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RME-GAN: A Learning Framework for Radio Map Estimation based on Conditional Generative Adversarial Network

Songyang Zhang, Achintha Wijesinghe, Zhi Ding

arXiv:2212.12817v1eess.SP

TL;DR

Fine-resolution outdoor radio maps must be estimated from sparse measurements despite shadowing, obstacles, and non-uniform sampling. The paper proposes RME-GAN, a two-phase cGAN framework that first learns global propagation patterns and then local shadowing effects. Experiments report improved and robust reconstruction across the evaluated observation settings.

  • Problem

    Fine-resolution radio map estimation from sparse RF measurements is difficult because existing methods inadequately handle shadowing, obstacles, and non-uniformly distributed observations.

  • Method

    RME-GAN combines radio propagation-model guidance with cGAN learning, using a first phase for global patterns and a second phase for local shadowing effects.

  • Results

    RME-GAN demonstrates performance advantages and robustness in radio map reconstruction across uniform, biased, and non-uniform observation settings.

  • Takeaways & Limitations

    The two-phase framework supports radio map estimation from sparse observations by combining global propagation information with local shadowing features.

Abstract

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Outdoor radio map estimation is an important tool for network planning and resource management in modern Internet of Things (IoT) and cellular systems. Radio map describes spatial signal strength distribution and provides network coverage information. A practical goal is to estimate fine-resolution radio maps from sparse radio strength measurements. However, non-uniformly positioned measurements and access obstacles can make it difficult for accurate radio map estimation (RME) and spectrum planning in many outdoor environments. In this work, we develop a two-phase learning framework for radio map estimation by integrating radio propagation model and designing a conditional generative adversarial network (cGAN). We first explore global information to extract the radio propagation patterns. We then focus on the local features to estimate the effect of shadowing on radio maps in order to train and optimize the cGAN. Our experimental results demonstrate the efficacy of the proposed framework for radio map estimation based on generative models from sparse observations in outdoor scenarios.

I. INTRODUCTION

Radio map estimation seeks fine-resolution spatial signal-power maps from sparse measurements, but shadowing, obstacles, and non-uniform sampling limit existing methods. RME-GAN addresses these issues with a two-phase cGAN framework combining propagation-model guidance and local-feature learning.

  • Motivation: Radio maps support spectrum planning, coverage analysis, resource allocation, and outage diagnosis by describing spatial RF signal-power distributions.In practice, fine-resolution maps must be estimated from sparse sensor or device measurements.
  • Limitations of Existing Methods: Existing model-based methods struggle with shadowing and obstacles, while model-free methods depend on measurement quality and often assume uniform spatial sampling.Real-world user-device measurements can be unevenly distributed, and propagation models may vary across training sets.
  • Proposed Framework: RME-GAN integrates radio propagation models with a conditional generative adversarial network for outdoor radio map estimation from sparse observations.The framework is designed specifically for the estimation stage using geographically sparse measurements.
  • Two-Phase Learning: The first phase extracts global radio-map information using model-based guidance, while the second uses sampling strategies to learn local shadowing and radio features.The two phases target complementary global propagation patterns and local effects caused by shadowing and obstacles.
  • Evaluation: Experiments report that the proposed strategies capture global model information and local shadowing features, improving radio-map reconstruction across evaluated observation settings.The study compares methods on reconstruction accuracy and fault diagnosis, including uniform, biased, and non-uniform observations.

A. Radio Map Estimation

Radio map estimation methods combine propagation models, neighborhood interpolation, or learned mappings to reconstruct spatial PSD from sparse observations. GAN and cGAN formulations provide generative frameworks that can condition reconstruction on additional information.

  • Model-based Radio Map Estimation: Model-based estimation represents radio maps using propagation-related functions of frequency and geographic location.The formulation sums transmitter-specific channel gains weighted by transmitted PSDs.
  • Model-free Radio Map Reconstruction: Model-free methods avoid a specific propagation model and use neighborhood information through interpolation or learning-based mappings.Interpolation combines observations using weights, while learning-based methods map geometric inputs to PSD outputs.
  • Model-free Radio Map Reconstruction: Interpolation methods estimate local PSD from observations using weighted combinations, including inverse-distance, radial-basis, and Kriging approaches.The cited methods differ in weighting, kernel choice, or estimation-error optimization.
  • Generative Adversarial Networks: GANs learn data distributions through generator–discriminator interaction, while cGANs condition both networks on additional information.Customized cGANs can combine adversarial and traditional losses for one-to-one mappings such as sketch-to-image generation.

