Variable Step Size Technique for the Parabolic Equation in Complex Environmental Conditions

Ying Gao,Jufei Chen,Binzhou Yan,Shuxia Guo,Qun Shao

doi:10.1109/access.2019.2942369

Abstract

In this paper, a variable step size method for the PE (Parabolic Equation) is proposed to solve the problem of low computational efficiency in the study of radio wave propagation at a large range of complex environments. Firstly, the relationship between the error and the step size, the frequency and other factors of the SSFT (Split-Step Fourier Transform) solution in the standard atmosphere is deduced, and then the basic selection range of the step size is given for the variable step size method. Secondly, the action mechanism of different environmental factors and the requirement of changing trend for step size are expounded through simulation, and the complex environment of PE application is classified according to the requirement of error. Finally, the electric wave characteristics of typical complex environment are advanced by the method. The simulation results show that compared with the small step method, the variable step size method of the PE can reduce the horizontal sampling point by 55.9% and the calculation time by 69.6% when the accuracy is close to the small step method, and the variable step size method is more accurate than the fixed large size step method. Therefore, the variable step size on the PE can not only ensure the accuracy of calculation, but also reduce the memory and time required, which greatly improves the reliability and efficiency. Moreover, it is suitable for solving the problem of the radio wave propagation in complex environment.

Highlights

With the wide applications of electronic information system, such as wireless communication, radar, remote sensing and so on, the electromagnetic environment in space is becoming more and more complex
Since Leontovich and Fock deduced the PE from the Helmholtz wave equation and established the theoretical framework for tropospheric wave propagation modeling, the parabolic equation model has been showing its strong adaptability in radio wave propagation [7]
The traditional parabolic equation fixed-step SSFT method is inefficient in long-distance wave prediction and cannot be predicted in real time

Summary

INTRODUCTION

With the wide applications of electronic information system, such as wireless communication, radar, remote sensing and so on, the electromagnetic environment in space is becoming more and more complex. Variable step size model can further improve the efficiency of SSFT solution while ensuring the accuracy of calculation It has practical significance in realtime prediction of electromagnetic wave propagation in a wide range of complex environments. The exp[i xk(n − 2)] indicates refractive effect of the medium, which is called the refractive factor; The exp i x k2 − p2 − k indicates the diffraction effect of the obstacle during the radio wave propagation, which is called the diffraction factor; u (x0, z) indicates the field distribution of the initial field It is worth noting, that the results obtained using the SSFT method are derived at ∂n/∂z = 0, the refractive index does not vary with the height. When solving the PE based on the SSFT algorithm, the form and the characteristics of SSFT algorithm determine that there are errors in formula solution They are related to the distribution form of n, the frequency of electromagnetic wave and the step size x. Radio frequency is determined, the magnitude of x is the main factor affecting the calculation accuracy and the speed

STEP SELECTION IN COMPLEX ENVIRONMENTS

ANALYSIS OF THE STEP SIZE SELECTION

Findings

CONCLUSION