Geometric Information Bounds for CSI Manifolds in Hybrid 6G Networks

This paper proposes a novel information-theoretic upper bound on the mutual information between the physical position of a user and the observed MIMO channel state information (CSI). Unlike classical Cram’er-Rao bounds or I-MMSE relations, our bound explicitly incorporates the spatial variability of the channel via the Jacobian of the channel with respect to position. We provide a derivation for both local linearized models and global nonlinear bounds, highlighting the dependence on array geometry and multipath structure. The results offer new insight into the intrinsic information available for position estimation and semantic localization in wireless networks.