Blind Separation of Multiple Convolved Colored Signals Using Second-order Statistics

The present paper deals with the blind separation of multiple convolved colored signals, that is, the blind deconvolution of an Multiple-Input Multiple-Output Finite Impulse Response (MIMO-FIR) system. To deal with the blind deconvolution problem using the secondorder statistics (SOS) of the outputs, Hua and Tugnait [3] considered it under the conditions that a) the FIR system is irreducible and b) the input signals are spatially uncorrelated and have distinct power spectra. In the present paper, the problem is considered under a weaker condition than the condition a). Namely, we assume that c) the FIR system is equalizable by means of the SOS of the outputs [6]. Under b) and c), we show that the system can be blindly identified up to a permutation, a scaling, and a delay using the SOS of the outputs. Moreover, based on this identifiability, we show a novel necessary and sufficiently condition for solving the blind deconvolution problem, and then, based on the condition, we propose a new algorithm for finding an equalizer using the SOS of the outputs.