Adaptive super-exponential algorithms for blind deconvolution of MIMO systems

Abstract

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

“…For example, we may take . Because we consider the case when the number of inputs is less than the number of outputs , i.e., , the correlation matrix is not of full rank and a singular matrix [7]. Therefore, we may apply the matrix pseudoinversion lemma to the recursive equation (36).…”

“…The case where the length of the block of the matrix pseudoinversion lemma is restricted to the case when the added matrix is a single dyad (i.e., is a column vector) [7]- [9]. An illustrative example and the simulation results of the matrix pseudoinversion lemma in this case and the application to adaptive blind deconvolution of MIMO systems are shown in [7]- [9].…”

“…An illustrative example and the simulation results of the matrix pseudoinversion lemma in this case and the application to adaptive blind deconvolution of MIMO systems are shown in [7]- [9].…”

Blind Deconvolution of MIMO-IIR Systems: A Two-Stage EVA

“…which is shown in [10] and its proof is found in [3]. Using this fact, the other remaining eigenvalues ofF †B are all zero.…”

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

“…We already proposed two type of adaptive multichannel super-exponential algorithms (AMSEAs), the one in covariance (correlation or Kalman-filter) form and the other in QR-factorization form, for the degenerate rank case of the correlations matrices [8]. We propose an AMSEDA using the matrix pseudo-inversion lemma (the covariance form) in this paper, and we show the effectiveness of the proposed algorithm by computer simulations in comparison with the AMSEDA using the QR-factorization [10].…”