Convergence behavior analysis of FxLMS algorithms with different leaky term - Wen, Shulin (2023)
In order to improve the robustness of conventional filtered-X LMS (FXLMS) algorithm, different leaky terms are introduced into the cost function. With different leaky term, the convergence behavior differs much. The detailed derivation of LASSO based FXLMS (L1-FXLMS) and elastic-net based FXLMS (L1/2-FXLMS) algorithms are presented. In addition, sufficient conditions for guaranteed convergence are derived for FxLMS algorithms with different leaky term. Furthermore, the convergence behavior of L1-FXLMS and L1/2-FXLMS algorithms are compared with conventional FXLMS and leaky FXLMS (L2-FXLMS) algorithms. It is indicated that L1-FXLMS could have faster convergence speed than L2-FXLMS with the premise of guaranteed convergence. Simulation and experiments are conducted to test the sufficient boundaries for guaranteed convergence of different FXLMS algorithms.