Mixed least-mean-squares/H/spl infin/-optimal adaptive filtering

We construct a so-called mixed least-mean squares/H/sup /spl infin//-optimal (or mixed H/sup 2//H/sup /spl infin//-optimal) algorithm for adaptive filtering. The resulting adaptive algorithm is nonlinear and requires O(n/sup 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/sup /spl infin//-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/sup /spl infin// adaptive filters.