Parabolic Equation Method Analysis Of Radio Wave Propagation In Complex Tunnels

The modern society witnesses the common occurrence of more and more complex infrastructure such as tunnels.More and more attention is paid to the characteristics of radio wave propagation in tunnels.There are three models to predict wave propagation,including empirical,deterministic and semi-empirical and semi-deterministic model.Among these models,the deterministic model mainly consists of accurate numerical and high-frequency approximation method.However,these two methods will bring the problems of low computational efficiency and low accuracy when analyzing the wave propagation characteristics in tunnel.The parabolic equation method derived from the wave equation provides a new method for predicting wave propagation in tunnel.In this work,parabolic equation method is used to analyze the propagation characteristics of radio waves in complex tunnel environment.The main work can be divided into three parts:Firstly,the basic theory of parabolic equation method is introduced,including scalar parabolic equation and vector parabolic equation.At the same time,the method for solving parabolic equation is explained,such as split-step Fourier transform and finite difference method.Considering the scenario of tunnel environment,the finite difference method is used to compute the parabolic equation later on.Secondly,in order to speed up the computation,the alternating direction implicit difference method is applied to predict the frequency domain characteristic.Then the modeling of tunnel section and the treatment of boundary conditions is studied.Afterwards,the parabolic equation suitable for bending conditions is derived.In addition,the model of refractive index and meteorological environment is constructed.By updating the refractive index in using parabolic equation method,the influence of complex environment is included.Finally,the frequency domain method is extended to the time domain to analyze the time domain characteristics of wave propagation in tunnel.The equations used alternating direction implicit method parabolic equation in time domain are derived.Then the treatment of boundary conditions in time domain is studied.In addition,the parabolic equation in time domain suitable for bending conditions is derived.Numerical stability analysis and dispersion error are given.The numerical results confirm the correctness of the proposed algorithm.