PC-TGS: Point-Cloud-Assistant Localized Statistical
Channel Prediction by Tangent Gaussian Splatting

Ye Xue, Yiheng Wang, Xinhua Shao, Qi Yan, Shutao Zhang, Tsung-Hui Chang
IEEE Transactions on Wireless Communications, 2026
Paper Code

Abstract

Accurate, site-specific channel information is crucial for optimizing next-generation wireless networks. Localized statistical channel modeling (LSCM) reconstructs the channel multipath angular power spectrum (APS) from RSRP measurements, but cannot predict APS at locations without measurements. We present PC-TGS, the first framework to extrapolate APS to unmeasured outdoor grids by integrating sparse radio measurements with dense LiDAR geometry. PC-TGS represents environmental scatterers as anisotropic 3D Gaussians, initialized and refined through a relaxed-mean reparameterization of the raw point cloud. A tangent-plane projection maps each Gaussian into the local angular domain, while a depth-aware electromagnetic splatting process aggregates their contributions. We derive a closed-form Gaussian-weighted average (GWA) for APS bin integration with a provable error bound. Evaluations on a city-scale dataset (5M LiDAR points, 6,310 RSRP samples) demonstrate that PC-TGS significantly outperforms state-of-the-art baselines in both accuracy and inference speed.

How It Works

PC-TGS Framework

Relaxed-Mean Reparameterization. A learnable selection matrix T softly selects N virtual scatterers from R raw LiDAR points, with a bias term for denoising. This bridges noisy, dense point clouds with compact, physically meaningful scatterer proxies.

Tangent-Plane Projection. Unlike camera-based 3DGS, we project each 3D Gaussian onto the tangent plane of the unit sphere at each angular bin (θ, φ), mapping environmental geometry into the antenna angular domain.

GWA-Based APS Integration. We replace the intractable bin integral with a moment-matched Gaussian window, yielding a closed-form weight formula with a provable O(Δθ³ + Δφ³) error bound.

Electromagnetic Splatting. Depth-sorted alpha compositing accumulates complex multipath contributions, reinterpreting visual rendering as multipath superposition. Each scatterer learns anisotropic covariance, complex spherical harmonic coefficients (degree 0–4), and an MLP-predicted attenuation & phase.

Results

City A dataset: 5M LiDAR points, 6,310 grids, 32 RSRP beams per grid

Method Type ST-1 (dB) ↓ ST-2 (dB) ↓ ST-3 (dB) ↓ Inf. Time (ms)
PC-TGS (ours) Offline 5.57 7.45 7.57 73.6
PC-TGS w/o RFT Offline 5.43 8.23 8.62 73.5
MM-LSCM Offline 5.76 9.12 9.94 379
SM-LSCM Offline 5.89 10.02 11.14 99
RadioUNet Offline — 10.31 — 2.1
WNOMP Online 6.12 13.35 15.07 1.5 / 8,032
TMSBL Online 6.03 11.69 11.77 134 / 9,743
Ray Tracing Online — 14.37 16.77 8,100

ST-1: rotated RSRP @ measured grids  |  ST-2: RSRP @ unmeasured grids  |  ST-3: rotated RSRP @ unmeasured grids  |  MAE in dB (lower is better)

At 50% measurement density, PC-TGS (9.25 dB) still outperforms RadioUNet trained at full density (10.31 dB).

Conclusion

We proposed point-cloud-assisted tangent Gaussian splatting (PC-TGS), a physically grounded framework that extrapolates the channel APS to grids where no signal measurements are available. PC-TGS fuses LiDAR geometry and RSRP data in an end-to-end differentiable pipeline integrating relaxed-mean scatterer parameterization, tangent-plane projection, and depth-aware electromagnetic synthesis, made possible by a novel GWA-based closed-form bin integration. Experiments on a city-scale dataset show clear accuracy gains over existing single- and multi-modal baselines. PC-TGS enables geometry-aware, data-efficient channel prediction for large-scale wireless digital twins.

Citation

@article{xue2026point,
  title={Point-Cloud-Assistant Localized Statistical Channel Prediction
         by Tangent Gaussian Splatting},
  author={Xue, Ye and Wang, Yiheng and Shao, Xinhua and
          Yan, Qi and Zhang, Shutao and Chang, Tsung-Hui},
  journal={IEEE Transactions on Wireless Communications},
  volume={25},
  pages={17816--17830},
  year={2026},
  publisher={IEEE},
  doi={10.1109/TWC.2026.3696997}
}