A Bayesian Approach to Blind Separation of Mixed Discrete Sources by Gibbs Sampling

Abstract

Blind source separation (BSS) is the process of separating the original signals from their mixtures without the knowledge of neither the signals nor the mixing process. In this paper, a Bayesian modeling approach for the separation of instantaneous mixture of linear modulation signals with memory in communication systems is developed, in which the finite alphabet (FA) property of the source signals, together with the correlation contained in the source signals are used for the purpose of accurate signal separation. And the Gibbs sampling algorithm is employed to estimate discrete source signals and mixing coefficients. Moreover, the approach takes into account noise levels in the model in order to provide precise estimations of the signals. The simulation results under determined mixture condition show that this new algorithm gives precise estimation of sources and coefficients of mixture. Furthermore, the efficiency of this proposed approach under underdetermined mixture condition is attested by a numerical simulation experiment.