An approximate representation of heavy-tailed noise: Bi-parameter Cauchy-Gaussian mixture model

Abstract

As a non-Gaussian statistic model, alpha stable distribution has gained much attention due to its generality to represent heavy-tailed and impulsive interference. Unfortunately, there is no closed form expression for the probability density function of alpha-stable distributions. Hereby, finding the approximate expressions is of importance for signal detection and denoising. In this paper, we present a novel approximate expression, which is a simplified version of Cauchy-Gaussian mixture (CGM) for symmetric alpha-stable (SalphaS) distribution, called Bi-parameter CGM (BCGM). Such a model has a complete closed-form expression, and hence is more tractable than classical GMM and CGM.