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Single-Voxel Wireless NeRF for Spatial Spectrum Prediction
Raj Bakhunchhe, Arun Paidimarri, Sara Garcia Sanchez, Asaf Tzadok, Ali Tajer, Ish Kumar Jain
TL;DR
Large wireless channel datasets are costly to collect, while wireless NeRFs use computationally demanding dense sampling. This paper tests single-voxel alternatives and finds SV-INGP matches NeRF2’s median SSIM of 0.78 with 184x lower training time on the real-world NeRF2 dataset.
Problem
Large channel datasets are costly to collect, and whether wireless spatial-spectrum prediction requires dense voxelization remains unclear.
Source: §I · p. 1Method
The paper introduces single-voxel variants of NeRF2 and INGP that represent each propagation ray with one voxel.
Source: §I · p. 2Results
On the real-world NeRF2 dataset, SV-INGP matches NeRF2’s median SSIM of 0.78 with 184x lower training time.
Source: §I · p. 2Takeaways & Limitations
For fixed-receiver spatial-spectrum prediction, dense volumetric sampling may be unnecessary, and current wireless NeRF models are over-parameterized.
Source: §VI · p. 7The evaluation is limited to image reconstruction, so performance of predicted spectra in actual wireless applications remains unstudied.
Source: §V · p. 7
Abstract
from arXiv · showhide
Wireless channel measurements across multiple spatial directions are crucial for AI-driven applications, such as RF digital twins and integrated communication and sensing. However, collecting channel data across large scenes is labor-intensive. Wireless NeRFs address this challenge by learning propagation behavior from sparse measurements and synthesizing channel spatial spectrum magnitude at unseen locations. However, existing wireless NeRFs inherit dense volumetric sampling from vision NeRFs, which requires substantial computation. This paper asks whether such dense sampling is necessary for predicting magnitudes of the wireless spatial spectrum. We empirically show that wireless NeRFs are over-parameterized for this task and introduce SV-INGP, a sparse volumetric sampling variant of Instant Neural Graphics Primitives (INGP). Across real-world and simulated datasets, SV-INGP matches the median Structural Similarity Index Measure (SSIM) of the NeRF2 baseline while reducing training time by 184x. These results generalize across LoS and NLoS scenes, sub-6 and millimeter-wave frequencies, and antenna array tapering configurations, suggesting a simpler and more efficient design path for RF digital twins
I. INTRODUCTION
The paper asks whether wireless spatial-spectrum prediction needs dense depth-wise voxelization, given the computational burden of existing wireless NeRFs, and studies single-voxel alternatives.
I. INTRODUCTION
- Large channel datasets support wireless AI applications, but simulation accuracy depends on environment models while real-world measurement campaigns are labor-intensive and difficult to scale.The paper asks whether dense volumetric representations are necessary for spatial-spectrum synthesis or whether current wireless NeRFs are over-parameterized.Source: §I · pp. 1–2
- Wireless NeRFs learn scene-dependent propagation from sparse channel measurements and synthesize spatial-spectrum magnitudes at unseen locations without explicit material properties or detailed environment models.Existing approaches use dense voxel sampling and aggregate voxel contributions along each ray, requiring substantial computational resources.Source: §I · p. 1
- Learned volume density has limited correspondence with dominant spatial-spectrum directions, challenging assumptions that dense depth-wise sampling provides scene-level interpretability.The paper presents a systematic study of voxelization, including learned density, voxel count, and placement along each direction.Source: §I · p. 2
- SV-NeRF2 and SV-INGP represent each propagation ray with a single voxel and are evaluated against their multi-voxel counterparts.The study compares accuracy, rendering complexity, and training and inference times.Source: §I · p. 2
- On the real-world NeRF2 dataset, SV-INGP matches NeRF2’s median SSIM of 0.78 with 184x lower training time.Compared with multi-voxel INGP, it also reduces training and inference time by 8x and 10x, respectively, with a 2.5% SSIM reduction.Source: §I · p. 2
II. RELATED WORK
Wireless NeRF work builds on vision NeRFs, while this paper focuses on whether dense volumetric rendering is needed for wireless spatial-spectrum prediction.
II. RELATED WORK
- Wireless NeRFs adapt continuous density and radiance fields to synthesize RF spatial-spectrum magnitudes, with NeRF2 combining volumetric rendering and wireless propagation models.Related work also applies NeRF-style representations to wireless scene reconstruction, sensing, and RF digital twins.Source: §II · p. 2
- Existing wireless NeRFs sample many voxels along each ray and aggregate their contributions, but this paper finds a single-voxel representation can preserve prediction accuracy while reducing rendering cost.The work examines whether dense depth-wise voxelization is necessary because wireless propagation is often dominated by a few strong paths.Source: §II · p. 2
- INGP accelerates neural representation learning with multi-resolution hash encoding while retaining dense ray sampling, making reduced sampling a distinct route to lower rendering complexity.Gaussian Splatting instead uses learnable Gaussian primitives rather than volumetric density fields; this paper focuses on NeRF-based representations.Source: §II · p. 2
III. SINGLE-VOXEL WIRELESS NERF DESIGN
The section presents a single-voxel wireless NeRF design and defines the receiver-side angular spectrum representation used in the scene model. It describes how transmitter-location spectra are formed, normalized, and used as network targets.
