Authors - Andrea Piroddi, Maurizio Torregiani Abstract - This paper introduces an information-theoretic framework for bounding the mutual information (MI) between the two-dimensional physical position of a user and the observed multiple-input multiple-output (MIMO) channel state information (CSI). Unlike classical Cram´er–Rao bounds or I-MMSE relations, the proposed approach explicitly incorporates the spatial variability of the channel via its Jacobian with respect to position. Two complementary results are derived: a local Jacobian-based characterization, valid under small prior spatial uncertainty with explicit validity conditions, and a global nonlinear upper bound via path-integral formulations that extends the analysis to arbitrary spatial distributions. Both are derived from first principles under clearly stated assumptions, and their relationship to classical Cram´er–Rao bounds, Fisher information, and Ziv–Zakai bounds is discussed. A quantitative tightness analysis across array sizes M ∈ {8, 16, 32, 64} shows that the local bound is nearly exact for small arrays and low SNR, while becoming progressively more conservative for larger configurations. A sensitivity analysis of the global bound to the reference point choice is provided, together with a principled method to reduce this sensitivity via the channel manifold centroid. Validation using Sionna RT ray tracing on the Munich urban scene reveals that realistic channels exhibit lower spatial variability than synthetic line-of-sight models, with direct implications for CSI-based localization design.
