Variable size LMS algorithm with fast convergence capabilities for Active Noise Control

Active Noise Control (ANC) applications can be divided into two groups: fixed, optimal or suboptimal, and adaptive. Adaptive ANC solutions use almost exclusively Least Mean Squares (LMS) algorithm (or its modifications) to perform adaptation. This simple, robust, and computationally inexpensive algorithm has one drawback: the need of careful step size adjustment. Too large step size may cause loss of stability; to small step size results in small adaptation speed and degrades ANC performance in nonstationary environments. Therefore, numerous Variable Step Size (VS) modifications can be found in the literature. This paper presents a contribution within this field: a VS-LMS algorithm designed with the aim of fast adaptation. Fast adaptation is crucial in many ANC applications, e.g. in large industrial halls, where the silence zone should follow persons moving in these rooms. The design procedure used in the presented work involved development of the new LMS stability condition. The condition was obtained through discrete system analysis rather than through statistical theory. Moreover, the condition does not use the small step size assumption which is not obeyed during the phase of fast convergence. Based on this condition the VS-LMS was designed that can use almost largest possible step size without loss of stability. Computer simulations validated the correctness of the new condition and showed high performance of the proposed VS-LMS algorithm.