RIS Aided Gridless 2D-DOA Estimation Via Decoupled Atomic Norm Minimization

Recently, atomic norm minimization (ANM) has been applied in the reconfigurable intelligent surface (RIS) aided direction of arrival (DOA) estimation problem in the non-line-of-sight (NLOS) propagation. However, most existing RIS-aided ANM (RIS-ANM) methods assume a uniform linear array (ULA) RIS which can only handle the one-dimensional (1D) DOA estimation. To this end, a novel RIS-aided gridless two-dimensional (2D) DOA estimation method is developed for a uniform planar array (UPA) RIS passive sensing system, where a general single-input multi-output (SIMO) transmission model is adopted. Specifically, a RIS-aided decoupled ANM (RIS-D-ANM) is proposed for gridless 2D-DOA retrieval. We show that the proposed RIS-D-ANM provides a decoupled formulation of the atomic norm instead of reshaping the 2D information via vectorization in the classic RIS-ANM method. Thus, the computational complexity of the original high-dimensional SDP problem is remarkably reduced without performance degradation. Furthermore, the computational cost is further reduced by integrating the alternating direction method of multiplier (ADMM), resulting in the RIS-aided decoupled ADMM (RIS-D-ADMM) method. Simulation results demonstrate the effectiveness of the proposed method.