Radio maps are essential for wireless decision-making tasks such as access-point placement, coverage planning, and localization, but their fine spatial details are governed by complex propagation effects and are costly to simulate accurately. Machine learning offers a path to high-fidelity radio-map prediction without running expensive high-fidelity simulations for every scene. However, generating high-quality training labels at scale is also difficult: the affordable labels come from finite-ray simulations, which are richer than low-fidelity inputs but carry residual Monte Carlo noise. We address this challenge with Physics-Unrolled Hybrid Neural Operator (PU-HNO), a three-stage cascade that predicts high-fidelity indoor radio maps from low-fidelity ray-tracing outputs and scene priors by progressively capturing reflection, diffraction, and scattering effects, rather than treating radio maps as generic images. We prove that, under conditionally unbiased label noise, the model can learn stable propagation structure and outperform its own training labels. Experiments across diverse floorplans show that PU-HNO outperforms image-to-image baselines, wireless learning models, and monolithic neural operators across both image-quality and wireless deployment metrics.
Figures & tables
Figure 1: PU-HNO predicts high-fidelity radio maps from low-fidelity inputs and intermediate-fidelity supervision.
Figure 2: Individual propagation mechanisms jointly shaping the radio map.
Figure 3: PU-HNO estimates high-fidelity radio maps using a three-stage neural-operator architecture that captures different wireless propagation mechanisms.
Wireless Performance
Computer Vision / Generic
Model Family
Model
Outage F1 ↑
Fading Ratio ≈1
Tail Error (5%) ↓
MCESE ↓
RMSE (dB) ↓
MAE (dB) ↓
SSIM ↑
LPIPS ↓
SIONNA
Training Labels
0.172
1.782
1.661
1.311
14.012
5.486
0.725
0.476
Computer Vision
CNN
0.490
0.799
1.043
1.443
4.798
3.152
0.904
0.277
UNET
0.178
0.815
0.448
1.076
3.851
2.326
0.919
0.266
RESNET
0.107
0.761
0.531
1.152
4.228
2.692
0.905
0.291
VIT
0.017
1.495
0.145
1.637
15.310
6.188
0.652
0.475
Table 1: Quantitative radio map prediction results showing that PU-HNO consistently outperforms all baselines across wireless and computer vision metrics.
Figure 4: PU-HNO recovers fine details from noisy labels and approaches the high-fidelity reference.
Category
Variant
Outage F1 ↑
Fading Ratio ≈1
Tail Error ↓
RMSE (dB) ↓
SSIM ↑
Learning Paradigm
1A: Single Target (No Curr)
0.637
1.124
0.927
3.787
0.927
1B: Progressive (No Curr)
0.784
0.956
0.217
3.407
0.926
Loss Formulation
2A: w/o Sobolev Gradient
0.111
0.814
0.381
3.584
0.923
2B: w/o Transport (Ray)
0.740
0.910
1.273
3.512
0.916
2C: Unweighted Masked Huber
0.128
0.818
0.197
3.655
0.916
Engineered Priors
3A: w/o Geometric Priors
0.780
0.967
0.110
3.660
0.923
Table 2: Ablation study showing that PU-HNO benefits from its staged architecture, geometry priors, and propagation-aware losses.
Figure 5: Model sensitivity to structural distribution shifts and training label noise.
Appendix figures & tables10 assets
Supplementary material from the paper’s appendix.
Appendix
Figure 6: Representative training and test floorplans. Environments are procedurally generated via recursive binary space partitioning (BSP) and randomized furniture spawning. The test set introduces structural distribution shifts by expanding the permitted range of room and obstacle counts beyond the training distribution.
Figure 7: Qualitative evaluation of radio map reconstruction. PU-HNO accurately recovers the High-Fidelity Ground Truth (HF-GT) field from sparse LF-Inputs. Baselines such as GeNeRT (a) and SFNO (b) struggle to preserve these sharp, deployment-critical details and exhibit significant over-smoothing.
