Blind separation of convolved cyclostationary processes

Abstract

A non-parametric method is presented for the blind separation of convolved cyclostationary processes such as those typically observed at the output of MIMO systems driven by periodically modulated random processes. The approach is formulated in the frequency domain and is deductive in the sense that it follows the lines of optimal supervised filtering—from which the relationships to be used in the unsupervised situation are derived. This leads to an algorithm where the successive diagonalisations of some cyclic spectral density matrices give rise to unique separating filters. One important result concerns the proposal of solutions to unambiguously recover the exact source permutation at each frequency. A statistical performance analysis of the method is also conducted, with the results suggesting some strategies to increase the robustness of the separation. Examples of successful separation are finally provided on realistic convolutive mixtures, both synthetic and from the real world, where impulse responses of several thousands of coefficients are dealt with.