Blind separation of uncorrelated sources via principal component analysis of observations for a symmetric mixing matrix

A well-known fact in blind deconvolution is that if the unknown source signal is white (temporally) and the unknown channel filter is minimum phase, it is possible to determine the inverse filter (equalizer) by evaluating simply the power spectral density (PSD) of the received signal. For blind source separation, however, a similar special case, equivalent to the situation in blind deconvolution, is not reported. In this paper, we identify the special conditions for which the solution of the blind source separation problem can be identified using only second order statistics of the observed mixtures. In this special case, the equivalent of minimum phase channel turns out to be a symmetric mixing matrix, and the equivalent of temporally white input signal translates to uncorrelated source signals. A fast-converging and robust on-line blind source separation algorithm using a recently introduced principal components analysis (PCA) algorithm named SIPEX-G is also presented and its performance is evaluated in simulations of source separation.