WINERT: TOWARDS NEURAL RAY TRACING FOR WIRELESS CHANNEL MODELLING AND DIFFEREN-TIABLE SIMULATIONS

Abstract

In this paper, we work towards a neural surrogate to model wireless electromagnetic propagation effects in indoor environments. Such neural surrogates provide a fast, differentiable, and continuous representation of the environment and enables end-to-end optimization for downstream tasks (e.g., network planning). Specifically, the goal of the paper is to render the wireless signal (e.g., timeof-flights, power of each path) in an environment as a function of the sensor's spatial configuration (e.g., placement of transmit and receive antennas). NeRFbased approaches have shown promising results in the visual setting (RGB image signal, with a camera sensor), where the key idea is to algorithmically evaluate the 'global' signal (e.g., using volumetric rendering) by breaking it down in a sequence of 'local' evaluations (e.g., using co-ordinate neural networks). In a similar spirit, we model the time-angle channel impulse response (the global wireless signal) as a superposition of multiple paths. The wireless characteristics (e.g., power) of each path is a result of multiple evaluations of a neural network that learns implicit ray-surface interaction properties. We evaluate our approach in multiple indoor scenarios and demonstrate that our model achieves strong performance (e.g., <0.33ns error in time-of-flight predictions). Furthermore, we demonstrate that our neural surrogate whitens the 'black-box' wireless simulators, and thus enables inverse rendering applications (e.g., user localization).

1. INTRODUCTION

Realistic simulations of physical processes are vital to many scientific and engineering disciplines. In this paper, we focus on simulation of wireless electromagnetic (EM) signals within a propagation environment. The physics of such EM wave propagation between a transmit and receive point are analytically given by Maxwell equations: the transmitted wave undergoes different interactions with the environment (e.g., reflection), and the receiver gets the wave through multiple paths with different time-of-flights and powers, and from different directions. However, solving the Maxwell equations with boundary conditions requires in-depth knowledge of the propagation environment, hence classically modelling EM propagation is intractable for most engineering applications. Existing techniques make such simulations tractable by trading-off accuracy for speed. At one end of the spectrum, such simulations are represented in a statistical sense where a probabilistic model roughly captures the marginalized distribution over time-of-flights, gains and direction of transmit-receive paths. However, this level of accuracy is insufficient for designing systems that efficiently operate in high frequency bands. This motivates solutions at the other end of the spectrum: wireless ray tracing simulators. Given a detailed CAD representation of the environment along with the material properties, and numerous wireless configuration parameters (e.g., placement of a base station), the simulators generate resulting propagation characteristics. Although wireless ray tracing simulators are appealing, there are a few drawbacks. First, they are generally slow, which poses a bottleneck for closed-loop design pipelines, as wireless configurations cannot be quickly mapped to propagation characteristics. Second, because they are non-

