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GSRF: Complex-Valued 3D Gaussian Splatting for Efficient Radio-Frequency Data Synthesis
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Extends 3D Gaussian Splatting to the radio-frequency domain with complex-valued Gaussians, Fourier-Legendre radiance, orthographic splatting and CUDA complex ray tracing for fast RF data synthesis (RSSI, spatial spectra, CSI).
Problem
Synthesizing RF data (RSSI, spatial spectra, complex CSI) from transmitter and receiver positions is accurate in NeRF-based methods but too slow to train and infer, limiting real-time wireless sensing applications.
Approach
Replace NeRF volumetric sampling with explicit complex-valued 3D Gaussians carrying Fourier-Legendre directional radiance and complex transmittance, splat them onto a spherical receiving plane orthographically, and perform complex-valued ray tracing in custom CUDA kernels, with no MLPs.
Key results
- On RFID spatial spectrum synthesis with sparse data, GSRF reaches median 21.2% PSNR and 56.4% MSE improvement over NeRF² and trains in 0.27 h versus 5.01 h for NeRF² (18.56x faster).
- On BLE RSSI synthesis, GSRF achieves 4.09 dBm average error versus 6.09 dBm for NeRF² (32.79% improvement) with 15.82x shorter training time.
- On 5G CSI synthesis, GSRF attains mean SNR 20.99 dB, outperforming R2F2 and FIRE, using 30% of the training data.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use GSRF instead of NeRF^2 | RFID spatial spectrum synthesis · RFID spatial spectrum, sparse measurements | PSNR: 21.2% median improvement | Helped |
| use GSRF instead of NeRF^2 | RFID spatial spectrum synthesis · RFID spatial spectrum, sparse measurements | MSE: 56.4% median improvement | Helped |
| use GSRF instead of NeRF^2 | RFID spatial spectrum synthesis · RFID spatial spectrum, sparse measurements | training time: 5.01 hours -> 0.27 hours; 18.56× faster | Helped |
| use GSRF instead of NeRF^2 | RFID spatial spectrum synthesis · RFID spatial spectrum | inference latency: 352.73 ms -> 4.18 ms; 84.39× speedup | Helped |
| use GSRF instead of WRF-GS | RFID spatial spectrum synthesis · RFID spatial spectrum, sparse measurements | PSNR: 5.7% | Helped |
| use GSRF instead of WRF-GS | RFID spatial spectrum synthesis · RFID spatial spectrum, sparse measurements | MSE: 19.3% | Helped |
| use GSRF instead of NeRF^2 | 5G CSI synthesis · 5G CSI synthesis | SNR | No clear effect |
| use GSRF instead of NeRF^2 | BLE RSSI synthesis · BLE RSSI synthesis | RSSI error: 6.09 dBm -> 4.09 dBm; 32.79% improvement | Helped |
| use GSRF instead of WRF-GS | BLE RSSI synthesis · BLE RSSI synthesis | RSSI error: 4.261±3.943 -> 4.094±3.908; 3.92% | Helped |
| use GSRF-generated fingerprints instead of NeRF^2-generated fingerprints | KNN BLE localization · BLE-based localization | localization accuracy: 31.40% | Helped |
| replace spherical-harmonic radiance with Fourier–Legendre radiance (ablation) | GSRF · RFID spatial spectrum | PSNR: 20.51 -> 22.64 | Helped |
| include the phase channel (ablation) | GSRF · RFID spatial spectrum | PSNR: 20.89 -> 22.64; 8.37% reduction when phase is removed | Helped |
Surprising findings
- Inference latency on RFID is 4.18 ms versus 352.73 ms for NeRF², and the BLE RSSI improvement over WRF-GS is only 3.92%.
Limitations
- No zero-shot generalization to unseen environments; per-scene training is required.
- Optimized for static scenes; scene changes require retraining or fine-tuning.
- Comparison to NeRF² on 5G uses 30% of training data for GSRF but full data for baselines, so efficiency comparisons are not strictly matched.
Experimental setup
Datasets: NeRF² RFID dataset BLE nursing home dataset Argos 5G CSI dataset
Benchmarks: RFID spatial spectrum synthesis (NeRF² dataset) BLE RSSI synthesis 5G CSI synthesis (Argos)
Metrics: MSE PSNR RSSI error (dBm) localization error (m) SNR (dB) training time inference latency
Baselines: NeRF² WRF-GS R2F2 FIRE
Builds on: 3D Gaussian Splatting NeRF Huygens-Fresnel principle spherical harmonics
Closest papers by meaning
- RxGS: Receiver-Generalizable 3D Gaussian Splatting for Radio-Frequency Data Synthesis (NeurIPS 2026 · similarity 0.89)
- GES : Generalized Exponential Splatting for Efficient Radiance Field Rendering (CVPR 2024 · similarity 0.84)
- COLMAP-Free 3D Gaussian Splatting (CVPR 2024 · similarity 0.83)
- RPC-GS: Gaussian Splatting with native RPC Rendering for Satellite Imagery (NeurIPS 2026 · similarity 0.83)
- Can NeRFs "See" without Cameras? (NeurIPS 2025 · similarity 0.83)
- POp-GS: Next Best View in 3D-Gaussian Splatting with P-Optimality (CVPR 2025 · similarity 0.83)
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