Evaluation progresion path loss model

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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

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evaluation progression path loss model

Transcript of Evaluation progresion path loss model

Page 1: Evaluation progresion path loss model

EVALUATION OF A TERRAIN-SENSITIVE,

PROPAGATION PATH LOSS MODEL BASED UPON THE

GEOMETRICAL THEOKY OF DIFFRACTION, MODIFIED FOR

FINITE C O N D U C T I V I T Y A N D LOCAL SURFACE HOUGHNESS:

A T h e s i s P r e s e n t e d t o

The F a c u l t y o f t h e C o l l e g e of E n g i n e e r i n g and Technology

Ohio U n i v e r s i t y

I n Par t ia l F u l f i l l m e n t

o f t h e Requi rements f o r t h e Degree

Master of S c i e n c e

R i c h a r d Ma.

November 1983

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I I N T R O D U C T I O N

The work p r e s e n t e d i n t h i s p a p e r was funded by

S o u t h e a s t e r n Confe rence f o r E l e c t r i c a l E n g i n e e r i n g E d u c a t i o n

u n d e r c o n t r a c t N60921-81-D-A191. The purpose of t h i s

r e s e a r c h i s t o i n v e s t i g a t e t h e f e a s i b i l i t y o f employing

G e o m e t r i c a l Theory o f D i f f r a c t i o n f o r mode l ing

e l e c t r o m a g n e t i c wave p r o p a g a t i o n p a t h l o s s o v e r i r r e g u l a r

t e r r a i n .

The G T D approach t o c a l c u l a t i n g e l e c t r o m a g n e t i c f i e l d s

c a n be d i v i d e d i n t o two p a r t s : a g e o m e t r i c a l p r o c e s s o f

f i n d i n g which r a y s e x i s t and where t h e i r r e f l e c t i o n a n d / o r

d i f f r a c t i o n p o i n t s l i e , and a ma themat i ca l p r o c e s s of

e v a l u a t i n g t h e magni tude and phase of t h e c o r r e s p o n d i n g

e l e c t r i c f i e l d a t t h e r e c e i v e r l o c a t i o n by summing t h e s e

r a y s . A t o t a l of f o u r t e e n d i f f e r e n t r a y - t y p e s a r e c o n s i d e r e d

by t h e model used i n t h i s s t u d y ( e . g . d i r e c t , r e f l e c t e d ,

d i f f r a c t e d , r e f l e c t e d - d i f f r a c t e d , and r e f l e c t e d - r e f l e c t e d -

d i f f r a c t e d ) . I n p u t p a r a m e t e r s t o t h e model i n c l u d e a

p i e c e w i s e - l i n e a r two-dimensional t e r r a i n p r o f i l e , t h e

l o c a t i o n s of t h e t r a n s m i t t i n g and r e c e i v i n g a n t e n n a s ,

f r e q u e n c y , d i s t a n c e s , and t h e e l e c t r i c a l c o n s t a n t s of t h e

ground. S i n c e t h e GTD method i s e n t i r e l y a n a l y t i c a l ,

t r o p o s p h e r i c a t t e n u a t i o n e f f e c t s a r e n o t i n c l u d e d i n t h e

model .

I n p a s t , GTD h a s been used t o d e t e r m i n e t h e I n s t r u m e n t

Landing System ( I L s ) g l i d e s l o p e per formance . F o r t h a t

Nguyen Minh Thu
Highlight
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a p p l i c a t i o n , t h e w a v e l e n g t h i s a p p r o x i m a t e l y I m , i n c i d e n c e

a n g l e s a r e u s u a l l y n e a r g r a z i n g , and t h e f i e l d s a r e

h o r i z o n t a l l y p o l a r i z e d . Under t h e s e c o n d i t i o n s , t h e g round

i t s e l f is assumed t o b e a p e r f e c t c o n d u c t o r , and t h e g r o s s

i r r e g u l a r i t i e s s u c h as d r o p o f f s and h i l l s a r e more i m p o r t a n t

t h a n s u r f a c e r o u g h n e s s . However, t o p r o v i d e more m e a n i n g f u l

r e s u l t s when e s t i m a t i n g p r o p a g a t i o n l o s s e s f o r a wide

v a r i e t y o f t e r r a i n and r e c e i v e r - t r a n s m i t t e r g e o m e t r i e s , t h e i

model was mod i f i ed t o a c c o u n t f o r f i n i t e c o n d u c t i v i t y and

l o c a l s u r f a c e r o u g h n e s s f o r b o t h h o r i z o n t a l and v e r t i c a l

p o l a r i z a t i o n . T h i s m o d i f i c a t i o n i s one of t h e c r u c i a l f a c e t s

o f t h i s r e s e a r c h .

