A distributed FxLMS algorithm for narrowband active noise control and its convergence analysis

A conventional multichannel narrowband active noise control (MNANC) system can effectively suppress low-frequency periodic noise. However, a large number of secondary sources and error sensors are required in the system, which leads to high computational complexity. To address this problem, a diffusion narrowband filtered-x least-mean-square (DNFxLMS) algorithm is proposed based on distributed acoustic sensor networks. The computational burden is dispersed among the nodes over the networks. A comprehensive statistical analysis of the algorithm is conducted to better understand its convergence properties. Specifically, we investigate the convergence behavior of the weight-error vector in the mean and mean-square sense. Based on this analysis, the stability bound of the system is discussed. The expressions for steady-state mean-square deviation (MSD) and excess mean-square error (EMSE) are derived. Extensive computer simulations are conducted to verify the theoretical analysis and to evaluate the usefulness of the DNFxLMS algorithm.