An optimum permutation test for nonparametric radar detection

A hypothesis H is parametric if every distribution from the process defined by H belongs to a family of distributions characterized by a finite number of parameters; on the other hand, if the distribution can not be defined by a finite number of parameters, the hypothesis is nonparametric. We analyze a detector based on the optimum permutation test, in the Neyman-Pearson sense, and under Gaussian noise conditions, which operates on a radar video signal. The computational complexity of the detector is high and its implementation in real time is difficult, due to the number of operations increases with the factorial of the number of samples. Also, we present an algorithm that reduces the computational work required. We also present the characteristic of detectability of the optimum permutation test under Gaussian noise environments and different types of target models (nonfluctuating, Swerling I and Swerling II). The detection probability versus signal-to-noise ratio is estimated by Monte-Carlo simulations for different parameter values (N pulse, M reference samples and false alarm probability P_fa)