EVALUATION OF A TERRAIN-SENSITIVE, PROPAGATION PATH LOSS MODEL BASED UPON THE GEOMETRICAL THEOKY OF DIFFRACTION, MODIFIED FOR FINITE CONDUCTIVITY AND LOCAL SURFACE HOUGHNESS: A Thesis Presented to The Faculty of the College of Engineering and Technology Ohio University In Partial Fulfillment of the Requirements for the Degree Master of Science Richard Ma. November 1983 I INTRODUCTION The work presented in this paper was funded by Southeast ern Conference for Electrical Engineering Education under contract N60921-81-D-A191. The purpose of this research is to investigate the feasibility of employing Geometrical Theory of Diffraction for modeling electromagnetic wave propagat ion path loss over irregular terrain. The GTD approach to calculating electromagnetic fields can be divided into two parts: a geometrical process of finding which rays exist and where their reflect ion and/or diffraction points lie, and a mathematical process of evaluating the magnitude and phase of the corresponding electric field at the receiver location by summing these rays. A total of fourteen different ray-types are considered by the model used in this study (e.g. direct, reflected, diffracted, reflected-diffracted, and reflected-reflected- diffracted). Input parameters to the model include a piecewise-linear two-dimensional terrain profile, the locations of the transmitting and receiving antennas, frequency, distances, and the electrical constants of the ground. Since the GTD method is entirely analytical, tropospheric attenuation effects are not included in the model. In past, GTD has been used to determine the Instrument Landing System (ILs) glide slope performance. For that application, the wavelength is approximately Im, incidence angles are usually near grazing, and the fields are horizontally polarized. Under these conditions, the ground itself is assumed to be a perfect conductor, and the gross irregularities such as dropoffs and hills are more important than surface roughness. However, to provide more meaningful results when estimating propagation losses for a wide variety of terrain and receiver-transmitter geometries, the i model was modified to account for finite conductivity and local surface roughness for both horizontal and vertical polarization. This modification is one of the crucial facets of this research. Although there exist other propagation path loss models, they all have limitations. The Physical Optics (PO) model, which calculates the field strength by summing fields re- radiated by ground currents has the disadvantage of requiring long computation time. Its performance is also limited by failing to provide a correct field interaction between linear segments comprising the profile. Another model, developed by Longley-Rice, which is intended to determine propagation loss for paths where only limited informationdefining terrain is available. In particular, the model is intended to estimate propagation path losses for terrain profiles given in the Continental United States (COWS) data base. The Longley-Rice model is Statistical in nature, and has been known to give results not as accurate in some circumstances such as short range paths. The shortcomings of existing models led to the developments of the GTD model as an alternative tool in predicting propagation path loss. Finally, GTD modeled data were compared against measured path loss data to provide an evaluation of prediction performance capability. These comparisons, which were made over a range of distances and frequencies, show that GTD is a feasible means for predicting short-range propagation path losses. I I GTD BACKGROUND and DEVELOPMENT The Geometrical Theory of Diffraction (GTD) is an analytical method for determining the amplitude and phase of electromagnetic wave behavior resulting from interact ion with conducting surfaces. The theory is basically an extension of Geometric Optics (GO) which includes diffraction. The theory has its origin in a mathematical work by Sommerfeld. His paper 11 1 published in 1896, describes the mathematics of diffraction for a perfectly conducting, inf inite-length half-plane. In it, he emplogs the Fresnel integral method to evaluate the nlezfric fie12 variation as the observation point changes in ;ccation f~om the illuminated region to the shadow region. However, the drawback of Sommerfeld's work is that it is only limited to half-plane ap2licaticns. Starting in 1953, it xas Keller [2,7,4J who systematically developed the Geometrical Theory of diffract ion for more general applications. Since then, this method has undergone improvements by many workers and is still undergoing changes 151 to meet various requirements. In Keller's original work, asymptotic expansions were used to describe field behavior. The result thus obtained yielded unrealistic singularities in the immediate vicinity of the shadow and reflect ion boundaries. Later, Kouyoum jian and co-workers modified Keller's work to a uniform solution which provides a continuous field everywhere; this revised theory is the Uniform Theory of Diffraction (UTD). The method addressed in