Exploiting 2nd-order statistics in Bayesian signal reconstruction problems

We study signal reconstruction with the aid of second order statistics (SOS) in some Bayesian multi-user setups. Under a Bayesian framework, the unknown mixing channel matrix is a random object. Furthermore, it is well known that the SOS of the received data can solve the channel matrix up to an orthogonal factor, which now becomes a random object. That is, the prior for the original channel matrix contracts to another prior for the residual orthogonal mixing matrix. This paper shows how to exploit this new prior over the orthogonal group in two different applications: blind separation of binary users and semi-blind channel identification. Computer simulations assess the benefits of our proposed solutions over some classical "textbook" solutions.