Mixed least-mean-squares/H^∞-optimal adaptive filtering

Abstract

We construct a so-called mixed least-mean squares/H-∞optimal (or mixed H^2/H^∞-optimal) algorithm for adaptive filtering. The resulting adaptive algorithm is nonlinear and requires O(n^2) (where n is the number of filter weights) operations per iteration. Such mixed algorithms have the properly of yielding the best average (least-mean-squares) performance over all algorithms that achieve a certain worst-case (H^∞-optimal) bound. They thus allow a tradeoff between average and worst-case performance and are most applicable in situations where the exact statistics and distributions of the underlying signals are not known. Simple simulations are also presented to compare the algorithm's behaviour with standard least-squares and H^∞ adaptive filters.

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