A transform domain optimization to increase the convergence speed of the multichannel filtered-X least-mean-square algorithm

Abstract

The main drawback of the multichannel filtered-X LMS (FX-LMS) algorithm for the active noise control (ANC) of broadband disturbances is its low convergence speed when the filtered reference signals are strongly correlated, producing a large eigenvalue spread in the global correlation matrix. This correlation can be caused either by autocorrelation of the signals of the reference sensors, or by coupling between the ‘‘error paths’’ which introduces intercorrelation in the filtered reference signals. Multichannel versions of fast convergence monochannel algorithms exist (Newton-LMS, RLS, fast Kalman), but these algorithms either require too many computations for practical implementations, or they require the optimization of the controller to be performed at each sample, which can be a serious constraint. The purpose of this paper is to introduce a multichannel algorithm that has a high convergence speed and a low computational load, close to the FX-LMS. It is called the cosine transform filtered-X LMS (CTFX-LMS) because it uses a discrete cosine transform to eliminate the correlation that slows down the convergence process. The fundamental differences between this algorithm and many previously published frequency domain algorithms will be explained. Results of active noise control experiments in ducts will validate the convergence behavior of the new algorithm.