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Sea Clutter: Scattering, The K Distribution and Radar Performance.pdf

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    Contents
    1 Introduction
    1.1 Prologue
    1.2 Maritime radar
    1.3 The modelling of radar returns from the sea
    1.4 Outline of the book
    2 The characteristics of radar sea clutter
    2.1 Overview
    2.2 The sea surface
    2.3 Sea clutter reflectivity
    2.4 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 ACF
    2.10.2 Power spectrum analysis of range-time intensity plots
    3 Modelling radar scattering by the ocean surface
    3.1 Introduction
    3.2 The sea surface
    3.3 EM scattering from the sea at high grazing angles
    3.4 Imaging ocean currents at high grazing angles
    3.5 The composite model for scattering at medium grazing angles
    3.6 Scattering at low grazing angles: beyond the composite model
    3.7 Scattering from breaking waves
    3.8 Average backscatter from the ocean at low gazing angles
    3.9 Imaging ocean currents at low grazing angles
    4 Statistical models of sea clutter
    4.1 Introduction
    4.2 Gaussian clutter models
    4.3 Non-Gaussian clutter
    4.3.1 Compound models of non-Gaussian clutter
    4.3.2 The gamma distribution of local power and the K distribution
    4.3.3 A coherent signal in K-distributed clutter
    4.3.4 K-distributed clutter with added thermal noise
    4.3.5 Phases of homodyned and generalised K processes
    4.3.6 Applications to interferometric and polarimetric processing
    4.4 Spikes in clutter
    4.4.1 The Class A and breaking area models
    4.4.2 Clutter spike models and K phenomenology
    4.4.3 An analysis of spiky clutter data
    4.5 The lognormal,Weibull and other non-Gaussian distributions
    4.6 Coherent clutter modelling
    4.6.1 The Doppler signatures of different scattering events
    4.6.2 Some typical experimental results
    4.6.3 Models of Doppler spectra
    5 The simulation of clutter and other random processes
    5.1 Introduction
    5.2 Generating un-correlated random numbers with a prescribed
    5.3 Generating correlated Gaussian random processes
    5.4 Fourier synthesis of random processes
    5.5 Approximate methods for the generation of correlated gamma distributed random numbers
    5.6 The correlation properties of non-Gaussian processes generated by MNLT
    5.7 Correlated exponential andWeibull processes
    5.8 The generation of correlated gamma processes by MNLT
    6 Detection of small targets in sea clutter
    6.1 Introduction
    6.2 Statistical models for probabilities of detection and false alarm
    6.3 Likelihood ratios and optimal detection
    6.4 Some simple performance calculations
    6.5 The generalised likelihood ratio method
    6.6 A simple Gaussian example
    6.6.1 A likelihood ratio based approach
    6.6.2 Generalised likelihood ratio based approach
    6.7 The detection of a steady signal in Rayleigh clutter
    6.7.1 Generalised likelihood ratio based approach
    6.7.2 Peak within interval detection
    6.8 Applications to coherent detection
    6.9 The estimation of clutter parameters
    6.9.1 Maximum likelihood estimators for gamma and Weibull parameters
    6.9.2 Tractable, but sub-optimal, estimators for K and Weibull parameters
    6.10 Implications of the compound form of non-Gaussian clutter
    6.10.1 Modified generalised likelihood ratio based detection
    6.10.2 Modified peak within interval detection
    6.11 Concluding remarks
    7 Imaging ocean surface features
    7.1 Introduction
    7.2 The analysis of correlated Gaussian data
    7.2.1 X processing
    7.2.2 Xa processing and the whitening filter
    7.2.3 Xo processing
    7.3 The Wishart distribution
    7.3.1 The real Wishart distribution
    7.3.2 The complex Wishart distribution
    7.4 Polarimetric and interferometric processing
    7.4.1 X processing of interferometric and polarimetric data
    7.4.2 Phase increment processing of interferometric data
    7.4.3 Coherent summation and discrimination enchantment
