Development and convergence analysis of new least-mean-square-based algorithm equipped with exponential-decay step size and disturbance compensation for active noise control

摘要

In real-world active noise control (ANC) applications, disturbance can be picked up by error sensors and significantly degrade the steady-state ANC performance. This study proposes two techniques in combination with a least-mean-square (LMS) based ANC algorithm, named normalized filtered-x LMS/commutation error (NFxLMS/CE) algorithm, to deal with the disturbance that is independent of a reference signal. A new stochastic method to analyze convergence properties of the NFxLMS/CE algorithm under influence of the disturbance is first established. Given that the reference signal is persistently exciting of sufficient order, exponential convergence of the algorithm is derived with a step-size condition. An exponential-decay step size (EDSS) is then proposed to obtain a new ANC algorithm referred to as EDSS-NFxLMS/CE algorithm. In addition, a disturbance-compensation (DC) technique is developed for the EDSS-NFxLMS/CE algorithm to obtain an EDSS-NFxLMS/CE_DC algorithm such that the influence of the disturbance can be reduced. It is shown that the EDSS-NFxLMS/CE_DC algorithm is exponentially convergent. Moreover, computer simulations show that the EDSS-NFxLMS/CE_DC algorithm can achieve a better ANC performance in terms of convergence rate and level of noise reduction as compared with that using the EDSS-NFxLMS/CE algorithm without DC and that using NFxLMS/CE_DC algorithm of constant step sizes. These results support the effectiveness of the proposed techniques and EDSS-NFxLMS/CE_DC algorithm.