Direction-of-arival estimation based on difference of L1 and L2 minimization

In this paper, we proposed an direction-of-arrival (DOA) estimation method based on difference L₁ and L₂ minimization. The dictionary is highly coherent in the application of DOA estimation, which brings about challenges to sparse signal reconstruction algorithms. Difference of L₁ and L₂ behaves closer to L₀ than L_p (0 <; p <; 2), and is able to produce better result in the case of highly coherent dictionary. Therefore, the better results are achievable when difference L₁ and L₂ minimization is employed to DOA estimation. In addition, the nested array is adopted in our method to improve the degrees of freedom (DOF). Simulation results illustrate that our method performs better than L_p minimization and spatial smoothing (SS)-MUSIC when snapshots are shortage.