Relation between Blind System Identification and Convolutive Blind Source Separation

1. INTRODUCTION. Traditionally blind source separation (BSS) has often been considered as an inverse problem. In this paper we show that the theoretically optimum convolutive BSS solution corresponds to blind multiple-input multiple-output (MIMO) system identification. By choosing an appropriate filter length we show that for broadband algorithms the well-known ambiguities can be avoided. Ambiguities in instantaneous BSS algorithms are scaling and permutation [1]. In narrowband convolutive BSS these ambiguities occur independently in each frequency bin so that arbitrary scaling becomes arbitrary filtering [2]. For additional measures to solve the internal permutation problem see, e.g., [2] and for the arbitrary filtering, e.g., [3]. On the other hand broadband time-domain BSS approaches are known to avoid the bin-wise permutation ambiguity. However, traditionally, multichannel blind deconvolution (MCBD) algorithms are often used in the literature [3, 4], which have the drawback of whitening the output signals when applied to acoustic scenarios. Repair measures for this problem have been proposed in [3] (minimum distortion principle) and [4] (linear prediction). In the following we consider the optimum broadband solution of mere separation approaches (MIMO systems, see Fig. 1b) as presented, e.g., in [5], and relate it to the known blind system identification approach based on single-input multiple-output (SIMO) models [6, 7, 8] (Fig. 1a).