Matched Myriad Filtering for Robust Communications

Weighted myriad filters is a robust nonlinear filtering framework motivated by the statistical properties of ff- stable distributions. Derived to be optimal in impulsive environments, the class of myriad filters includes a rich variety of filtering operations which can be controlled by simply adjusting a tuning parameter k. Weighted myriad filters range from highly robust mode-like selection filters (k = 0) to the efficient class of linear FIR filters (k = 1). In this paper we introduce the matched myriad filter (MMyF) as an application of weighted myriad filters to the robust estimation problem in communications. In order to develop matched filter applications with passband and multidimensional signals, we introduce the vector myriad filter (VMyF) as a weighted maximum likelihood location estimator of spherically symmetric Cauchy distributions. The complex MMyF is then formulated as a two-dimensional VMyF. Finally, the improved performance of MMyF's is demonstrated through simulation..