Joint 3D User and 6D Hybrid Reconfigurable Intelligent Surface Localization

The latest assessments of the emerging technologies for reconfigurable intelligent surfaces (RISs) have indicated the concept's significant potential for localization and sensing, either as individual or simultaneously realized tasks. However, in the vast majority of those studies, the RIS state (i.e., its position and rotation angles) is required to be known a priori. In this paper, we address the problem of the joint three-dimensional (3D) localization of a hybrid RIS (HRIS) and a user. The most cost- and power-efficient hybrid version of an RIS is equipped with a single reception radio-frequency chain and meta-atoms capable of simultaneous reconfigurable reflection and sensing. This dual functionality is controlled by adjustable power splitters embedded at each hybrid meta-atom. Focusing on a downlink scenario where a multi-antenna base station transmits multicarrier signals to a user via an HRIS, we propose a multistage approach to jointly estimate the metasurface's 3D position and 3D rotation matrix (i.e., 6D parameter estimation) as well as the user's 3D position. Our simulation results verify the validity of the proposed estimator via extensive comparisons of the root-mean-square error of the state estimations with the Cram\'{e}r-Rao lower bound (CRB), which is analytically derived. Furthermore, it is showcased that there exists an optimal hybrid reconfigurable intelligent surface (HRIS) power splitting ratio for the desired multi-parameter estimation problem. We also study the robustness of the proposed method in the presence of scattering points in the wireless propagation environment.