this thesis is a direct application of UTD. Since UTD is an extension of GTD concept, it is commonly referred to as GTD. Geometrical Optics (GO) Geometrical Optics, or ray optics, was originally developed to analyze the propagation of light, where the frequency is sufficiently high that the wave nature of light need not be considered. GO theory assumes the flow of electromagnetic radiation between two points in space can be viewed as travelling in straight lines called rays; further, rays are assumed to not interfere with one another and hence can be summed vectoriaily i.,I conform to the laws of superposition). Two fundamental ray types are considered in GO. They are direct and reflected rays (*) as illustrated in Figure 2-1. A direct ray exists if there is no blockage along the ray path between the transmitting antenna and receiving antenna. A reflected ray is generated if there are points on the terrain profile which satisfy Snell's Law of reflection, viz, there is a reflection area which causes the angle of incident of the incident ray to equal to theangle of (*) Refraction phenomenon is excluded in this application because the amplitude of the refracted ray transmitted through hills would be too weak to be significant. reflection as shown in the Figure. In the application here, the wavelength of GO field is assumed to be small compared to terrain variations, so that reflection is considered to be a local phenomenon. Consequently, reflection is assumed to eminate from a point rather than an area. That point is commonly called point of reflect ion. Also, Geometrical Optics assumes the phase of the direct and reflected ray to be proportional to the total optical path length of the ray from a reference point, where the phase is defined to be zero. The amplitude varies according ta the principle of conservation of energy; thus field iztensity decreases with increasing distance as described below. Throughout this thesis, the receiving point is located in the far field of the antenna, and hence, a ray is considered to be in the form of plane wave at the point of reflection. For a far-field application, a GO field such as the direct ray can be obtained by considering only the leading term in the asymptotic, high-frequency solution of Maxwell's equation 16 1. The solution thus obtained indicates that field intensity decreases inversely with distance and incurs a phase variation of e-1 BR, where R is the path distance measured from the transmitting antenna to the receiving antenna, and B=2n/X is the phase constant of the wave. To illustrate the reflected ray and the method for calculating its contribution, refer to Figure 2-2, which depicts the direct and reflected rays, and an image representation of the source. Both the direct and reflected rays are eminated from the source antenna radiating at a height h above a flat ground plane, assuming perfect conductivity. The observation point is located as indicated in the figure, and is in the far-field region of the antenna. Image theory 171 states that an equivalent configuration will result if the ground plane is removed, and an image source is added at a distance -h from where the ground plane had been, as indicated in the figure. The anpiitude of tze imge mirre.~L- aqua1 to the amplitude of the direct source and is in phase for vertical polarization and out of phase for horizontal 2olarization as is shown in Fig~re2-3. The distanse 2, Setween the observer and the inage source is equal to: where h is the height of the antenna from the ground. For practical applications, the reflecting surface will introduce losses and phase shift to the incident field due to imperfect conductivity and surface roughness. These effects are accounted for by the complex valued reflection coefficient ( r ). In case of perfect conductivity, (r ) reduces to +1 for vertical polarization and -1 for horizontal polarization, both of which indicates incident field is totally reflected to the observation point. Given the above information about the phase shift and losses incurred by the earth surface, the reflected ray contribution can be written as: where Eo is a constant representing the field intensity at the reference point. The direct field which travels along the line joining the source and observation point and is similar to reflected ray; the energy density decreases inversely with distance and a phase variation of e-jBRd , where Rd is the path distance from the source antenna to the observation point The composite signal received at the observation can be calculated by summing the direct field and reflected field as follows: where Er is the received field at the observation point. Knowing the electrical properties of the reflection surface, which determines the value of the reflection coefficient, and the location of the observation point, signal can be readily determined. Deficiency of Geometrical Optics The reflected ray and direct ray configuration considered in SO can cause a serious deficiency if used in VHF wave propagation modelling over irregular terrain because it fails to account for diffraction.