Independent component analysis in noise

Estimating statistically independent sources in the presence of unknown channel distortion and additive white Gaussian noise is considered. A geometrical approach is presented to the analysis of the class of minimum entropy (ME) receivers. It is shown that ME receivers have the signal space property, i.e., all ME receivers reside in the column space of the channel mixing matrix. A necessary and sufficient condition that ME and the minimum mean square error (MMSE) receivers are co-linear is given. Two examples are presented to illustrate effects of source statistics. It is shown that ME receiver may deviate considerably from the MMSE receiver when there are both sub-Gaussian and super-Gaussian sources.