An alternating descent algorithm for the off-grid DOA estimation problem with sparsity constraints

In this paper, we present an iterative alternating descent algorithm for the problem of off-grid direction-of-arrival (DOA) estimation under the spatial sparsity assumption. Using a secondary dictionary we approximate the off-grid DOAs exploiting the method of Taylor expansion. In that way, we overcome the limitation of the conventional sparsity-based DOA estimation approaches that the unknown directions belong to a predefined discrete angular grid. The proposed method (SOMP-LS) alternates between a sparse recovery problem solved using the Simultaneous Orthogonal Matching Pursuit algorithm and a least squares problem. Experiments demonstrate the performance gain of the proposed method over the conventional sparsity approach and other existing off-grid DOA estimation algorithms.