and (f) sea state 3, across swell, 1 grazing Sea clutter: scattering, the K distribution and radar performance 30 of a few seconds duration giving the dominant return. Figure 2.8(a–c) shows a grazing angle in the region of 1 . If this is reduced to 0.1 , as shown in Figure 2.8(d) for a rough sea (sea state 5, significant wave height 3 m), the well-defined wave structure of Figure 2.8(b) becomes concentrated into spikes of much higher amplitude (relative to the overall mean). However, there is still a fairly regular structure. Occasionally there is very long wavelength swell present in the sea wave spectrum. It may not be easily identified visually, but the grazing incidence radar backscatter is dominated by its effects. Figure 2.8(e) shows an averaged plot at 1 incidence looking into the swell. The sea roughness is medium (sea state 3) but the swell produces a very clear pattern. As can be seen, the sea wavelength is much longer than any of the other plots. An interesting effect is the dependence of the structure on viewing aspect. Looking down the swell propagation direction produces a plot similar to Figure 2.8(e), but looking across the swell direction breaks up the wave pattern (Figure 2.8(f)). This can be explained in terms of the radar footprint. Although the range resolution is 4 m, the cross-range resolution is determined by the beamwidth of 1.2 . At a range of 16 km, used for Figure 2.8(e,f), the azimuth patch dimension is 320 m. Thus, when looking into the swell, the radar resolves structure greater than 4.2 m. Across the swell, only structure greater than 320 m is resolved, and then not in range but in time as the swell moves through the beam. The 'across swell' picture is therefore not expected to show the wavelike pattern of the 'into swell' pictures. The effect of range resolution can be considered in a similar manner. Figure 2.9 shows qualitatively the effects of changing range resolution on the sea clutter returns. Figure 2.9(a) was collected from a radar with a pulse length of 28 ns (equivalent to a range resolution of 4.2 m) and the long wave features in the clutter are clearly resolved. In Figure 2.9(b), the resolution has been reduced to 200 ns (a range resolution of 30 m) and it is clear that the high-resolution spatial features have been averaged out. These varying characteristics can all be described within the compound formulation for sea clutter. Empirical results relating the parameters of the (a) 10 (b) 8 6 Time (s) Time (s) 8 10 4 2 6 4 2 0 0 0 100 200 300 Range (m) 400 500 0 100 200 300 Range (m) 400 500 Figure 2.9 Range-time plots of averaged sea clutter showing the effect of different synthesised pulse widths: (a) pulse width ¼ 28 ns and (b) pulse width ¼ 200 ns The characteristics of radar sea clutter 31 compound amplitude distribution to the prevailing conditions are described in Chapter 3, where the following results emerge: ● ● ● ● Sea clutter is more spiky at lower grazing angles and higher spatial resolution. It is more spiky when a sea swell is present, with the spikiest conditions observed when looking up or down swell. Horizontally polarised returns are generally more spiky than those for vertical polarisation. No significant statistical trend has been established for variations of spikiness with sea state, wind speed or aspect angle relative to wind direction. Further observations on the variation of distribution shape with radar and environmental parameters are reported by Hair et al. [9]. This work shows that the compound formulation is a good model over radar frequencies from 1 to 16 GHz and for range resolutions from 0.375 to 15 m. 2.7 Polarisation characteristics We have seen that sea clutter characteristics depend on the polarisation of the radar signal. Polarisation is defined by the direction of the electromagnetic fields, and if these are deterministic, the wave is defined as being polarised. When the direction of the electric and magnetic field vectors, E and H respectively, reside in fixed planes as the wave progresses it is said to be linearly polarised, the plane of polarisation being defined by the E vector. In general, however, the directions of E and H vary with time and the wave is said to be elliptically polarised or, as a special case of this, circularly polarised. In circular polarisation the directions of E and H rotate, while the magnitudes remain constant. (Circular polarisation may be synthesised by adding vertical and horizontal linear polarisations with a phase difference of 90 .1) On scattering the polarisation of the wave may change. The polarisation scattering matrix, S, describes the amplitude and relative phase of returns from different combinations of polarisations on transmit and receive. In order to investigate the effects of polarisation further, it is of interest to examine polarisation agile recordings; these provide more insight into the polarisation characteristics evident in Figure 2.8(a–f). The data are from a clifftop radar with the following basic parameters: ● ● ● ● I-band (9.75 GHz) 100 MHz pulse bandwidth, giving about 2 m range resolution Pulse-to-pulse switching of transmitter polarisation between V and H at 1 kHz Two receiver channels for recording simultaneous V and H Thus, every two pulses, recordings are made of VV, VH, HV and VV scattering. A flat plate reflector is used for calibration. Figure 2.10 shows range-time intensity plots of the four polarisation combinations from a 12 s record of data recorded 1 Left-hand circular polarisation is defined as EV ¼ iEH; right-hand circular is EV ¼ iEH. 32 Sea clutter: scattering, the K distribution and radar performance VV Polarisation HH Polarisation 2 2 4 4 Time (s) (b) 0 Time (s) (a) 0 6 6 8 8 10 10 12 12 0 100 200 300 400 500 Range (m) 0 VH Polarisation HV Polarisation (d) 0 2 2 4 4 Time (s) (c) 0 Time (s) 100 200 300 400 500 Range (m) 6 6 8 8 10 10 12 12 0 100 200 300 400 Range (m) 500 0 100 200 300 400 Range (m) 500 Figure 2.10 Range-time intensity plots for HH, VV, HV and VH polarisations using V and H polarisations. The similarity of the VH and HV is evident, as is expected from reciprocity. Also the characteristic spikiness of HH compared to VV can be