Nonlinear secondary-path effects on the transient behavior of the multiple-error FXLMS algorithm

This paper presents a statistical analysis of the multiple-error Filtered-X Least Mean Square algorithm with nonlinearities in the secondary paths. Each nonlinearity is modelled by a scaled error function that can represent the saturation behavior of the transducers and associated hardware in active noise control applications. Deterministic recursions are derived for the mean weight and mean square error behavior for white Gaussian inputs and slow adaptation. The independence theory is not used in the derivations. Monte Carlo simulations show excellent agreement with the behavior predicted by the theoretical models. The new results predict the behavior of the algorithm for different amounts of nonlinear distortion