Stochastic analysis of the delayed LMS algorithm for a new model

This paper presents a stochastic analysis of the delayed least mean square (DLMS) adaptive algorithm using a new model. The new model does not use independence theory. Recursive difference equations are derived for the weight vector first and second moments. These equations yield new analytical results for the mean square error behavior. These results are compared to those of previous models. The new model is shown to be more general. The algorithm's properties are explained that could not be explained using existing models. The theoretical behavior is in close agreement with Monte Carlo simulations for the cases studied. This provides support for the accuracy of the theoretical model.

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