A modified least mean square Newton algorithm based on block coordinate descent for multi-reference active noise control

In some feedforward active noise control systems, more references are required to increase the noise reduction performance; however, the convergence speed of adaptive algorithms usually decreases, and the computational complexity increases when the number of reference channels increases. In this paper, a modified least mean square Newton (LMS-Newton) algorithm based on block coordinate descent is proposed. By dividing the control filter into channel-wise blocks and updating each block sequentially, the proposed algorithm reduces computational complexity while retaining the convergence performance of conventional LMS-Newton algorithms. Theoretical analysis demonstrates that the proposed algorithm can converge to the Wiener solution under a reliable estimation of the correlation function. The simulation results using the measured road noise data with 42 reference signals show that the proposed algorithm reduces the convergence time of the filtered-x normalized least mean square (FxNLMS) algorithm and achieves 11.1 dBA and 9.9 dBA noise reduction at the left and right ears within 40 s. The proposed algorithm achieves a 74% reduction in computational complexity compared to the FxNLMS algorithm and a 98% reduction compared to the LMS-Newton algorithm.