# BeamMix: 3D Gaussian Mixture-of-Experts for Element-Space Wireless Channel Modeling

Authors: William Bjorndahl and Joseph Camp.
Affiliation: Southern Methodist University.

Website: https://beammix.net/
DOI: https://doi.org/10.1145/3745756.3809247
PDF: https://beammix.net/beammix.pdf
Published in: Proceedings of the 24th Annual International Conference on Mobile Systems, Applications and Services, pages 928–940 (2026).

## Abstract

Many-antenna base stations must rapidly select beams and compute multi-user precoders from uplink measurements. This requires accurate, decision-ready models of the downlink channel in element space. Recent work has ported radiance field graphics techniques to the RF domain to learn how the propagation environment shapes the wireless channel. These scene-centric methods first learn a volumetric RF field or a cloud of 3D Gaussian primitives that encodes this propagation. They then ray-march or splat through this field to render channel state information (CSI) or spatial spectra at the array. For scheduling and multi-user precoding, however, this workflow is indirect. The models are designed to learn the 3D RF field, and the downlink channel information needed for resource allocation (CSI or spatial spectra) only becomes available after the rendering step. To bypass rendering we propose BeamMix, a map-free, element-space model that represents the channel as a mixture of physics-guided 3D Gaussian primitives. Each primitive has structure inspired by geometry-based stochastic channel models, with a learnable spatial footprint, direction, delay, and frequency response. An uplink-conditioned mixture-of-experts gate selects a top set of active primitives per observation. Their complex-valued contributions are splatted directly onto the antenna manifold. This produces element-space CSI for schedulers and precoders without additional rendering. We evaluate BeamMix on: (i) site-level uplink-to-downlink CSI prediction, (ii) full-array uplink-to-downlink CSI prediction, and (iii) RF spectrum synthesis. When directly compared, BeamMix improves accuracy over wireless radiance field baselines on site-level CSI and spectrum synthesis.

## Method

BeamMix connects wireless radiance fields, radio radiance fields, radio Gaussian splatting, and mixture-of-experts modeling with the element-space CSI used by beam selection and MU-MIMO precoders. Its CSI tasks use uplink measurements and fixed antenna coordinates, without transmitter position, scene maps, or ray directions. Spectrum synthesis uses transmitter position and queries the primitives over receive directions.

## Site-level uplink-to-downlink CSI prediction

The NeRF² MIMO benchmark uses measured Argos channels from eight base-station elements. Each method predicts downlink CSI from uplink CSI using the same frame-based data splits and global amplitude normalization.

![Median CSI prediction SNR versus training time on the NeRF squared MIMO benchmark. BeamMix reaches approximately 25.1 dB in 10 minutes. Reference lines show the final WRF-GS+ result of 24.5 dB after 130 minutes and NeRF squared result of 20.7 dB after 313 minutes.](https://beammix.net/assets/beammix-site-convergence.png)

Results: BeamMix-Site achieves 25.13 dB median prediction SNR, compared with 24.48 dB for WRF-GS+ and 20.75 dB for NeRF². Training takes 10.1 minutes versus 130.2 minutes for WRF-GS+, about 12.9 times faster on the same NVIDIA RTX 3090. Here, prediction SNR measures channel reconstruction accuracy; higher is better.

Impact: Learning the downlink channel directly can improve prediction accuracy while reducing training time. This makes adapting a channel model to measured conditions more practical without first reconstructing a volumetric RF scene.

## Full-array channel prediction and beam decisions

The full-array Argos evaluation predicts a complex channel over 96 antennas in a 12 × 8 array and 26 downlink tones. It covers line-of-sight and non-line-of-sight captures at 2.4 GHz, plus a 5 GHz capture, with 70/10/20 train/validation/test frame splits.

![Six heatmaps show three active Gaussian primitive footprints across a 12 by 8 antenna array. The top row is a line-of-sight sample with broad contributions; the bottom row is a non-line-of-sight sample with more concentrated contributions.](https://beammix.net/assets/beammix-array-footprints.png)

Results: Median prediction SNR reaches 26.9–27.0 dB at 2.4 GHz and approximately 19 dB at 5 GHz. DFT beam selection agrees with true-CSI decisions in roughly 93–96% of top-1 choices, with 100% top-3 accuracy on the reported captures. Accuracy is close to the strong per-antenna MLP baseline.

Impact: The output retains complex amplitude and phase at every antenna, allowing direct beam selection and multi-user precoding. The Gaussian decomposition also exposes where each component contributes across the array, adding an inspectable structure to otherwise similar prediction accuracy.

## RF spatial spectrum synthesis

In the NeRF² RFID dataset, a fixed 4 × 4 receiver array measures angular received power as the transmitter moves through an indoor space. All methods use the same training and held-out transmitter positions and predict a 90 × 360 elevation–azimuth spectrum. This task uses transmitter position as input.

![Angular received-power spectra for four held-out transmitter positions. Columns compare ground truth, BeamMix, WRF-GS+, NeRF squared, WRF-GS, and GSRF. BeamMix retains the dominant lobes and fine angular structure visible in the measured spectra.](https://beammix.net/assets/beammix-spectrum-comparison.png)

Results: BeamMix achieves 0.9267 median SSIM, 25.88 dB PSNR, and −19.58 dB NMSE. The strongest baseline, WRF-GS+, achieves 0.8795 SSIM, 24.324 dB PSNR, and −17.40 dB NMSE. Higher SSIM and PSNR, and lower NMSE, indicate more faithful spectra.

Impact: The learned primitives preserve dominant arrival directions and finer multipath structure. This provides a common benchmark against wireless radiance field methods and shows that the representation can explain angular RF structure as well as model channels at the antenna elements.

## Citation

```bibtex
@inproceedings{10.1145/3745756.3809247,
author = {Bjorndahl, William and Camp, Joseph},
title = {BeamMix: 3D Gaussian Mixture-of-Experts for Element-Space Wireless Channel Modeling},
year = {2026},
isbn = {9798400720277},
publisher = {Association for Computing Machinery},
address = {New York, NY, USA},
url = {https://doi.org/10.1145/3745756.3809247},
doi = {10.1145/3745756.3809247},
booktitle = {Proceedings of the 24th Annual International Conference on Mobile Systems, Applications and Services},
pages = {928–940},
numpages = {13},
keywords = {3D gaussians, mixture-of-experts, element space, multiple input multiple output},
location = {University of Cambridge, Cambridge, United Kingdom},
series = {MobiSys '26}
}
```