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DyRadio: Spatiotemporal Diffusion for Dynamic Radio Map Reconstruction

Zhijie Fan, Zhifeng Zhao, Rongpeng Li

arXiv:2611.01603v1cs.LGcs.AI

TL;DR

Dynamic radio-map reconstruction must make use of temporally distributed sparse observations while handling evolving propagation states and unknown measurement noise. DyRadio combines propagation-guided, noise-conditioned spatiotemporal diffusion with iterative blind-area predictive-likelihood noise estimation. It reports the best MSE, NMSE, PSNR, and SSIM across evaluated settings against four baselines.

  • Problem

    Single-frame methods do not explicitly exploit dependencies among temporally distributed observations, while direct temporal pooling can mismatch changing propagation states and sparse data complicates noise estimation.

    Source: A. Related Works · p. 2

  • Method

    DyRadio uses a propagation-guided, noise-conditioned spatiotemporal diffusion model for joint RM reconstruction and alternates blind-area prediction with predictive-likelihood updates to estimate noise.

    Source: B. Contributions · pp. 2–3, A. Framework Overview · p. 5

  • Results

    Across sampling rates and noise levels, DyRadio achieves the lowest MSE and NMSE and highest PSNR and SSIM among four baselines.

    Source: 1) Overall Reconstruction Performance · p. 10

  • Takeaways & Limitations

    DyRadio demonstrates reconstruction accuracy and robustness against measurement noise compared with existing methods.

    Source: §V · p. 12

Abstract

from arXiv · show

Accurate radio map (RM) reconstruction is essential for environment-aware wireless networks. Sampling-based methods, which infer radio conditions from sparse measurements, are widely adopted because they do not require explicit knowledge of transmitter configurations. However, in dynamic environments, time-varying propagation conditions cause RMs to evolve, complicating reconstruction from temporally distributed sparse observations. Although cross-frame observations provide complementary spatial information, their direct aggregation can introduce temporal state mismatch. Furthermore, unknown measurement noise adds to the reconstruction difficulties. To address these challenges, we propose DyRadio, a framework that integrates spatiotemporal RM reconstruction with unknown noise estimation. Specifically, a propagation-prior-guided, noise-conditioned spatiotemporal diffusion model (DM) jointly reconstructs consecutive RMs by capturing cross-frame dependencies, while adapting to measurement noise levels. To estimate the noise level, an iterative predictive likelihood method alternates between DM-based blind-area prediction and noise-level updates. The estimated noise level then conditions reconstruction of the complete RM sequence. Experimental results demonstrate superior reconstruction accuracy and robustness against measurement noise, with peak signal-to-noise ratio (PSNR) improvements of 1.18-5.75 dB over the best-performing baseline across all evaluated settings.

I. INTRODUCTION

Dynamic radio maps are needed as wireless networks increasingly depend on spatial radio conditions, but sparse observations across evolving environments complicate reconstruction. DyRadio combines propagation-guided, noise-conditioned spatiotemporal reconstruction with iterative estimation of unknown measurement noise.

I. INTRODUCTION

  • Radio maps characterize spatial radio quantities such as received signal strength, with potential uses in spectrum management, predictive communication, and handover.The introduction motivates dynamic reconstruction alongside growing vehicular, robotic, and agentic applications.Source: §I · p. 1

A. Related Works

  • Existing sampling-based methods primarily reconstruct single frames, while dynamic reconstruction must use complementary observations without conflating their distinct propagation states.Direct temporal pooling can distort propagation patterns near moving vehicles, and sparse observations make measurement noise difficult to distinguish from changing propagation conditions.Source: A. Related Works · p. 2

B. Contributions

  • DyRadio’s propagation-guided, noise-conditioned spatiotemporal diffusion model jointly reconstructs consecutive maps while capturing cross-frame dependencies.A DiT with spatiotemporal attention uses propagation-prior features, while noise-modulated cross-attention adapts the contribution of sparse observations.Source: B. Contributions · pp. 2–3
  • An iterative predictive-likelihood method estimates unknown measurement noise by alternating blind-area RM prediction and noise updates without complete RMs or an additional estimation network.The resulting estimate conditions reconstruction under varying noise conditions.Source: B. Contributions · p. 3
  • DyRadio’s reported experiments use a dynamic urban-traffic RM dataset and show PSNR gains of 1.18–5.75 dB over the strongest baseline.The dataset is constructed using CARLA and Sionna RT.Source: B. Contributions · p. 3

A. Diffusion Model Preliminaries

  • Diffusion models learn generation through forward noising and reverse denoising, with conditional generation using available information during denoising.DDIM can accelerate sampling by denoising over a selected subsequence of steps; deterministic DDIM adds no random noise during reverse updates.Source: A. Diffusion Model Preliminaries · pp. 3–4

B. Problem Formulation

The problem is to reconstruct a sequence of complete radio maps from sparse, temporally distributed, noisy measurements and environmental information. Because the noise level is unknown and coupled to map reconstruction, DyRadio estimates it using the model’s predictive distribution and then conditions sequence reconstruction on that estimate.

