PETOOL: MATLAB-based one-way and two-way split-step parabolic equation tool for radiowave propagation over variable terrain

A MATLAB-based one-way and two-way split-step parabolic equation software tool (PETOOL) has been developed with a user-friendly graphical user interface (GUI) for the analysis and visualization of radio-wave propagation over variable terrain and through homogeneous and inhomogeneous atmosphere. The tool has a unique feature over existing one-way parabolic equation (PE)-based codes, because it utilizes the two-way split-step parabolic equation (SSPE) approach with wide-angle propagator, which is a recursive forward–backward algorithm to incorporate both forward and backward waves into the solution in the presence of variable terrain. First, the formulation of the classical one-way SSPE and the relatively-novel two-way SSPE is presented, with particular emphasis on their capabilities and the limitations. Next, the structure and the GUI capabilities of the PETOOL software tool are discussed in detail. The calibration of PETOOL is performed and demonstrated via analytical comparisons and/or representative canonical tests performed against the Geometric Optic (GO) + Uniform Theory of Diffraction (UTD). The tool can be used for research and/or educational purposes to investigate the effects of a variety of user-defined terrain and range-dependent refractivity profiles in electromagnetic wave propagation.Program summaryProgram title: PETOOL (Parabolic Equation Toolbox)Catalogue identifier: AEJS_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEJS_v1_0.htmlProgram obtainable from: CPC Program Library, Queenʼs University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 143 349No. of bytes in distributed program, including test data, etc.: 23 280 251Distribution format: tar.gzProgramming language: MATLAB (MathWorks Inc.) 2010a. Partial Differential Toolbox and Curve Fitting Toolbox requiredComputer: PCOperating system: Windows XP and VistaClassification: 10Nature of problem: Simulation of radio-wave propagation over variable terrain on the Earthʼs surface, and through homogeneous and inhomogeneous atmosphere.Solution method: The program implements one-way and two-way Split-Step Parabolic Equation (SSPE) algorithm, with wide-angle propagator. The SSPE is, in general, an initial-value problem starting from a reference range (typically from an antenna), and marching out in range by obtaining the field along the vertical direction at each range step, through the use of step-by-step Fourier transformations. The two-way algorithm incorporates the backward-propagating waves into the standard one-way SSPE by utilizing an iterative forward–backward scheme for modeling multipath effects over a staircase-approximated terrain.Unusual features: This is the first software package implementing a recursive forward–backward SSPE algorithm to account for the multipath effects during radio-wave propagation, and enabling the user to easily analyze and visualize the results of the two-way propagation with GUI capabilities.Running time: Problem dependent. Typically, it is about 1.5 ms (for conducting ground) and 4 ms (for lossy ground) per range step for a vertical field profile of vector length 1500, on Intel Core 2 Duo 1.6 GHz with 2 GB RAM under Windows Vista.

► A MATLAB-based tool (PETOOL) is introduced with a user-friendly interface.
► One- and two-way split-step parabolic equation (SSPE) algorithms are implemented.
► The tool can handle both forward and backward waves in radio-wave propagation.
► Arbitrary terrain and atmosphere profiles can easily be defined.
► Validation, verification and calibration are performed by numerical tests.