Unified Channel Estimation and Localization for RIS-Assisted Near-Field Terahertz Systems

Reconfigurable intelligent surfaces (RISs) have emerged as a key enabling technology for next-generation (xG) Internet-of-Things (IoT) networks operating in high-frequency bands such as terahertz (THz). Due to the large number of reflecting elements, RIS-assisted communications predominantly occur in the near-field region, where signal propagation is governed by spherical wavefronts. This far-field to near-field transition induces a nonlinear coupling between the channel response and the user position, which significantly complicates channel estimation and localization in RIS-assisted THz systems. Existing approaches typically address these two tasks separately, leading to redundant processing and error propagation between channel and position domains. To overcome these limitations, we propose a unified framework, termed near-field unified channel estimation and localization (NF-UCL), that exploits the intrinsic bijective correspondence between the near-field channel and the user position. We introduce the concept of a near-field channel map and show that its image, termed the near-field channel manifold, exhibits a smooth Riemannian structure. This geometric characterization enables the application of manifold optimization techniques for efficient joint processing. Specifically, we develop an Riemannian conjugate gradient (RCG)-based algorithm that performs channel estimation and localization directly on the near-field channel manifold. Simulation results demonstrate that the proposed NF-UCL framework outperforms conventional methods in terms of channel normalized mean square error (NMSE) and user position root mean square error (RMSE).