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 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 and receiving antenna.

A reflected ray is generated if there are points on the terrain profile which satisfy Snell's Law of , 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 modelling over irregular terrain because it fails to account for diffraction. For example, consider a

two dimensional conducting edge as illustrated in Figure 2-4. If observations are made on a circle of constant radius

as illustrated, starting in region I, moving clockwise to

region 11, the following will be observed. First, the reflected ray disappears at and below the reflection boundary because the point of reflection migrates beyond the

edge. Consequently, GO predicts a field discontinuity at the reflection boundary. Also, consider the immediate vicinity

oi ?he shadzw 3oundsry where the direct ray is blocked by the tip of the edge; GO again predicts a field discontinuity st the shadow boundary due to the loss of the direct ray.

Since Geometric-Optics fails to account for the phenomena of diffraction, abrupt and unrealistic field discontinuities across the shadow and reflect ion boundaries are predicted by

GO. In addition, region I11 (shadow region) will be determined by GO to have zero field intensity, again an unrealistic calculation. These deficiencies led to the development of GTD.

Diffraction

Diffracted rays, according to Keller 18 1, have certain properties : 1. The diffracted field propagates along ray paths that include points on the boundary surface. These ray

paths obey the principle of Fermat, also known as the principle of the shortest optical path.

2. A diffracted wave propagates along its ray path so that the energy density decreases inversely with increasing in distance, and the phase delay equals the

wave number times the distance along the ray path. 3. Diffraction, like reflection and transmission, is a

local phenomenon at high frequencies. That is, it depends only on the nature of the boundary surface and the incident field in the immediate neighborhood of

the point of diffraction.

Contemporary GTD theory can be used to calculate diffraction from cones, curve surfaces, and wedges 131. However, the

work addressed here models terrain as +UWU-u ~~~~CILOAULL~L,---'---' piecewise-linear segments; hence only wedge diffract ion is considered, although it is likely that propzgation paths may be encountered where other types of diffraction may provide more meaningful results.

The value of a diffracted ray is calculated by the value of the incident plane wave at the point of diffraction multiplied by a diffraction coefficient. This is similar to the reflected ray, which is obtained by multiplying the incident ray by a reflection coefficient. The diffraction coefficient for a wedge configuration is determined by the geometry in the immediate neighborhood of the point of diffraction. To illustrate how field continuity near the shadow and reflection boundaries is preserved as a result of the diffracted-ray contribution, consider a ray incident on a two-dimensional edge as illustrated in Figure 2-5. GTD employs the following expression to describe the field behavior of diffraction [I01 : I I I I i'i D (@,@'I = ~d'(@-$') + Dn (@-@I)

I I II where Dd' and D, are the vertical and horizontal polarization diffract ion coefficient terzas for the edge faces o and n respectively.

These four terms are used to camn~naater - --- for the discontinuity in the geometrical-optics field at a shadow and reflection boundary for the two faces of the wedge. For instance, the terms of the form (@-@I) are to compensate for the loss of the direct ray at the shadow boundary; those of the form + are to compensate for the loss of the reflected ray at reflection boundary. Thus, the GTD diffraction coefficient enables a realistic field to be calculated regardless of the location of the observation point.

The overall electric field in any of the three region in space can now be written as: where the electric field contribution from diffract ion is obtained by GTD method. While the above equation applies only to a perfectly conducting edge, modification for finite conductivity applications have been performed, and is described in the next chapter. I I I GTD Modified for Finite Conductivity and Surface Roughness

In the early development of GTD, the theory assumed that diffract ive edges were perfectly conducting, which simplified the diffraction coefficient expression. Because propagation modeling involves diffract ion from imperfectly-

conducting surfaces, GTD theory was modified in order to provide more meaningful results when estimating terrain diffraction. The objectives sought in implementing the modification were to match the reflected Tay :ontribution at tlmmi+$e.2 the reflection boundary, an2 "LA.. r aY contribution at the shadow boundary. These objectives were met, and subsequent continuity checks at the shadow and reflect ion boundaries indicated that continuity had not been violated by the modification.

In order to provide insight into wave interaction with terrain, this chapter begins with a discussion of the effects of finitely-conducting and locally-rough terrain on wave reflection, which is then extended to defining those constraints imposed by the effects on the diffraction coefficient . Finite Conductivity Reflect ion Coefficient

The behavior of the vertical and horizontal reflection coefficient for finite conductivity is illustrated in Figure 3-1, where the percentage of reflection is plotted against the incidence angle for fresh water and commonly-encountered earth surfaces. The conductivity and permittivity of the medium are shown in the figure.

In Figure 3-1, it is seen that as the incidence angle changes to 90 degrees (i.e. grazing angle), the magnitude of the reflect ion coefficient approaches unity. In such case, the phase angle of the reflection coefficient, approaches

-180 degrees as depicted in Figure 3-2. As a result, a reflection coefficient of -1 will occur at grazing zr,gle for all common ground planes.

Rough Surfaces

The laws of reflection by a perfectly smooth surface cannot, in general, be directly applied to terrain due to surface irregularities. One of the major difference in the characteristics of a smooth surface and a rough surface is that a smooth plane (of sufficiently large dimensions) will reflect the incident wave specularly, or in a single direct ion, while a rough surface will scatter energy diffusely. The degree of roughness depends upon the wavelength and angle of incidence. To account for surface d

hori zon ta L In P --

m LL u -- D 00 In --

rn lL conductivity = 0.01 2 O/m u relative permittivity = 15.0 oI frequency = 300MHz

U) N --

0 0

I -- -- - I 1 1 I 1 I 18.00 36.00 54.00 72.00 90 INCIDENT RNGLE Figure 3-1 Amplitude of reflection coefficient as a function of incident angle 0 0 vertical polarization rn 0

0 conductivity = 0.01 2 U/m Wo relative permittivity = 15.0 -Id frequency = 300MHz =co-- ZIa

WZ cn rn a0 n I

0 0 rn 0 00 horizontal polarization d 1 1 1 1 I I I I I I 0.00 18.00 36.00 54.00 72.00 90.00 INCIDENT ANGLE Figure 3-2 Phase of reflection coefficient as a function of incident angle roughness, a factor is used to modify the reflection coefficient. This modified reflection coefficient is defined by LII]:

where is the plane-wave reflection coefficient for 4' L II from a rough surface, Ro is the plane-wave reflection coefficient for a flat smooth surface

( R' is for horizontal polarization, and R " is for vertical polarization), and 6s is the surface roughness factor.

