AVOIDING ILL-CONVERGENCE OF FINITE-DIMENSIONAL BLIND ADAPTATION SCHEMES EXCITED BY DISCRETE SYMBOL SEQUENCES

A general framework for convergence analysis of finite-dimensional bli nd adaptation algorithms of Bussgang type is presented. The approach a llows discrete symbol sets and can be used for analysis of systems wit h both poles and zeros. The main tool of analysis is an associated dif ferential equation whose stability properties are proved to be tied to the convergence properties of a general blind stochastic approximatio n algorithm. The recently highlighted ill-convergence problem of for e xample the constant modulus algorithm (CMA) is then addressed. The pro blem is partially solved using new blind adaptation algorithms which a re not derived by criterion minimization. Instead, the averaged updati ng directions of the suggested stochastic gradient schemes are designe d to guarantee global stability of the associated differential equatio ns. (C) 1997 Elsevier Science B.V.