Component
Trainable parameters
Shared encoder, conditioning, and projection heads
∼187 K
Stage 1 (specular)
∼1.56 M
Stage 2 (diffraction)
∼614 K
Stage 3 (scattering)
∼147 K
Total
∼2.50 M
Appendix
Table 3: Parameter budget by component. Counts are obtained by instantiating the model used for the reported results and summing over the corresponding submodules. Totals are rounded to the nearest thousand.
Term
Symbol
Value
Stage-1 reconstruction
λ1
0.55
Stage-2 reconstruction
λ2
1.00
Stage-3 reconstruction
λ3
1.60
Sobolev gradient
λsob
0.15
Stage-1 transport feature
μ1
0.20
Stage-2 transport feature
μ2
0.28
Appendix
Table 4: Loss hyperparameters used for all reported runs. “Distance scale” refers to rscale in Eq. ( 14 ), in physical units relative to the 15m×15m floorplan.
Symbol
Quantity
Value
Tout
Outage threshold
−100 dBm
B
Bandwidth
20 MHz
F
Receiver noise figure
7 dB
NdBm
Thermal noise floor (per Eq. ( 25 ))
≈−94 dBm
Ymin
Simulator floor for valid mask
−150 dB
R
Dynamic range for PSNR
170 dB
Appendix
Table 5: Constants used by the wireless deployment metrics. These values are fixed across all reported experiments and are taken from standard 5–6 GHz indoor wireless practice.
Figure 8: Performance comparison across generic and wireless-specific metrics with 95% bootstrap confidence interval.
Family
Model
F1 ↑
R ↑
Fad. ≈1
SE5 ↓
MCESE ↓
RMSE ↓
MAE ↓
PSNR ↑
SSIM ↑
ESSIM ↑
LPIPS ↓
DISTS ↓
Grad ≈1.58
Label
IF-GT
0.172
0.991
1.782
1.661
1.311
14.012
5.486
21.679
0.725
0.405
0.476
0.294
9.348
CV
CNN
0.490
0.348
0.799
1.043
1.443
4.798
3.152
30.989
0.904
0.548
0.277
0.202
1.380
CV
U-Net
0.178
0.100
0.815
0.448
1.076
3.851
2.326
32.897
0.919
0.551
0.266
0.199
1.388
CV
ResNet
0.107
0.058
0.761
0.531
1.152
4.228
2.692
32.085
0.905
0.509
0.291
0.211
1.368
CV
ViT
0.017
0.045
1.495
0.145
1.637
15.310
6.188
20.909
0.652
0.157
0.475
0.336
10.313
Wireless
NeRF 2
0.026
0.015
0.696
1.725
3.406
5.671
3.041
27.291
0.857
0.399
0.345
0.203
1.935
Appendix
Table 6: Extended quantitative comparison on the HF-GT indoor test set. R denotes outage recall. Fad. is the local fading ratio and should be close to 1 . SE5 is the absolute 5th-percentile spectral-efficiency tail error in high-variation regions. Grad is the mean spatial RSS-gradient magnitude. The HF-GT reference has GradMean 1.58 ; hence Grad should be interpreted by closeness to 1.58 , not by monotone increase or decrease. Bold marks the best learned predictor.
Model
Outage F1 ↑
Recall ↑
Missed area (m2)
Extra APs
Extra cost
CNN
0.490
0.348
652
3
$4,500
GeNeRT
0.000
0.000
1,000
4
$6,000
WNO
0.191
0.108
892
4
$6,000
PU-HNO
0.820
0.852
148
1
$1,500
Appendix
Table 7: Engineering interpretation of outage detection for AP placement on a 10,000m2 enterprise floorplan. The assumed true hard-coverage area is 1,000m2 .
Model
SE5 error ↓
Throughput loss
Achieved edge throughput ↑
CNN
1.043
83.4 Mbps
16.6 Mbps
GeNeRT
1.405
112.4 Mbps
0.0 Mbps
WNO
0.373
29.8 Mbps
70.2 Mbps
PU-HNO
0.100
8.0 Mbps
92.0 Mbps
Appendix
Table 8: Engineering interpretation of 5% tail spectral-efficiency error as achieved cell-edge throughput. The target edge throughput is 100 Mbps and the assumed bandwidth is 80 MHz.
