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

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

A Comparison of the Machine Learning Algorithm for Evaporation Duct Estimation

In this research, a comparison of the relevance vector machine (RVM), least square support vector machine (LSSVM) and the radial basis function neural network (RBFNN) for evaporation duct estimation are presented. The parabolic equation model is adopted as the forward propagation model, and which is used to establish the training database between the radar sea clutter power and the evaporation duct height. The comparison of the RVM, LSSVM and RBFNN for evaporation duct estimation are investigated via the experimental and the simulation studies, and the statistical analysis method is employed to analyze the performance of the three machine learning algorithms in the simulation study. The analysis demonstrate that the M profile of RBFNN estimation has a relatively good match to the measured profile for the experimental study; for the simulation study, the LSSVM is the most precise one among the three machine learning algorithms, besides, the performance of RVM is basically identical to the RBFNN

Characterizing Evaporation Ducts Within the Marine Atmospheric Boundary Layer Using Artificial Neural Networks

We apply a multilayer perceptron machine learning (ML) regression approach to infer electromagnetic (EM) duct heights within the marine atmospheric boundary layer (MABL) using sparsely sampled EM propagation data obtained within a bistatic context. This paper explains the rationale behind the selection of the ML network architecture, along with other model hyperparameters, in an effort to demystify the process of arriving at a useful ML model. The resulting speed of our ML predictions of EM duct heights, using sparse data measurements within MABL, indicates the suitability of the proposed method for real-time applications.Comment: 13 pages, 7 figure

Influence of Sea Surface Roughness on the Electromagnetic Wave Propagation in the Duct Environment

This paper deals with a study of the influence of sea surface roughness on the electromagnetic wave propagation in the duct environment. The problem of electromagnetic wave propagation is modeled by using the parabolic equation method. The roughness of the sea surface is computed by modifying the smooth surface Fresnel reflection coefficient to account for the reduction in the specular reflection due to the roughness resulting from sea wind speed. The propagation model is solved by the mixed Fourier split-step algorithm. Numerical experiments indicate that wind-driven roughened sea surface has an impact on the electromagnetic wave propagation in the duct environment, and the strength is intensified along with the increment of sea wind speeds and/or the operating frequencies. In a fixed duct environment, however, proper disposition of the transmitter could reduce these impacts

Forward scatter radar for air surveillance: Characterizing the target-receiver transition from far-field to near-field regions

A generalized electromagnetic model is presented in order to predict the response of forward scatter radar (FSR) systems for air-target surveillance applications in both far-field and near-field conditions. The relevant scattering problem is tackled by developing the Helmholtz-Kirchhoff formula and Babinet's principle to express the scattered and the total fields in typical FSR configurations. To fix the distinctive features of this class of problems, our approach is applied here to metallic targets with canonical rectangular shapes illuminated by a plane wave, but the model can straightforwardly be used to account for more general scenarios. By exploiting suitable approximations, a simple analytical formulation is derived allowing us to efficiently describe the characteristics of the FSR response for a target transitioning with respect to the receiver from far-field to near-field regions. The effects of different target electrical sizes and detection distances on the received signal, as well as the impact of the trajectory of the moving object, are evaluated and discussed. All of the results are shown in terms of quantities normalized to the wavelength and can be generalized to different configurations once the carrier frequency of the FSR system is set. The range of validity of the proposed closed-form approach has been checked by means of numerical analyses, involving comparisons also with a customized implementation of a full-wave commercial CAD tool. The outcomes of this study can pave the way for significant extensions on the applicability of the FSR technique

An Atmospheric Sensitivity and Validation Study of the Variable Terrain Radio Parabolic Equation Model (VTRPE)

The Variable Terrain Radio Parabolic Equation (VTRPE) computer model is a powerful and flexible program that provides calculations of the radar propagation conditions of the atmosphere. It is limited however, by the accuracy and resolution of the input data. This study quantifies the sensitivity of the VTRPE model to the accuracy and resolution of the atmospheric parameters that go into it. Also, two case studies are examined to test the utility of VTRPE in operational use. The sensitivity to measurements of pressure, temperature, and humidity was found to be dependent on the meteorological environment. In standard and subrefractive environments, average values of Root Mean Squared Error in calculating propagation pathloss were greatest for measurement errors in humidity. While the overall RMSE averaged only 0.5% to 5%, in certain regions the errors in calculating pathloss were as high as 20%. VTRPE was used to calculate possible height errors when birds were detected at long ranges from a WSR-88D radar in a ducting environment. While the radar assumes a standard atmosphere when calculating height, results from VTRPE suggest that this resulted in possible height errors of over 3 km. Another case study of detected anomalous propagation was examined to determine the effects of multiple soundings in the VTRPE calculation of propagation pathloss. In this example, the effect of assuming a homogeneous atmosphere resulted in propagation pathloss errors of up to 30%

Radar cross section studies

The ultimate goal is to generate experimental techniques and computer codes of rather general capability that would enable the aerospace industry to evaluate the scattering properties of aerodynamic shapes. Another goal involves developing an understanding of scattering mechanisms so that modification of the vehicular structure could be introduced within constraints set by aerodynamics. The development of indoor scattering measurement systems with special attention given to the compact range is another goal. There has been considerable progress in advancing state-of-the-art scattering measurements and control and analysis of the electromagnetic scattering from general targets

Application of coupled-wave Wentzel-Kramers-Brillouin approximation to ground penetrating radar

This paper deals with bistatic subsurface probing of a horizontally layered dielectric half-space by means of ultra-wideband electromagnetic waves. In particular, the main objective of this work is to present a new method for the solution of the two-dimensional back-scattering problem arising when a pulsed electromagnetic signal impinges on a non-uniform dielectric half-space; this scenario is of interest for ground penetrating radar (GPR) applications. For the analytical description of the signal generated by the interaction of the emitted pulse with the environment, we developed and implemented a novel time-domain version of the coupled-wave Wentzel-Kramers-Brillouin approximation. We compared our solution with finite-difference time-domain (FDTD) results, achieving a very good agreement. We then applied the proposed technique to two case studies: in particular, our method was employed for the post-processing of experimental radargrams collected on Lake Chebarkul, in Russia, and for the simulation of GPR probing of the Moon surface, to detect smooth gradients of the dielectric permittivity in lunar regolith. The main conclusions resulting from our study are that our semi-analytical method is accurate, radically accelerates calculations compared to simpler mathematical formulations with a mostly numerical nature (such as the FDTD technique), and can be effectively used to aid the interpretation of GPR data. The method is capable to correctly predict the protracted return signals originated by smooth transition layers of the subsurface dielectric medium. The accuracy and numerical efficiency of our computational approach make promising its further development