B. Problem Formulation

  • The target is a sequence of complete radio maps whose consecutive propagation states are distinct yet temporally correlated.The environment is represented over an H × W spatial grid, and each time’s observations sample only a limited number of locations.Source: B. Problem Formulation · p. 4
  • Measurement noise is modeled with standard deviation σobs, which is generally unknown despite its importance to reconstruction.The problem formulation treats noise-level estimation as maximizing its posterior probability.Source: B. Problem Formulation · p. 4
  • Map reconstruction and noise estimation are coupled through their joint posterior, so DyRadio uses the noise-conditioned model’s predictive distribution to estimate noise before reconstructing the full sequence.The resulting estimate conditions reconstruction of the entire T-length RM sequence.Source: B. Problem Formulation · p. 4

III. THE PROPOSED METHOD

DyRadio reconstructs a complete sequence in L-frame subsequences, using propagation priors and noise-conditioned spatiotemporal attention. It first estimates a shared noise level through blind-area predictive likelihood, then uses that estimate to condition reconstruction.

A. Framework Overview

  • DyRadio processes the complete T-frame sequence one L-frame subsequence at a time to limit the computational cost of joint reconstruction.The framework consists of noise estimation followed by RM reconstruction.Source: A. Framework Overview · p. 5
  • A U-Net supplies coarse RM predictions and propagation features to a noise-conditioned spatiotemporal DiT that jointly reconstructs each subsequence.The DiT uses 3D patch embeddings and spatiotemporal self-attention; measurement noise modulates observation cross-attention to adjust sparse-observation contributions.Source: A. Framework Overview · p. 5
  • The framework estimates measurement noise by alternating blind-area RM prediction with predictive-likelihood updates that account for predictive uncertainty.It assumes one shared noise level across the T-frame sequence, and the final estimate conditions subsequent L-frame subsequences.Source: A. Framework Overview · p. 5

B. Noise-Conditioned Spatiotemporal DM

DyRadio uses a two-stage model: a propagation-guided U-Net extracts features, and a noise-conditioned spatiotemporal DiT reconstructs RM subsequences from sparse observations. Noise-level conditioning modulates observation fusion, while alignment supervision uses clean RM values at sampled locations.

Stage I: Propagation-Guided Feature Extraction

  • A propagation-guided U-Net takes scene information and sparse RM observations to produce an auxiliary RM prediction and features that guide Stage II reconstruction.Obstacle and transmitter locations add location-specific propagation-prior losses; transmitter locations are used only during training.Source: 1) Stage I: Propagation-Guided Feature… · p. 5

Stage II: Spatiotemporal Diffusion Reconstruction

  • A noise-conditioned DiT predicts diffusion noise from a noisy L-frame RM subsequence, conditioning on scene information, sparse observations, measurement-noise level, and propagation-prior features.Reverse DDIM sampling starts from Gaussian noise and uses predicted diffusion noise to recover the clean RM subsequence.Source: 2) Stage II: Spatiotemporal Diffusion… · p. 5
  • Stage I features are incorporated into generation features through multiplicative feature guidance, without establishing when this fusion occurs relative to DiT processing.The features come from the second- and third-last decoder layers of Uϕ at 64×64 and 32×32 resolutions, then guide Stage II spatiotemporal RM reconstruction.Source: 1) Stage I: Propagation-Guided Feature… · p. 5, 2) Stage II: Spatiotemporal Diffusion… · p. 6
  • The noise-level embedding conditions observation cross-attention and gates observation residuals injected into generation tokens.Generation features provide queries, while observation features provide keys and values.Source: 2) Stage II: Spatiotemporal Diffusion… · p. 6
  • Spatiotemporal self-attention and a feed-forward network process fused features to predict diffusion noise, with timestep embeddings modulating each DiT block.The diffusion loss is normalized over spatial locations and frames; an observation-alignment loss uses clean ground-truth RM values to avoid directly fitting measurement noise.Source: 2) Stage II: Spatiotemporal Diffusion… · pp. 6–7

1) Blind-area prediction with the learned RM prior:

Blind-area prediction with the learned RM prior holds out subsets of observed locations and predicts them using the remaining observations, scene information, and current noise estimate. Multiple generated sequences provide predictive mean and variance for the held-out measurements.

