Adaptive Criteria Optimization as a Least Squares Problem

"In this work, we propose an approach to the analysis of adaptive filtering criteria, based on an original formulation via least squares. This proposal, though based on some model considerations, possesses great generality and simplicity, encompassing many filtering structures and criteria. The approach is used on the study of three blind techniques (decision-directed, constant modulus and modified Sato) and of its relations to the supervised Wiener criterion. The method allows us to view adaptive techniques in a simple and unusual fashion and brought out theoretical insights on blind receivers and their relationship. The whole theoretical framework has a deep geometric appeal and highlights the relevance of separation conditions to static criteria analysis."