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

Authors:
Márcio Holsbach Costa;Leandro Ronchini Ximenes;José Carlos Moreira Bermudez
Affiliations:
Department of Electrical Engineering, Federal University of Santa Catarina, Florianópolis 88040-900, SC, Brazil;Department of Electrical Engineering, Federal University of Santa Catarina, Florianópolis 88040-900, SC, Brazil;Department of Electrical Engineering, Federal University of Santa Catarina, Florianópolis 88040-900, SC, Brazil
Venue:
Signal Processing
Year:
2008

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Abstract

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.