An adaptive super-exponential deflation algorithm for blind deconvolution of MIMO systems using the QR-factorization of matrix algebra

Kohno, Kiyotaka; Inouye, Yasushi; Kawamoto, Mitsuru; Okamoto, Toshio

doi:10.1109/mwscas.2004.1354384

Cited by 2 publications

(1 citation statement)

References 13 publications

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“…Theorem 1: Under the same conditions in Lemma 1, it follows that (10) where and are defined by (7) and (8), respectively. The proof of Theorem 1 is shown in Appendix B.…”

Section: Matrix Pseudo-inversion Lemmamentioning

confidence: 87%

A Matrix Pseudo-Inversion Lemma for Positive Semidefinite Hermitian Matrices and Its Application to Adaptive Blind Deconvolution of MIMO Systems

Kohno

Inouye

Kawamoto

2008

IEEE Trans. Circuits Syst. I

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Abstract-In the simplest case, the matrix inversion lemma gives an explicit formula of the inverse of a positive-definite matrix added to a rank-one matrix as follows:(1 It is well known in the literature that this formula is very useful to develop a recursive leastsquares algorithm for the 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 pseudo-inversion lemma along with some illustrative examples. 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. This lemma is important in its own right, but in order to show the usefulness of the lemma, we apply it to develop an adaptive superexponential algorithm for the blind deconvolution of multi-input multi-output systems.Index Terms-Adaptive super-exponential algorithm (SEA), matrix pseudo-inversion lemma, recursive algorithms.

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“…Theorem 1: Under the same conditions in Lemma 1, it follows that (10) where and are defined by (7) and (8), respectively. The proof of Theorem 1 is shown in Appendix B.…”

Section: Matrix Pseudo-inversion Lemmamentioning

confidence: 87%

A Matrix Pseudo-Inversion Lemma for Positive Semidefinite Hermitian Matrices and Its Application to Adaptive Blind Deconvolution of MIMO Systems

Kohno

Inouye

Kawamoto

2008

IEEE Trans. Circuits Syst. I

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An Adaptive Super-Exponential Deflation Algorithm for Blind Deconvolution of MIMO Systems Using the Matrix Pseudo-Inversion Lemma

Kohno

Kawamoto

Inouye

2005 IEEE International Symposium on Circuits and Systems

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The multichannel blind deconvolution of finite-impulse response (FIR) or infinite-impulse response (IIR) channels is investigated using the multichannel super-exponential deflation methods. We propose a new adaptive approach to the multichannel super-exponential deflation methods using the matrix pseudo-inversion lemma (which is extended from the matrix inversion lemma in the full-rank case to the rank-degenerate case) and the higher-order cross correlations of the channel and the equalizer outputs. In order to see the effectiveness of the proposed approach, many computer simulations are carried out for time-invariant MIMO channels along with time-variant MIMO channels. It is shown through computer simulations that the proposed approach is effective for even time-variant channels.

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An adaptive super-exponential deflation algorithm for blind deconvolution of MIMO systems using the QR-factorization of matrix algebra

Cited by 2 publications

References 13 publications

A Matrix Pseudo-Inversion Lemma for Positive Semidefinite Hermitian Matrices and Its Application to Adaptive Blind Deconvolution of MIMO Systems

A Matrix Pseudo-Inversion Lemma for Positive Semidefinite Hermitian Matrices and Its Application to Adaptive Blind Deconvolution of MIMO Systems

An Adaptive Super-Exponential Deflation Algorithm for Blind Deconvolution of MIMO Systems Using the Matrix Pseudo-Inversion Lemma

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