This paper deals with the problem of detecting a radar target signal against correlated non-Gaussian clutter, which is modeled by the compound-Gaussian distribution. We prove that if the texture of compound-Gaussian clutter is modeled by an inverse-gamma distribution, the optimum detector is the optimum Gaussian matched filter detector compared to a data-dependent threshold that varies linearly with a quadratic statistic of the data. We call this optimum detector a linear-threshold detector (LTD). Then, we show that the compound-Gaussian model presented here varies parametrically from the Gaussian clutter model to a clutter model whose tails are evidently heavier than any K-distribution model. Moreover, we show that the generalized likelihood ratio test (GLRT), which is a popular suboptimum detector because of its constant false-alarm rate (CFAR) property, is an optimum detector for our clutter model in the limit as the tails get extremely heavy. The GLRT-LTD is tested against simulated high-resolution sea clutter data to investigate the dependence of its performance on the various clutter parameters.

Coherent Radar Target Detection in Heavy-Tailed Compound-Gaussian Clutter

This paper deals with covariance matrix estimates in impulsive noise environments. Physical models based on compound noise modeling [spherically invariant random vectors (SIRV), compound Gaussian processes] allow to correctly describe reality (e.g., range power variations or clutter transitions areas in radar problems). However, these models depend on several unknown parameters (covariance matrix, statistical distribution of the texture, disturbance parameters) that have to be estimated. Based on these noise models, this paper presents a complete analysis of the main covariance matrix estimates used in the literature. Four estimates are studied: the well-known sample covariance matrix MSCM and a normalized version MN, the fixed-point (FP) estimate MFP, and a theoretical benchmark MTFP. Among these estimates, the only one of practical interest in impulsive noise is the FP. The three others, which could be used in a Gaussian context, are, in this paper, only of academic interest, i.e., for comparison with the FP. A statistical study of these estimates is performed through bias analysis, consistency, and asymptotic distribution. This study allows to compare the performance of the estimates and to establish simple relationships between them. Finally, theoretical results are emphasized by several simulations corresponding to real situations.

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Performance Analysis of Covariance Matrix Estimates in Impulsive Noise

As the undesired echo from a radar environment (clutter) is often not Rayleigh distributed, problems arise in specifying the clutter as a non-Gaussian random process and in computer-generating realisations of clutter for simulation purposes. The paper shows that modelling the clutter as a compound Gaussian or a spherically invariant random process allows a complete specification of the clutter suitable for use in radar design. It also lends itself readily to computer simulation procedures. Specific procedures for generating clutter realisations with assigned correlation properties and with K or Weibull amplitude distributions are suggested, and are validated by statistical tests. Then the issue of resolving between the Weibull and K distributions is considered, and empirical operative characteristics of the associated hypothesis test are computed.

Modelling and simulation of non-Rayleigh radar clutter

We develop computer simulation procedures which enable us to generate any correlated non-Gaussian radar clutter that can be modeled as a spherically invariant random process (SIRP). In most cases, when the clutter is a correlated non-Gaussian random process, performance of the optimal radar signal processor cannot be evaluated analytically. Therefore, in order to evaluate such processors, there is a need for efficient computer simulation of the clutter. We present two canonical simulation procedures for the generation of correlated non-Gaussian clutter. A new approach for the goodness-of-fit test is proposed in order to assess the performance of the simulation procedure. >

Computer generation of correlated non-Gaussian radar clutter

Deals with the problem of detecting subspace random signals against correlated non-Gaussian clutter exploiting different degrees of knowledge on target and clutter statistical characteristics. The clutter process is modeled by the compound-Gaussian distribution. In the first part of the paper, the optimum Neyman-Pearson (NP) detector, the generalized likelihood ratio test (GLRT), and a constant false-alarm rate (CFAR) detector are sequentially derived both for the Gaussian and the compound-Gaussian scenarios. Different interpretations of the various detectors are provided to highlight the relationships and the differences among them. In particular, we show how the GLRT detector may be recast into an estimator-correlator form and into another form, namely a generalized whitening-matched filter (GWMF), which is the GLRT detector against Gaussian disturbance, compared with a data-dependent threshold. In the second part of this paper, the proposed detectors are tested against both simulated data and measured high resolution sea clutter data to investigate the dependence of their performance on the various clutter and signal parameters.

Vector subspace detection in compound-Gaussian clutter. Part I: survey and new results

The paper deals with the problem of radar detection of a target echo embedded in Weibull clutter and white Gaussian noise (WGN). Relevant features of the paper, with respect to previous papers on the same subject, refer to the coherent nature of the Weibull process (that modelling the clutter) and of the processing chain. In more detail, the in-phase and quadrature components of the clutter echoes have been modelled to give a Weibull probability density function (PDF) of the amplitude and a uniform PDF of the phase. Any shape of the correlation function among consecutive clutter samples is also allowed in the model. The so called 'coherent Weibull clutter' (CWC) introduced in the paper represents a suitable generalisation of the conventional ?coherent Gaussian clutter? (CGC). The processing chain is also coherent, i.e. it operates on the in-phase and quadrature components of the signals. To derive a suitable processing scheme, we resort to the general theory of radar detection which applies to any type of PDF and autocorrelation function (ACF) of the target and clutter. Briefly, it is found that the processing scheme is based on two nonlinear estimators of the clutter samples in the two alternative hypotheses (i.e. H0 and H1 the fully fledged architecture being discussed in the paper. The detection processor turns out to be a suitable generalisation of that concerning the CGC case. A new family of processing schemes is derived in accordance with the statistical model assumed for the useful target. The following cases are covered: target known a priori, Swerling 0, 1 and 2 models, and partially fluctuating target. Attention is also paid to the interesting case of a target modelled as a coherent Weibull process. The detection of such a target against white Gaussian noise is worked out. The detection performance of the a

Theory of radar detection in coherent Weibull clutter

In this correspondence, a new model for the Weibull clutter is presented. Then attention is turned to the design of the optimum radar processor to detect an a priori known target signal embedded in coherent Weibull clutter. An original detection scheme is presented and the corresponding performance is assessed.

F. Scannapieco

Papers

Theory of radar detection in coherent Weibull clutter

Radar detection in coherent Weibull clutter

On a coherent model for log-normal clutter

Target detection and classification with very high range resolution radar

Reply: On a coherent model for log-normal clutter