Feedforward Active Noise Control With a New Variable Tap-Length and Step-Size Filtered-X LMS Algorithm

Abstract

The fixed tap-length and step-size filtered-X least mean-square (FxLMS) algorithm is conventionally used in active noise control (ANC) systems. A tradeoff between the performance and the convergence rate is a well-known problem due to the choice of the step size. Although the variable-step-size FxLMS algorithms have been proposed for fast convergence, a long tap-length filter is frequently required in order to deal with different environments such that the convergence rate is still subject to a small step size for the long tap length. In this paper, we study a new ANC system with a variable tap-length and step-size FxLMS algorithm. Based on the assumption of an unsymmetric and two-sided exponential decay response model for the ANC control filter, the new FxLMS algorithm has the minimum mean-square deviation for the optimal filter coefficients. In the online secondary path modeling ANC system, simulation results show that the new algorithm with different kind of variable step sizes can provide significant improvements of convergence rate and noise reduction ratio, compared to the fixed-tap-length FxLMS algorithms.Index Terms-Active noise control, exponential decay response, filtered-X LMS, mean-square deviation, noise reduction ratio, secondary path model.

Adaptive variable step-size neural controller for nonlinear feedback active noise control systems

“…It is noted that in available variable step-size LMS algorithms (e.g. [25][26][27][28]), the convergence property of such adaptive parameters have rarely been addressed, and the ANC system stability with variable step-size is still not fully solved in the literature. Thus, the results of this paper may fill in this gap.…”

“…However, the convergence rate of conventional FXLMS algorithms may be unsatisfactory because the adopted constant learning gains (or step-size) may not be able to handle the wider operation regimes. To improve the convergence speed, several modifications have been introduced in [25][26][27][28]. The adjustment of the step-size parameter in [25] is implemented by minimizing the square of the control error.…”

“…Thus, an extra time average of the error variables was further incorporated in [26] to retain its performance in the presence of measurement noise. In the recent work [27,28], novel leakage terms have been imposed on the gradient-based algorithms to update the step-size parameters [27] and to adjust the tap length [28]. Although better performance can be obtained in comparison to [25], the increased computational costs and more stringent assumptions (e.g.…”

Multichannel Filtered-X Error Coded Affine Projection-Like Algorithm with Evolving Order

“…Therefore, implementation of the MFXLMS algorithm for multichannel systems demands considerable computational resources, making certain applications unfeasible. Variants of the FXLMS algorithm that improve the convergence speed using a variable step-size are proposed in [6,7]; nevertheless, they also require more computations. Other approaches enhance the convergence using different strategies such as convex combination of adaptive filters [8], adaptive IIR filters [9], training mechanism based on recursive least square algorithm [10], and the use of two adaptive filters [11]; however, those strategies involve a higher computational burden than the classic adaptive filters.…”

A recursive least square algorithm for active control of mixed noise

“…In [15], a variable tap-length and step-size FxLMS algorithm was proposed by Chang et al; this can self-adjust the required tap-length according to the environment and achieve fast convergence compared to the standard FxLMS algorithm. Although great progress has been made in active noise control, the techniques mostly target noise with relatively singular characteristics such as broadband noise, narrowband noise, harmonic noise, and sudden, instant, highintensity, discontinuous impulse noise.…”