Design of causal preconditioning filters for adaptive filtering algorithms in real-time multi-channel active noise control applications

Abstract

Least-mean-square (LMS) algorithm has been widely used in the area of active noise control (ANC). One practical concern of LMS-based algorithms is its slow convergence rate in multi-channel broadband noise control applications. To improve the convergence speed of traditional LMS algorithm, preconditioning filters were added to the LMS system in previous studies to remove the correlation between the reference signals and decouple the plant responses. However, the preconditioning filters implemented previously are usually obtained through singular value decomposition of the cross spectral matrix of reference signals and the plant response matrix, which does not lead to causal preconditioning filters and, thus, it can only be applied in spatial audio applications when delay is not an important concern, but cannot be implemented in real-time active noise control applications. In the current work, a method is proposed to obtain a casual multi-channel preconditioning filter for real-time active noise control applications through a numerically robust algorithm to perform a spectral factor decomposition to the reference signal cross spectral matrix and a minimum-phase and all-pass decomposition to the multi-channel secondary path. Simulation results show that, by applying the proposed preconditioning filter, the convergence speed of the LMS algorithm can be significantly improved.