Asymptotically Optimum Radar Detection in Compound-Gaussian Clutter

A substantial bulk of work is now available in the literature about detection in non-Gaussian noise. Starting with the experimental evidence that the Gaussian assumption is no longer met in many situations of practical interest, much effort has been directed towards the study of conventional detectors under non-Gaussian clutter as well as the design and the analysis of new optimized structures. Both strategies entail preliminary statistical inference on measured data so as to work out a model for clutter returns, to be applied for analysis and synthesis purposes. A general agreement has been reached about the validity of the so-called compound-Gaussian model for radar clutter. The baseband equivalent of clutter returns can be deemed as the product of two mutually independent processes: a complex, zero-mean, possibly correlated Gaussian process, also referred to as speckle, times a real, nonnegative, spiky component, which exhibits much longer decorrelation time than the former [1—3]. Otherwise stated, the measured amplitude probability density function (apdf) is a Rayleighian process whose mean square value is itself a slowly varying random process, carrying the information on the texture of the illuminated patch. Mathematically, such a scattering mechanism is very accurately described, for observation times on the order of the coherent processing interval (CPI) of radar systems, by means of the spherically invariant random processes (SIRPs), wherein the spiky component is a random constant, rather than a process, so that the overall clutter correlation coincides, except for a scale factor, with that of the speckle [4]. A further advantage of this model is that it is fully compatible with some widely reported properties of radar clutter, primarily with the invariance of its apdf under some linear, even time-varying transformations, such as moving target indicator (MTI) techniques and discrete Fourier transform (DFT) processing [5, 6]. Performance analysis of the conventional radar detectors subject to compound-Gaussian disturbance showed that they suffer a remarkable degradation as the actual clutter apdf deviates from the Rayleigh law [7, 8]. Better performance can be achieved by means of ad hoc processors, namely detection structures properly optimized with reference to specific instances of clutter apdf and covariance matrix. The problem of optimized detection in K-distributed clutter is handled in [9], showing that those receivers may yield noticeable improvement over the conventional ones. Nonetheless, not only does implementing optimized detectors require knowledge of clutter statistics, which in practice must be estimated from observables, but their performance assessment has highlighted that