Statistical analysis of the LMS adaptive algorithm subjected to a symmetric dead-zone nonlinearity at the adaptive filter output

This work presents a statistical analysis of the Least Mean Square (LMS) adaptive algorithm subjected to the existence of a symmetric dead-zone nonlinearity at the adaptive filter output. Such configuration can be representative of low-cost active noise control systems where the canceling signal drives a class B power amplifier or a nonlinear actuator. Recursive deterministic equations are derived for the mean coefficient and mean-square error behaviors assuming Gaussian signals and slow adaptation. The steady-state algorithm behavior is determined for given filter parameters and degree of nonlinearity. Monte Carlo simulations and laboratory experiments are presented which corroborate the theoretical results.