Differentiable and Learnable Wireless Simulation with Geometric Transformers

TL;DR

This work introduces Wi-GATr, a fully learnable wireless channel surrogate based on a Geometric Algebra Transformer that exploits $\,mathrm{E}(3)\, $-equivariance and a dedicated geometric tokenizer to map 3D scene geometry and antenna configurations to channel observations. It supports forward prediction, inverse problems (e.g., receiver localization), and probabilistic inference via diffusion models, enabling both accurate predictions and uncertainty-aware generation of scene variables. The authors contribute two large indoor 3D wireless datasets, Wi3R and WiPTR, and demonstrate strong performance on simulated data and real-world measurements (DICHASUS), including substantial improvements over hybrid and calibrated ray tracing baselines. The approach offers a fast, data-efficient, differentiable alternative to traditional ray tracers and lays groundwork for joint sensing and communication applications, while acknowledging limitations in data requirements and the non-exact replacement of model-based methods.

Abstract

Modelling the propagation of electromagnetic wireless signals is critical for designing modern communication systems. Wireless ray tracing simulators model signal propagation based on the 3D geometry and other scene parameters, but their accuracy is fundamentally limited by underlying modelling assumptions and correctness of parameters. In this work, we introduce Wi-GATr, a fully-learnable neural simulation surrogate designed to predict the channel observations based on scene primitives (e.g., surface mesh, antenna position and orientation). Recognizing the inherently geometric nature of these primitives, Wi-GATr leverages an equivariant Geometric Algebra Transformer that operates on a tokenizer specifically tailored for wireless simulation. We evaluate our approach on a range of tasks (i.e., signal strength and delay spread prediction, receiver localization, and geometry reconstruction) and find that Wi-GATr is accurate, fast, sample-efficient, and robust to symmetry-induced transformations. Remarkably, we find our results also translate well to the real world: Wi-GATr demonstrates more than 35% lower error than hybrid techniques, and 70% lower error than a calibrated wireless tracer.

Figures (10)

• Figure 1: Geometric surrogates for modelling wireless signal propagation.(a): Predictive modelling of channels from 3D geometry, transmitter, and receiver properties. Wi-GATr is a fast and differentiable surrogate for ray tracers. (b): A probabilistic approach with diffusion models lets us reconstruct 3D environments (c) and antenna positions (d) from the wireless signal.
• Figure 2: Qualitative signal prediction results. We show a single floor plan from the WiPTR test set. The black lines indicate the walls and doors, the colors show the received power as a function of the transmitter location (brighter colours mean a stronger signal). The transmitting antenna is shown as a black cross. The $z$ coordinates of transmitter and receiver are all fixed to the same height. We compare the ground-truth predictions (top left) to the predictions from different predictive models, each trained on only 100 WiPTR floor plans. Wi-GATr is able to generalize to this unseen floor plan even with such a small training set.
• Figure 3: Signal prediction. We show the mean absolute error on the received power as a function of the training data on Wi3R (left) and WiPTR (right). Wi-GATr outperforms the transformer and PLViT baselines at any amount of training data, and scales better to large data or many tokens than SEGNN.
• Figure 4: Rx localization error, as a function of the number of Tx. Lines and error band show mean and its standard error over 240 measurements.
• Figure 5: Probabilistic modelling. We formulate various tasks as sampling from the unconditional or conditional densities of a single diffusion model. (a): Unconditional sampling of wireless scenes $p({\bm{F}}, {\bm{x}}^{\text{tx}}, {\bm{x}}^{\text{rx}}, h)$. (b): Receiver localization as conditional sampling from $p({\bm{x}}^{\text{rx}} | {\bm{F}}, {\bm{x}}^{\text{tx}}, h)$ for two different values of $h$ and ${\bm{x}}^{\text{rx}}$. (c): Geometry reconstruction as conditional sampling from $p({\bm{F}}_u | {\bm{F}}_k, {\bm{x}}^{\text{tx}}, {\bm{x}}^{\text{rx}}, h)$ for two different values of $h$, keeping ${\bm{x}}^{\text{tx}}$, ${\bm{x}}^{\text{rx}}$, ${\bm{F}}_k$ fixed.