Representation of the Middleton class B model by symmetric alpha-stable processes and chi-distributions

Abstract

Signal processing in non-Gaussian noise environments has attracted much attention recently, due to the poor performance of conventional systems based on the Gaussian assumption. The Middleton class B model has been shown in the literature as an appropriate model to describe certain non-Gaussian interference phenomena. However, its use is often limited because the probability density function has a very complicated form. We derive a mixture representation for the Middleton class B model where the density function is expressed as a weighted sum of chi-distributions with positive and monotonically decreasing coefficients. Therefore, the user can chose a finite linear combination of these simple distributions to approximate the Middleton class B density function to any desirable accuracy. The results presented help to extend the applicability of the Middleton class B model in practice.