Performance Analysis of Gini Correlator for Detecting Known Signals in Impulsive Noise

Abstract

Detection of known signals embedded in additive noise is a fundamental problem in signal processing. For normally distributed noise, it is well known that the popular matched filter detector (MFD) is optimal. However, for impulsive noise whose distribution has a heavier tail, the performance of MFD will deteriorate severely. To deal with such problem, in this paper, we propose a novel detector, termed as Gini correlator (GC), and derive the analytic forms of its expectation and variance, under a specified contaminated Gaussian model (CGM) emulating a frequently encountered scenario in practice. In order to further understand its properties, we compare the proposed GC with five state-of-the-art detectors permeating in the literature, in terms of Pitman asymptotic relative efficiency (ARE), as well as time-delay estimation. Monte Carlo simulations not only validate our theoretical discoveries, but also demonstrate the advantages of GC in the aspects of 1) accurate control of false alarm probability without prior knowledge of noise distribution, 2) comparable performance with MFD for Gaussian noise, 3) better performances over the classical detectors in the aspects of greater ARE and smaller bias and standard deviation for time-delay estimation. The theoretical and empirical findings in this work enable GC to be a useful alternative to the existing detectors whether or not impulsivity exists in noise.

Keywords

• Gini correlator (GC)
• Kendall’s tau (KT)
• locally optimal detector (LOD)
• Pitman asymptotic relative efficiency (ARE)
• sign correlator (SC)
• Spearman’s rho (SR)