On the blind implementation of the ultimate source separators for arbitrary noisy mixtures

Since the beginning of the 1980s the blind second-order (SO) and higher-order (HO) narrow-band (NB) methods of source separation have received a great interest. However, despite this fact, the situations of practical interest for which these blind methods may blindly implement the ultimate ones, such as the spatial matched filter (SMF) or the weighted least square (WLS) source separators, are not still identified for general noisy situations, which may limit the use of these blind methods in operational contexts. Assuming instantaneously mixed NE sources, the purpose of this paper is to enlighten the previous important problem through the analysis of the SO correlation and the FO cross-cumulants at the outputs of the SMF and the WLS separators for arbitrary noisy mixtures of sources. (C) 1999 Published by Elsevier Science B.V. All rights reserved.