Fast Low-rank Filtered-x Least Mean Squares for Multichannel Active Noise Control

The canonical algorithm for active noise control is the filtered-x least mean squares (FxLMS) algorithm. In the multichannel case, as the number of loudspeakers and microphones increases, the algorithm becomes very computationally costly. The dominant computational cost stems from a large number of linear convolutions with long impulse responses. In this paper a multichannel FxLMS algorithm is derived which makes use of and adaptively identifies a low-rank decomposition of the desired impulse responses. The low-rank decomposition can be used to implement a low-cost convolution, leading to an overall reduction in computational cost. This method does not add any latency, unlike frequency-domain approaches, which is important for broadband noise reduction. It is demonstrated through simulations that the proposed algorithm also provides similar or better noise reduction performance compared to the conventional FxLMS.