Abstract:

To improve the performance of existing two-dimensional (2-D) grid-less irection of arrival(DOA) estimation methods using the uniform rectangular array(URA) or sparse rectangular array(SRA), a novel 2-D grid-less DOA estimation method based on doubly Toeplitz matrix reconstruction and 2-D ESPRIT is proposed. First, using URA or SRA, the doubly Toeplitz structure of the associated covariance matrix is established. Second, by applying the log-det sparse metric and semi-definite positive constraints, the constrained optimization problem is presented and solved by the majorization-minimization (MM) algorithm. Finally, the azimuth angles and elevation angles are estimated by the 2-D ESPRIT method. The proposed method needs to solve semi-definite programming (SDP) problems repeatedly, which results in a high complexity, while it always provides a superior performance of DOA estimation. In simulations, the proposed method has a very small root-mean-square error (RMSE) in the case of URA and SRA, which can approach the Crammer-Rao bound. Simulation results prove the good performance of the proposed method.

Key words: 2-D direction of arrival estimation, grid-less, rectangular array, semi-definite programming, majorization-minimization