Two-Dimensional Direction-of-Arrival Estimation via a Sparse Penalty Likelihood Method

This article proposes a two-dimensional $l_{1}$-penalized maximum likelihood (ML) method for estimating two-dimensional directions of arrival (2-D DOA) in L-shaped arrays. The method employs an $l_{1}$ -norm penalty term to promote sparsity in grid directions and uses complex elliptical symmetry (CES) distributed array outputs, which are robust. The 2-D DOA is decoupled into two independent one-dimensional (1-D) DOA estimations by angle decoupling, dramatically reducing computational complexity. Subsequently, the two 1-D DOAs are paired using the sub-dictionary spatial spectrum reconstruction (SSRSD) method. To solve the non-convex penalized ML optimization problem, an optimization function majorization-minimization (MM) algorithm is developed, and an improved Bayesian information criterion (BIC) is used to select suitable penalty parameters. Simulation results demonstrate that the proposed method exhibits high robustness, estimation accuracy, and pairing effectiveness in low signal-to-noise ratio scenarios.