Mean weight behavior of the FXAFA LMS algorithm

In this correspondence, the recently proposed filtered-X adaptive filtering with averaging (FXAFA) algorithm is analyzed. This adaptive algorithm is aimed at applications of active control of noise and vibration. The FXAFA least-mean-square (LMS) algorithm is a member of the family of filtered-X LMS (FXLMS) algorithms; thus, its stochastic analysis must be carried out without invoking the independence assumption. This fact is shown here by deriving an analytical model for the mean behavior of the adaptive filter weights. It is also shown that both FXAFA and FXLMS algorithms have the same steady-state value of the adaptive weight vector. Monte Carlo simulations verify the accuracy of the theoretical model here derived.