Stochastic simulation of urban environments. Application to Path-loss in wireless systems

TL;DR

This paper develops stochastic 3D city models to statistically analyze electromagnetic path-loss, showing that power attenuation follows a distance-dependent law influenced by city morphology.

Contribution

It introduces fast, calibrated stochastic city models and uses Monte-Carlo ray tracing to estimate and analyze path-loss behavior in complex urban environments.

Findings

Power expectancy follows a 1/d^γ law with environment-dependent γ

Models reproduce main city features and are computationally efficient

Monte-Carlo simulations provide statistical insights into urban path-loss

Abstract

We are interested in the assessment of electromagnetic Path-Loss in complex environments. The Path-loss is the attenuation function $P$ of the electromagnetic power at a distance $d$ of an antenna. In free-space, $P(d) \propto 1/d^2$, in complex environments like cities, wave trajectory is altered by successive reflections and absorptions, the path-loss is not theoretically known and engineering rules postulate that $P(d) \simeq 1/d^{\gamma}, \, \gamma>2$. We place in a stochastic geometry context to answer the problem statistically. We present random models of 3D-city. These models reproduce main real cities' features, can be calibrated with simple mean formulae and can be fast simulated. For collections of random cities with the same mean morphology, we estimate by Monte-Carlo ray tracing techniques their attenuation maps. By averaging these maps, we show that the power expectancy actually follows a function $\sim 1/d^{\gamma}$ with $\gamma$ depending on the environment morphology.