Distributed FxLMS Algorithm Design and Analysis for Sinusoidal Reference Signal

This paper proposes a diffusion filter-x least mean square (FxLMS) algorithm when the input is the sinusoidal signal. By applying the z-transform technique, we obtain the transfer function between error signals and vibration signals, and further obtain the explicit expression of the steady-state of the error signal without algorithm iteration. Our algorithm has lower computational complexity than that with stochastic input signals on one hand, and on the other hand, the explicit expression can be used to estimate the vibration reduction magnitude of the algorithm in practical scenarios. Simulation is performed to validate the theoretical analysis.