RLS algorithm with convex regularization

In this letter, the RLS adaptive algorithm is considered in the system identification setting. The RLS algorithm is regularized using a general convex function of the system impulse response estimate. The normal equations corresponding to the convex regularized cost function are derived, and a recursive algorithm for the update of the tap estimates is established. We also introduce a closed-form expression for selecting the regularization parameter. With this selection of the regularization parameter, we show that the convex regularized RLS algorithm performs as well as, and possibly better than, the regular RLS when there is a constraint on the value of the convex function evaluated at the true weight vector. Simulations demonstrate the superiority of the convex regularized RLS with automatic parameter selection over regular RLS for the sparse system identification setting.