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

Kohno,; Kawamoto,; Inouye,

doi:10.1109/iscas.2010.5537446

Cited by 2 publications

(5 citation statements)

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“…Some details concerning this formula and its application to block-based adaptive blind deconvolution of MIMO systems can be found in [18] and [19]. However, we have not yet extended it to the case where and become linear bounded operators with a closed range.…”

Section: Discussionmentioning

confidence: 99%

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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Section: Discussionmentioning

confidence: 99%

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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“…. Results of calculating 's and recovering original sources 's are found in [14]. We considered a MIMO system with two inputs and five outputs and assumed that the system is of FIR and the length of channel is three, i.e., 's in (17) were set to be (58) Two source signals were 4-and 8-PSK signals, respectively.…”

Section: Simulation Resultsmentioning

confidence: 99%

“…It can be seen from Fig. 2(a) and (b) that the accuracy of the matrix pseudoinversion lemma is a little worse than the built-in function "pinv," but the formula (14) of the matrix pseudoinversion lemma can treat the changes of the channel.…”

Section: Simulation Resultsmentioning

confidence: 99%

“…Theorem 1: Under the same conditions in Lemma 1, it follows that (14) where and are defined by (7) and (8), respectively. The proof of Theorem 1 is shown in Appendix C.…”

Section: Matrix Pseudoinversion Lemma: a General Case With A Blocmentioning

confidence: 90%

“…We also include simulation results for the performance of the proposed algorithm in order to show its effectiveness, where we compare the performance of the proposed algorithm using the lemma with that of the algorithm using the built-in function in MATLAB version 7.1.0 for calculating pseudoinverses of the relevant matrices instead of using the lemma. We should note that a performance result of a block-based adaptive multichannel superexponential deflation algorithm is shown in [14].…”

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confidence: 99%

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

Kohno

Kawamoto²,

Inouye

2010

IEEE Trans. Circuits Syst. I

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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.

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

Cited by 2 publications

References 5 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

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

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