Blind signal separation in noisy environments using a three-step quantizer

Abstract

Independent component analysis in noisy channels needs special considerations, since standard solutions lead to a bias in the estimate of the parameters. We show three different approaches to mitigate the effects of additive noise in the transfer medium. A principal component subspace method can reduce the noise to more favorable levels, so that any following algorithm shows reduced bias effects. Although stochastic-gradient algorithms for maximum-likelihood solutions to the problem can easily be found, they are computationally prohibitive. A very successful approach is, therefore, to assume zero noise power for the derivation of the adaptive algorithm and subsequently trying to compensate for any bias introduced by such a solution. The threshold nonlinearity (three-step quantizer) is suitable for the blind separation of a large class of sub-Gaussian distributions. Stability regions are explored followed by algorithmic extensions to suppress the bias in the estimation of the separation matrix.