In the field of echo cancellation, the normalized least mean squares (nlms) algorithm is the most popular adaptive algorithm due to its simplicity and ease of implementation. However, this category of algorithms prese...
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In the field of echo cancellation, the normalized least mean squares (nlms) algorithm is the most popular adaptive algorithm due to its simplicity and ease of implementation. However, this category of algorithms presents a conflict between several performance criteria: the initial convergence speed, the tracking ability and the root mean square error of filtering (MSE) in the steady state. Variable-step algorithms (VSS) address the trade-off between convergence speed and low final MSE. Nevertheless, due to a fairly small adaptive step-size in the steady-state regime, they fail to adequately track variations of the unknown system and they are all implemented with the original nlmsalgorithm. In this contribution, a new improved variable adaptation step algorithm capable to track time variations of the unknown system even after good convergence in the steady state is suggested. It is based on the use of the fast-normalized adaptive algorithm (Fnlms) for system identification and acoustic echo cancellation context. The purposes of using the Fnlmsalgorithm in the field of VSS are on the one hand to improve its final MSE and, on the other hand, to obtain a VSS algorithm with better convergence and tracking compared to the VSS nlmsalgorithms. Simulation results show that the proposed VSS-fast nlms algorithm outperforms the original Fnlmsalgorithm in terms of steady-state error reduction and minimization after the initial transition phase while maintaining similar convergence speed and tracking capacity. Furthermore, it achieves visible improvements in terms of two objective criteria, i.e., a faster initial convergence rate and a better tracking ability than the ones of the non-parametric VSS-nlms (NPVSS-nlms) and traditional nlmsalgorithms.
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