Norm-constrained adaptive algorithms for sparse system identification based on projections onto intersections of hyperplanes

•A new approach for developing norm-constrained adaptive algorithms is presented.•The new approach uses projections onto intersections of hyperplanes.•Adaptive algorithms based on the l0 and the l1 norms are developed.•Enhanced algorithms with reduced number of parameters are also developed.•Simulation results ratify the effectiveness of the proposed algorithms.

This paper introduces a novel approach to derive norm-constrained adaptive algorithms for sparse system identification. In contrast to other similar approaches found in the literature, the proposed approach is focused primarily on keeping the a posteriori error equal to zero (which is a characteristic of the normalized least-mean-square algorithm) while seeking to satisfy a norm constraint. To this end, the proposed algorithms look directly for a vector belonging to the intersection of a zero-error hyperplane and a hyperplane resulting from a relaxed norm constraint. This somewhat simpler strategy leads to effective sparsity-promoting adaptive algorithms that exhibit low computational complexity and use parameters that are easy to adjust. In this context, a general framework that allows obtaining adaptive algorithms using different norm functions is devised. From this framework, two norm-constrained algorithms based on the ℓ1 and ℓ0 norms are obtained. Moreover, enhanced versions of these algorithms are developed aiming to make them independent of user-defined norm-bound parameters. Numerical simulation results corroborate the effectiveness of the proposed framework as well as the very good performance of the obtained algorithms.