DoA Estimation in RIS-Assisted Network via Element Sampling and Sparse Reconstruction

This work addresses a direction-of-arrival (DoA) estimation problem in a reconfigurable intelligent surface (RIS)-assisted network scenario. The accurate DoA information enables precise tracking and positioning of users for navigation, surveillance, and wireless communications. A strong direct link between the access point (AP) and the user is essential for DoA estimation. However, when the direct path between the AP and the user is obstructed, RIS is utilized as an alternate solution to provide the reflected path for localization. RIS has tunable and low-cost reflective elements that are uniformly placed on a panel. In this work, a novel strategy to sample the optimal number and locations of the RIS elements is proposed to enhance the DoA estimation accuracy. The proposed method optimally samples the RIS elements from a uniform linear RIS array (RIS ULA) while ensuring that the peak side lobe of the sampled sub-array is less than the fully populated RIS. Then, utilizing the sparsity of the target in the spatial domain, an atomic norm-based DoA estimation problem is formulated, keeping the number of elements, side-lobe level, and RIS reflection parameters in the constraint. This problem is solved using a modified semi-definite programming (SDP) algorithm. The numerical results show that the proposed method achieved a significant improvement in the DoA estimation performance as compared to existing methods.