Performance of CA-CFAR receivers in alpha-stable clutter

We analyze the performance of a cell averaging constant false alarm rate (CA-CFAR) receiver that operates in a heavy-tailed clutter environment that is modeled by an alpha-stable distribution. Stable distributions are usually characterized with known characteristic function but their probability distribution are not known in closed form except for some special cases of the characteristic exponent α. Therefore, previous performance studies of CFAR in alpha-stable clutter have been limited to only some very special cases of α that correspond to the Gaussian, Cauchy and Pearson distributions, for which the statistical distribution of the clutter is available in closed-form. In this paper, we derive the distribution of the receiver output for arbitrary values of α in terms of the Fox's H-function. The derived statistical distribution is useful in evaluating the false alarm and detection probabilities of the system.