Maximum likelihood blind separation of convolutively mixed discrete sources

In this paper, a Maximum Likelihood (ML) approach, implemented by Expectation-Maximization (EM) algorithm, is proposed to blind separation of convolutively mixed discrete sources. In order to carry out the expectation procedure of the EM algorithm with a less computational load, the algorithm named Iterative Maximum Likelihood algorithm (IML) is proposed to calculate the likelihood and recover the source signals. An important feature of the ML approach is that it has robust performance in noise environments by treating the covariance matrix of the additive Gaussian noise as a parameter. Another striking feature of the ML approach is that it is possible to separate more sources than sensors by exploiting the finite alphabet property of the sources. Simulation results show that the proposed ML approach works well either in determined mixtures or underdetermined mixtures. Furthermore, the performance of the proposed ML algorithm is close to the performance with perfect knowledge of the channel filters.