Research and verification for parabolic equation method of radio wave propagation in obstacle environment

Abstract

In recent years, the two-way parabolic equation method (2WPE) has been widely utilized for studying the tropospheric ground-wave propagation under the irregular terrain. This algorithm can deal with the influences of the irregular terrain characteristic and the different electromagnetic parameters of the surface structure on wave propagation. However, there are still some defects in 2WPE method. Firstly, the method considers the irregular terrain and obstacles as a whole, so it cannot deal with the situation where the medium parameters of obstacles and the ground are different. Secondly, its calculation precision is limited with the inclination of the undulating terrain: if there are obstacles the upper bound of the inclination is easily broken through. Therefore, in this paper, a novel two-way parabolic equation method is proposed for analyzing the radio wave propagation in obstacle environment. According to the principle of domain decomposition, the obstacle zones are divided into two domains in the new algorithm, and the two subdomains are calculated, respectively. Meanwhile, in order to avoid the calculation error caused by the abrupt truncation of the obstacle zone, the field at the upper boundary of obstacles is modified to ensure the continuity of tangential field. To further improve the accuracy of the new algorithm, according to the historical transmission paths, we exactly retrieve the phases of each forward and backward wave, especially when stepping in and out of the obstacles. Furthermore, the method of moment (MoM) is used to verify the calculation accuracy of the new algorithm in obstacle environment. Although the accuracy of the MoM is very high, it also requires a great deal of calculation resources: it can only be employed to compute the fields in short distance. To overcome the difficulty, we use the image principle in the obstacle environment and do not subdivide the ground into segments; therefore the verification accuracy can be improved. On this basis, to unify the source setting of the new algorithm and the MoM, the equivalent source model is used to set the initial field. Finally, through numerical experiments, the simulation results of both methods agree very well, so the effectiveness of the boundary correction and the phase correction which are presented in this paper are both verified. The accuracy and superiority of the new algorithm in obstacle environment are also demonstrated. To sum up, the novel two-way parabolic equation method can be used to accurately calculate the field of the space in the obstacle environment, and lays the foundation for the field calculation of radio wave propagation in real environment.