A Frequency Domain Method for Blind Source Separation of Convolutive Audio Mixtures

IEEE Transactions on Speech and Audio Processing, Vol. 13, No.5, September 2005.
Kamran Rahbar, J.P. Reilly and Jonathan H. Mantony

Abstract   This paper discusses a frequency domain method for blind identification of MIMO convolutive channels driven by white quasi-stationary sources. The sources can assume arbitrary probability distributions and in some cases they can even be all Gaussian distributed. We also show that under slightly more restrictive assumptions the algorithm can be applied to the case when the sources are colored, non-stationary signals. We demonstrate that by using the second order statistics of the channel outputs, under mild conditions on the non-stationarity of sources, and under the condition that channel is column-wise coprime, the impulse response of the MIMO channel can be identified up to an inherent scaling and permutation ambiguity. We prove that by using the new algorithm, under the stated assumptions, a uniform permutation across all frequency bins is guaranteed, and the inherent frequency dependent scaling ambiguities can be resolved. Hence no post processing is required as is the case with previous frequency domain algorithms. We further present an efficient, two step frequency domain algorithm for identifying the channel. Numerical simulations are presented to demonstrate the performance of the new algorithm.