Direction-of-Arrival Estimation through Exact Continuous l20-Norm Relaxation

On-grid based direction-of-arrival (DOA) estimation methods rely on the resolution of a difficult group-sparse optimization problem that involves the l20 pseudo-norm. In this work, we show that an exact relaxation of this problem can be obtained by replacing the l20 term with a group minimax concave penalty with suitable parameters. This relaxation is more amenable to non-convex optimization algorithms as it is continuous and admits less local (not global) minimizers than the initial l20-regularized criteria. We then show on numerical simulations that the minimization of the proposed relaxation with an iteratively reweighted l21 algorithm leads to an improved performance over traditional approaches.