On the Relationships between Blind Equalization and Blind Source Separation – Part I: 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. This first part, which is essentially a tutorial, begins with a systematic exposition of the basic concepts that form the core of equalization theory, starting from the fundamental idea that characterizes the zero-forcing solution and reaching, after an explanation of the supervised Wiener paradigm, an analysis of the unsupervised or blind techniques. Afterwards, the problem of blind source separation and the main approaches to solving it are studied; important concepts are discussed, such as those of principal component analysis (PCA), independent component analysis (ICA) and strategies founded on bases as diverse as the use of mutual information as a measure of independence, the idea of nongaussianity and the employment of the classical process of estimation via the method of maximum-likelihood.