A l t h o u g h t h e r e e x i s t o t h e r p r o p a g a t i o n p a t h l o s s m o d e l s ,

t h e y a l l have l i m i t a t i o n s . The P h y s i c a l O p t i c s ( P O ) mode l ,

which c a l c u l a t e s t h e f i e l d s t r e n g t h by summing f i e l d s r e -

r a d i a t e d by g round c u r r e n t s h a s t h e d i s a d v a n t a g e of

r e q u i r i n g l o n g c o m p u t a t i o n t i m e . I t s p e r f o r m a n c e i s a l s o

l i m i t e d b y f a i l i n g t o p r o v i d e a c o r r e c t f i e l d i n t e r a c t i o n

be tween l i n e a r s egmen t s c o m p r i s i n g t h e p r o f i l e . A n o t h e r

mode l , d e v e l o p e d by Long ley -R ice , which i s i n t e n d e d t o

d e t e r m i n e p r o p a g a t i o n l o s s f o r p a t h s whe re o n l y l i m i t e d

i n f o r m a t i o n d e f i n i n g t e r r a i n i s a v a i l a b l e . I n p a r t i c u l a r ,

t h e model i s i n t e n d e d t o e s t i m a t e p r o p a g a t i o n p a t h l o s s e s

f o r t e r r a i n p r o f i l e s g i v e n i n t h e C o n t i n e n t a l U n i t e d S t a t e s

(COWS) da ta base. The Longley-Rice model is S t a t i s t i c a l i n

n a t u r e , a n d h a s b e e n known t o g i v e r e s u l t s n o t as a c c u r a t e

i n some c i r c u m s t a n c e s s u c h as s h o r t r a n g e p a t h s . The

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s h o r t c o m i n g s o f e x i s t i n g m o d e l s l e d t o t h e d e v e l o p m e n t s o f

t h e GTD m o d e l as a n a l t e r n a t i v e t o o l i n p r e d i c t i n g

p r o p a g a t i o n p a t h l o s s .

F i n a l l y , GTD modeled d a t a w e r e compared a g a i n s t m e a s u r e d

p a t h l o s s d a t a t o p r o v i d e a n e v a l u a t i o n o f p r e d i c t i o n

p e r f o r m a n c e c a p a b i l i t y . T h e s e c o m p a r i s o n s , w h i c h were made

o v e r a r a n g e of d i s t a n c e s a n d f r e q u e n c i e s , show t h a t GTD i s

a f e a s i b l e means f o r p r e d i c t i n g s h o r t - r a n g e p r o p a g a t i o n p a t h

l o s s e s .

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I I G T D BACKGROUND and DEVELOPMENT

The G e o m e t r i c a l Theory o f D i f f r a c t i o n (GTD) i s a n

a n a l y t i c a l method f o r d e t e r m i n i n g t h e a m p l i t u d e and p h a s e o f

e l e c t r o m a g n e t i c wave b e h a v i o r r e s u l t i n g f rom i n t e r a c t i o n

w i t h c o n d u c t i n g s u r f a c e s . The t h e o r y i s b a s i c a l l y a n

e x t e n s i o n o f G e o m e t r i c O p t i c s (GO) which i n c l u d e s

d i f f r a c t i o n . The t h e o r y h a s i ts o r i g i n i n a m a t h e m a t i c a l

work by Sommerfeld. H i s p a p e r 11 1 p u b l i s h e d i n 1896,

d e s c r i b e s t h e ma thema t i c s o f d i f f r a c t i o n f o r a p e r f e c t l y

c o n d u c t i n g , i n f i n i t e - l e n g t h h a l f - p l a n e . I n i t , h e emplogs

t h e F r e s n e l i n t e g r a l method t o e v a l u a t e t h e n l e z f r i c f i e 1 2

v a r i a t i o n as t h e o b s e r v a t i o n p o i n t c h a n g e s i n ; c c a t i o n f ~ o m

t h e i l l u m i n a t e d r e g i o n t o t h e shadow r e g i o n . However, t h e

drawback o f Sommerfe ld ' s work i s t h a t i t i s o n l y l i m i t e d t o

h a l f - p l a n e a p 2 l i c a t i c n s . S t a r t i n g i n 1953, i t xas K e l l e r