    7.5 Feature detection by matched filtering
    7.6 False alarm rates for matched filter processing
    7.6.1 A simple model for the global maximum single point statistics
    7.6.2 The global maximum of a 1D Gaussian process and the matched filter false alarm curve for a time series
    7.6.3 Extension to 2D matched filters
    7.7 A compound model for correlated signals
    8 Radar detection performance calculations
    8.1 Introduction
    8.2 Radar equation and geometry
    8.3 Normalised sea clutter RCS models
    8.4 Sea clutter fluctuations and false alarms
    8.5 Target RCS models and detection probability
    8.6 Detection performance
    8.7 Modelling other types of radar
    9 CFAR detection
    9.1 Introduction
    9.2 Adaptation to changing clutter amplitude
    9.2.1 Control of received signal dynamic range
    9.2.2 Log FTC receiver for Rayleigh clutter
    9.2.3 Cell-averaging CFAR detector
    9.2.4 Linear prediction techniques
    9.2.5 Non-linear predictors
    9.3 Adaptation to changing clutter pdf
    9.3.1 Fitting to a family of distributions
    9.3.2 Distribution-free detection
    9.3.3 Estimation of the K distribution shape parameter
    9.3.4 Estimation of aWeibull shape parameter
    9.4 Other CFAR detection techniques
    9.4.1 Site specific CFAR
    9.4.2 Closed loop systems
    9.4.3 Exploitation of transient coherence
    9.4.4 Scan-to-scan integration
    9.5 Practical CFAR detectors
    10 The specification and measurement of radar performance
    10.1 Introduction
    10.2 Performance specification issues
    10.2.1 Discussion
    10.2.2 Adaptive radars
    10.2.3 Specification of adaptive systems
    10.2.4 Practical performance specification
    10.3 Performance prediction
    10.3.1 Clutter amplitude statistics
    10.3.2 Clutter speckle component
    10.3.3 False alarms
    10.4 Measuring performance
    10.4.1 Trials
    10.4.2 Factory measurements
    10.4.3 Modelling and simulation
    10.5 Measurement methods and accuracies
    10.5.1 Probability of detection
    10.5.2 Probability of false alarm PFA
    10.5.3 Statistical analysis of trials
    Appendix 1 Elements of probability theory
    A1.1 Introduction
    A1.2 Finite numbers of discrete events
    A1.3 An infinite number of discrete events
    A1.4 Continuous random variables
    A1.5 Functions of random variables
    A1.6 The normal process
    A1.7 The time evolution of random processes
    A1.8 Power spectra and correlation functions
    A1.9 The complex Gaussian process
    A1.10 Spatially correlated processes
    A1.11 Stochastic differential equations and noise processes
    A1.12 Miscellaneous results
    Appendix 2 Some useful special functions
    A2.1 Introduction
    A2.2 The gamma function and related topics
    A2.3 Some properties of the K distribution pdf
    A2.4 The Bessel functions In, Jn
    A2.5 Expansions in Hermite and Laguerre polynomials
    Appendix 3 Scattering from a corrugated surface
    A3.1 The integral formulation of the scalar scattering problem
    A3.2 Helmholtz equation Green's functions in two and three dimensions
    A3.3 Derivation of the Fresnel formulae
    A3.4 Approximate de-coupling of the integral equations - the impedance boundary condition
    A3.5 Scattering by a perfectly conducting surface
    A3.5.1 The physical optics or Kirchoff approximation
    A3.5.2 Small height perturbation theory - PC case
    A3.5.3 The half-space and reciprocal field formalisms
    A3.6 Scattering by an imperfectly conducting surface: small height perturbation theory
    A3.7 Numerical solutions of the scattering problem
    A3.7.1 Scattering from a perfect conductor
    A3.7.2 Scattering from an imperfect conductor; modification of the F/B method
    A3.8 Incorporation of the impedance boundary condition in F/B calculations
    A3.9 Evaluation of adjunct plane contributions
    A3.10 Summary
    Index
    IET RADAR, SONAR, NAVIGATION AND AVIONICS SERIES 20 Series Editors: Dr N. Stewart Professor M. Griffiths Sea Clutter: Scattering, the K Distribution and Radar Performance
