Statistical-mechanical analysis of the FXLMS algorithm for multiple-channel active noise control

We analyze the behaviors of the Filtered-X LMS (FXLMS) algorithm for active noise control (ANC). Correlations between the impulse response of an adaptive filter and a primary path are treated as macroscopic variables. To obtain the correlations, we analytically solve the equations and finally compute the MSE. In particular, we analyze the behaviors of multiple-channel ANC. We theoretically show that the MSE is affected by the secondary paths that are not directly connected.