The theory describing the effects of rough surfaces on the reflection assume that terrain elevation are Gaussianly distributed with respect to the mean elevation. According to Central Limit Theorem 11 21, random 2-dimensional terrain roughness will converge to a Gaussian distribution as the number of terms in the sum is large (The terrain investigated in this paper ranges from 0.5 kilometer to 120 kilometers with various shapes and features so that the number of terms are considered large). For a Gaussian

Model, 6s is defined by 11 31 :

A+ is the phase shift between the shortest and the longest reflected path. Consider rays 1 and 2 (Figure 3-3) incident on a surface with irregularities of height Ah at a grazing angle Y . The path difference between the two rays is :

Ar =2Ah siny

and hence the phase difference is:

-4rAh siny where Ah is the standard deviation of the terrain elevation along each piecewise-1 inear sect ion of the terrain defining the profile and X the wavelength. The vai1~ -n. . is assumed to be constant throughout the entire propagation path, however, the model could be modified to accept different values for different parts of the profile. If A@ , the phase difference is small, the two rays will be airnost in phase as they are in the case of a perfectly smooth surface. This A@ is the same variable as is used in the

Rayleigh criterion 11 41 in determining whether the surface is smooth for a given frequency. Finite Conductivity Diffraction Coefficient

To illustrate the edge diffraction coefficients for two dielectric plates and to show how field continuity near shadow and reflection boundaries is preserved, consider a ray incident on a dielectric edge as depicted in Figure 3-4. In the two dimensional case the diffraction coefficient is expressed as 1151:

I A I I I1 II II I1 + AoDo (@+@'I + A,D,(++@') fiiII I where Lo , L, , A, , A: are finite conductivity correction constants necessary to preserve field continuity at the reflection boundary and shadow boundary for the dielectric wedge. In the case of the perfectly conducting edge discussed in Chapter 2, these fozr cz;.sta~"~ts are equal to 1 I I I I I unity. The terms Lo and Ln are correction terms to account for variations in phase and amplitude due to differences between finitely conducting wedges and perfectly conducting wedges at the shadow boundary for the dielectric plate o and I n respectively; while A! and Anrf account for such differences at the reflection boundary. At shadow boundaries, the difference between finite and perfect conductivity is that energy may be transmitted through the finitely-conducting medium. If transmission does occurs, I I I I this must be accounted for by the constants L! and L, . For high-frequency terrain modeling, ray transmitted through ;i 4 hills and mountains is negligible, thus Lo =Ln =l.

The reflected field which is modified by the reflection coefficient vanishes at the reflection boundary; as a result, the diffracted field is required to increase in amplitude to compensate for the reflected ray loss at the reflect ion boundary so that the total high-f requency field is continuous everywhere. In this application, A, and A, are set to equal to the reflection coefficients of the edge I is surfaces 0 and n, respectively. Therefore, A! = Rg for the L two dimensional case. 4 is equal to the modified reflection coefficient for rough surfaces application as described earlier.

To demonstrate that the above changes to the diffraction coefficients do not violate continuity constraints, continuity tests were performed. The results of these tests presented in Appendix A show that the modifications zbcxre ds not violate any GTD concepts. The following chapter will presents a model evaluation by comparison with measured IV Measured and Modeled Data Comparisions

The GTD model modified for rough surfaces and finite conductivity has been used to predict propagation path loss for a variety of terrain profiles. This chapter presents those results along with measured data for terrain profiles of different lengths and contours. These results enable a realistic evaluation of the model's performance, which in turn determines the feasibility of employing the model in general propagation path loss prediction.

Yeaauzsd data were obtained from a propagation experiaent report by McQuate, et. al. 11 6J and were reduced to digital f3rmat to sfford comparison with modeled data.

~h~ referenced report contains tabulations 0 f electromagnetic propagation loss data resulting from propagation measurements over irregular terrain in Colorado with path lengths ranging from 0.5 to 120 km at seven frequencies in the 230- to 9200-MHz range. These reduced data consist primarily of graphs showing basic transmission loss vs. receiving antenna height derived from the measurement of each path. Information about the propagation path are given by photographs, a terrain profile, and a description of vegetation cover. All transmissions were continuous wave and frequencies of 230, 410, 751, 910, 1846, 4595, and 9190 MHz were used with horizontal polarization only. To adopt the McQuatels terrain profile as input data to the GTD model, the profile was first approximated by piecewise-linear segments which represent the original path. In some cases, this process can proceed in a straightforward manner, if the predominant slopes and diffractive edges are well defined. However, in other cases, the process is not so straightforward, particularly those profiles involving multiple peaks and large irregular roughness. Often, a profile can be represented by more than one piecewise-linearized approximation. Under this r' -,-::-~+3r,,-i= fi 2 i.r- +n ------"-*-", =, ." the user, based onhis uwn experiznce, ,a ia~er-ine whether an edge constitutes diffraction or reflectian; or if the edge is merely a source of local surface roughness. Thus, there is no well- deficed methodology established to aid in the linearization process, aithougn it is known that the number of edges defining the terrain should be kept to a minimum due to the cumulative effect of computer errors. These factors are discussed where applicable along with the presentation of terrain profile and piecewise-linear approximation.

rn, A, Au ,,,.-:VVLU~ a "vnchiiiark for the GTD model performance, modeled data from the Longley-Rice Point-to-Point model

L17 ,I 81 is also plotted along with GTD-modeled results and measured data. The Longley-Rice model was developed at the Institute for Telecommunication Science, and is referred to here as the ITS model. Input data required by both the GTD and ITS models are identical. Since the inclusion of ITS modeled data serves only as baseline information, a discussion of its performance is not included.

