Development of a Block-Based Adaptive Blind Deconvolution Algorithm Using the Matrix Pseudo-Inversion Lemma and Its Application to MIMO Systems

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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 BB^H). 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 pseudo-inversion lemma along with some illustrative examples. Based on this result, we propose a block-based adaptive multichannel super-exponential algorithm. We present simulation results for the performance of the block-based algorithm in order to show the usefulness of the matrix pseudo-inversion lemma.