Convergence analysis of multichannel ANC system using FXLMS algorithm with inexact secondary path model

The paper conducts the convergence analysis of multichannel an active noise control (ANC) system using a filtered-X least-mean-square (FXLMS) algorithm with inexact secondary path modeling. An update equation of the excess mean-square error (MSE) is developed first. A criterion on secondary path modeling for the convergence of the excess MSE is then derived, which reveals that the convergence rate can be enhanced by choosing the secondary path models appropriately. Next, an upper bound on the step size of the update equation is derived. Furthermore, the steady-state excess MSE is expressed explicitly for a thorough insight into the steady-state response of the system. Computer simulations verify that our theoretical analysis can predict accurately the performance of a feedforward multichannel ANC system with inexact secondary path modeling.