Detection performance of some nonparametric rank tests and an application to radar

The detection performance of some one-sample nonparametric rank tests for signals in Gaussian noise exhibiting a characteristic trend is presented in this paper for a finite number of observations and asymptotically. The tests considered are the Kendall tau, the Spearman rho, and a version of the normal-scores test; both coherent and incoherent signal processing are considered. The asymptotic performance is determined through a simple extension of existing analytical results, whereas for a finite number of observations a direct Monte Carlo simulation is used. The latter requires a preliminary determination of false-alarm probability versus decision threshold. For the Spearman rho and the tests an importance-sampling technique is used in a Monte Carlo simulation to determine the required results. Finally an application of the Kendall tau test to conventional radar is considered, in which the characteristic trend due to the amplitude modulation of the received train of echoes by the scanning of the antenna is used for detecting the presence of a target.