Detection performance of the narrow-band Wilcoxon detector against Gaussian noise (Corresp.)

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 of
P_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.