Blind Source Separation and Channel Identification: Exploiting 2nd Order Statistics in Bayesian Frameworks

Abstract

We study how 2nd order statistics (SOS) can be exploited in two signal processing problems, blind separation of binary sources and trained-based multi-user channel iden­ tification, in a Bayesian context where a prior on the mixing channel matrix is available. It is well known that the SOS of the received data permit to resolve the unknown mixing matrix, up to an orthogonal factor. In a Bayesian framework, this residual orthogonal mixing matrix becomes a random ob­ ject in its own right, with an associated distribution over the group of orthogonal matrices. This distribution is induced by the prior on the mixing matrix, and must be known for opti­ mum statistical processing. \Ve rely on a previous theoretical work to provide these answers, and discuss applications for this induced probability density function (pdf) over the or­ thogonal group, in the two aforementioned signal processing problems. Preliminary results, obtained through computer simulations, demonstrate the effectiveness of incorporating this induced distribution associated with the residual orthog­ onal matrix into the design of several estimators.