Signal processing in non-Gaussian noise using mixture distributions and the EM algorithm

Many techniques have been developed and optimized for processing signals that are corrupted by additive, Gaussian noise. The schemes designed for Gaussian noise typically perform very poorly when the noise is non-Gaussian. An approach for non-Gaussian signal processing is presented in this paper that is based on modeling the probability density function (pdf) of the additive noise with a finite mixture of Gaussian pdfs. Model parameters are estimated using iterative procedures derived from the expectation-maximization (EM) algorithm. Explicit algorithms are presented for several signal processing problems using this framework, including linear regression, array processing, and sequence estimation for intersymbol interference communication channels. The resulting algorithms are data-adaptive, in that they characterize the non-Gaussian noise and then modify the signal processing accordingly.