A Novel Vector-Decomposition-Based Structure for Enhancing the Normalized Filtered-X Least Mean Square Algorithm Under the High-Power Low-Frequency Noise

The normalized filtered-x least mean square (NFxLMS) algorithm adopts a normalized step size to improve the convergence and reduce the gradient noise caused by the high-power input signal. However, this normalization would introduce an even larger misadjustment than the FxLMS algorithm when this high-power noise is in a low-frequency range. To improve the performance of the NFxLMS algorithm in such an environment, a novel vector-decomposition-based structure (VDBS) is proposed in the paper. In this study, the filter weight vector is decomposed into two sub-vectors that are updated by different algorithms. The first sub-vector is updated by the NFxLMS algorithm, whereas the second one is updated by the FxLMS algorithm. In this way, the total misadjustment can be minimized by setting relevant parameters appropriately, while a faster convergence rate and smaller round-off errors can also be reached. The stability analysis proves that the proposed structure can enlarge the convergence range of the step size in the first sub-vector. The results of simulations and experiments justify that the VDBS can improve the performance of the NFxLMS algorithm for high-power low-frequency noise. The proposed structure can make the traditional NFxLMS algorithm perform better in a high-power low-frequency noise environment.