The presentation of data are arranged according to the path length, starting with the shortest path; in all, eleven paths are presented. Preceeding each of the paths investigated, a brief description is offered on the salient characteristics of the path (e.g. whether it is within line

of sight or beyond line of sight), assumptions made in the linearization process, and where appropriate, comments on

the behavior of GTD modeled results. The terrain profile itself is a redrawn from McQuate's report, along with the

piecewise linear approximation of the profile, represented by dotted lines superimposed on the terrain profile. The

input data files for those eleven profiles can be found in Appendix 3.

A. DATA REDUCTION

All terrain information and measured propagation path loss data were obtained from a hard copy of the McQuate report. To retrieve those data from graphs in the report,

an electronic digitizer was used to facilitate the process.

A single data point was obtained by moving an optical viewer (using the front panel controls) over the desired location on the curve and then pressing a button on the digitizer. The co-ordinate of that point was automatically scaled and

translated into the appropriate values as appeared in the report, which was stored discretely in computer disk storage. The only data that the operator had to enter during

the process was: for the case of Path loss data, the path loss scale increment on the Y-axis; and for the terrain profile, the length and height of the path.

Path loss data were sampled at the interval of every 1/2 meter over the entire antenna height movement range of 13 meters. By following a predefined procedure of digitizing

the path loss data, the seven curves corresponding to the seven different frequencies in the McQuate's report were

organized into a natrix file.

A dewlett-Packard 7225A Graphics Plotter equipped vith a optical viewer was employed for this effort (the optical viewer is loaded like a pen for viewing).

The plotter was connected in a parallel configuration

with an ADM-3A CRT terminal. The computer to which this hardware was connected was an IBX 4341 running under -$%/SP CMS timeshare mode. To provide proper handshaking for data transfer between the host computer and plotter, an ASSEMBLER

routine was written. Plotter ~zsolutlon in both axes exceeds 0.001 inch, indicating that quantization and truncation errors can be considered insignificant. The hard

copy report from which these data were taken was a Xerox copy of the original report. Thus, data were likely contaminated by photocopy errors. Evidence of

such errors appear as slightly curved axes, non-squareness, and distortion. To compensate for such errors, the end points of the axes were entered, from the plotter, to the software; this information was then used to correct subsequent data from the plotter via a linear interpolation method. All data files thus obtained were checked against the original data; any errors, which were usually obvious when they existed, were corrected by editing the associated data file.

i'leasured path loss data are plotted versus receiver antenna height, with one plot for each frequency. The ITS modeled and GTD modeled data are also plotted on the same graph to enable a direct performance evaluation to be made; these model results represent absolute path loss, rather than relative loss. B. Presentation of data

1. Path R1-0.5-TI (0.5~n., flat, within line of sight)

This terrain profile is shown in Figure 4-1. As can be seen, the profile is made up of flat ground sloping down

towards the transmitting antenna. Because of profile simplicity, the linearization process was straightforward, resulting in a modeled profile defined solely by the endpoints.

This profile was the first one to be chosen in the

development stage of the GTD model to verify that no gross errors existed.

The second reason in selecting this profile was to study

the local surface roughness factor and its effects on the vertical lobe structure which arises from the interference between the direct ray and reflected rays. For a flat ground

plane, such as the one discussed here, the GTD model operates as a Geometrical Optics model since there are no

diffractive edges. Thus, GTD model estimates of path loss are based exclusively on a singly-reflected ray and direct ray For such a configuration, the behavior of the modified reflect ion coefficient for local surface roughness can be study explicitly.

Measured and Modeled data for this terrain profile are plotted in Figures 4-2 through 4-8, with the ground electric constants used as shown in the figure. During the investigation of this profile, the electrical constants of the ground plane were varied over a wide range of values to determine its effects on the received field. The result of this experiment showed that field strength did not change appreciably. This is an expected result for horizontal polarization because its properties at low angles of incidence are similar to perfectly conducting ground planes. However, this result would not be expected for vertical polarization or for paths involving high incidence angles.

Additionally, a range of local surface roughness

,siY1*1-3-,~-.F\-a+I..c. were investigated to determine its effect on the modeled data. Generally, the model is sensitive to the local surface roughness; the larger the modeled surface roughness, the smaller %he modeled lobing depth. The actual profile foreground consists of alternating strips of plowed ground and wheat stubble; therefore a range of surface roughness values from 6-1 8 inches were used, which is reasonable based upon the description of the profile. Those values provided good results in the modeled data, although greatest agreement between modeled and measured results were obtained using a roughness value equal to 9 inches. Hence, 9 inches of local surface roughness is used for all subsequent modeled data for this profile.

For the first three lower frequencies plots using the 9 inches local surface roughness factor, the lobing effect is not prominent, and the modeled data is in close agreement with the measured data. At higher frequencies, vertical lobing does becoming more noticeable with the size and the depth of the lobe nulls, and as well as the spacing between those nulls being in good agreement for both measured and modeled data. In some instances, the modeled lobing occurs at different receiver antenna heights than does the measured lobing, causing an apparent divergence between the measured and modeled data. However, this separation is considered to be caused by errors in terrain profile definition or antenca helgAt hats rstfier t:sn >"> -3deling error. 7 :& "OC 0 a 2 aJ Fi 4 Q,aaJ Qua g2gffl Pam bQ,b UXH m G -0 ZR 0) 0) C Cm 2 a0 er U a 'ti k 3 LO 4 L?- -Y

0 0

1: I

I I

o-OOI- oo-ori- oo-oai- oo-osi- oo-oni- [BQI SSOl Hltfd

'(I a 0) 0) d d Q,'(Ial a0)m g2g LO Par/] E aJ E-r WEH

2. Path R1-5-T6A (4.6 km., Mixed Path with Double Diffract ive Edges)

This terrain profile, shown in Figure 4-9, is made up of rolling hills. The piecewise linear approximation process was straightforward, resulting in the seven edges represented by the dotted line in the figure. Of primary interest in this profile is the doubly-diffractive edges which has its shadow boundary corresponding to a receiving antenna height of 9 meter. At that height, the receiving antenna is in a straight line along the two diffractive edges ~diththe transmitting antenna. Below this height, the patn is blocked, and is below line of sight. Above the 9 meter antenna height, the path is within line of sight.

