Closed-Form Solution for CFAR Detection Threshold in G⁰ Distributed SAR Clutter

We propose to devise a constant false alarm rate (CFAR) detector for detecting targets in clutter regions with varying degree of heterogeneity. The CFAR detector employs the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">G</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub>-distribution for characterizing the statistics of background Synthetic Aperture Radar (SAR) clutter amplitude data. We express the Method of Log-Cumulants (MoLC) estimator for the shape parameter of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">G</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub>-distribution in closed-form using an approximation of the polygamma function. Monte-carlo simulation results are presented to illustrate the effectiveness of employing polygamma approximation in MoLC estimation for clutter regions with varying heterogeneity levels. Exploiting the dependencies between hypergeometric functions and the Fisher-Snedecor distribution function, we formulate a closed-form solution for the CFAR detection threshold. Furthermore, we derive a closed-form expression of the detection probability for the proposed CFAR detector in terms of clutter model parameters and the signal-to-clutter ratio (SCR). Analytical results are presented to illustrate the efficacy of the CFAR detector in various clutter environments as well as for different SCR levels compared to the CFAR-WBL, CFAR-LGN, CFAR-K and existing CFAR-<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">G</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> detectors. We further assess the performance of the CFAR detector on ALOSPALSAR and MSTAR (Moving and Stationary Target Acquisition and Recognition) data representing sea clutter and vegetation clutter, respectively. The proposed detector achieves accurate detection result compared to the aforementioned state-of-the-art CFAR detectors. Finally, experimental results illustrate the computational effectiveness of the proposed CFAR-<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">G</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> detector over CFAR-K and the conventional CFAR-<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">G</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> detectors.