Direction-of-Arrival Estimation Through Exact Continuous ℓ2,0-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
$\ell _{2,0}$
pseudo-norm. In this work, we show that an exact relaxation of this problem can be obtained by replacing the
$\ell _{2,0}$
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
$\ell _{2,0}$
-regularized criteria. We then show on numerical simulations that the minimization of the proposed relaxation with an iteratively reweighted
$\ell _{2,1}$
algorithm leads to an improved performance over traditional approaches.