III. PROBLEM FORMULATION

The problem formulation targets fine-resolution outdoor radio-map reconstruction from sparse regional observations. RME-GAN relaxes assumptions about observation placement, observation counts, and transmitter parameters while training a generator for full-map estimation.

  • Problem Setup: Each region is represented on a 256 × 256 grid with transmitter positions, an urban map, and sparse sensor observations.Observed samples contain non-negative PSD values and geographic coordinates.
  • Problem Setup: Training regions with fine-resolution ground-truth maps supervise a learning machine that estimates maps for other regions.The stated objective is to estimate the full radio map from the available regional inputs.
  • Relaxed Conditions: RME-GAN does not require sparse observations to be uniformly distributed across each region.The formulation permits either uniform or uneven spatial placement.
  • Relaxed Conditions: The framework also permits different observation counts and radio-propagation parameters across regions.These relaxed conditions motivate the proposed two-phase GAN-based radio-map estimation framework.

IV. RADIO MAP RECONSTRUCTION VIA RME-GAN

RME-GAN maps region features to full radio maps using a cGAN-style generator and discriminator. Its customized objective uses two training phases to capture global propagation patterns and local details.

  • RME-GAN learns a mapping from region features F_i to an estimated full radio map.Sparse observations are first interpolated to the region size to reformat the input features.
  • The framework uses a general cGAN structure for the one-to-one mapping between input region features and radio-map outputs.The discriminator receives prior information indicating whether the radio map is generated or real.
  • An 18-layer Unet provides the generator sketch, with its parameters specified in Table I.
  • The generator and discriminator are trained iteratively by splitting the min-max optimization into separate subproblems.The framework defines separate loss functions for optimizing D and G.
  • The cGAN objective is customized with two-phase loss terms for global and local information.This design targets the global propagation pattern and local radio-map details, respectively.

B. Two-phase Customization in RME-GAN

The first phase integrates radio-propagation modeling with learning to capture global information from sparse observations. Model-based interpolation produces an upsampled template that guides radio-map reconstruction despite missing local shadowing and obstacle effects.

  • The framework addresses global propagation modeling and detail estimation from biased, non-uniform observations as separate challenges.
  • Sparse observations are upsampled into a 256×256 radio-map template using model-based interpolation and pathloss modeling.The approach uses an LDPL model to represent global pathloss.
  • The upsampled template and fitted model parameters capture global propagation patterns and provide guidance during radio-map reconstruction.The template does not fully capture obstacle and shadowing effects, but it supplies global information for training.

2) Downsampling for detailed features:

The second phase downsamples observations to emphasize local radio-map details and correct reconstruction errors. Geometry-wise sampling addresses spatial imbalance, while frequency-wise sampling targets high-frequency details and outliers.

  • The second phase downsamples sparse observations to correct errors in reconstructed radio-map details.
  • Geometry-wise downsampling: Geometry-wise downsampling uses spatial partitions to balance samples across locations and selects one peak-energy observation per piece.Superpixels can be built from an urban map or interpolated template; Voronoi diagrams and spectral clustering are alternatives.
  • Frequency-wise downsampling: Frequency-wise downsampling transforms the estimated radio map into Fourier space and selects high-frequency coefficients as additional loss information.The selected coefficients represent details or outliers in the radio map.
  • Phase 1 emphasizes global model information, while Phase 2 emphasizes local details, with the transition controlled by a decision variable.Validation accuracy or training-epoch length can determine the phase-change point.
  • Phase 1 loss functions: The first-phase baseline uses MSE between the generated radio map and ground truth, together with total variation to model smoothness.The MSE is normalized by the 256×256 map size.
  • Phase 1 loss functions: A gradient-based global-information loss compares generated and model-based-template gradient patterns using cosine similarity.The gradients are computed in the up, down, right, and left directions for each pixel.

2) Phase 2 - Local Shadowing Estimation:

Phase 2 focuses the loss design on local shadowing and fine-resolution details. It combines baseline accuracy and smoothness terms with geometric, frequency-domain, and multi-scale structural information.

  • Baseline loss function: The second phase uses total variation and MSE, assigning MSE a smaller weight than in the first phase to emphasize details.
  • Geometric loss function: The geometric loss minimizes MSE between downsampled observations and generated radio-map values at the same positions.This favors downsampled observations to mitigate non-uniform spatial sampling.
  • Frequency domain loss function: The frequency-domain loss minimizes MSE between selected high-frequency coefficients of the reference and generated radio maps.The selected feature vector contains the first N_f high-frequency Fourier coefficients.
  • Multi-scale structural similarity index: MS-SSIM is added to improve generated-radio-map quality by comparing fine-resolution details with the coarse model-based template.The measure evaluates image quality through luminance, contrast, and structure across scales.