seen. The dominant spikes on the HH record persist for about 1 or 2 s and have associated depolarised signals in VH and HV. In contrast, the shorter spikes in HH (only lasting a small fraction of a second) do not tend to have cross-polar returns. As discussed earlier, circular polarisation can be synthesised by the linear transformation of linear polarisations. This requires careful balancing of the gain and phase responses of the transmitter and receiver channels. This may be achieved by measuring the returns from a flat plate and a depolarising target, such as a tilted dihedral. Figures 2.11–2.13 compare VV and HH data, recorded with the same radar as above, with RR and RL circularly polarised data, obtained by transforming The characteristics of radar sea clutter HH VV RR RL 33 Figure 2.11 Range-time intensity plots for HH and VV, compared with RR and RL for the same data, with a wind speed of 0–5 kn (the time axis is vertical and displays 7 s, starting from the top; the range axis is horizontal, and displays 256 range cells, i.e. 384 m) the coherent scattering matrix of the linearly polarised data. These figures are range-time intensity plots of three sea conditions, recorded using the same radar as above: ● ● ● Figure 2.11, wind speed 0–5 kn Figure 2.12, wind speed 6–10 kn Figure 2.13, wind speed 18–20 kn All of the images show 7 s of data from 256 range cells (384 m of range). The low wind speed data are very spiky. As the wind speed increases the contributions from spatially distributed scattering increase, tending to mask the discrete-like spikes. The dominant sea wavelength increases with the wind speed, and at high wind speed the wave pattern is very clear, with different wavelengths evident, travelling at different speeds due to their dispersion relation. The co- and cross-circular polarisation images look similar to each other, containing the features present in both the VV and HH images. As we will see in Section 2.9, the shape of the Doppler spectrum of sea clutter is also dependent on the polarisation used. Horizontally polarised returns tend to have a higher absolute Doppler frequency than vertically polarised returns. Taken together, all of these observations of polarisation effects suggest that there are a number of different mechanisms at work. 34 Sea clutter: scattering, the K distribution and radar performance HH VV RR RL Figure 2.12 Range-time intensity plots for HH and VV, compared with RR and RL for the same data, with a wind speed of 6–10 kn (the time axis is vertical and displays 7 s, starting from the top; the range axis is horizontal and displays 256 range cells, i.e. 384 m) 2.8 Clutter spikes and modulations The data illustrated in Figures 2.6–2.13 show examples of smooth modulations and what may broadly be classified as clutter 'spikes'. Together, the modulation and spikes contribute to the non-Gaussian nature of the clutter, a feature that is generally referred to as 'spikiness'. Thus, we must remember that wavelike modulation (which seems to arise from Bragg scattering), for example as shown in Figure 2.8(e), contributes to the clutter 'spikiness' despite not actually being made up of spikes.2 The spikes themselves seem to divide into two classes that are most easily differentiated by their time evolution. Short spikes, which we will refer to as 'bursts', last for a small fraction of a second (200 ms is typical) and do not fluctuate much within that time. Longer spikes, which we will refer to as 'whitecaps', last for a second or so and have a noise-like fluctuation that decorrelates in a few milliseconds (at a fixed radar frequency). Thus, we have three distinct features and may consider potential mechanisms for their origin [10]. Figure 2.14 illustrates these three features from recordings of real data, using the same radar as for Figure 2.10, which employed pulse-to-pulse frequency agility. The plots show two examples of returns from single range cells; the time histories of simultaneous returns from VV and HH are compared. In Figure 2.14(a), the 2 This may seem perverse, but we cannot change 50 years of common usage in the literature. The characteristics of radar sea clutter HH VV RR RL 35 Figure 2.13 Range-time intensity plots for HH and VV, compared with RR and RL for the same data, with a wind speed of 18–20 kn (the time axis is vertical and displays 7 s, starting from the top; the range axis is horizontal, and displays 256 range cells, i.e. 384 m) Amplitude 0 (a) 64 56 48 40 32 24 16 8 0 Amplitude HH pol 1 2 3 Time (s) 4 5 VV pol 0 1 2 3 Time (s) 4 5 64 56 48 40 32 24 16 8 0 HH pol 0 6 Amplitude Amplitude 64 56 48 40 32 24 16 8 0 Specular (burst) scattering spikes Bragg resonant scattering Whitecap scattering spikes (b) 2 64 56 48 40 32 24 16 8 0 3 4 5 6 7 Time (s) 8 9 10 11 12 5 6 7 Time (s) 8 9 10 11 12 VV pol 0 6 1 1 2 3 4 Figure 2.14 Pairs of simultaneous pulse-by-pulse time histories of a range clutter cell with VV and HH polarisations (using pulse-to-pulse frequency agility; sea state 3) 36 Sea clutter: scattering, the K distribution and radar performance overall behaviour of the two polarisations is similar. However, the detailed structure is different, indicating that different scatterers are contributing. This is an example of whitecap scattering. An example of another area of the record, which does not contain dominant HH spikes, is shown in Figure 2.14(b). Here there are occasional large amplitudes in the HH record. These 'bursts' are highly polarisation sensitive and appear to be discrete in nature because of the lack of fluctuation in their time history. The effect of the bursts on the average RCS and the distribution appears to be small compared to the whitecaps of Figure 2.14(a). These plots also show the modulated Bragg scattering. We see rapid fluctuations in both VV and HH polarisations, but VV returns have a much higher amplitude than the HH returns. Walker [11, 12] investigates the Doppler characteristics in these scattering mechanisms in the controlled environment of the wave tank and through the analysis of real sea clutter data. His discussion both draws on and supports earlier wave tank measurements and clutter analysis [13–15]. Together