On the Relationships between Blind Equalization and Blind Source Separation – Part II: Foundations

Abstract

The objective of this two-part work is to present and discuss the relationships between the problems of blind equalization and blind source separation. Both tasks appear, at first sight, to be essentially distinct, since equalization theory was developed mainly under single-input / single-output (SISO) and single-input/ multiple-output (SIMO) models, whereas the very idea of source separation strongly suggests the need for considering models with multiple inputs and multiple outputs (MIMO). However, in this second part, equivalences between the Benveniste-Goursat-Ruget theorem and the approach to blind source separation based on maximum-likelihood, between the Shalvi-Weinstein techniques and the separation methods that employ kurtosis and, finally, between the Bussgang algorithms and the ICA tools built from concepts such as negentropy and nonlinear principal component analysis are indicated. Finally, some connections previously unexplored in the literature are presented that are derived from ideas such as that of temporality and that of considering the parallels existing between a two-stage (magnitude and phase) equalization procedure and the classical pair PCA / ICA.