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Blind Deconvolution of MIMO-FIR Systems with Colored Inputs Using Second-Order Statistics
Mitsuru KAWAMOTO Yujiro INOUYE
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Publication Date: 2003/03/01
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Blind Signal Processing: Independent Component Analysis and Signal Separation)
Category: Convolutive Systems
blind deconvolution, MIMO-FIR systems, equalizable, colored sources, second-order statistics,
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The present paper deals with the blind deconvolution of a Multiple-Input Multiple-Output Finite Impulse Response (MIMO-FIR) system. To deal with the blind deconvolution problem using the second-order statistics (SOS) of the outputs, Hua and Tugnait 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. 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, while Hua and Tugnait have not proposed any algorithm for solving the blind deconvolution under the conditions a) and b).