Blind-area prediction with the learned RM prior

  • Observed spatiotemporal locations are partitioned into disjoint blind areas, and each prediction excludes one area from its conditioning observations.The setup assumes measurement noise is independent of the clean RM and across observed locations, with a common standard deviation throughout the sequence.Source: 1) Blind-area prediction with the… · p. 7
  • For each blind area, the pretrained DM uses scene information, retained observations, and the current noise estimate to produce a predictive distribution.The method generates S independent RM sequences for each blind area.Source: 1) Blind-area prediction with the… · p. 7
  • Monte Carlo samples estimate the predictive mean and variance, while the clean RM value at each held-out location is approximated by a Gaussian distribution.Source: 1) Blind-area prediction with the… · p. 7

2) Noise estimation through predictive likelihood:

DyRadio estimates the shared measurement-noise standard deviation by maximizing a composite predictive likelihood over blind-area measurements. It alternates likelihood-based updates with new blind-area predictions until convergence or a maximum iteration count.

Noise estimation through predictive likelihood

  • The predictive density of each blind-area measurement marginalizes over the clean RM value and accounts for uncertainty in its prediction.The predictive variance combines clean RM prediction variance and measurement noise variance.Source: 2) Noise estimation through predictive… · pp. 7–8
  • Gaussian predictive densities across blind areas form a composite likelihood that is maximized to estimate the shared noise standard deviation.The likelihood terms account for location-dependent predictive uncertainty.Source: 2) Noise estimation through predictive… · p. 8
  • A relaxed update combines the current noise estimate with the likelihood-based estimate; prediction and update repeat until the change is below δ or Rmax is reached.The final estimate conditions the pretrained spatiotemporal DM, together with scene information and all available measurements, to reconstruct the complete RM sequence.Source: 2) Noise estimation through predictive… · p. 8

IV. EXPERIMENTAL SETTINGS AND RESULTS

The evaluation constructs dynamic radio maps by combining CARLA vehicle motion with Sionna RT propagation simulations. The dataset spans multiple scenes and trajectories, and evaluation reconstructs complete 96-frame sequences.

IV. EXPERIMENTAL SETTINGS AND RESULTS

  • DyRadio is compared with four representative reconstruction methods spanning single- and multi-frame settings, as well as diffusion-based and supervised approaches.Source: §IV · p. 8

1) Dataset:

  • The dataset combines CARLA-generated vehicle movements and scene geometry with Sionna RT raytracing-based radio propagation simulations.The simulations account for multipath propagation through surface reflections and Lambertian diffuse scattering from buildings, roads, and vehicles.Source: 1) Dataset · p. 8
  • The dataset contains 12,000 RSS radio-map sequences across 16 scenes, each represented on a 128 × 128 grid over a 96 × 96 m2 area.Each sequence has 96 frames generated at 10 Hz; the scenes are divided into 12 training, one validation, and three testing scenes with no scene overlap.Source: 1) Dataset · p. 9

2) Implementation Details:

DyRadio is evaluated against single- and multi-frame reconstruction methods under varying sampling rates and measurement noise. It achieves the strongest reported reconstruction metrics and shows smaller performance degradation as noise increases.

2) Implementation Details:

  • DiT blocks are grouped into first, middle, and last stages with different feature dimensions and attention-head counts, and both stages are trained jointly from scratch.Noise estimation uses 10-step DDIM sampling; reconstruction uses 50-step DDIM sampling. Training uses four NVIDIA RTX PRO 6000 GPUs.Source: 2) Implementation Details · pp. 9–10

3) Comparison Methods:

  • The comparison includes single-frame diffusion methods RadioDiff and PhyRMDM, single-frame supervised RadioUNet, and multi-frame supervised RadioMapMotion.Baselines lacking sparse-observation support are adapted, and all are retrained with identical dataset splits and validation-loss early stopping.Source: 3) Comparison Methods · p. 10

1) Overall Reconstruction Performance:

  • DyRadio achieves the lowest MSE and NMSE and highest PSNR and SSIM across evaluated settings, reducing MSE by 25.1%–73.3% versus RadioMapMotion.Single-frame methods lack explicit cross-frame modeling; RadioMapMotion’s predictions can smooth local variations and blur shadow boundaries.Source: 1) Overall Reconstruction Performance · p. 10

2) Impact of Sampling Rate and Measurement Noise on RM Reconstruction Performance:

  • 2.83 dB: DyRadio’s PSNR improves by this amount as sampling rises from 1% to 3%; its drop is 1.53 dB as noise rises from 0.03 to 0.09, versus approximately 6.0 dB for RadioMapMotion.The reported smaller noise-related reduction is attributed to DyRadio’s noise-conditioned design preserving reconstruction quality under increasingly noisy observations.Source: 2) Impact of Sampling Rate and… · pp. 10–11, Figure 6 · p. 11

3) Effectiveness of Temporal Modeling:

DyRadio’s temporal modeling improves with longer input sequences, while direct pooling degrades. The reported noise-estimation results and ablations support the framework’s reconstruction performance, and noise estimation adds limited inference overhead.

