Two variants of the FxLMS algorithm

We present a time-domain feedback analysis of the FxLMS algorithm, which has been receiving increasing attention in the literature due to its potential application in the active control of noise. In particular, we introduce a generalized FxLMS variant and derive conditions for its l ₂-stability. We also show that the algorithm can in fact be regarded as a member of the class of filtered-error variants. A special case of the generalized algorithm is the so-called MFxLMS recursion, which refers to a recent modification of the standard FxLMS update. While this modification significantly improves the convergence behaviour of FxLMS, it requires of the order of 3M elementary computations per time step. This is in contrast to the 2M operations required by the standard FxLMS. We suggest two new modifications that keep the computational load at the 2M level, and which present improved convergence over the FxLMS algorithm. Simulation results are included to demonstrate the points raised in the paper