An Efficient Algorithm for Active Noise Control

Active noise control (ANC) systems have been increasingly researched and developed [1]. The use of the modified filtered-x structure for ANC using finite impulse response (FIR) adaptive filtering [2] will be assumed in the rest of this paper (Fig. 1). The multichannel versions of the filtered-x least-mean-square (FX-LMS) and the modified FX-LMS (MFX-LMS) algorithms are the benchmarks to which most adaptive filtering algorithms are compared, because they are widely used [1, 2]. In the field of adaptive filtering it is well known that fast affine projection (FAP) algorithms for ANC provide a good tradeoff between convergence speed and computational complexity [3–9, 11, 14]. It was also reported that in realistic cases where noisy plant models are used, FAP algorithms can be much more robust to plant model noise than more complex algorithms based on recursive least-squares, and they can achieve a better convergence performance at a lower cost [4, 6]. In [6], an efficient implementation based on Gauss-Seidel method has been proposed and adapted for nonlinear ANC using Volterra filtering in [15]. Also, a similar approach with that of [6] has been adapted for filtered-X structures in [7–9]. The numerical complexity of previously published affine projection (AP) algorithms for