A Sheaf-Theoretic Framework for Distributed Multi-Site Channel Charting

Channel charting (CC) enables data-driven user localization in wireless networks by embedding channel state information (CSI) into low-dimensional representations. In multi-cell scenarios, each base station independently learns a local chart via neural encoders, leading to misaligned representation spaces across overlapping coverage areas. This lack of consistency hinders network-level tasks such as user tracking, handover prediction, and resource allocation. To address this issue, we propose a principled framework for multi-site channel charting based on topological signal processing. We model the collection of local charts as a network sheaf, which encodes consistency constraints across the network and enables the coherent integration of locally learned representations into a shared global structure. This formulation introduces an interpretable inductive bias that promotes alignment across base stations while preserving local geometric fidelity. Building on this model, we develop a multi-site channel charting architecture and an alternating optimization algorithm that jointly updates neural encoders and inter-site orthogonal transport maps, with theoretical guarantees on consistency. Experimental results validate the effectiveness of the proposed approach, demonstrating improved cross-site alignment without degrading the quality of local embeddings.