GSRF: Complex-Valued 3D Gaussian Splatting for Efficient Radio-Frequency Data Synthesis

TL;DR

GSRF provides a fast, high-fidelity RF data synthesis framework by extending 3D Gaussian Splatting to the RF domain with complex-valued 3D Gaussians and a Fourier-Legendre radiance basis. It introduces orthographic splatting on a Ray Emitting Spherical Surface and a complex-valued ray tracing pipeline implemented on RF-optimized CUDA kernels, enabling real-time synthesis. Across RFID, BLE, and 5G tasks, GSRF demonstrates substantial gains in training data efficiency, training time, and inference latency while maintaining fidelity in spatial spectra and CSI. The approach offers a compelling, MLP-free alternative to NeRF-based RF synthesis with practical impact on indoor localization and sensing in wireless networks.

Abstract

Synthesizing radio-frequency (RF) data given the transmitter and receiver positions, e.g., received signal strength indicator (RSSI), is critical for wireless networking and sensing applications, such as indoor localization. However, it remains challenging due to complex propagation interactions, including reflection, diffraction, and scattering. State-of-the-art neural radiance field (NeRF)-based methods achieve high-fidelity RF data synthesis but are limited by long training times and high inference latency. We introduce GSRF, a framework that extends 3D Gaussian Splatting (3DGS) from the optical domain to the RF domain, enabling efficient RF data synthesis. GSRF realizes this adaptation through three key innovations: First, it introduces complex-valued 3D Gaussians with a hybrid Fourier-Legendre basis to model directional and phase-dependent radiance. Second, it employs orthographic splatting for efficient ray-Gaussian intersection identification. Third, it incorporates a complex-valued ray tracing algorithm, executed on RF-customized CUDA kernels and grounded in wavefront propagation principles, to synthesize RF data in real time. Evaluated across various RF technologies, GSRF preserves high-fidelity RF data synthesis while achieving significant improvements in training efficiency, shorter training time, and reduced inference latency.

Figures (12)

• Figure 1: Overview of GSRF architecture. The RF scene is represented by Gaussian primitives with mean $\mu$, covariance $\Sigma$, and complex-valued radiance $\psi$ and transmittance $\rho$, whose attributes are updated via gradient-based optimization with adaptive density control. For rendering, rays $\gamma$ are emitted from the receiver, Gaussians are splatted onto a 2D receiving RF plane, and the received data is obtained by aggregating complex-valued contributions along each ray.
• Figure 2: Visualization comparison of synthesized spatial spectrum at different positions.
• Figure 3: Metric comparison for a sparse measurement density of $0.8\,\text{measurements}/\text{ft}^3$.
• Figure 4: Training times for spectrum synthesis.
• Figure 5: Test times for spectrum synthesis.