Convergence behavior analysis of FxLMS algorithm with different leaky term

In order to improve the robustness of conventional filtered-X LMS (FXLMS) algorithm, different leaky terms are introduced into the cost function. With di erent 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, su cient conditions for guaranteed convergence are derived for FxLMS algorithms with different leaky term. Furthermore, the convergence behavior of Ll-FXLMS and L1/2- FXLMS algorithms are compared with conventional FXLMS and leaky FXLMS (L2-FXLMS) algorithms. It is indicated that Ll-FXLMS could have faster convergence speed than L2- FXLMS with the premise of guaranteed convergence. Simulation and experiments are conducted to test the su cient boundaries for guaranteed convergence of different FXLMS algorithms.