Two adaptations of the nonparametric Wilcoxon test for use in detecting a coherent train of narrow-band signal pulses with unknown starting phase in a background of statistically undefined noise have been proposed in the literature. The performance of these detectors when the noise is stationary Gaussian is determined and compared. For a finite train of signal pulses, results were obtained by Monte Carlo simulation using the variance-reducing technique of importance sampling. For the best of the two narrow-band Wilcoxon detectors a comparison with the optimum parametric detector shows that for a train of 30 signal pulses and a false-alarm probability ofP_f = 10^{-6}the loss is about 2 dB, while for 50 signal pulses the loss is reduced to 1 dB. The theoretical asymptotic loss is 0.2 dB.

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 thec_1normal-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 thec_1tests 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.