Abstract
A general framework for convergence analysis of finite-dimensional blind adaptation algorithms of Bussgang type is presented. The approach allows discrete symbol sets and can be used for analysis of systems with both poles and zeros. The main tool of analysis is an associated differential equation whose stability properties are proved to be tied to the convergence properties of a general blind stochastic approximation algorithm. The recently highlighted ill-convergence problem of for example the constant modulus algorithm (CMA) is then addressed. The problem is partially solved using new blind adaptation algorithms which are not derived by criterion minimization. Instead, the averaged updating directions of the suggested stochastic gradient schemes are designed to guarantee global stability of the associated differential equations.
Published Version
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