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

Abstract

We devise a constant false alarm rate (CFAR) detector for detecting targets in clutter regions with varying degrees of heterogeneity. The CFAR detector employs the $\mathcal {G}^{0}$ 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 $\mathcal {G}^{0}$ -distribution in closed-form using an approximation of the polygamma function. We quantify the effectiveness of employing a polygamma approximation in MoLC estimation for clutter regions with varying levels of heterogeneity using a Monte Carlo simulation. 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). We present analytical results that confirm 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- $\mathcal {K}$ , and existing CFAR- $\mathcal {G}^{0}$ detectors. We further assess the performance of the CFAR detector on ALOSPALSAR and MSTAR (Moving and Stationary Target Acquisition and Recognition) data, which represent sea clutter and vegetation clutter, respectively. The proposed detector achieves accurate detection results compared to the aforementioned state-of-the-art CFAR detectors. Finally, experimental results illustrate the computational effectiveness of the proposed CFAR- $\mathcal {G}^{0}$ detector compared to CFAR- $\mathcal {K}$ and conventional CFAR- $\mathcal {G}^{0}$ detectors.