A block-based adaptive super-exponential deflation algorithm for blind deconvolution of MIMO systems using the matrix pseudo-inversion lemma

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 already extended this result to the case when the matrix A is singular, and presented the matrix pseudo-inversion lemma. Such a singular case may occur in a situation where a given problem is overdetermined in the sense that it has more equations than unknowns. In this paper, based on these results, we propose a block-based adaptive multichannel super-exponential deflation 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.