III. SINGLE-VOXEL WIRELESS NERF DESIGN
- The single-voxel wireless NeRF is presented as a lower-computation approach with performance comparable to related methods and as a way to assess voxel density.The section frames the design as serving both purposes.Source: §III · p. 2
A. RF Scene Model
- For a fixed K × K receiver array, each transmitter position yields a channel response represented over elevation and azimuth directions.The sampled front-facing angular domain uses 1° resolution in both dimensions.Source: A. RF Scene Model · p. 2
- The directional spectrum is formed by projecting the array-channel response onto steering vectors, with each direction corresponding to a receiver-originating ray.The spectrum magnitude varies by direction, and dominant peaks correspond to strong signal arrival directions.Source: A. RF Scene Model · p. 3
- Existing NeRF models sample multiple points along each ray, while the scene model includes an explicit free-space propagation factor for a sample at depth l.The propagation factor uses c for the speed of light and fc for carrier frequency.Source: A. RF Scene Model · p. 3
- Each transmitter location produces a 90×360 spectrum image normalized by its own maximum pixel value, and that normalized spectrum is the network target.Per-spectrum normalization lets spectra from different transmitter locations contribute comparably during training.Source: A. RF Scene Model · p. 3
B. Proposed Single-Voxel INGP
The proposed design uses one voxel per receiver-originating ray because a fixed wireless receiver provides no cross-view constraint on how a ray’s contribution is distributed over depth. SV-INGP combines this sparse sampling with a learned density and radiance pipeline and INGP-style location encoding.
B. Proposed Single-Voxel INGP
- With a fixed receiver, each scene point lies on one ray direction and contributes to one spectrum pixel, unlike vision scenes where camera poses provide shared constraints across views.The measurement constrains the ray’s accumulated contribution, so multiple voxels along that ray are not needed to distribute it over depth.Source: B. Proposed Single-Voxel INGP · p. 3, Figure 3 · p. 3
- SV-INGP takes transmitter location, direction, and single-voxel location as inputs and predicts spatial-spectrum magnitude using density and radiance MLPs.The density MLP outputs density and a feature vector; the radiance MLP uses that vector, direction, and transmitter location to predict the complex retransmitted signal.Source: B. Proposed Single-Voxel INGP · pp. 3–4
- The single voxel represents the entire ray segment, so its effective thickness is set to the maximum ray depth d.The predicted density maps to a bounded attenuation weight, and the learned voxel contribution is combined with an explicit propagation factor.Source: B. Proposed Single-Voxel INGP · p. 4
- The model is trained to match ground-truth spatial-spectrum magnitude using mean-squared error over a batch of directions.The supplied passage specifies a batch of M directions.Source: B. Proposed Single-Voxel INGP · p. 4
- SV-INGP uses sinusoidal positional encoding for direction and transmitter location, and a global multiresolution hash grid for the single-voxel location.The hash grid is queried across coarse and fine resolutions, retaining INGP’s compact high-resolution representation while evaluating one learned spatial sample per ray.Source: B. Proposed Single-Voxel INGP · p. 4
C. Multi-Voxel INGP Baseline
The multi-voxel counterpart extends the single-voxel estimate by sampling multiple locations along each ray and accumulating their contributions.
C. Multi-Voxel INGP Baseline
- The multi-voxel counterpart samples multiple locations per ray and accumulates their contributions.Source: C. Multi-Voxel INGP Baseline · p. 4
- For N voxels per ray, the single-voxel estimate is extended to a multi-voxel form.Source: C. Multi-Voxel INGP Baseline · p. 4
- The j-th voxel is at P_j = x(l_j, ω), where l_j is its distance from the receiver.Source: C. Multi-Voxel INGP Baseline · p. 5
D. Insights into single-voxel model
With a fixed receiver, multi-voxel sampling reparameterizes the single-voxel model rather than expanding its prediction set; normalization further favors the single-voxel form.
D. Insights into single-voxel model
- Under fixed-receiver geometry, the multi-voxel model is a reparameterization of the single-voxel model’s predictions, not a more expressive model.Source: D. Insights into single-voxel model · p. 5
- The single-voxel depth factor depends only on direction, while radiance receives direction and transmitter location and can absorb that factor.Source: D. Insights into single-voxel model · p. 5
- Normalizing each spectrum by its maximum removes absolute signal level, leaving an angular energy distribution that a single voxel represents directly.Source: D. Insights into single-voxel model · p. 5
A. Implementation Details
The evaluation compares single-voxel models with multi-voxel baselines on real and simulated wireless data. On the real-world NeRF2 dataset, SV-INGP matches NeRF2’s median SSIM while training substantially faster.
