On adaptive filtering with combined least-mean-squares and H^∞ criteria

Abstract

We study the possibility of combining least-mean-squares, or stochastic, performance with H^∞-optimal, or worst-case, performance in adaptive filtering. The resulting adaptive algorithms allow for a trade-off between average and worst-case performances and are most applicable in situations, such as mobile communications, where, due to modeling errors and rapid time-variation of system parameters, the exact statistics and distributions of the underlying signals are not known. We mention some of the open problems in this field, and construct a nonlinear adaptive filter (requiring O(n^2) operations per iteration, where n is the number of filter weights) that recursively minimizes the least-mean-squares error over all filters that guarantee a specified worst-case H^∞ bound. We also present some simple examples to compare the algorithm's behaviour with standard least-squares and H^∞ adaptive filters.