Kiyotaka Kohno

Eigenvector Algorithms Incorporated With Reference Systems for Solving Blind Deconvolution of MIMO-IIR Linear Systems

This letter presents an eigenvector algorithm (EVA) for blind deconvolution (BD) of multiple-input multiple-output infinite impulse response (MIMO-IIR) channels (convolutive mixtures), using the idea of reference signals. Differently from the conventional researches on EVAs, the proposed EVA utilizes only one reference signal for recovering all the source signals simultaneously. Computer simulations are presented for demonstrating the effectiveness of the proposed algorithm.

Adaptive super-exponential algorithms for blind deconvolution of MIMO systems

Multichannel blind deconvolution of finite-impulse response (FIR) or infinite-impulse response (IIR) systems is investigated using the multichannel super-exponential method. First, some properties are shown for the rank of the correlation matrices relevant to the multichannel super-exponential method. Then, the matrix inversion lemma is extended to the degenerate rank case. Based on these results, two types of adaptive multichannel super-exponential algorithms are presented, that is, the one in covariance form and the other in QR-factorization form.

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

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 BBH) 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 A is singular, and present a matrix pseudo-inversion lemma. Based on this result, we propose a block-based adaptive multi-channel super-exponential algorithm (BAMSEA). We present simulation results for the performance of the block-based algorithm in order to show the usefulness of the matrix pseudo-inversion lemma.

Super-exponential Methods Incorporated with Higher-Order Correlations for Deflationary Blind Equalization of MIMO Linear Systems

The multichannel blind deconvolution of finite-impulse response (FIR) or infinite-impulse response (IIR) systems is investigated using the multichannel super-exponential deflation methods. In the conventional multichannel super-exponential deflation method [4], the so-called “second-order correlation method” is incorporated in order to estimate the contributions of an extracted source signal to the channel outputs. We propose a new multichannel super-exponential deflation method using higher-order correlations instead of second-order correlations to reduce the computational complexity in terms of multiplications and to accelerate the performance of equalization. By computer simulations, it is shown that the method of using fourth-order correlations is better than the method of using second-order correlations in a noiseless case or a noisy case.

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

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

Eigenvector Algorithms Using Reference Signals

This paper presents an eigenvector algorithm (EVA) derived from a criterion using reference signals, in which the EVA is applied to the blind source separation (BSS) of instantaneous mixtures. The proposed EVA works such that source signals are simultaneously separated from their mixtures. This is a new result, which has not been clarified by the conventional researches. Simulation results show the validity of the proposed EVA

Eigenvector algorithms using reference signals for blind source separation of instantaneous mixtures

This paper presents an eigenvector algorithm (EVA) derived from a criterion using reference signals, in which the EVA is applied to the blind source separation (BSS) of instantaneous mixtures. The proposed EVA works such that source signals are simultaneously separated from their mixtures. This is a new result, which has not been clarified by the conventional researches. Moreover, by modifying the criterion, the corresponding EVA which is robust to Gaussian noise is derived. Simulation results show the validity of the proposed EVAs

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

In the simplest case, the matrix inversion Lemma gives an explicit formula of the inverse of a positive-definite matrix A added to a rank-one matrix bb^H as follows:(A + bb^H )^-1 = A^-1-A^-1 b(1 + b^H A^-1b)^-1b^HA^-1. It is well known in the literature that this formula is very useful to develop a recursive least-squares algorithm for the 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. Such a singular case may occur in a situation where a given problem is overdeter-mined 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 super-exponential algorithm for the blind deconvolution of multi-input multi-output systems.

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 BBH). 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.

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

The multichannel blind deconvolution of finite-impulse response (FIR) or infinite-impulse response (IIR) systems is investigated using the multichannel super-exponential deflation methods. We propose a new adaptive approach to the multichannel super-exponential deflation methods using the QR-factorization of matrix algebra and the higher-order cross correlations of the (channel) system and equalizer outputs. In order to see the effectiveness of the proposed approach, many computer simulations are carried out for time-invariant MIMO systems along with time-variant MIMO systems. It is shown through computer simulations that the proposed approach is effective for time-invariant systems, but is not so effective for time-variant systems as we expected in advance.