Direction-of-Arrival Estimation Using a Mixed $\ell _{2,0}$ Norm Approximation

A set of vectors is called jointly sparse when its elements share a common sparsity pattern. We demonstrate how the direction-of-arrival (DOA) estimation problem can be cast as the problem of recovering a joint-sparse representation. We consider both narrowband and broadband scenarios. We propose to minimize a mixed ℓ2,0 norm approximation to deal with the joint-sparse recovery problem. Our algorithm can resolve closely spaced and highly correlated sources using a small number of noisy snapshots. Furthermore, the number of sources need not be known a priori. In addition, our algorithm can handle more sources than other state-of-the-art algorithms. For the broadband DOA estimation problem, our algorithm allows relaxing the half-wavelength spacing restriction, which leads to a significant improvement in the resolution limit.