CFAR Strategy Formulation and Evaluation Based on Fox’s H-function in Positive Alpha-Stable Sea Clutter

Abstract

The problem of target detection in impulsive non-Gaussian sea clutter has attracted a lot of attention in recent years. The positive alpha-stable (PαS) distribution has been validated as a suitable model for the impulsive non-Gaussian sea clutter. Since the probability density function (PDF) of the PαS variable cannot be expressed as a closed-form expression, the research into constant false alarm rate (CFAR) detectors in PαS distributed sea clutter is limited. This paper formulates and evaluates some CFAR detectors, such as Greatest Of-CFAR (GO-CFAR), Smallest Of-CFAR (SO-CFAR), Order Statistic-CFAR (OS-CFAR) and censored mean level (CML) detectors, in PαS distributed sea clutter. Firstly, the Fox’s H-function is adopted to express the PDF of the PαS variable, and the cumulative density function based on Fox’s H-function is derived in this paper. Then, by use of the properties of the H-function and PαS distribution, exact expressions of the probabilities of false alarm and detection for CFAR detectors in the PαS background are derived. Some CFAR properties of these detectors in the PαS background are also explored. Numerical results based on derived expressions are given and verified by Monte Carlo simulation. Some analyses of detection performance from a practical perspective are also given.