Series expansion of gaussian-gaussian mixture probability distribution

Abstract

This paper demonstrates that Gaussian - Gaussian mixture (GGM) density function could be conceived as the result of sum of a Gaussian process and a Non Gaussian process which are independent of each other. Expressions for the even order moments of the Non Gaussian process are obtained as a function of the parameters of the mixture distribution. The mixture density function is then expanded in terms of these moments and even order Hermite polynomials. It is shown that first few terms of the series expansion provides reasonably good approximation of the mixture density function. The series representation would lead to simplification of the likelihood ratio function and hence is easier to implement than GGM likelihood ratio receiver.