A Matrix Pseudoinversion Lemma and Its Application to Block-Based Adaptive Blind Deconvolution for MIMO Systems

作者：Kohno Kiyotaka^*; Kawamoto Mitsuru; Inouye Yujiro

来源：IEEE Transactions on Circuits and Systems I-Regular Papers, 2010, 57(7): 1449-1462.

DOI：10.1109/TCSI.2010.2050222

• Adaptive superexponential algorithm
• blind deconvolution
• block-based recursive least squares algorithm
• matrix pseudoinversion lemma

The matrix inversion lemma gives an explicit formula of the inverse of a positive definite matrix added to a block of dyads ( represented as) as follows: (A + BB(H))(-1) = A(-1) - A(-1) B(I + B(H) A(-1) B)(-1) B(H) 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 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.

• 出版日期2010-7