    Other volumes in this series: Optimised radar processors A. Farina (Editor) Radar development to 1945 R. W. Burns (Editor) Volume 1 Volume 2 Volume 3 Weibull radar clutter M. Sekine and Y. H. Mao Volume 4 Volume 7 Volume 8 Advanced radar techniques and systems G. Galati (Editor) Ultrawideband radar measurements L. Yu. Astanin and A. A. Kostylev Aviation weather surveillance systems: advanced radar and surface sensors for flight safety and air traffic management P. Mahapatra Volume 10 Radar techniques using array antennas W. D. Wirth Volume 11 Air and spaceborne radar systems P. Lacomme, J. C. Marchais, J. P. Hardange and E. Normant Introduction to RF Stealth D. Lynch Volume 12 Principles of space-time adaptive processing R. Klemm Volume 13 Volume 14 Applications of space-time adaptive processing R. Klemm (Editor) Volume 15 Ground penetrating radar, 2nd edition D. J. Daniels (Editor) Volume 16 Volume 17 Volume 18 Volume 19 Radar imaging and holography A. Pasmmov and S. Zinoviev Target detection by marine radar J. Briggs Strapdown inertial navigation technology D. H. Titterton and J. L. Weston Introduction to radar target recognition P. Tait
    Sea Clutter: Scattering, the K Distribution and Radar Performance Keith D. Ward Robert J.A. Tough Simon Watts The Institution of Engineering and Technology
    Published by: The Institution of Engineering and Technology, London, United Kingdom © 2006: The Institution of Engineering and Technology 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 forms 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. Inquiries concerning reproduction outside those terms should be sent to the publishers 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 authors and the publishers believe that the information and guidance given in this work are correct, all parties must rely upon their own skill and judgment when making use of them. Neither the authors nor the publishers assume any liability to anyone for any loss or damage caused by any error or omission in the work, whether such error or omission is the result of negligence or any other cause. Any and all such liability is disclaimed. The moral rights of the authors to be identified as authors of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act 1988. British Library Cataloguing in Publication Data Watts, Simon Sea Clutter : scattering, the K-distribution and radar performance 1. Incoherent scatter 2. Radar - Interference - Mathematical models 3. Boats and boating - Radar equipment I. Title II. Tough, Robert III. Ward, Keith IV. Institution of Electrical Engineers 015118 623.8 933 ISBN (10 digit) 0 86341 503 2 ISBN (13 digit) 978-086341-503-6 Typeset in India by Newgen Imaging Systems (P) Ltd, Chennai, India Printed in the UK by MPG Books Ltd, Bodmin, Cornwall
    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 25 years. This includes recent support from the EMRS DTC. Work was also supported by funding from the authors’ own organisations, TW Research 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 1 2 Prologue Introduction 1.1 1.2 Maritime radar 1.3 1.4 The modelling of radar returns from the sea Outline of the book The characteristics of radar sea clutter 2.1 2.2 2.3 2.4 Overview The sea surface Sea clutter reflectivity Amplitude statistics 2.4.1 The compound nature of sea clutter amplitude statistics Frequency agility and sea clutter Observations of amplitude distributions Polarisation characteristics Clutter spikes and modulations Coherent properties of radar sea clutter 2.5 2.6 2.7 2.8 2.9 2.10 Spatial characteristics Range ACF Power spectrum analysis of range-time intensity plots 2.10.1 2.10.2 3 Modelling radar scattering by the ocean surface 3.1 3.2 3.3 3.4 3.5 3.6 3.7 Introduction The sea surface EM scattering from the sea at high grazing angles Imaging ocean currents at high grazing angles The composite model for scattering at medium grazing angles Scattering at low grazing angles: beyond the composite model Scattering from breaking waves 1 1 1 5 7 13 13 15 17 19 22 23 24 27 29 32 36 37 40 45 45 47 54 60 70 75 88
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