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.

Estimating path loss for a transmitter-receiver location is key to many use-cases including network planning and handover. Machine learning has become a popular tool to predict wireless channel properties based on map data. In this work, we present a transformer-based neural network architecture that enables predicting link-level properties from maps of various dimensions and from sparse measurements. The map contains information about buildings and foliage. The transformer model attends to the regions that are relevant for path loss prediction and, therefore, scales efficiently to maps of different size. Further, our approach works with continuous transmitter and receiver coordinates without relying on discretization. In experiments, we show that the proposed model is able to efficiently learn dominant path losses from sparse training data and generalizes well when tested on novel maps.

Abstract Conventional decision trees have a number of favorable properties, including a small computational footprint, interpretability, and the ability to learn from little training data. However, they lack a key quality that has helped fuel the deep learning revolution: that of being end-to-end trainable. Kontschieder et al. (ICCV, 2015) have addressed this deficit, but at the cost of losing a main attractive trait of decision trees: the fact that each sample is routed along a small subset of tree nodes only. We here present an end-to-end learning scheme for deterministic decision trees and decision forests. Thanks to a new model and expectation–maximization training scheme, the trees are fully probabilistic at train time, but after an annealing process become deterministic at test time. In experiments we explore the effect of annealing visually and quantitatively, and find that our method performs on par or superior to standard learning algorithms for oblique decision trees and forests. We further demonstrate on image datasets that our approach can learn more complex split functions than common oblique ones, and facilitates interpretability through spatial regularization.

State-of-the-art stixel methods fuse dense stereo and semantic class information, e.g. from a Convolutional Neural Network (CNN), into a compact representation of driveable space, obstacles, and background. However, they do not explicitly differentiate instances within the same class. We investigate several ways to augment single-frame stixels with instance information, which can similarly be extracted by a CNN from the color input. As a result, our novel Instance Stixels method efficiently computes stixels that do account for boundaries of individual objects, and represents individual instances as grouped stixels that express connectivity. Experiments on Cityscapes demonstrate that including instance information into the stixel computation itself, rather than as a post-processing step, increases Instance AP performance with approximately the same number of stixels. Qualitative results confirm that segmentation improves, especially for overlapping objects of the same class. Additional tests with ground truth instead of CNN output show that the approach has potential for even larger gains. Our Instance Stixels software is made freely available for non-commercial research purposes.