3) Effectiveness of Temporal Modeling:

  • 32.22 to 34.24 dB: DyRadio’s PSNR rises as sequence length increases from 4 to 16, while direct pooling falls from 31.12 to 27.63 dB.RadioMapMotion’s PSNR rises from 14.72 to 31.94 dB, but DyRadio already reaches 32.22 dB at sequence length 4.Source: 3) Effectiveness of Temporal Modeling · p. 11

4) Noise Estimation Accuracy and Impact on Reconstruction:

  • At σobs = 0.03, increasing sampling from 1% to 3% reduces noise-estimation MAE from 2.755 × 10−3 to 1.218 × 10−3 and absolute relative bias from 2.34% to 0.38%.MAE decreases across noise levels as sampling increases, and relative bias generally approaches zero; additional observations improve estimation reliability even under sparse sampling.Source: 4) Noise Estimation Accuracy and… · pp. 11–12, Table V · p. 11
  • At p = 2%, estimated-noise inputs perform within 0.002 dB PSNR of ground-truth-noise inputs and improve PSNR over fixed-noise input by 0.546, 0.149, and 0.296 dB at σobs = 0.03, 0.07, and 0.09.The comparison evaluates ground-truth, estimated, and fixed (σ = 0.05) noise inputs.Source: Table VI · p. 11, 4) Noise Estimation Accuracy and… · p. 12

5) Ablation Study:

  • Removing Stage I reduces PSNR by 7.07–8.28 dB, removing temporal attention by 5.43–7.33 dB, and removing noise-conditioned fusion by 3.01 dB at p = 2% and σobs = 0.09.For the last ablation, SSIM falls from 0.9785 to 0.9429; the full model performs best across evaluated settings.Source: 5) Ablation Study · p. 12, Table VII · p. 12

6) Inference Efficiency:

  • DyRadio achieves superior reconstruction performance with inference time comparable to diffusion-based RadioDiff and PhyRMDM, and noise estimation takes 1.842 s, or 11.9% of total inference time.Timing is measured on one NVIDIA RTX PRO 6000 GPU; DyRadio and RadioMapMotion generate 16 frames per inference.Source: 6) Inference Efficiency · p. 12, Table VIII · p. 12

V. CONCLUSION

  • DyRadio combines a noise-conditioned spatiotemporal diffusion model with iterative noise-level estimation for dynamic RM reconstruction from sparse observations.The conclusion describes propagation-prior features and spatiotemporal attention for joint reconstruction, alongside blind-area prediction and noise-estimate updates.Source: §V · p. 12

APPENDIX EVALUATION METRICS

The appendix defines reconstruction metrics over complete RM sequences and noise-estimation metrics across test sequences, with lower MSE and NMSE and higher PSNR and SSIM indicating better reconstruction quality.

1) MSE:

  • MSE is the squared reconstruction error between ground-truth and reconstructed RM values, evaluated over the complete sequence and averaged across test sequences.The metric passage identifies the compared values at each frame and spatial location.Source: APPENDIX EVALUATION METRICS · p. 12, 1) MSE · p. 13

2) NMSE:

  • NMSE normalizes squared reconstruction error by the ground-truth RM energy.Source: 2) NMSE · p. 13

3) PSNR:

  • PSNR evaluates reconstruction fidelity using the ratio of maximum signal power to MSE.Its stated formula is PSNR = 10 log10(MAX2/MSE).Source: 3) PSNR · p. 13

4) SSIM:

  • SSIM evaluates local luminance, contrast, and structural similarity between reconstructed and ground-truth RMs.The definition uses local-patch means, variances, covariance, and stabilization constants.Source: 4) SSIM · p. 13

5) Average estimated noise:

6) MAE:

  • Noise-estimation MAE is the average absolute error in the estimated noise level.Source: 6) MAE · p. 13

7) Relative Bias:

  • Relative bias measures the percentage deviation of the mean estimated noise level from the ground-truth noise level.Source: 7) Relative Bias · p. 13
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