Local stable minima of the Sato recursive identification scheme

Abstract

A common recursive identification scheme used in a class of adaptive systems problems involving blind channel equalization (but potentially usable elsewhere) is an algorithm due to Sato. The authors study the convergence properties of the Sato blind algorithm by characterizing the mean cost surface. The results show the important feature that the equalizer parameters may converge to parameter settings which fail to achieve the ideal objective which is to approximate the inverse with sufficient accuracy. A proof that a well-posed Sato algorithm can misbehave is presented. Examples are used to illustrate the results.