A novel approach based on non-unitary joint block-diagonalization for the blind MIMO equalization of cyclo-stationary signals

In this paper, 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. In our case, the considered input signals are cyclo-stationary processes whose cyclic frequencies are not necessarily known. To tackle that problem, we propose to use a new algorithm that performs the (nonunitary) joint block diagonalization (JBD) of a given set of complex matrices. It is based on a gradient approach. But first, the matrices set to be joint block-diagonalized has to be built: this is done using a particular linear operator on the correlation matrices of the observations and taking advantage of some specific algebraic properties of the aforementioned “transformed” matrices (for instance, the frequencies that correspond to the matrices belonging to that set happen to be the cyclic ones). Then, the JBD of this matrices set enables to estimate the mixing system and, consequently, to recover the source signals. Computer simulations are provided in order to illustrate the behavior and the usefulness of the proposed approach in the context of digital communications and a comparison with another existing method is also performed.