A theoretical study of convergence characteristics of a multiple channel ANC system

Most active noise control (ANC) systems are based on feedforward structure with adaptive filters, which are updated with the filtered-x LMS algorithm or the multiple error filtered-x (MEFX) LMS algorithm. The convergence characteristics of these algorithms have been studied mostly in the time domain, and it was found that the convergence properties are subject to the distribution of the eigenvalues of the autocorrelation matrix of the filtered reference signal. Analysis in the time domain, however, requires a great deal of computation, and its physical meaning is unclear. This paper presents a method for evaluating the adaptive algorithm for the ANC system with multiple noise sources and multiple control points in the frequency domain. In this method, the convergence characteristics of the MEFX LMS algorithm are evaluated separately by the determinant or eigenvalues of the matrix, which are composed of transfer functions between the secondary sources and the control points, and the correlations among the outputs of the reference sensors.