Performance analysis of single-frequency FxLMS algorithm without slow adaptation assumption

Abstract

Most performance analysis of filtered-x least mean square (FxLMS) was involved with slow adaptation assumption. However, this assumption introduces analytical errors in the transient stage of the algorithm, especially for long secondary paths. This paper presents a detailed analysis of single-frequency FxLMS algorithm for narrowband active noise control (NANC) removing slow adaptation assumption. Difference equations are derived by examining the convergence behavior of the discrete Fourier coefficients (DFC) of the secondary source. Closed-form steady-state expressions are obtained for the mean square error (MSE) and residual noise energy. An upper bound for the algorithm in the mean-square sense is also established. Simulation results indicate that the proposed analysis method is a better match with the simulation results. Furthermore, the narrowband update matrix is shown to be constant, unlike the signal-dependent matrix used in broadband ANC systems.