An LMS viewpoint on the local stability of second order blind source separation

Abstract

The local stability of blind source separation (BSS) algorithms has been mostly investigated in the vicinity of the mixing system inverse, i.e. assuming not only separation but also deconvolution of the sources. In the case of convolutive mixtures, other equilibrium points exist that do not deconvolve the sources. In this paper, we examine the local stability at such an equilibrium point for a second-order BSS algorithm based on the source non-stationarity. Considering explicitly source silences (for example with speech sources) greatly simplifies the obtained local stability conditions and allows a comparison with the classical LMS noise canceller. This analysis reveals a discrepancy between causal and double-sided (acausal) mixing channels.