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

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. Copyright © 2012 John Wiley & Sons, Ltd.