D. Summary of Two-Phase Training Strategy

The generator is trained with weighted loss terms across two phases: first to learn a propagation-based template, then to correct local detail using shadowing and obstacle effects.

  • The final generator objective combines the previously defined loss terms, with λi controlling each term’s contribution.The weights can differ between the two training phases.
  • Phase 1 emphasizes model-based interpolation so RME-GAN learns a template representing radio propagation.
  • Phase 2 favors local information to correct template details by learning shadowing and obstacle impacts.

V. EXPERIMENTAL RESULTS

The experiments evaluate RME-GAN on RadioMapSeer under uniform, regionally unbalanced, and non-uniform sparse-observation settings. The dataset uses urban maps and sparse samples to test radio-map reconstruction.

  • Dataset: RadioMapSeer contains 700 maps with 80 transmitter locations per map, covering metropolitan areas including Ankara, Berlin, Glasgow, Ljubljana, London, and Tel Aviv.Transmitters and receivers are set to 1.5 m, buildings to 25 m, and transmitter power to 23 dBM.
  • Data representation: Urban maps represent building segmentation, and sparse observations are sampled from each radio map for training and testing.The dataset examples include urban maps with buildings and corresponding pathloss radio maps.
  • Sampling setups: The experiments sample sparse observations under uniform, regionally unbalanced, and non-uniform distributions.Setup 1 samples 1% uniformly; Setup 2 samples each region at a random 1%–10% ratio; Setup 3 samples 1% from one side and 10% from the other.
  • Dataset split: The dataset is split into 500 training, 100 testing, and 100 validation regions for each experimental scenario.

3) Parameters of Learning Models:

The learning models use an 18-layer Unet generator and a 4-layer discriminator, while experiments compare RME-GAN with interpolation, model-based, autoencoder, Unet, Kriging, and cGAN baselines. RME-GAN performs best across observation-distribution settings, while visualization and validation results support its ability to recover detailed radio-map structure.

  • Learning-model parameters: RME-GAN uses an 18-layer Unet generator and a 4-layer discriminator.The two training phases use different loss-term weights, with the second phase favoring the downsampled radio map for detail correction.
  • Setup 1: RME-GAN outperforms all compared methods when observations are uniformly distributed in Setup 1.The comparison includes MBI, RBF, radioUnet, AE, deep AE, traditional Unet, Kriging, and traditional cGAN, evaluated with NMSE and RMSE.
  • Setups 2 and 3: RME-GAN achieves the best results under both regionally biased observations in Setup 2 and non-uniform observations in Setup 3.The reported advantage is attributed to the design of the sampling strategies and RME-GAN.
  • Visualization: Visualization results show interpolation methods failing to capture environmental effects, Kriging producing blurred maps, and RME-GAN capturing the PSD distribution.The comparison covers radio-map reconstructions from the different methods.
  • Two-phase training: Validation error drops when training moves from phase 1 to phase 2, indicating improved correction of detailed errors using shadowing information.

2) Zero-shot Learning:

The paper tests RME-GAN beyond its training observation pattern, in low-power regions, and for coarse outage-map reconstruction. Across these evaluations, RME-GAN retains superior or more accurate performance, supporting robustness and practical applicability within the tested settings.

  • Zero-shot learning: RME-GAN trained on uniformly sampled data retains superior performance when tested on regionally unbalanced and non-uniform data.This zero-shot evaluation assesses robustness and generalization across different observation distributions.
  • Selected low-power areas: RME-GAN outperforms other methods in all three selected low-power areas and displays greater robustness in those regions.The evaluation targets low-power areas because they are more sensitive to environmental effects.
  • Outage analysis: RME-GAN provides more accurate outage-map reconstruction than competing approaches at thresholds 5 and 25.Outage maps classify locations as normal or outage according to whether PSD falls below a preset threshold, with performance measured by segmentation error.
  • Conclusion: The paper concludes that RME-GAN combines a global propagation template with second-phase shadowing estimation and delivers performance advantages and robustness for sparse RF radio-map estimation.
  • Future directions: The authors identify fault diagnosis from sparse RF observations and integration of model-based approaches with learning machines as future directions.
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