RIS-Enabled Joint Near-Field 3D Localization and Synchronization in SISO Multipath Environments
Han Yan, Hua Chen, Wei Liu, Songjie Yang, Gang Wang, Chau Yuen
Abstract
In this paper, we tackle the challenges of reconfigurable intelligent surfaces (RIS)-aided 3D localization and synchronization in multipath environments, focusing on the near-field of mmWave systems. Specifically, a maximum likelihood (ML) estimation problem is formulated for the channel parameters. To initiate this process, we leverage a combination of canonical polyadic decomposition (CPD) and orthogonal matching pursuit (OMP) to obtain coarse estimates of the time of arrival (ToA) and angle of departure (AoD) under the far-field approximation. Subsequently, distances are estimated using <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$l_{1}$ </tex-math></inline-formula>-regularization based on a near-field model. A refinement phase is introduced by employing the spatial alternating generalized expectation maximization (SAGE) algorithm. Finally, a weighted least squares approach is applied to convert channel parameters into position and clock offset estimates. To extend the estimation algorithm to ultra-large (UL) RIS-assisted localization scenarios, it is further enhanced to reduce errors associated with far-field approximations, especially in the presence of significant near-field effects, achieved by narrowing the RIS aperture. Moreover, the Cram<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\acute {\text {e}}$ </tex-math></inline-formula>r-Rao Bound (CRB) is derived and the RIS phase shifts are optimized to improve the positioning accuracy. Numerical results affirm the efficacy of the proposed estimation algorithm.