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.
Highlights
The main goal of radar detection is to detect targets embedded in clutter
The probability density function (PDF) of the PαS distribution generally cannot be expressed in a closed form, and it is generally defined by its characteristic function (CF)
The analyses of CA-constant false alarm rate (CFAR) based on the derived probability of a false alarm (Pfa) and probability of detection (Pd) expressions in [24,25] are adopted for comparison
Summary
The main goal of radar detection is to detect targets embedded in clutter. Detectors with a constant false alarm rate (CFAR) are needed when background clutter fluctuates with time. Some research [19,24,26] indicates that the clutter shows heavy-tailed characteristic properties in a high-resolution radar system and/or in the case of a low grazing angle, and suggests that some clutter power samples can be modeled as PαS variables. It is known that the probability density function (PDF) of the PαS variable cannot be expressed in a closed form except for in the case of a Pearson distribution (α = 1/2) [13] Limited by this problem, much previous research just evaluates the CFAR detectors in the Pearson distribution [6,20,21,22,23].
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