1Regularized Least-Mean-Square Algorithms

Abstract—We consider adaptive system identification problems with convex constraints and propose a family of regularized Least-Mean-Square (LMS) algorithms. We show that with a properly selected regularization parameter the regularized LMS provably dominates its conventional counterpart in terms of mean square deviations. We establish simple and closed-form expres-sions for choosing this regularization parameter. For identifying an unknown sparse system we propose sparse and group-sparse LMS algorithms, which are special examples of the regularized LMS family. Simulation results demonstrate the advantages of the proposed filters in both convergence rate and steady-state error under sparsity assumptions on the true coefficient vector. Index Terms—LMS, NLMS, convex regularization, sparse system, group sparsity, l1 norm I