Multilevel Monte Carlo Coupled with the Parabolic Wave Equation Method for Uncertainty Analysis of Radio Wave Propagation in Tunnels

Radio wave propagation modeling in tunnels is crucial to design reliable wireless communication systems. Among the techniques available, the parabolic wave equation (PWE) methods have been widely utilized, due to their balance of accuracy and efficiency. However, the accuracy of the PWE methods depends on precise knowledge of tunnel environments, which are subject to uncertainties. While Monte Carlo (MC) methods are reliable for uncertainty analysis, they are computationally intensive. Polynomial chaos expansion (PCE) methods, though efficient, struggle with high-dimensional inputs. This paper applies the multilevel Monte Carlo (MLMC) method to the PWE method in a non-intrusive way. MLMC is employed to address uncertainties arising from various sources. Such MLMC-PWE method provides efficient estimations of the mean and variance of quantities of interest (QoI) by utilizing a multiscale hierarchy of spatial discretization. Numerical examples across different tunnel geometries demonstrate that the MLMC-PWE method achieves lower computational costs and improved efficiency relative to the MC-PWE method and the PCE-PWE method.