Time-Domain Blind Signal Separation of Convolutive Mixtures via Multidimensional Independent Component Analysis

Abstract

An algorithm for blind signal separation (BSS) of convolutive mixtures is presented. In this algorithm, the BSS problem is treated as multidimensional independent component analysis (ICA) by introducing an extended signal vector which is composed of current and previous samples of signals. It is empirically known that a number of conventional ICA algorithms solve the multidimensional ICA problem up to permutation and scaling of signals. In this paper, we give theoretical justification for using any conventional ICA algorithm. Then, we discuss the remaining problems, i.e., permutation and scaling of signals. To solve the permutation problem, we propose a simple algorithm which classifies the signals obtained by a conventional ICA algorithm into mutually independent subsets by utilizing temporal structure of the signals. For the scaling problem, we prove that the method proposed by Koldovský and Tichavský is theoretically proper in respect of estimating filtered versions of source signals which are observed at sensors.