Improved Adaptive Algorithm for Active Noise Control of Impulsive Noise Muhammad Tahir Akhtar * , and Wataru Mitsuhashi † * The Education and Research Center for Frontier Science, † Department of Information and Communication Engineering, University of Electro-Communications, 1-5-1 Chofugaoka, Chofu 182-8585, Tokyo, JAPAN. (Emails: akhtar@ice.uec.ac.jp, mit@ice.uec.ac.jp) Abstract— The paper concerns active control of impulsive noise. The most famous filtered-x least mean square (FxLMS) algorithm for active noise control (ANC) systems is based on the minimization of variance of mean-squared-error signal. The impulsive noise can be modeled using non-Gaussian stable process for which second order moments do not exist. The FxLMS algorithm, therefore, becomes unstable for the impulsive noise. Among the existing algorithms for ANC of impulsive noise, one is based on the minimizing least mean p-power (LMP) of the error signal, resulting in FxLMP algorithm. The other is based on modifying; on the basis of statistics properties; the reference signal in the update equation of the FxLMS algorithm. In this paper, the proposed algorithm is an extension of the later approach. Extensive simulations are carried out, which demonstrate the effectiveness of the proposed algorithm. It achieves the best performance among the existing algorithms, and at the same computational complexity as that of FxLMS algorithm. I. I NTRODUCTION Active noise control (ANC) is based on the principle of destructive interference between acoustic waves [1]. Essen- tially, the primary noise is canceled around the location of the error microphone by generating and combining an antiphase canceling noise [2]. As shown in Fig. 1, a single-channel feedforward ANC system comprises one reference sensor to pick up the reference noise x(n), one canceling loudspeaker to propagate the canceling signal y(n) generated by an adaptive filter W (z), and one error microphone to pick up the residual noise e(n). The most famous adaptation algorithm for ANC systems is the filtered-x LMS (FxLMS) algorithm [3], which is a modified version of the LMS algorithm [4]. Here the reference signal x(n) is filtered through a model of the so- called secondary path S(z), following the adaptive filter, and hence the name filtered-x algorithm. The FxLMS algorithm is a popular ANC algorithm due to its robust performance, low computational complexity and ease of implementation [3]. Over the past few decades a great progress has been made in ANC, yet the practical applications are limited. One important challenge comes the control of impulsive noise. In practice, the impulsive noises are often due to the occurrence of noise disturbance with low probability but large amplitude. An impulsive noise can be modeled by stable non-Gaussian distribution [5]. We consider impulse noise with symmetric α- stable (SαS) distribution f (x) having characteristic function of the form [5] ϕ(t)= e −γ|t| α (1) NOISE SOURCE LMS _ FxLMS Algorithm Fig. 1. Block diagram of FxLMS algorithm based single-channel feedforward ANC systems. where 0 <α< 2 is the shape parameter called as charac- teristics exponent, and γ> 0 is the scale parameter called as dispersion. If a stable random variable has a small value for α, then distribution has a very heavy tail, i.e., it is likely to observe values of random variable which are far from its central location. For α =2 it is Gaussian distribution, and for α =1 it is the Cauchy distribution. An SαS distribution is called standard if γ =1. In this paper, we consider ANC of impulsive noise with standard SαS distribution, i.e., 0 <α< 2 and γ =1. For stable distributions, the moments only exist for the order less than the characteristic exponent [5], and hence the mean-square-error criterion, which is bases for FxLMS algorithm, is not an adequate optimization criterion. Thus FxLMS algorithm may become unstable, when the primary noise is impulsive. There has been a very little research on active control of impulsive noise, at least up to the best knowledge of authors. In practice the impulsive noises do exist and it is of great meaning to study its control. In [6], the filtered-x least mean p-power algorithm (FxLMP) has been proposed, which is based on minimizing a fractional lower order moment (p-power of error) that does exist for stable distributions. It has been shown that FxLMP algorithm with p<α shows better robustness to ANC of impulsive noise. However, due to the calculation of fractional power at each iteration, the computational complexity of FxLMP algorithm may be formidable. In [7] a simplified variant of FxLMS algorithm has been proposed for ANC of impulsive noise. The basic idea is here to ignore the samples of the reference signal x(n) if its amplitude is above a certain value set by its statistics. This algorithm gives stable and robust performance, as compared with the FxLMS algorithm, for impulse noises with large α, 978-1-4244-2167-1/08/$25.00 ©2008 IEEE 330