This type of configuration is of considerable interest with regards to GTD modeling theory because it involves caiculations of two rapidly varying fields near the transition region; if GTD has a region in which the theory is not strictly applicable, it would be in a transition region such as the one presented in this profile.

Figures 4-10 through 4-1 6 present plots of measured and modeled results. Referring to the 230 MHz plot in Figure 4-10, a field discontinuity of about 5 seen at the transition region discribed above. This discontinuity is the largest observed in model response and is not considered to be significantly detrementel with regards to propagation modeling. As the frequency becomes higher, the discontinuity vanishes as is seen in the figure. The reason for this behavior is that the area of the transition region defining the rapidly-vary ing fields decreases with increasing frequency. Although the discontinuities may still be present, they are apparently bypassed in the sampling scheme used for data retrieval.

Generally good agreement is demonstrated between the modeled data and the measured data although there is a bias error that tends to increase with frequency. This increasing -. oiaa error, according to previous experience 11 9) gained lros- ~ropagationmodeling, is likely due to trees within the path that are not taken into account by the model, whose absorptive effects increase with frequency.

0 0

a >

+XI ! ----- OO'OL- 00 08- 00 08- 00' 0 0 m )8 1P I a M 8X l OX j a X a X 8 X I- 8 X a X a 0

8 [f Q > 8 0 8 I 8

8 X

+ -- '+.- ooqor- 00-od- 00-od- 00-oor- oo 011- oo 021- oo orr- 00-ohi- oo.0~1--A" (90)SSQ~ HL~M

0 0 ex T~ B# I ex I ex I 8X 8X X 1' e 8 X I 8 X 1:: 0 X 8 X 8 X

e xx 8 X r-a 8 X 1;; 8 X 8 8 8 i"" 0 8 a X i" oo-ooi-- oo*oz;- OO.DO;-

0 LQ - a3 rn. 2 s2 3 2 5 C 0 -4 U a 0 '+I k 7 II K' ; 2 S 'Z 3. Path R1-5-T5A (5.0 Km., beyond Line of sight)

Refering to the drawing of the terrain profile in Figure

4-7, it is seen that the direct path is blocked for all antenna height. The piecewise-linearized model is approximated by 3 plates.

GTD calculated results from this piecewise linear terrain model for the lower frequencies are extremely close to the measured data as can be seen fromPigures 4-18 through 4-23. As frequency becomes higher, discrepancies between measured and modeled data increases. The reason may be due to losses caused by trees or other intervening objects as was observed with the previous path.

x x x x x GTD Modeled - Measured

QDBOQ ITS Modeled

Local Surface Roughness (one

sic~ma)= 9 inches (0.2286 meters)

Frequency = 910 MHz

Conductivity = 0.012 U/m

Relative Permittivity = 15.0

Figure 4-21 . Path loss vs. receiving antenna height for Profile R1-5-T5A , Figure 4-17 . Transmitter height is at 7.3 meters. 'r.oo s; 00 5; 00 7: 00 B; 00 1i.00 19.00 RCVR. ANT. HT. [MI

4. Path RI -10-T2A (9.8 Km. , Beyond Line of Sight)

The terrain profile along with the piecewise linear approximation are shown in Figure 4-24. The path is beyond line of sight, with the direct ray blocked by a hill. A total of 7 edges are used as input data.

The measured and modeled data are shown in Figures 4-25 through 4-31; close agreement between the two were obtained for all frequencies. Also, the measured data do not suffer the high-frequency errors evident in the previous two profiles; zne reason may be due to the absence of trees along the path.

5. Path R1-10-T3 (9.6 Km., Line of Sight)

- .-- The terrain profile for this path is shown in Figure 4-32 Because the piecewise-linear approximation does not fit the actual terrain profile as closely as the previous profiles, the local terrain roughness factor was adjusted during the experiment to investigate its effects. In this effort, local terrain roughness values of .2286 meter and 2 meters were used. The GTD program was run with the same linearized terrain profile using these different local surface roughness parameters.

The first set of calculated results using 9 inches local surface roughness are shown from Figures 4-33 through 4-39.

GTD modeled results are in close agreenent with the measured data, except at 751 MHz. At 751 LVIHZ, an anomaly is obvious in the measured data, where the path loss at 751 MHz is inconsistent with the reported losses at higher or lower frequencies; hence comments on GTD modeled performance at that frequency are not offered. At 1846 MHz, GTD over estimates the depth of the vertical lobe.

Secondly, the roughness factor was adjusted over a wide range of values. It was found that by increasing the roughness factor to 2 meters, the depth of the lobing was closer to the measured data. The new path loss estimate for 1846 31Hz is plotted on Figure 4-44; and other frequencies are shown in Figures 4-40 through 4-46. Generally, the local terrain roughness factor does not incur a not iceable effect on frequencies lower than 1 GHz. Other values of terrain roughness factor ranging from 0.5 to 5 meters were attempted, but based upon the size and the depth of the lobe, and taking into consideration the variation of the of the linearized profile with respect to the actual terrain profile, a final value of 2 meter was selected.

0 . 0 e 5" X e x e X e X e x e x e X 0 X X.

a

I X +.---- +.---- AX ooaoL- 00 08- oo 08- o 0-oo.oci-oo.oni-oososr-@ (gal SSO-I ~ltid

0 0 B m 8L I 8( j

I

- 8 oo-0:- 00-00- 00-06- 00-001- o~*o~i-00-ozi~ oo'06i- 00-obi- (801 SSOl Hltfd

4 4 aaa, aa,a g:i?ffl Clam EaI3 WXH

6. Path R1-20-TI (27.7 Km., Beyond Line of sight)

The terrain profile along with the piecewise-linear approximation are presented in Figure 4-47. The approximation only tends to include the major peaks and slopes of the actual terrain. The approximation consists of 5 edges as seen in the figure. Because of variations of the actual terrain with respect to the linear approximation,

a modeled local roughness parameter of 2 meter was chosen.

