Nonparametric Radar Extraction Using a Generalized Sign Test

Abstract
A nonparametric procedure used in a constant false alarm rate (CFAR) radar extractor for detecting targets in a background of noise with unknown statistical properties is described. The detector is based on a generalization of the well-known two-sample sign test and thus requires a set of reference noise observations in addition to the set of observations being tested for signal presence. The detection performance against Gaussian noise is determined for a finite number of observations and asymptotically, for both nonfluctuating and pulse-to-pulse Rayleigh fluctuating target statistics. It is noted that the performance loss, as compared to the optimum parametric detector, depends critically on the number of reference noise observations available when the number of hits per target is not large. In the same case a much larger loss is also found for a pulse-to-pulse fluctuating target even though the asymptotic loss is the same as for a nonfluctuating target. A comparison is finally made with a detector based on the Mann-Whitney test, which usually is considered to be one of the better nonparametric procedures for the two-sample case.