Exploring permutation inconsistency in blind separation of speech signals in a reverberant environment

We study and explore the limitations of methods for blind separation of a mixture of multiple speakers in a real reverberant environment. To support our results, we analyze a frequency-domain method, which achieves blind source separation (BSS) by transforming the time-domain convolutive problem to multiple short-term problems in the frequency domain. We show that treating the problem independently at different frequency bins introduces a "permutation inconsistency" problem, which becomes worse as the length of room impulse response increases. Our studies prove that the ideas proposed in the existing literature are not capable of effectively handling this problem and a need exists for its satisfactory solution. We speculate that time-domain BSS techniques may also suffer from an equivalent permutation inconsistency problem when long un-mixing filters are used.