Resumo-Algoritmos de filtragem adaptativa apresentam comprometimento da aprendizagem na presença de ruído aditivo, seja no sinal de referência, seja no sinal de entrada. Este artigo combina duas estratégias-reúso de coeficientes e compensação de viés-para obter algoritmos robustos para ambos os tipos de ruído. Tais algoritmos são capazes de melhorar significativamente o desempenho em regime estacionário sem implicar uma perda significativa na taxa de convergência. Melhorias no algoritmo resultante (redução do custo computacional e aumento da taxa de convergência) se mostraram possíveis através do recurso a fatores de reúso variáveis no tempo.

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Adaptive filtering algorithms are widespread today owing to their flexibility and simplicity. Due to environments in which they are normally immersed, their robustness against noise has been a topic of interest. Traditionally, in the literature it is assumed that noise is mainly active in the reference signal. Since this hypothesis is often violated in practice, recently some papers have advanced strategies to compensate the bias introduced by noisy excitation data. The contributions of this paper are twofold. The first one establishes that, in some conditions, the bias-compensated least mean square algorithm implements an optimum estimator, in the sense that it presents the smallest variance of the set of unbiased estimators. Since the asymptotic mean-square performance of this algorithm has not yet been investigated in detail, the second contribution adopts an energy conservation relationship to derive its theoretical steady-state mean squared distortion. The final result is presented in a closed form, is consistent with simulations and is able to provide important guidelines to the designer.