Calculated results from GTD modeled and measured data are . -. aiio%-~i ii4-48 through 4-54. As aasn from these

figures, 223 results show a larger loss than the measured data as the frequency increases, especially those above 910

-MU?., ---- These excessive variations may be caused by modeled

~~it;r\at'ri reflection from the comparatively smooth segments used to approximate the irregular terrain.

C, P-a C -4 m $ 4 .rl aJLJ UOC a, CJ tn k I .4 4 a, .Ir;C ?ah .-I a, rn .4 4J rnu-ic, 0 0 .4 d k hW C 5kld ldOh hWB

rl d aalaa5 Q) OLIO E25: ardrn E-1 s E-( WEH

0 0 X a x 0 X I . X a X a X a X a a rn XO X. X a X X . x .X .X X .X ex 8( a ex 00-oat-'--T-'- 00 on- -m*mi- 00-osi- w-osi- oo*o~i- (80)SSOl Hltfd X X X X X GTD Modeled - Measured

8Qaec) ITS Modeled

Local Surface Roughness (one

sigma) = 2 meters Frequency = 1846 MHz Conductivity = 0.012 U/m

Relative Permittivity = 15.0

Figure 4-52 . Path loss vs. receiving antenna height for Profile R1-20-Ti , Figure 4-47 . Transmitter height is at

I 7.3 meters. 7- 1.00 3.00 5.00: - --+------I---+------I 7.00 8-00 11-00 13.00 RCVR. FINT. HT. (MI 0

X a X '3 XO I xm xe is Xb X. xe* :" Y Cr W m i X. X a X a X X X X X i"" X X X X

Y 1 L < - oo.oo:- w-oti- 00-ozi- ooosi- oonmi- oo*osi- h*osi- 00-o~i- ooos~--AX (001 SSQl Hltld X X X X X GTD Modeled

--- Measured

a Q a @J Q ITS Modeled

Local Surface Roughness (one

sicpa) = 2 meters Frequency =9190 MHz Conductivity = 0.012 U/m Relative Permittivity = 15.0

Figure 4-54 . Path loss vs. receiving antenna height for Profile Rl-20-T1 I , g r Figure 4-47 . Transmitter height is at

-_t__ _1 7.3 meters. '1.00 3.00 5.00 7.00 8.00 11.00 19.00 RCVR. RNT. HT. (MI 7. Path TI-2044 (20.7 Km., Beyond Line of Sight)

The linearized approximation and terrain profile for this path are shown in Figure 4-55. The linearized model consists of 6 edges which follow only the major terrain features; again, alocal terrain roughness factor of 2 meters was used for modeling.

The modeled and measured data for this profile are shown in Figures 4-45 through 4-61. As can be seen from the

Figures, the plots are similar to that of the previous

,7 .n 7. przlf lie. At frequencies below 1 GZZ? ~TLUmodeled results show close agreement with meaanred data; vhilz above that frequency, GTD consistently gives a higher value than the rne~qured data,

0

X B X 8 X e X. i"0 X X X X X X X X X X X X X X X X i'" X X X X , Yl oo*oo:- 00-01 i- 00-ozi- oo9osi- oo *mi.- 00 *bi- OO-mi- 00-o~i- (90)SSOl Hltfd

8. 49.0 Km., Beyond Line of Sight Path.

The terrain profile for this profile is shown in Figure 6-62. Because of the complexity of this profile, two piecewise-linear approximations were used. The purpose of investigating both approximations is to determine the relationship between modeled terrain variation and the local surface roughness parameter. The first approximation, consisting of 17 edges, is shown by the dotted line in Figure 4-62. This model defines more accurately the terrain profile, hence, a roughness parameter of 9 inches is used.

P4eas:ired and GTD modeled data for the 17 edge profile are givan iz Pigure 4-63 through Figure 4-69. As seen in these figures, evidence of excessive vertical lobing is observed for frequencies above 410 MHz.

A less-accurately defined linearized profile for the same path is shown in Figure 4-70. Since this modeled profile has a greater variation with respect to the actual profile than the 17 edge approximation, a local terrain roughness factor of 2 meter is used. GTD modeled and measured data for this linearized profile are presented in Figures 4-71 through 4-77. These figures show GTD estimated path loss and vertical lobing are in closer agreements with the measured data than previous model employing smaller surface roughness

factor, especially at frequencies of 751 MHz and above.

An important observation is provided by the simple two- profile investigation presented above. The accuracy of the

GTD model does not solely depend on the accuracy of the input linearized terrain profile; some combinations of profile definition and local surface roughness factor are necessary for model accuracy. The rules for determining what combination constitutes an optimum combination would require an in-depth study which is beyond the scope of the feasibility study offered in this thesis.

u D -a ..I ..I E: m 3 d' .r( -4 a 5' 4J UOC QaD k I .r( rl 0) *dC m

0 9 X X 0 X. X 0 X. X. X. \ X. X. X. X0

e

'--T+- 00'001- 000tr- 00.0~i- 00*06i i- rnooei- (80) SSQl Hltfd '8 a rl d Q)a Q) a Q) a 29gcn Clam BQ)E UXH

X s -.: \, L - - A:! M*M:- w-oti- 00-ozi- oo-osi- oo'mi- oo-ost- oo-wi- oo*o~i- m*oet-- (901 SSBl Hltfd (I) (I) aJ C J2 a 9) 2 rl rl $%aaJ OkO z;x Clam BalE UEH

9- Path TI-50-TI (52.5 Km., Line of Si&t)

The terrain profile, along with linearized model are given in Figure 4-78. As can be seen, the path is unblocked and a totalof of five edges are usedin the linear approximation, with a modeled surf ace roughness factor of 2 meters.

Measured and modeled data are shown in Figures 4-79 through 4-84. GTD modeled results do not show the degree of vertical lobing as is evident in the measured data. The reason may be due to an excessive local surface roughness parameter and/or improper placement of terrain profile edges. Since the profile does not consist diffractive edge, the limit of GTD model's capability in predicting long paths cannot be determined.

