Posterior Error Energy Minimization Based Combined FxNLMS and FxLMS Algorithm for Active Noise Control

The filtered-x normalized least mean square (FxNLMS) algorithm is widely used in active noise control (ANC) systems. However, for cyclostationary input signals, the noise reduction performance of the FxNLMS algorithm is affected by the periodic power of cyclostationary inputs, which leads to a larger steady-state mean square deviation (MSD) than the filtered-x least mean squares (FxLMS) algorithm. In this paper, a new adaptive combination algorithm of FxNLMS and FxLMS is proposed to suppress cyclostationary input noise with fast convergence and low steady-state MSD. The mixing parameter for combining the two algorithms is obtained by minimizing the energy of the posterior error and updated using the time-average method. The mathematical analysis including the mean square convergence and computational complexity are performed. The simulation results show that the proposed combined-FxNLMS-FxLMS algorithm can efficiently combine the respective advantages of FxNLMS and FxLMS algorithms and improve the noise reduction performance of the ANC system.