The performances of order statistic (OS) constant false alarm rate (CFAR) detectors are analyzed for non-Gaussian
clutters modeled by heavy-tailed complex isotropic symmetric
alpha-stable random processes whose amplitude is the
generalized Rayleigh distribution. The detection and false alarm probabilities of the amplitude OS-CFAR detectors are
presented assuming that the target signal is Rayleigh distributed. Exact closed-form solutions are derived for the special
case of Cauchy-Rayleigh distribution where the characteristic exponent is 1. Numerical results are presented for
detection and false alarm rates as functions of the generalized signal-to-noise ratio, reference window sizes, and rank
order indexes. It is shown that the window size and rank order do not have significant effects on the performances. It is
also shown that the amplitude detectors provide similar performances as the square-law detectors in the heavy-tailed
clutter environment.
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