Separation of convolutive mixtures of cyclo-stationary signals using a non-unitary block-diagonalization algorithm

In this communication, we address the problem of the blind separation of convolutive mixtures of sources also known as blind equalization of linear time invariant multi-input multi-output systems in digital communications. The considered input signals are cyclo-stationary processes whose cyclic frequencies are not necessarily known. We propose a new method which, by some aspects, generalizes previous works developed in the instantaneous case of mixtures. The key idea consists of applying a particular linear operator on the correlation matrices of the observations and, then, to take advantage of some specific properties of the aforementioned "transformed" matrices in order to build a particular set of matrices (for instance, the frequencies that correspond to the matrices belonging to that set do happen to be the cyclic ones). Then, the (non-unitary) joint block diagonalization of this matrices set makes it possible to estimate the mixing system and, consequently, to recover the sought after source signals. Finally, computer simulations are provided in order to illustrate the behaviour and the usefulness of the proposed approach in the context of digital communication.