Convex Optimization-Based 2-D DOA Estimation with Enhanced Virtual Aperture and Virtual Snapshots Extension for L-Shaped Array

We address the two-dimensional direction-of-arrival (2-D DOA) estimation problem for L-shaped ULA by developing an algorithm represented by the convex optimal method. In this paper, the generalized conjugate symmetry property of L-shaped ULA is fully developed to increase not only virtual array aperture but virtual snapshots, which not only increases the maximum resolvable sources but yields better 2-D DOA estimation performance. Specifically, we first formulate the cost function as a quadratically constrained complex quadratic programming (QCCQP) problem via the subspace theory. The QCCQP problem can then be relaxed to a series of semidefinite programming (SDP) problems, which can be solved via the CVX solvers in polynomial time complexity per iteration. To avoid complex 2-D global iterations during the implementation of SDP problems, the PM-ESPRIT-like method is first applied to estimate azimuths, based on which, the proposed method can then be transformed to 1-D local iterations with no additional angles pairings needed. Furthermore, the superb performance of the proposed method still holds whether the spatial angles are very close or separate apart. Performances evaluations are confirmed based on multiple simulations examples and some criteria.