Physics-Aware Query-Conditioned Graph Attention Networks for Radio Map Estimation

Radio map estimation from sparse measurements is fundamental to wireless network planning, optimization, and localized map updating. Most recent learning-based approaches formulate the problem as dense map completion over a predefined grid, whereas many practical deployments require estimating transmitter-specific received signal strength only at queried locations or refining an existing map after local changes. This paper proposes a physics-aware query-conditioned hierarchical graph attention network for transmitter-resolved point-wise radio map estimation. For each queried target--transmitter pair, the proposed encoder constructs a bounded local graph over sampled reference observations and aggregates reference-to-query evidence through transmitter-referenced geometric descriptors. A global graph then exchanges representation-level context among nearby target locations to improve neighborhood consistency without revisiting a large number of reference measurements. On top of this shared architecture, we instantiate three operating regimes: direct RSS estimation, prior-conditioned residual correction, and post-hoc gated attenuation of the learned correction. The framework uses only measurement-side quantities and does not rely on environment-side inputs. Simulations on the DeepMIMO scenario show that, in the direct regime, the proposed HGAT achieves the lowest RMSE and MAE among the evaluated learning-based baselines on all reported sites. When conventional prior estimate is available, the residual and gated regimes further reduce the prior error.