Stability analysis and optimization of time-domain convolutive source separation algorithms

In this paper, we investigate the self-adaptive source separation problem for convolutively mixed signals. The proposed approach uses a recurrent structure adapted by a generic rule involving arbitrary separating functions. We first analyze the stability of this generic algorithm and we apply these results to some classical rules that were proposed in the literature but only partly analyzed. We then derive the expression of the asymptotic error variance achieved by this rule (for strictly causal mixtures). This enables us to determine the optimum separating functions that minimize this error variance. They are shown to be only related to the probability density functions of the sources. The performance improvement achieved by this approach is illustrated by simulations performed with real mixtures of speech signals.