Convergence Analysis of the Phase-Scheduled-Command FXLMS Algorithm with Phase Error

In this paper, a phase-scheduled-command filtered-x least mean square (FXLMS) algorithm with a phase error between the disturbance and command signal is analyzed in detail. The influence of the phase error on the control effort, convergence time constant and performance of convergence is explained for both stationary and nonstationary disturbance signal cases. An estimation ratio, in both stationary and nonstationary disturbance cases, of the pseudo-error MSE convergence performance is also developed and discussed. Simulation results were collected to verify the analysis. The results show that, for both stationary and nonstationary disturbance, the phase error may heavily increase the distance of the optimum vector from the initial value, leading to a large control effort, a large convergence time constant and poor convergence performance. The estimation ratio also has a satisfactory performance for estimating the influence of the phase error.