Statistical Modeling of Electromagnetic Wave Propagation in Tunnels With Rough Walls Using the Vector Parabolic Equation Method

The vector parabolic equation (VPE) method is a very efficient methodology for high-fidelity modeling of electromagnetic wave propagation. While the VPE has been widely applied to model wave propagation in tunnel environments, most of the work involves only smooth surface walls and leaves out of consideration scenarios with rough surfaces. Although it is often disregarded, surface roughness, as an additional source of path loss, is very important in the accurate modeling of tunnel propagation. This paper presents a rigorous approach to incorporate surface roughness into VPE-based models. To that end, the rough surface is first parameterized using a Karhunen-Loève expansion and then embedded into the VPE. The proposed approach can be applied to realistic tunnel geometries with arbitrary cross sections and curvature variations. Validations are provided by comparisons with experimental data in various practical tunnel cases.