Geometry-Aligned Differential Privacy for Location-Safe Federated Radio Map Construction

Radio maps that describe spatial variations in wireless signal strength are widely used to optimize networks and support aerial platforms. Their construction requires location-labeled signal measurements from distributed users, raising fundamental concerns about location privacy. Even when raw data are kept local, the shared model updates can reveal user locations through their spatial structure, while naive noise injection either fails to hide this leakage or degrades model accuracy. This work analyzes how location leakage arises from gradients in a virtual-environment radio map model and proposes a geometry-aligned differential privacy mechanism with heterogeneous noise tailored to both confuse localization and cover gradient spatial patterns. The approach is theoretically supported with a convergence guarantee linking privacy strength to learning accuracy. Numerical experiments show the approach increases attacker localization error from 30 m to over 180 m, with only 0.2 dB increase in radio map construction error compared to a uniform-noise baseline.