Symbol
Meaning
Domains and spaces
Ω⊂R2
2D floorplan/deployment domain
Y
Separable Hilbert space of RSS fields on Ω
⟨⋅,⋅⟩Y , ∥⋅∥Y
Inner product and norm on Y
G
Space of scene encodings (geometry, materials) on Ω
C
Space of coordinate priors (Rx grid, Tx/Rx elevations)
Appendix
Table 9: Comprehensive notation. Symbols are used consistently across this appendix.
Radio maps describe how wireless signals propagate across space and are essential for wireless communication, sensing, and network planning. However, constructing accurate radio maps traditionally requires either dense measurements or computationally expensive physical simulations, which limits scalability and real-time deployment. Recent advances in generative artificial intelligence offer a promising alternative, but existing approaches lack fine-grained control and physical consistency when applied to real-world wireless environments. Here we present ControlRadio, a controllable generative framework that produces radio maps from natural-language descriptions and environmental layouts, including building structures and transmitter locations. Joint semantic and spatial conditioning enables interpretable, propagation-plausible generation, while a controlled latent prior and layout-aware conditioning improve stability and structural consistency. Extensive experiments demonstrate that ControlRadio achieves state-of-the-art accuracy and strong generalization across diverse urban scenarios, while reducing computation time by more than four orders of magnitude compared with conventional simulation-based methods. Such results suggest a new paradigm for scalable and controllable wireless environment modeling, with broad implications for next-generation communication systems and data-driven radio sensing.
Kangjun Liu, Xiying Pan, Shuhang Zhang +3
Pengcheng Laboratory, China · South China University of Technology and the Pengcheng Laboratory, China · Peking University, China +2
Real measurements are too limited to train an accurate indoor pathloss predictor that works across a wide range of buildings. Large-scale synthetic pretraining offers a way forward, but real building layouts are also scarce, and accurate ray-tracing simulators are slow, expensive, and often proprietary. We address both problems by introducing a generator that automatically creates diverse indoor layouts and a fast, open-source approximate ray tracer that computes radio maps for them. Using this pipeline, we generate 128M synthetic samples, pretrain ResNet-101 and Swin-T encoder-decoders, and fine-tune them on high-quality benchmark data. Despite simulator mismatch, our ResNet-101 model reduces error by 15% on average relative to the best known methods across five indoor radio-map prediction tasks and improves transfer on a small real-measurement dataset. Both architectures show predictable data-scaling trends: power laws fitted on 2M-16M samples predict the mean normalized downstream RMSE at 32M-128M with 3.33% mean absolute percentage error for ResNet-101 and 7.10% for Swin-T. These results show that pretraining on large amounts of cheap simulated data can improve indoor radio-map prediction, even when real measurements and high-quality simulations are limited.
High-fidelity radio fields are typically simulated for every scene--transmitter configuration or fitted separately to each scene, failing to exploit propagation structures shared across environments. We present Point2Radio, a foundation model that learns a transferable propagation prior from multiple environments. Given a material-aware point cloud and a transmitter (TX) setting, a common encoder produces a TX-conditioned scene representation that can be queried at arbitrary receiver (RX) locations. Task-specific query decoders map this representation to different radio quantities, e.g., three-dimensional (3D) path-gain (PG) fields and power angular spectra (PAS). At inference for a new scene, the model uses only a material-aware point cloud and transceiver queries, running in milliseconds on a single GPU without meshes or explicit path tracing. We evaluate PG prediction on a scene-disjoint split of a 337-scene corpus containing 86,272 TX-conditioned fields. Point2Radio achieves 0.871 dB mean absolute error (MAE), reducing error by 76.7% relative to a same-split UNet-style baseline. The same encoder also supports PAS prediction via a task-specific decoder. Experiments further show that light target-scene fine-tuning improves adaptation to a specific environment.