A filtered-x weighted accumulated LMS algorithm: Stochastic analysis and simulations for narrowband active noise control system

In narrowband active noise control (NANC) systems, several modifications of the well-known filtered-x least-mean-square (FXLMS) algorithm have been proposed for improved operation. The filtered-x weighted accumulated LMS (FXWALMS) algorithm is a variant of the FXLMS algorithm obtained by introducing the momentum LMS (MLMS) algorithm into the conventional FXLMS algorithm. The version with momentum term of the adaptive algorithm is used in practical implementations aiming to increase convergence with moderate computational cost. In order to better understand the influence of the FXWALMS algorithm on the NANC system, statistical performance of such an algorithm is investigated in both the transient and steady-state behaviors. Different equations which describe the convergence behaviors of the mean and mean squared estimation errors for the discrete Fourier coefficients (DFCs) of the secondary source are derived and discussed in detail. Using related difference equations, the steady-state expressions for DFCs estimation mean square error and the residual noise mean square error are developed in closed forms. Moreover, a modified FXWALMS (MFXWALMS) algorithm is proposed to improve the overall performance of the system. Extensive simulations are conducted to prove the effectiveness of analytical results and the superior performance of the MFXWALMS algorithm in various scenarios.

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