A. Implementation Details
- The real-world evaluation uses the NeRF2 dataset, while simulated Sionna RT data come from a metal-walled 3 m × 3 m indoor scene; the baselines are NeRF2 and Wireless INGP.Source: A. Implementation Details · p. 5
- Baselines use 64 samples per ray and single-voxel variants use one; models train for 30,000 iterations, with SSIM and training and inference times reported.Source: A. Implementation Details · p. 5
B. Single-Voxel Wireless NeRF Evaluation
- SV-NeRF2 and SV-INGP have SSIM reductions of 5.5% and 2.5%, respectively, while mean SSIM stays flat from 1 to 32 voxels per ray.Source: B. Single-Voxel Wireless NeRF Evaluation · p. 5, Figure 5 · p. 6
- Single-voxel predictions preserve the ground truth’s dominant spatial patterns and high-power regions across four transmitter locations.Source: B. Single-Voxel Wireless NeRF Evaluation · p. 5, Figure 5 · p. 6
- SV-INGP trains in 2.5 minutes, an 8x reduction relative to multi-voxel INGP.Source: B. Single-Voxel Wireless NeRF Evaluation · p. 5
- SV-INGP matches NeRF2’s median SSIM of 0.78 with 184x lower training time on the real-world NeRF2 dataset.Source: B. Single-Voxel Wireless NeRF Evaluation · p. 6
C. Interpretability: Understanding the Role of Volume Density
The learned maximum volume-density map does not align clearly with predicted spatial-spectrum peaks, so it is not a reliable scene-geometry representation for this task.
C. Interpretability: Understanding the Role of Volume Density
- The loss constrains overall signal strength but not its individual factors, allowing multiple density values to fit the data.Source: C. Interpretability: Understanding the… · p. 6
- NeRF2’s maximum volume-density map does not clearly align with predicted spatial-spectrum peaks.Source: Figure 6 · p. 6, C. Interpretability: Understanding the… · p. 6
- Unlike the occupancy-like density interpretation in vision NeRFs, a fixed receiver leaves density values without geometric alignment to scene structure.Source: C. Interpretability: Understanding the… · p. 6
D. Interpretability: Understanding Single Voxel Placement
Single-voxel NeRF2 performance is insensitive to voxel placement, and SV-INGP remains close to multi-voxel INGP across the tested propagation scenarios and frequencies. Array tapering improves SSIM by suppressing sidelobes, with a wider-main-lobe tradeoff.
D. Interpretability: Understanding Single Voxel Placement
- A flat SSIM response across voxel placements shows that single-voxel NeRF2 performance does not depend on where the voxel sits along the ray.In the 64-voxel model, most response was concentrated in the first voxel, where the explicit path-loss factor caused the smallest attenuation.Source: D. Interpretability: Understanding… · p. 7
- Because measurements are indexed by direction rather than depth, the radiance network absorbs voxel-location changes; in NLoS, blockers remove energy from a direction.The model therefore assigns low intensity in that direction whether the voxel is in front of or behind the blocker.Source: D. Interpretability: Understanding… · p. 7
E. Generalization Across Wireless Scenarios
- SV-INGP and INGP retain a small SSIM gap in both LoS and NLoS scenes, including when a metal obstacle attenuates the direct path.Both models achieve lower SSIM in NLoS than LoS.Source: E. Generalization Across Wireless… · p. 7, Figure 8 · p. 7
- SSIM distributions remain close at 2.4 GHz and 27 GHz, suggesting that millimeter-wave prediction in this setting does not require more voxels per ray.The comparison uses the same scene geometry, model architecture, and ray-sampling configuration.Source: E. Generalization Across Wireless… · p. 7, Figure 9 · p. 7
- Array tapering improves SSIM by suppressing sidelobes and angular artifacts, with the tradeoff of a wider main lobe.Untapered arrays can produce strong sidelobes that are not due to separate propagation paths.Source: E. Generalization Across Wireless… · p. 7, Figure 9 · p. 7
V. LIMITATIONS AND FUTURE WORK
The conclusion reports that a single-voxel design matches NeRF2’s median SSIM while greatly reducing training time. The paper also identifies limits in normalization, scene conditions, and evaluation scope, and leaves non-volumetric representations as an open question.
V. LIMITATIONS AND FUTURE WORK
- The evaluation uses locally normalized spectra and static indoor scenes, and assesses image reconstruction rather than performance in actual wireless applications.Local normalization discards relative power levels across transmitter locations, which matters for applications such as path planning; robustness to environmental change and outdoor extension remain untested.Source: §V · p. 7
VI. CONCLUSION
- A single-voxel design achieves median SSIM of 0.78, matching the NeRF2 baseline, while reducing training time by 184x.The conclusion attributes this to fixed-receiver geometry: direction-indexed measurements leave depth unconstrained and make learned volume density uninterpretable as scene structure.Source: §VI · p. 7
- Whether the same conclusion applies to representations without volumetric density, such as Gaussian Splatting, remains open.Source: §VI · p. 8