Computation-efficient solution for fully-connected active noise control window: analysis and implementation of multichannel adjoint least mean square algorithm

Abstract

The multichannel active noise control (MCANC) system, in which multiple reference sensors and actuators are used to enlarge the noise-cancellation zone, is widely utilized in complex acoustic environments. However, as the number of channels increases, the practicality decreases due to the exponential rise in computational complexity. This paper, therefore, revisits the adjoint least mean square (ALMS) algorithm and its multichannel applications. The computational analysis reveals that the multichannel adjoint least mean square (McALMS) algorithm1 has a significantly lower computation cost when implementing the fully connected active noise control (ANC) structure. In addition to this advantage, the theoretical analysis presented in this paper demonstrates that the McALMS algorithm can achieve the same optimal solution as the standard adaptive algorithm without the assumptions of input independence and white Gaussian noise. In addition, a practical step-size estimation strategy based on the Golden-section search (GSS) method is proposed to predict the fast step size of the McALMS algorithm. The numerical simulations in a multichannel ANC system demonstrate the effectiveness of the McALMS algorithm and validate the derived theoretical analysis. Furthermore, the McALMS algorithm with proposed step-size approach is used to implement a multichannel noise cancellation window that achieves satisfactory global noise reduction performance for tonal, broadband, and even real-world noises.