A matrix pseudoinversion lemma and its application to block-based adaptive blind deconvolution for MIMO systems

Authors:
Kiyotaka Kohno;Mitsuru Kawamoto;Yujiro Inouye
Affiliations:
Department of Electronic Control Engineering, Yonago National CoIlege of Technology, Yonago, Japan;Information Technology Research Institute, National Institute of Advanced Industrial Science and Technology, Tokyo, Japan;Department of Electronic and Control Systems Engineering, Shimane University, Matsue, Japan
Venue:
IEEE Transactions on Circuits and Systems Part I: Regular Papers
Year:
2010

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Abstract

The matrix inversion lemma gives an explicit formula of the inverse of a positive definite matrix A added to a block of dyads(represented as BBH) as follows: (A + BBH) -1 = A-1 - A-1 B(I + BH A-1 B) -1 BH A-1. It is well known in the literature that this formula is very useful to develop a block-based recursive least squares algorithm for the block-based recursive identification of linear systems or the design of adaptive filters. We extend this result to the case when the matrix A is singular and present a matrix pseudoinversion lemma along with some illustrative examples. Based on this result, we propose a block-based adaptive multichannel superexponential algorithm. We present simulation results for the performance of the block-based algorithm in order to show the usefulness of the matrix pseudoinversion lemma.