The Finite-Difference Method To Parabolic Equation And Its Application In Complex Electromagnetic Environments

Research on long range radio wave propagation plays a significant role in both mobile communication and electromagnetic environment. Impedance boundary and propagation medium are the environment factors for wave propagation mainly. Modern progress in information science and technology research shows that accurately predict radio wave propagation is not only benefit to improve communication quality, but also helpful to research on the character of propagation medium and boundary through analysis on the receive signals. This thesis shows the research on the propagation theory and numerical method, including initial field, terrain boundary and propagation space model, prediction on propagation loss under particular complex electromagnetic environment and some applications based on the research.The approximate procedure of Parabolic equation (PE) from Maxwell equations and its solution with Finite difference method (FDM) for narrow-angle and wide-angle propagation under impedance boundary condition are shown in the thesis. To achieve the numeric results, the initial field of Gaussian antenna suitable to PE is investigated based on antenna theory, the Harming window model for absorbing boundary is improved to enhance the absorbing effect, staircase terrain and shift map model is used to deal with complex terrain. For the application of terrain, the backward propagation, inverse algorithm and target positioning are researched briefly. Also atmospheric duct propagation is included under standard atmosphere and various kinds of duct and the propagation simulation of several example duct environments are conducted. The research on GPS signal propagation is elaborated for low gazing angle to the sea surface, in which the model of initial field of GPS signal is improved, the propagation loss formula including satellite-earth path are modified, a hybrid method to deal with circular polarization wave propagation is proposed, GPS signal propagation in typical atmospheric duct is calculated and the differences between GPS signal and Gaussian antenna are summarized based on the calculated results. The accuracy of the simulations are validated by the comparisons with the results of Fourier method and AREPS.The research achievements are the use of FDM to solve parabolic equation with accurate and available results, which is demonstrated through the comparison with other algorithms. The new ideas are proposed as follows:a method to improve the existing absorbing layer, establishment of some GPS initial field models which are suitable in different conditions with circular polarization wave included. In addition, conclusions of low gazing GPS signals propagation on sea surface are summarized.