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The Pareto distribution has been shown to be an excellent model for X-band high-resolution maritime surveillance radar clutter returns. Given the success of mixture distributions in radar, it is thus of interest to consider the effect of Pareto mixture models. This paper introduces a formulation of a Pareto intensity mixture distribution and investigates coherent multilook radar detector performance using this new clutter model. Clutter parameter estimates are derived from data sets produced by the Defence Science and Technology Organisation's Ingara maritime surveillance radar.

In recent years at the Australian Defence Science and Technology Organisation (DSTO), clutter mixture models have been analysed, since they can provide tighter fits to spiky clutter in the distribution’s upper tail region [

Recently, the Pareto distribution has been proposed as an alternative clutter model and has also been validated for high-resolution radar clutter returns [

The paper is structured by introducing the Pareto distribution in Section

As maritime surveillance radar resolution has improved over the years, the backscattering from the sea surface, known as sea clutter, has been found to deviate significantly from the traditional Gaussian model [

The Pareto distribution [

In the intensity domain, the Pareto distribution has a power law density given by

Figure

An example of correlated Pareto clutter returns, where the correlation is small. (a) shows the clutter in the time domain, while the (b) is the result of a fast Fourier transform (FFT) applied to the same clutter.

Figure

Correlated Pareto clutter, where the correlation is strong.

These figures show the difficulty of performing target detection in a spiky clutter environment. Both Figures

The extension of the Pareto model (

Figure

Clutter fit example, showing the empirical distribution functions

This figure shows the Ingara data corresponding to run 34690, at azimuth angle of

Neyman-Pearson detectors [

For the case of a fixed target model (so that

In order to examine the performance of detectors based upon a Pareto mixture distribution assumption, it is necessary to specify the SIRP that generates the desired marginal intensity distributions. To generate a Pareto mixture SIRP, one uses the characteristic function:

Using the DSTO Ingara data sets, the performance of the optimal detector, and GLRT, for Pareto mixture clutter models was assessed. Due to the fact that the Ingara data is pure clutter, a synthetic Gaussian target model has been used throughout, as in [

The comparison of detectors based upon the Pareto and Pareto mixture clutter models produced some very interesting results. In most cases it was observed that the mixture distribution assumption did not improve detector performance significantly. This is illustrated in Figure

Comparison of detector performance curves for Pareto and Pareto mixture models. The probability of detection (Pd) is plotted as a function of the signal to clutter ratio (SCR). The optimal detectors are denoted Optimal (PP) for the mixture model and Optimal (P) for the standard Pareto counterpart. The GLRT for the Pareto mixture is denoted GLRT (PP), while the same for a single Pareto model is GLRT (P). The figure shows that the mixture model provides only a very small detection gain.

Figure

A second example of detector performance, with same legend as for Figure

Varying the number of looks, normalised Doppler frequency and Toeplitz covariance factor did not significantly alter the results. Hence it appears that although the KK-mixture distribution provides significant detection performance relative to that provided by a detector based upon a single K-Distributed clutter assumption [

Although a Pareto mixture model can provide a better fit to the upper tail region in real radar clutter returns, this has been observed to not significantly improve detection performance, which is the primary application of radar. Increasing the number of degrees of freedom in a model adds computational cost, slowing the radar’s ability to perform its operation in real time. Hence it is computationally better to use a nonmixture model when designing radar detection schemes, under the basic Pareto clutter model assumption.