Performance of Rank Sum Nonparametric Detector at Clutter Edge

The performance of a Constant False Alarm Rate (CFAR) detector is often evaluated in three typical backgrounds - homogeneous environment, multiple targets situation and clutter edges described by Prof. Rohling. However, there is a lack of the analytic expression of the false alarm rate for the Rank Sum (RS) nonparametric detector at clutter boundaries, and lack of a comparison of the ability for the RS detector to control the rise of the false alarm rate at clutter edges to that of the conventional parametric CFAR schemes; which is incomplete and imperfect for the detection theory of nonparametric detectors. The analytic expression of the false alarm rate P_fa for the RS nonparametric detector at clutter edges is given in this paper, and the ability of the RS nonparametric detector to control the rise of the false alarm rate at clutter edges is compared to that of the Cell Averaing (CA) CFAR, the Greatest Of (GO) CFAR and the Ordered Statistic (OS) CFAR with incoherent integration. When both of the heavy and the weak clutters follow a Rayleigh distribution, it is shown that the rise of the false alarm rate for the RS detector at clutter edges lies between that of the CA-CFAR and that of the OS-CFAR with incoherent integration. If a non-Gaussian distributed clutter with a long tail moves into the reference window, the rise of the CA-CFAR, the GO-CFAR and the OS-CFAR with incoherent integration reaches a peak of more than 3 orders of magnitude, and can not return to the original pre-designed P_fa. However, the RS nonparametric detector exhibits its inherent advantage in such situation, it can maintain a constant false alarm rate even the distribution form of clutter becomes a different one.