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CGFormer: A Cross-Attention Based Grid-Free Transformer for Radio Map Estimation

Haihan Nan, Emmanuel Obeng Frimpong, Zhi Tian, Yue Wang, Lingjia Liu

Abstract

Radio map estimation (RME), which predicts wireless signal metrics at unmeasured locations from sparse measurements, has attracted growing attention as a key enabler of intelligent wireless networks. The majority of existing RME techniques employ grid-based strategies to process sparse measurements, where the pursuit of accuracy results in significant computational inefficiency and inflexibility for off-grid prediction. In contrast, grid-free approaches directly exploit coordinate features to capture location-specific spatial dependencies, enabling signal prediction at arbitrary locations without relying on predefined grids. However, current grid-free approaches demand substantial preprocessing overhead for constructing the spatial representation, leading to high complexity and constrained adaptability. To address these limitations, this paper proposes a novel cross-attention grid-free based transformer model for RME. We introduce a lightweight spatial embedding module that incorporates environmental knowledge into high-dimensional feature construction. A cross-attention transformer then models the spatial correlation between target and measurement points. The simulation results demonstrate that our proposed method reduces RMSE by up to 6%, outperforming grid-based and gridfree baselines.

CGFormer: A Cross-Attention Based Grid-Free Transformer for Radio Map Estimation

Abstract

Radio map estimation (RME), which predicts wireless signal metrics at unmeasured locations from sparse measurements, has attracted growing attention as a key enabler of intelligent wireless networks. The majority of existing RME techniques employ grid-based strategies to process sparse measurements, where the pursuit of accuracy results in significant computational inefficiency and inflexibility for off-grid prediction. In contrast, grid-free approaches directly exploit coordinate features to capture location-specific spatial dependencies, enabling signal prediction at arbitrary locations without relying on predefined grids. However, current grid-free approaches demand substantial preprocessing overhead for constructing the spatial representation, leading to high complexity and constrained adaptability. To address these limitations, this paper proposes a novel cross-attention grid-free based transformer model for RME. We introduce a lightweight spatial embedding module that incorporates environmental knowledge into high-dimensional feature construction. A cross-attention transformer then models the spatial correlation between target and measurement points. The simulation results demonstrate that our proposed method reduces RMSE by up to 6%, outperforming grid-based and gridfree baselines.
Paper Structure (20 sections, 12 equations, 6 figures, 1 table)

This paper contains 20 sections, 12 equations, 6 figures, 1 table.

Table of Contents

  1. Introduction
  2. Problem Formulation and Model Preliminaries
  3. Problem formulation
  4. Grid-based and Grid-free paradigms for RME
  5. Encoder-Style Transformer Blocks
  6. Proposed method
  7. Overall framework
  8. Spatial semantic embedding module
  9. Cross-attention enhanced prediction module
  10. Experimental Results
  11. Experimental setting
  12. Dataset
  13. Baselines
  14. Evaluation metrics
  15. Implementation details
  16. ...and 5 more sections

Figures (6)

  • Figure 1: Comparison of different RME paradigms. (a) grid-based RME, where the region is discretized into fixed grids, and (b) grid-free RME, where predictions are made at arbitrary spatial locations. External side information is not incorporated.
  • Figure 2: Overall architecture of the proposed CGFormer framework.
  • Figure 3: Architecture of the SSE module, which encodes spatial coordinates $\mathbf{p}$ and environmental priors $\mathcal{E}$ into NeRF-style sinusoid coordinate embeddings $E\left(\mathbf{p}\right)$ and global semantic embeddings $\mathbf{e}_\mathrm{B}\left(\mathbf{p}\right)$ and $\mathbf{e}_\mathrm{S}\left(\mathbf{p}\right)$ for buildings and measurements, respectively.
  • Figure 4: RMSE comparison of different methods under varying numbers of measurements on the Wireless InSite dataset.
  • Figure 5: Visualization of sampled, ground-truth, and estimated maps produced by CGFormer, STORM, and DCAE under sampling factors of 0.05, 0.25, and 0.5. White regions correspond to building areas.
  • ...and 1 more figures