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

Wangqian Chen; Hao Wang; Yumeng Zhang; Chenghong Bian; Junting Chen; Jun Zhang

cs.NIOct 27, 2026

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

Authors: Wangqian Chen, Hao Wang, Yumeng Zhang, Chenghong Bian, Junting Chen, Jun Zhang

Organizations: The Hong Kong University of Science and Technology · The Chinese University of Hong Kong, Shenzhen

Abstract

Radio maps provide essential wireless propagation knowledge for network optimization and autonomous platforms. Acquiring dense measurements, however, is prohibitively costly, requiring active sampling to prioritize informative measurements. Existing active sampling methods typically rely on variances from prescribed spatial models or learned pointwise uncertainty, which may not fully capture the spatial correlation of different measurements. This paper proposes GraphBARC, a graph-structured active radio map construction framework that integrates learned spatial modeling with analytical Bayesian inference. A graph network learns correlated node and edge factors using only acquired measurements, inducing a joint full-map belief that supports analytical observation updates without retraining. Rather than immediate one-step acquisition, it adopts a nonmyopic sensing strategy that evaluates joint map-wide Bayes risk reduction over feasible multi-step routes, accounting for information redundancy among planned measurements. We reuse candidate responses and derive residual-based bounds directly on route-value differences, retaining shared response-error structure to avoid uniformly high-accuracy evaluation. An error-aware continuation bound screens unpromising prefixes, after which only responses needed for unresolved comparisons are refined. We further establish a computable decision-gap bound and show that certified exclusions remain valid during refinement. Experiments show that GraphBARC reduces mean root-mean-square error (RMSE) by over 16% relative to the evaluated baselines and core planning time by 56% compared with the fixed-accuracy, unpruned implementation.

Figures & tables

Figure 1: System scenario for active radio map construction, where a sensing platform sequentially acquires measurements and selects the sensing locations under sensing-budget constraints to improve overall reconstruction accuracy.

Figure 2: Overall implementation pipeline of GraphBARC. The graph-factor generator maps measurement context into interpretable Gaussian node and edge factors, which are assembled with new measurement information into the posterior system. Numerical posterior queries provide the map estimate and candidate responses for the decision-controlled multi-step planner, forming a closed loop between posterior inference and active sensing.

Figure 3: Observation-aware graph-factor generator. Local message passing and graph attention aggregate sparse measurement context, and the output heads produce Gaussian node factors and edge factors, which jointly define the full-map belief used for analytical assimilation and active sensing.

Figure 4: Visual comparison of reconstructed radio maps, normalized uncertainty maps, and spatial MAE distributions under 15% observation coverage.

Scheme	MAE (dB)	RMSE (dB)	NMSE
Flow Matching	$7.845$	$11.475$	$0.162$
DRUE	$7.726$	$11.110$	$0.292$
BAL-EGP	$4.307$	$6.311$	$0.176$
Proposed ( $K=1$ )	$3.886$	$5.711$	$0.107$
Proposed ( $K=4$ )	$\mathbf{3.609}$	$\mathbf{5.293}$	$\mathbf{0.103}$

Table 1: Reconstruction accuracy on common unobserved cells

Scheme	RMSE $\leq$ 5.5 dB		NMSE $\leq$ 0.11
	Num.	Relative	Num.	Relative
Flow Matching	$13{,}504$	$7.67\times$	$1{,}708$	$1.87\times$
DRUE	$11{,}140$	$6.33\times$	$4{,}248$	$4.66\times$
BAL-EGP	$2{,}908$	$1.65\times$	$4{,}428$	$4.85\times$
Proposed ( $K=1$ )	$1{,}840$	$1.05\times$	$1{,}132$	$1.24\times$
Proposed ( $K=4$ )	$\mathbf{1{,}760}$	$\mathbf{1.00}\times$	$\mathbf{912}$	$\mathbf{1.00}\times$

Table 2: Observations required to meet target reconstruction errors

Figure 5: RMSE versus observation coverage on a representative radio map.

Figure 6: Sampling trajectories generated by different active strategies.

Scheme	KNN	RBF	Matérn-GPR
Random	$6.201$	$5.529$	$5.675$
Flow Matching	$8.965$	$7.225$	$7.869$
DRUE	$7.975$	$6.269$	$6.657$
BAL-EGP	$6.566$	$5.696$	$5.841$
Proposed ( $K=1$ )	$5.979$	$5.520$	$5.735$
Proposed ( $K=4$ )	$\mathbf{5.470}$	$\mathbf{5.233}$	$\mathbf{5.332}$

Table 3: RMSE of independent reconstruction methods using measurements acquired by different sensing strategies

Scheme	10%		15%
	MAE	RMSE	MAE	RMSE
Random	4.326	6.569	3.559	5.481
1% + Active	3.742	5.704	3.160	4.774
2% + Active	4.019	6.217	3.162	4.891
3% + Active	4.073	6.336	3.209	4.846
4% + Active	3.879	5.986	3.194	4.916

Table 4: Sensitivity of reconstruction to the initialization ratios

Figure 7: Validity and tightness of decision-error bounds: a) Reference decision regret

r_{t}

versus the reported decision-gap bound

g_{t}

; b) Shared-to-separate error-radius ratio versus the number of shared measurement locations.

Scheme	Time (s)	PCG iterations ( $\times 10^{-3}$ )	Generated prefixes ( $\times 10^{-3}$ )	Route comp. ( $\times 10^{-3}$ )


Fixed-Gram	3.344	23.33	1558.3	672.7
Adaptive-Gram	2.886	14.42	1558.3	673.1
Pruned-Gram	1.348	14.42	58.34	15.98
Shared-Pruned	1.443	14.42	58.24	15.90

Table 5: Runtime and computational workload of four-step planning over 50 frozen states

Active Sensing

Active sensing studies how agents choose when, where, and what to measure to improve decisions under limited sensing budgets.

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Apr 7, 2026J/K move · Enter open · S save

Sparse Gain Radio Map Reconstruction With Geometry Priors and Uncertainty-Guided Measurement Selection

Zhihan Zeng, Ning Wei, Kaihe Wang, Phee Lep Yeoh+3

National Key Laboratory of Wireless Communications, University of Electronic Science and Technology of China (UESTC), Chengdu 611731, China · University of Electronic Science and Technology of China (UESTC), Chengdu 611731, China · School of Science, Technology and Engineering, University of the Sunshine Coast, Moreton Bay Campus, Petrie, QLD 4502, Australia+1

Radio Propagation Modeling Active Sensing Uncertainty Quantification

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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.

Abstract

Active Sensing

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