Radiomap Blind Prediction under Incomplete Observation: Error Characterization and Correctable Propagation-Prior Learning

Radiomap blind prediction infers radiomaps from observable representations of the propagation environment and base station (BS) configuration without field measurements. These representations are inherently incomplete and cannot uniquely determine the target radiomap. Under squared loss, we identify the conditional-mean radiomap as the population-optimal deterministic target and decompose domain risk into target-approximation error and irreducible uncertainty. The train-test risk gap motivates propagation priors as cross-domain guidance, although their partial or simplified forms may bias the attainable predictor. We therefore propose RadioDecomp, which treats a prior-guided predictor as a correctable base and uses deterministic residual refinement to learn its remaining predictable discrepancy. We instantiate RadioDecomp as RadioLSR (LoS-Shadow-Residual). Experiments under cross-configuration and cross-environment settings show that RadioLSR is especially effective for cross-configuration generalization and provides overall gains over a controlled monolithic counterpart under cross-environment generalization.

Diffusion models achieve high-fidelity radio map construction through iterative denoising, yet their sampling cost limits practicality in dynamic wireless systems where radio maps must be refreshed repeatedly. Meanwhile, classical propagation models encode valuable scene-level knowledge that standard diffusion inference discards entirely by initializing from pure Gaussian noise. This paper bridges propagation priors and diffusion refinement through a mid-start sampling strategy. A matched propagation prior is perturbed to an intermediate diffusion timestep, and the pretrained diffusion backbone executes only the remaining reverse steps, focusing computation on multipath-aware refinement rather than full reconstruction from noise. We provide theoretical analysis establishing an upper bound on the initialization gap, a sufficient condition under which truncation improves reconstruction fidelity, and a formal characterization of prior-quality sensitivity under aggressive truncation. Experiments on IRT4HighRes show that, at $P_{\text{start}}=0.5$, the proposed method achieves a $2.01\times$ speedup while simultaneously improving NMSE, RMSE, SSIM, and PSNR over the full-step baseline. A prior-quality ablation across three propagation models of different fidelity confirms that reconstruction quality tracks prior quality, with the sensitivity amplified under shorter reverse trajectories, consistent with the theoretical predictions. These results also suggest that mid-start reconstruction quality can serve as a proxy for ranking the scene-level fidelity of different propagation models.

Radio maps are important for environment-aware wireless communication, network planning, and radio resource optimization. However, dense radio map construction remains challenging when only a limited number of measurements are available, especially in complex urban environments with strong blockages, irregular geometry, and restricted sensing accessibility. Existing methods have explored interpolation, low-rank cartography, deep completion, and channel knowledge map (CKM) construction, but many of these methods insufficiently exploit explicit geometric priors or overlook the value of predictive uncertainty for subsequent sensing. In this paper, we study sparse gain radio map reconstruction from a geometry-aware and active sensing perspective. We first construct UrbanRT-RM, a controllable ray-tracing benchmark with diverse urban layouts, multiple base-station deployments, and multiple sparse sampling modes. We then propose GeoUQ-GFNet, a lightweight network that jointly predicts a dense gain radio map and a spatial uncertainty map from sparse measurements and structured scene priors. The predicted uncertainty is further used to guide active measurement selection under limited sensing budgets. Extensive experiments show that our proposed GeoUQ-GFNet method achieves strong and consistent reconstruction performance across different scenes and transmitter placements generated using UrbanRT-RM. Moreover, uncertainty-guided querying provides more effective reconstruction improvement than non-adaptive sampling under the same additional measurement budget. These results demonstrate the effectiveness of combining geometry-aware learning, uncertainty estimation, and benchmark-driven evaluation for sparse radio map reconstruction in complex urban environments.