On the Approximation of Correlated Non-Gaussian Noise Pdfs using Gaussian Mixture Models

Gaussian mixture probability density functions (pdfs) have been po pular for modeling nonGaussian noise. The majority of non-Gaussian noise research has been restri cted to independent and identically distributed observation sequences due to the difficulty i n characterizing multidimensional pdf’s. There has been very few studies on the ability of Gaussian m ixture pdfs to model correlated non-Gaussian noise processes. In this paper, we initiate such a tudy and demonstrate that in practical cases, Gaussian mixture pdfs with a small number of mixin g terms can give good approximations to non-Gaussian noise pdfs. Some general models for co rrelated non-Gaussian interference and noise are reviewed. The focus is on three approaches. The first i s the Gaussian mixture model approach. The second is an approach based on spherically invariant random v ect rs. The final approach involves the combination of linear filters and nonlinearities, gen erally in anad-hoc manner. The three approaches are compared and the Gaussian mixture model is shown to approximate models generated from the other approaches.