A Generalized 2-D DOA Estimation Method Based on Low-Rank Matrix Reconstruction

While the sparse methods for 1-D direction-of-arrival (DOA) estimation are extensively studied in literature, the research for 2-D DOA estimation is rare. The main reason is that, for utilizing the on-grid or off-grid sparse methods, the 2-D continuous angle space should have to be discretized, which, however, may bring unacceptable computations due to the high dimensionality of the angle space. Hence, incorporating the gridless sparse methods which require no discretization into the 2-D DOA estimation is essential. In this paper, we propose a gridless 2-D DOA estimation method based on the low-rank matrix reconstruction and the Vandermonde decomposition theorem. We first reconstruct the covariance matrix with certain structure (i.e., low-rank, Toeplitz, and positive semidefinite), and then, retrieve the DOAs by using the Vandermonde decomposition theorem. We also present a theorem to guarantee that the true DOAs can be exactly recovered in certain condition. A faster algorithmic implementation is then given by deriving the dual problem of the original one. Our proposed method is applicable for both the uniform rectangular arrays and the sparse rectangular arrays. Extensive simulations are provided to evaluate its estimation performance and the adaptability to various array geometries.