Adaptive filters with nonlinear RLS algorithm in impulse noise

Adaptive filter using the nonlinear recursive least square (RLS) algorithm in impulse noise is presented. Its mean and mean square behaviors are studied for a Gaussian input signal and the class A impulse noise. Necessary and sufficient conditions for the stability of the algorithm are derived. A class of nonlinear functions including the linear one, which can be incorporated into RLS for assuring stable learning, is introduced. By simulations it is shown that the nonlinear algorithm not only provides convergence rate as fast as but also has excess mean squared error smaller than the linear counterpart in impulse noise.