Stochastic gradient adaptive algorithms for blind source separation

Abstract The aim in blind source separation is to separate linear mixtures of statistically independent non-Gaussian signals without resorting to an a priori knowledge of the sources or the mixing system. In this paper we propose a new family of adaptive algorithms that recursively compute the optimum separating system. The algorithms are of the gradient ascent type and maximize a statistical criterion that involves only second- and fourth-order cumulants. We present a complete analysis of all the stationary points in the proposed criterion for an arbitrary number of complex sources. We demonstrate that the algorithms can only converge to points where perfect separation is achieved provided that the mixing system is a square invertible matrix and all the sources have the same kurtosis sign. We also prove that the criterion is free of undesirable maxima.