Three-Dimensional Modeling of Wave Propagation over Different Types of Terrains and Environments Using the Parabolic Equation Solved by Higher Order Approximation of the Finite Difference Method

Mohammad Ahmad,Dayalan Kasilingam

doi:10.52549/ijeei.v9i2.2845

Abstract

Designing communications and radar systems depends on accurate modeling of ground waves in three-dimensional environment. Propagation of ground waves in the VHF and UHF bands affected by the characteristics of the terrain and the troposphere. Although some three-dimensional modeling of ground waves was found in the literature based on solving the parabolic equation, they were limited to a specific terrain and/or environment. Also, a lot of important factors such as the refractive index of the troposphere were ignored. In this paper, a computational model was developed for predicting the electromagnetic wave propagation over different types of terrains and environments under three-dimensional conditions. The model is based on solving the parabolic equation using higher order approximation of the finite difference method. The model allows specifications of an antenna and the electrical characteristics of the ground. Moreover, the model treats flat and non-flat terrains, mixed path with different electrical characteristics, and forest environment. Furthermore, the model enables calculations to be performed under standard and non-standard refractive conditions of the troposphere that varies in height, width, and range. The results were compared with two-dimensional parabolic equation solved by Fourier split-step and showed excellent agreement.

Highlights

Modeling of ground waves in three-dimensional (3D) environment is a major planning and design problem in communications and radar systems
The dielectric slab for both models is given by complex refractive index n = √εr − jσ⁄ωε0 where εr and σ are relative permittivity and conductivity of forest dielectric slab layer respectively
Where RjFDM and Rjref are the results that have been gotten from higher order finite difference method (FDM) and a reference solution of the parabolic equation respectively

Summary

INTRODUCTION

Modeling of ground waves in three-dimensional (3D) environment is a major planning and design problem in communications and radar systems This is because it gives a complete picture of the field variation in all directions at any desired point. One important and effective method used to model wave propagation is based on the parabolic equation (PE) [1]-[2]. This is because it provides complete wave solution for the field in the existence of terrain and environment that dependent on range, altitude, and width. The 3D PE is solved via higher order approximation of finite difference method (FDM) to model wave propagation over different types of terrains and environments under 3D conditions. Matched Layer method is used in this paper for that purpose [13]

Initial field

RESULTS AND DISCUSSION

CONCLUSION