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

TL;DR

This work tackles joint 3D localization of a user and an unknown-pose hybrid RIS in a downlink multi-carrier system. It develops a multistage estimator that first extracts channel parameters (delays, AOAs/AODs, gains) and then computes the 3D positions, clock biases, and the HRIS rotation via an orthogonal Procrustes step, with FIM-based CRBs used to benchmark performance. The approach demonstrates CRB-attainment at moderate/high transmit powers, reveals a critical trade-off in the HRIS power-splitting ratio, and proves robustness to scattering paths. The results indicate that joint UE-HRIS localization is feasible with a single HRIS RX chain and a fusion center, potentially reducing calibration overhead for 6G sensing and positioning applications.

Abstract

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 Cramér-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.

Figures (6)

• Figure 1: The considered wireless system comprising a multi-antenna BS, a single-antenna UE, and a single-RX-RF HRIS. The 3D location of the UE and the 6D state of the HRIS are unknown.
• Figure 2: The evaluation of the proposed channel parameter estimator. The power splitting factor is set to $\rho=0.5$. (a) The RMSE of the TOAs; (c) The RMSE of the AOA/AODs.
• Figure 3: The evaluation of the proposed UE and RIS state estimator. The power splitting factor is set to $\rho=0.5$. (a) The RMSE of the position estimations; (b) The RMSE of the HRIS's rotation matrix estimation.
• Figure 4: The role HRIS position estimation on the UE positioning accuracy, and vice versa. The HRIS common power splitting factor and the BS transmit power were set to $\rho=0.5$ and $P_\text{B} = 15~\text{dBm}$, respectively.
• Figure 5: The effect of the HRIS common power splitting ration $\rho$ on the estimation performance when the BS transmit power is set to $P_\text{B}=\text{25dBm}$. (a) The effect on the position, TOA, and rotation matrix estimations; (b) The effect on the angles estimations.