Homotopy RLS-DCD adaptive filter

In this paper, we propose a computationally efficient adaptive filtering algorithm for sparse identification. The algorithm is based on a recently proposed sparse recovery technique that exploits homotopy iterations, dichotomous coordinate descent iterations, and reweighting iterations. When combined with a low-complexity warm-start in RLS-like adaptive filters and leading DCD iterations for l1 (lasso) penalized least squares fitting, this homotopy technique results in an efficient RLSlike adaptive filtering algorithm. A significant advantage of the proposed algorithm compared to many other advanced sparse adaptive algorithms is that its computational complexity is only linear in the filter length. Moreover, most of the computations in the proposed algorithm are performed on the support, which can be significantly smaller than the filter length, thus making the complexity low. Numerical examples show that the proposed technique achieves an identification performance better than that of advanced sparse adaptive filters, such as SPARLS, l1-RLS and l0-RLS, and its performance is close to the oracle performance.