Efficient NLMS and RLS algorithms for a class of nonlinear filters using periodic input sequences

The paper discusses computationally efficient NLMS and RLS algorithms for a broad class of nonlinear filters using periodic input sequences. The class comprises all nonlinear filters whose output depends linearly on the filter coefficients. The algorithms presented in the paper are exact, suitable for identification and tracking of every nonlinear system in the class, and require a real-time computational effort of a single multiplication, an addition, and a subtraction per input sample. The transient and steady-state behavior of the algorithms are discussed and the effect of a model mismatch between the unknown system and the adaptive filter is also analyzed. The low computational complexity, good performance, and applicability of the algorithm to a large class of nonlinear systems make the approach of this paper a valuable alternative to the current techniques for nonlinear system identification.