Efficient Parabolic Equation-Driven CNN Propagation Model in Tunnels Based on Frequency Conversion

Parabolic equation (PE) methods have been widely utilized for modeling radio wave propagation in tunnels due to their notable efficiency and fidelity. However, as emerging wireless communication systems in railway environments shift to higher frequency bands, the computational costs associated with PE methods become prohibitively high. To that end, this article proposes a convolutional neural network (CNN)-based propagation model that provides predictions of radio wave propagation at high frequencies by leveraging data obtained by the PE method at a lower frequency. The proposed model significantly enhances the efficiency of wave propagation modeling in tunnels. Meanwhile, by explicitly incorporating prior knowledge from PE simulations and carefully designing the input, output, and structures of the CNN, the proposed model is more generalizable and robust compared to existing data-oriented machine learning (ML) models. Numerical results are compared with predictions from conventional PE methods for various tunnel geometries, and the proposed model is also validated against experimental measurements in a realistic tunnel scenario.