Detection of known signals in additive impulsive noise based on Spearman’s rho and Kendall’s tau

Abstract

In this paper, we apply Spearman’s rho (SR) and Kendall’s tau (KT) to the long-lasting problem of detecting known signals in additive impulsive noise. Under a specified contaminated Gaussian model (CGM), which emulates a frequently encountered scenario in radar, sonar and/or communication, we derive the analytic forms of their expectations and variances. For a better understanding of their properties, we further compare SR and KT with three classical detectors, namely, the locally optimal detector (LOD), the matched filter based detector (MFD), and the sign correlator (SC), in terms of the receiver operating characteristic (ROC) curve, area under the ROC curve (AUC), as well as the detection probability. Monte Carlo simulations not only validate our theoretical discoveries, but also demonstrate the advantages of SR and KT in the aspects of 1) accurate false alarm probability control without knowledge of noise distribution, 2) relatively high performances for white Gaussian noise, and 3) gap-bridging properties between LOD and SC in both normal and impulsive noise. The theoretical findings in this work enable SR and KT to be useful alternatives to the MFD and SC whether or not the distribution of noise is Gaussian or Contaminated Gaussian.