I$ i'"

8 X +--y-t--- oo.oo:- on-o~i- oo-oai- no-ori- &*mi- oo*osi- ^oo-wt-- OOOLI- (001 SSOl Hltfd

0 0 j4

l%g 0. C t x i"" X 8 i' +--Ft- Js ooWoor- w otr- w-ozi- on*oei- OO-mi-wb*~~i- m-osi- OO*OL~- on*o~r-~- [aa) SSQ~HLU~ ;s f -;

1 - is oo*w!- oo*o~i- oo*ozi- w*ori- oo-mi- %-mi- oo-ow- ooocr- ~*osr-~ (001 SSQ1 Hltfd

4J g-a

0 0 X X T" X I X X X X X 0 X X X X X 0 X x a X e X a x a X x a i"" x a x a X X m.oor- watt- ao=ozi- oagoci- m*lai-". w-mi- w-OQI-Y an-o~i- - (801 SSQl Hltfd

10. Path R3-80-T3 (80 Km., Line of Sight)

The terrain profile for this long path is shown in Figure 4-86. Again, the path is within line of sight. consists no najor diffractive edges, The linear approximation for GTD input uses 12 edges as is shown in the Figure.

The measured and modeled data are offered in Figures 4-86 through 4-91. GTD modeled data has a biased error on all frequencies, perhaps due to tropospheric effects not considered by the computer model; thus this free-space loss estimate does not appear unreaiistic. iiowever, it shouid be noted that this path can not conclusively determine GTD aodel performance limits due to tropospheric effects not being taken into account by the model. A more representative evaluation of GTD model for longer ~aths would be provided by a path containing pronuounced diffractive edges; unfortunately, such a path is not given

in McQuate, et.al.

0 x X X X X X X X X X X x X X X X X X X X I"" X X X X

Y 1 +' 00-oor-- 00-011- oo-ozi- oo.osi- ao-mi- w0osr- wmosi- OO*OL~- (00)SSOl Hltfd >a& d a, cnuuV) .rl 4J 0 8 -4 d 5 Sk,C (dOk Q'Hh

11. Path R2-120-TI (1 15 km., Line of Sight)

As seen in Figure 4-92, this terrain profile is the longest investigated in this thesis. Again, it does not include any diffractive edges, so that the potential performance of GTD on long paths can not be evaluated.

Measured and GTD modeled data for this path are shown in Figure 4-93 through 4-95. GTD modeled data shows unrealistically large vertical lobing, which although can be decreased by raising the surface roughness factor, the bias error between measured and modeled results as existed in the previous model will not decrease. This bias error is again considered to be due to tropospheric effect. Higher frequencies data are not available from the McQuatels and hence comparisons cannot be made. a a al al 4 4 .a aJ aaga al a aav) UxHBaJB

V RECOMMENDATIONS

While undergoing the GTD model performance evaluation on propagation path loss, certain suggestions and observations led to the following recommendations.

1. The terrain linearization process should be calculated analytically by computer algorithm to determine the actual mechanism of scattering from the terrain edges, and hence eliminate the present user dependent factor.

2. The value of local terrain roughness factor should be obtained by the actual gaussian average of the terrain irregularities in addition to the two values being chosen in this thesis. However, if irregularities vary grossly over different path segments, GTD model should be capable to assign variable values to different edge segments.

3. GTD model does not include the effects of forested areas in predicting path loss although it has been demonstrated that these effects can be estimated accurately

11 91. Consequently, GTD model should be modified to include the known effects of forested areas.

4. In this study, only the horizontal polarized field was investigated. Similiar studies should be undertaken for vertical and circular polarized wave so as to expose further capabilities of the GTD model.

5. As presently configured, GTD model can only calculate diffractive edges that are perpendicular to the propagation path. Modification of GTD model to account for diffraction from obliquely-angled edges would improve prediction accuracy for certain profiles.

6. Effects of troposphere such as: refraction (bending) of wave by nonhomogeneous atmosphere; absorbtion by oxygen and water vapor molecules, absorbtion and scattering by precipitation of clouds that are not included at present should be implemented in future work. VI Conclusion

A computer model has been developed to estimate electromagnetic wave propagation over irregular terrain using the Geometrical Theory of Diffraction (GTD) modified to account for finite conductivity and local ground surface roughness. Based upon comparisons of GTD modeled data with measured data, the following conclusions are offered :

1. GTD provides accurate predict ion capabilities for irregular terrain with path lengths from 0.5 to 80 Km., at seven frequencies in the 230- to 9200- MHz range; both within and beyond line of sight paths for horizontally- polarized wave.

2. The modified diffraction coefficient used to account for finite conductivity and local surface roughness does not affect field continuity at and near the vicinity of the shadow and reflection boundaries.

3. The presence of double diffracted edges within the field transition region caused minor field discontinuities, although these effects are not considered detremental to prediction accuracy.

4. GTD accuracy depends upon on an optimized combination of both the localsurface roughness parameter and the piecewise-linearized terrain data.

5. GTD accuracy decreases for longer paths investigated, apparently due to tropospheric attenuation effects not accounted for by the model.

b. Thevalue of the localsurface roughness factor necessary for realistic vertical lobe estimates tends to increase with path length, and thus the size of the Fresnel

Zone. V I1 ACKNOWLEDGEMENTS

The author is indebted to his advisor Dr. Kent Chamberlin who generously gave his time, endless patience, and guidance during this effort.

Special gratitude is due to Dr. R.J. Luebbers and Dr. Vichate Unguichian, who developed the basic GTD model.

Thanks also to Wong Sheung Shun for technical drawings. VIII REFERENCE

11 1 Sommerfeld, A. "Mathematische Theorie der Diffraktion," Math. Ann., vol. 47, pp. 317-374, 1896. 121 Keller, J. B., "The Geometrical Theory of Diffraction," Symposium on Optics, McGill University, Montreal, Canada; June 1953.

L3J Keller, J. B., " The Geometrical Theory of Diffraction." in The Calculus of Variations --and Its ~~~lications, McGraw Hill Book cK, Inc., New York, N.Y., 1958. 141 Keller, J. B, "Geometrical Theory of Diffraction," J. Opt. Soc. Am., 52, pp.116-130, February 1962. 151 Robert C. Hansen, Editor, "Geometric Theory of Diffraction," IEEE Press, New York, N.Y., 1981.

