ABSTRACT In this paper, a novel and exact mathematical formulation of three mean level constant false alarm rate (CFAR) detectors has been developed considering a homogeneous gamma-distributed (GM) clutter. These detectors include the cell averaging (CA), the greatest-of (GO), and the smallest-of (SO)-CFAR detection schemes. To do so, we derived closed-form expressions for the probability density function (pdf), and the cumulative distribution function (cdf) of the sum of an exponential fluctuating target submerged in gamma-distributed sea clutter. Then, we developed exact and explicit expressions for the probability of false alarm (P fa ) and probability of detection (P d ) of the optimal fixed threshold detector and the three considered CFAR detectors. The correctness of our expressions is then examined and validated via numerical simulations. Assuming a homogeneous GM background, the detection performance of these three detectors is carried out, discussed, and compared with that of the optimal detector. Experimental results with Sentinel-1 synthetic aperture radar (SAR) data demonstrate the effectiveness of the proposed closed-form expressions and show that the considered CFAR schemes are efficient for ship detection in sea clutter backgrounds.
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