Dirasat, Engineering Sciences, Volume 34, No. 1, 2007
- 1 -
Modeling of Wave Propagation over Different Realistic Types of
Environments Using the Parabolic Equation
(Research Note)
Mohammad H. Ahmad and Mohamed K. Abdelazeez*
ABSTRACT
In this paper, a computational model is developed for predicting the electromagnetic wave propagation over
different realistic types of environments for some realistic conditions. The model allows specification of
frequency, polarization, antenna radiation pattern, antenna altitude and elevation angle. It also treats standard and
non-standard refractive conditions; super-refractive, sub-refractive, and ducts. In addition, the model allows
specification of the electrical characteristics of the ground (permittivity and conductivity). Furthermore, the
model is used to deal with mixed path situation composed of user-defined number of sections each with a
different electrical characteristic, and it treats flat and non-flat terrain configurations with residential areas and
forest environment.
Keywords: Electromagnetic, Wave Propagation, Parabolic Equation, Fourier Split Step.
I. INTRODUCTION
Modeling of wave propagation over different types of
environments is a major planning and design problem in
communications and radar systems. Although there are
different available methods used to model Electro-
Magnetic (EM) wave propagation, these methods are
appropriate for some types of environments, i.e. forest
(Tamir, 1967; Swarup and Tewari, 1979), residential
(Walfisch and Bertoni, 1988; Chung and Bertoni, 2002),
non-flat terrain (Luebbers, 1984; Ott, 1971), sea (Barrick,
1971; Kuo, 1988), mixed path (Wait, 1961; Damboldt,
1981). These methods cannot be used to model wave
propagation over other types of environments. One
important and effective method used to model wave
propagation is based on the Parabolic Equation (PE)
(Fock, 1946). There are many advantages in using the PE
to model radio wave propagation. It gives full wave
solution for the field in the presence of range-dependent
environments. Also, the solution of PE exhibits excellent
robustness and accuracy for complicated problems
involving vertically and horizontally varying refractive
conditions. Solution of PE is performed using Finite
Difference (FD) method (McDaniel, 1975), which is a
straightforward method in implementing boundary
conditions; or/and using Fourier Split Step (FSS) method
(Harden and Tappert, 1973), which is significantly more
stable numerically, and more efficient in computation
times. The derivation of the PE from Maxwell’s
equations is found in Kuttler and Dokery (1991) and
Ryan (1991); were FSS solution of the PE is summarized
by both Ryan (1991) and Levy and Craig (1991). The
standard and non-standard refractive index of the
troposphere was discussed in Kuttler and Dockery
(1991), Dockery (1988) and Barrios (1994). The
electrical characteristic of the ground incorporated in the
FSS solution of the PE was discussed by Kuttler and
Dockery (1991), Dockery and Kuttler (1996), and Kuttler
* Al-Quds College, Amman, Jordan; and Department of
Electrical Engineering, Faculty of Engineering and
Technology, University of Jordan. Received on 14/12/2005
and Accepted for Publication on 17/12/2006.
© 2007 DAR Publishers/University of Jordan. All Rights Reserved.