. , --- I?!- "!'"a - J ------7 Pi., t'An Asymptotic Solution of Maxwell's Zquations" published in "The Theory of Electromagnetic - * --Naves, " a Symposium, Interscience hblishers, Inc. , New +, -- 3.11 . See also M. KLi2e, "Electromagnetic 2hzo.q and Geometerical Optics," published in "Electromagnetic Waves" by L.E. Langer; Univeristy of iJ4nlubvlLu;Lr mn nv,n - m Press, Madison; 1962. i7j Weeks, W.L., "Antenna EngineeringH, McGraw-Hi 11 Publishing Company LTD, New York, N.Y., pp 39-40, 1968.

131 Keller, J. B., "Geometrical Theory of Diffraction" J. Opt. Soc. Amer., vol. 52, pp. 116-130. 131 Ibid., Robert C. Hansen, pp. 83-218. L101 Kouyoumjian, R. G., "A Uniform Geometrical Theory of Diffraction for an Edge in a Perfectly Conducting Surface", Proc. IEE, vol. 62, pp. 1448-1461, Nov. 1974.

Ll 11 Beckmann, P. and Spizzichino, A. The Scatterin6 of Electromagnetic Waves from Rough Surfaces, Pergamz Press, New York, 1963, Chapter 12. 11 21 Larson, H. and Shubert. B., Probabilistic Models in Engineering Sciences, vol 1 , John Wiley & ~onnc., New York, pp 358, 1979.

L13j Ibid., Bechmann, P. and Spizzichino, A. Sect. 5.3. 114J Rayleigh, Lord, "On The Light Dispersed from Fine Lines Ruled upon Reflecting Surfaces or Transmitted by Very Narrow Slits," Phil. Mag. 14, pp. 350-359, 1907. 11 51 Rojas-Teran, R. G., and Burnside, W. D., "GTD Analysis of Airborne Antenna in the Presence of Lossy Dielectric Layers", Ohio State University Electro-Science Laboratory Report. 1161 McQuate, P. L. et al, "Tabulations of Propagation Data over Irregular Terrain in the 230-920OMHz Fr equency Range", ESSA Report ERL-65-ITS-58, U. S. Department of Commerce, March 1968.

1171 Longley, A. G. and Rice, P. L. "Prediction of Tropospheric Radio Transmission Loss Over Irregular Terrain", ESSA Report ERL79-ITS-67, U.S. Department of Commerce, 1968.

1181 Rice, P. L. et al, "Transmission Loss Predictions for Tropospheric Communication Circuits", Volume I, Report AD-687-820, U. S. Department of Commerce, January, 1967.

1131 Chamberlin, K. A. "Investigation and Development of VHF Ground-Air Propagation Nodeling INncluding the Attenuating Effects of Forested Areas for Within-Line- of-Sight Propagation Paths", Ohio University Avionics Engineering Center, March 1982. X Appendix

A. Diffraction Coefficient Boundaries Continuity Checks

Several critical boundaries continuity checks for different ray types have been devised to ensure that the modified diffract ion coefficient does not violate the basic theory of the GTD fundamentals. In total, three sets of

edges are studied; they are: at the shadow boundary for a singly-diffracted ray geometry; at the reflection boundary for a direct, singly-reflected and singly-diffracted ray;

and at tne reflection boundar~?J Ad-Fnr tws cases involving higher-order rays.

Verification of field continuity at those boundaries for lower-order ray types and as well as higher-order ray types are considered sufficient proof of proper GTD operation. Both the horizontal and vertical field polarization are

investigated in these checks. In addition, continuity check are carried out in perfect conductivity for the same profile which represent the GTD model before it is modified so as to provide a baseline information. A aore detailed explanat ion of each of the field continuity check operation are included in their corresponding sect ion. 1 . Reflect ion Boundary Check

The geometry used for singly diffracted ray continuity check at reflection boundary is shown in Figure A-1 . The profile, which consists of a transmitting antenna radiating over the horizontal ground plane is truncated at 13 meter to create a reflection boundary. The receiving antenna is allowed to elevate from 1 meter to 81 meter height and is located at the vertical coordinate. Three ray types exist : direct ray, singly reflected ray and single diffracted ray; and since by the special configuration of this edge, other ray types' existence is ruled out over the entire receiving antenna height range. The refleGion -:a7=dsA7, ,islined by the point at which the reflected ray vanishes, occurs at 11 meters of the antenna height for the geometry shown.

The purpose of reflection boundary continuity check is to ensure a proper electric field transition at the reflection boundary when the reflection ray vanishes. Since field intensity decreases, the diffracted ray should rise in amplitude to compensate the loss of reflected ray so that field continuity would be preserved. The diffracted ray also provides field value at the shadow region. Any abrupt changes at the boundary indicates that an error in the diffracted field calculation has occured.

'dith the above facts, refer to Figure A-2 which is a plot of the GTD estimated path loss for the geometry of Figure

A-1 assuming perfect conductivity. As seen in this Figure, calculated fields are continuous at the reflect ion boundary as is expected, because GTD model operates according to the conventional GTD before modification.

The finite conductivity path loss for a singly reflected ray of the same geometry is plotted on Figure A-3, with the ground electric constants indicated in the Figure. Since only the singly reflected ray exists the field disappears below the reflection boundary at 1 1 meter receiver antenna height. Field contribution below the reflect ion boundary is provided by the diffracted and direct rays. Figure A-4 shows this contribution in the finite conductivity case. And also can be seen in the Figure, the field transition is smooth across the reflection boundary. The vertical polarization ray suffers a higher loss than the perfect conductivity case; and the horizontal polarization field value for the finite conductivity case is essentially unchanged from the perfect conductivity case of Figure A-2. The smooth field transit ion across the reflection boundary verifies the GTD reflection boundary operation for lower order rays.

2. Shadow Boundary Check

The purpose of this shadow boundary continuity check is to ensure that field continuity is preserved at the shadow boundary so that GTD fundamental is not violated. The testing involves singly diffracted ray and direct ray. The profile geometry employed is shown in Figure A-5.

