RIS-Enabled Joint Near-Field 3D Localization and Synchronization in SISO Multipath Environments

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 $l_{1}$ -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 $\acute {\text {e}}$ 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.