The performance surface in nonlinear mean square estimation: application to the active noise control problem

This paper investigates the properties of the performance surface for a problem of nonlinear mean-square estimation of a random sequence. The problem studied has direct application to the study of active noise control (ANC) systems when the transducers are driven into nonlinear behavior. A deterministic expression is derived for the mean-square error (MSE) surface as a function of the system´s degree of nonlinearity. It is shown how the presence of the nonlinearity deforms the MSE surface. It is demonstrated that the surface is unimodal, and the expression for the optimum weight vector is determined. The new results are then used to quantify the behavior of ANC systems employing the LMS adaptive algorithm. Important algorithm properties are derived from this study. Examples are presented to verify the analytical models derived