Fuzzy adaptive filters, with application to nonlinear channel equalization

Two fuzzy adaptive filters are developed: one uses a recursive-least-squares (RLS) adaptation algorithm, and the other uses a least-mean-square (LMS) adaptation algorithm. The RLS fuzzy adaptive filter is constructed through the following four steps: (1) define fuzzy sets in the filter input space Rn whose membership functions cover U; (2) construct a set of fuzzy IF-THEN rules which either come from human experts or are determined during the adaptation procedure by matching input-output data pairs; (3) construct a filter based on the set of rules; and (4) update the free parameters of the filter using the RLS algorithm. The design procedure for the LMS fuzzy adaptive filter is similar. The most important advantage of the fuzzy adaptive filters is that linguistic information (in the form of fuzzy IF-THEN rules) and numerical information (in the form of input-output pairs) can be combined in the filters in a uniform fashion. The filters are applied to nonlinear communication channel equalization problems