Learning Graph Beliefs for Active Radio Mapping With Decision-Certified Multi-Step Sensing

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.

Learning-based radio map estimation (RME) plays a critical role in UAV-assisted wireless sensing, enabling tasks such as coverage prediction and network optimization. Most current methods assume an independently and identically distributed (i.i.d.) training and testing setting based on random sampling. However, practical UAV measurements are collected sequentially along feasible trajectories, resulting in highly structured and spatially correlated patterns. This mismatch introduces a sampling distribution shift that increases the intrinsic difficulty of spatial field recovery and compromises the generalization of models trained under i.i.d. assumptions. To mitigate this issue, we propose a trajectory-aware training paradigm based on Stochastic-Triggered Trajectory-Based Sampling (ST-TBS), which preserves trajectory continuity while introducing sampling variability. Moreover, from a statistical perspective, we show that trajectory-based sampling reduces spatial diversity and increases information redundancy compared to random sampling. Extensive experiments on the RadioMapSeer and SpectrumNet datasets demonstrate that models trained with random sampling suffer significant performance degradation under trajectory-based observations, with RMSE increasing from 0.0391 to 0.2632 on SpectrumNet. Conversely, our proposed ST-TBS method effectively reduces the RMSE to 0.0571. These results highlight the necessity of aligning training and deployment sampling distributions for reliable RME.

Radio map (RM) estimation aims to reconstruct the spatial distribution of wireless signal characteristics, such as received signal strength (RSS), from sparse measurements, a task that is critical for spectrum management, interference mitigation, and localization in modern wireless networks. Traditional approaches, including interpolation and deep learning, either struggle to capture complex propagation effects or require large-scale retraining for each new sampling pattern, which limits their generalization. More recently, prior-based methods have combined pre-trained generative models with measurements to reduce the need for deployment-time model fine-tuning, but they typically treat the prior as a simple regularizer and lack explicit transmitter-aware integration. In this paper, we propose RadioTrace, a novel RM estimation framework without deployment-time fine-tuning that tightly integrates sparse RSS measurements with a frozen pre-trained diffusion prior. RadioTrace incorporates transmitter (Tx) location estimation directly into the denoising loop, iteratively refining Tx coordinates based on reconstruction quality to guide the generative process. To further enhance robustness, we introduce a propagation-guided K-means initialization that mitigates poor local minima in the Tx update and provides a geometry-consistent starting point. Moreover, we provide a stochastic stability analysis for the Tx-coordinate refinement component, showing that the Tx update remains stable under perturbations induced by diffusion sampling and Tx-map relaxation. Extensive experiments demonstrate that RadioTrace achieves competitive performance with state-of-the-art learning-based methods under random sampling, and maintains strong reconstruction quality under restricted-area sampling, highlighting its adaptability, robustness, and practical relevance.