Grid-less two-dimensional DOA estimation methods using uniform or sparse rectangular array

Two grid-less two-dimensional (2-D) direction of arrival (DOA) estimation methods using uniform rectangular array (URA) or sparse rectangular array (SRA) are proposed in this paper. Firstly, based on URA or SRA, the doubly Toeplitz structure of the covariance matrix of observed signals is established. Secondly, two reconstruction methods of the doubly Toeplitz matrix are presented, i.e., the least squares (LS) method and the reweighted atomic norm (RAN) methods. At last, the azimuth angles and elevation angles are estimated by the 2-D ESPRIT method efficiently. For simplicity, the two DOA estimation methods are denoted by LS and RAN, respectively. The LS method has lower complexity than recently proposed fast grid-less maximum likelihood (FGML) method, while maintain a similar DOA estimation performance. The RAN method has high complexity, while can achieve superior performance of DOA estimation. Numerical experiments verify the effectiveness and good performance of the proposed methods.