A Matrix Pseudoinversion Lemma and Its Application to Block-Based Adaptive Blind Deconvolution for MIMO Systems
Kiyotaka Kohno, Mitsuru Kawamoto, Yujiro Inouye · IEEE Transactions on Circuits and Systems I Regular Papers · 2010
The matrix inversion lemma gives an explicit formula of the inverse of a positive definite matrixAadded to a block of dyads (represented asBBH) as follows: (A+BBH)-1=A-1-A-1B(I+BHA-1B)-1BHA-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 matrixAis 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.