Convergence of a decision-directed adaptive equalizer

An adaptive decision directed equalizer, wherein the estimates of the transmitted data are used for the adaptation of the equalizer parameters, is analyzed. In the paper the stability of the limit equation associated with the stochastic adaptation algorithm is proved. The convergence of the stochastic algorithm then follows by the application of the standard weak convergence theory. The approach of this paper is different from the earlier such analysis in the literature. Thus in the paper we work with the discrete probability distribution of the transmitted symbols, as is the case in practice, rather than assuming a continuous distribution of these for the sake of theoretical convenience.