As one can see from the figure, the transmitting antenna is located at the right-hand end of the two plates that constitute the profile, whereas the receiving antenna is located st zne pcoordinate as before, being capajle of elevated from one meters height through twenty-f ive meter. Since the trmittix &~tenna height is the sane as the peak ~f the profile, the shadow boundary becomes a straight horizontal line extending from the peak to the receiving antenna ordinate at 15 meter. The existence of other ray types are not possible in this geometrical configuration, as the reflected ray from the transmitting antenna on the two plates will travel outside the range of the receiving antenna. As a result, interference from rays other than the singly diffracted and direct ones does not exist.

The case for perfect conductivity edges which represents

GTD results before modification is presented first. Figure A-6 is a plot of receiver antenna height versus path loss the singly diffracted ray. As evident from the figure, field discontinuity occurs for both polarizations at the shadow boundary. This is caused by the disappearance of the direct ray at the boundary. Thus, by the addition of the direct rays, continuity is again presvered across the shadow boundary as seen in the plot of Figure A-7 for the perfectly conducting case.

Finite conductivity plot of path loss for the geometry of Figure A-5 is shown on Figure A-7. Again, as in the previous case of perfectly conducting edges diffracted ray, discontinuity occurs at the shadow boundary due to the disapperance of the direct ray. Refering to Figure A-9, which plots the total field contributions of the diffracted and also the direct ray, it is seen that the field continuity is win pssznerl z% the shadow, proving that the modified diffraction coefficient is performing in a fashion consistant with GTD.

3. Reflect ion Boundary check for Higher-order rays

The geometry used for this test is shown on Figure A-10, which consists of seven edges. The reflection boundary for the reflected-diffracted-diffract ed ray and reflected- diffracted-reflected ray is located at 11 meter of the receiving antenna height. The purpose of this test is to check that lower-order rays and higher-order rays compensate each another to preserve field 1 continuity at reflection boundary.

Assuming perfect con&uc-tivity edges, Figure A-l l &ws a plot of the path loss for the reflected-diffracted-reflected and reflected-diffracted-diffracted rays as the receiving antenna moves from the shadow region to the lite region. P_ field discontinuity in excess of 18 db can be observed at the reflection boundary. This is due to the fact that lower order rays are absented (i.e. diffracted-reflected, diffracted, or singly diffracted) to compensate the higher- order reflected ray losses at the boundary. Total path loss for the geometry of Figure A-10 is plotted in Figure A-12 for the perfect conductivity case; and as expected, field is again continuous with the addition of lower-ordered ray types although the intensity is rapidly-varying due to the number of rays interacting in the vincinity of the boundary and their relatively strong level because of perfect conductivity. Path loss versus receiving antenna height for the finitely conducting edges for the reflect ed-diffract ed- reflected ray and the reflected-diffracteddiffracted ray is plotted on Figure A-13. Again, more than 23 db of field discontinuities can be observed at the reflect ion boundary at 11 meters. The reason that this figure is higher than the 18 db in the perfectly conducting edges is because fields are further attenuated by finite conductivity edges. Total path losses with the contributions of all existing ray types is shown in Figure A-14, assuming the same ground electrical properties as before. Once again, the fieid

continuity is preserved at the reflection boundary at 11 meter, which sufficiently indicates that the modified GTD

theory in the higher and lower ray types combinations is kept.

B. Modeled Path Profile

All the terrain profiles input data investigated in this thesis are given in this section. These data are in the original form being read in by the GTD model to generate the calculated path loss in decibels, which were subsequently plotted versus receiving antenna height. First, an explaination of the input data format and its function to the GTD model is given. It is then followed by the terrain profile files.

A typical input data file will look like the following:

NE, ICON, YMIN, YMAX, EPSIR, SIGMA, DELTAG

XN YN ZN

FREQ 1 --> RAY-TYPE CONTRGL PARAMZTERS Where

HE, (15) number of edges ICON, (15) information output control ICON = 1 detailed print out

ICON = 0 brief output summary YMIN, (FIO.5) min db value of plot axis YMAX, (F10.5) max db value of plot axis EPSIR, (F10.5) relative permittivity of ground SIGMA, (F10.5) ground conductivity in MHO/METER DELTAG, (F10.5) surface roughness factor in meter

Second record to the n-th record: X,Y,Z coordinate of the edge in 32'10.5 format, where n is equal to NE (no. of edges), in the previous record.

Ray-type control parameters (Format = 1311 ) JDIR DIRECT RAY JREF SINGLY REFLECTED RAY

JRR REFLECTED-REFLECTED RAY JRD REFLECTED-D IFFRACTED RAY JRRD REFLECTED-REFLECTED-DIFFRACTED RAY

JRDR REFLECTED-D IFFRACTED-REFLECTED RAY JDIR SINGLY DIFFRACTED RAY

JDR DIFFRACTED-REFLECTED RAY

J DRD DIFFRACTED-REFLECTED-D IFFRACTED RAY JDD DOUBLY-D IFFRACT ED RAY JDDR DIFFRACTED-D IFFRACT ED-REFLECTED RAY

JDRR DIFFRACTED-REFLECTED-REFLECT ED RAY JRDD REFLECTED-D IFFRACTED-DIFFRACTED RAY

If any of the above parameter is being set to 1, that specific raytype is ignored during the computations. Other values simply implied that raytype is included.

Frequencies in megahertz should be entered in F10.3 format.

2. Listings of Path Profile Data

1. Path R1-0.5-T1 2. Path R1-5-T~A

3. Path R1-5-T5A 5. Path R1-10-T3

6. Path R1-20-TI

7. Path R1-20-T4 6 0-2 10 .OOOOO -90 .00000 15.OOOOO 0.01200 2.00000 0.0 00 .ooo 1589.320 0.0 8197.234 1500.574 0.0 10636.652 1542.418 0.0 13536.961 1~~3.03-j 0.0 18889.855 1566.680 0.0 20740.242 1551.000 230.0 0000000000000000 410.0 751.0 910.0 1846.0 4595.0 9190.0 9. Path R1-50-T1 11. Path R2-120-T1 11. 0-210.00000 -go.ooooo 15.00000 0.01200 0.22860 I? .? 9.0 2556.481