[ 2 , 7 , 4 J who s y s t e m a t i c a l l y d e v e l o p e d t h e G e o m e t r i c a l Theory

o f d i f f r a c t i o n f o r more g e n e r a l a p p l i c a t i o n s . S i n c e t h e n ,

t h i s method h a s undergone improvements by many w o r k e r s and

is s t i l l u n d e r g o i n g c h a n g e s 151 t o meet v a r i o u s

r e q u i r e m e n t s .

I n K e l l e r ' s o r i g i n a l work , a s y m p t o t i c e x p a n s i o n s were

u s e d t o d e s c r i b e f i e l d b e h a v i o r . The r e s u l t t h u s o b t a i n e d

y i e l d e d u n r e a l i s t i c s i n g u l a r i t i e s i n t h e immedia te v i c i n i t y

o f t h e shadow a n d r e f l e c t i o n b o u n d a r i e s . L a t e r , Kouyoum j i a n

and co-workers m o d i f i e d Ke l l e r ' s work t o a u n i f o r m s o l u t i o n

which p r o v i d e s a c o n t i n u o u s f i e l d eve rywhere ; t h i s r e v i s e d

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t h e o r y i s t h e Uni form Theory o f D i f f r a c t i o n (UTD). The

method a d d r e s s e d i n t h i s t h e s i s i s a d i r e c t a p p l i c a t i o n o f

UTD. S i n c e U T D i s an e x t e n s i o n o f G T D c o n c e p t , i t is

commonly r e f e r r e d t o as GTD.

G e o m e t r i c a l O p t i c s (GO)

G e o m e t r i c a l O p t i c s , o r r a y o p t i c s , was o r i g i n a l l y

deve loped t o a n a l y z e t h e p r o p a g a t i o n of l i g h t , where t h e

f r e q u e n c y i s s u f f i c i e n t l y h i g h t h a t t h e wave n a t u r e o f l i g h t

need n o t be c o n s i d e r e d . GO t h e o r y a s sumes t h e f l o w o f

e l e c t r o m a g n e t i c r a d i a t i o n b e t w e e n two p o i n t s i n s p a c e c a n b e

v i ewed as t r a v e l l i n g i n s t r a i g h t l i n e s c a l l e d r a y s ; f u r t h e r ,

r a y s a r e assumed t o n o t i n t e r f e r e w i t h one a n o t h e r and h e n c e

I c a n be summed v e c t o r i a i l y i . , conform t o t h e laws o f

s u p e r p o s i t i o n ) .

Two f u n d a m e n t a l r a y t y p e s a r e c o n s i d e r e d i n G O . They a r e

d i r e c t and r e f l e c t e d r a y s ( * ) as i l l u s t r a t e d i n F i g u r e 2-1.

A d i r e c t r a y e x i s t s i f t h e r e is no b l o c k a g e a l o n g t h e r a y

p a t h be tween t h e t r a n s m i t t i n g a n t e n n a and r e c e i v i n g a n t e n n a .

A r e f l e c t e d r a y i s g e n e r a t e d i f t h e r e a r e p o i n t s on t h e

t e r r a i n p r o f i l e which s a t i s f y S n e l l ' s Law o f r e f l e c t i o n ,

v i z , t h e r e i s a r e f l e c t i o n a r e a which c a u s e s t h e a n g l e of

i n c i d e n t of t h e i n c i d e n t r a y t o e q u a l t o t h e a n g l e o f

( * ) R e f r a c t i o n phenomenon i s e x c l u d e d i n t h i s a p p l i c a t i o n b e c a u s e t h e a m p l i t u d e o f t h e r e f r a c t e d r a y t r a n s m i t t e d t h r o u g h h i l l s would b e t o o weak t o b e s i g n i f i c a n t .

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r e f l e c t i o n as shown i n t h e F i g u r e . I n t h e a p p l i c a t i o n h e r e ,

t h e w a v e l e n g t h o f GO f i e l d i s a s s u m e d t o b e small c o m p a r e d

t o t e r r a i n v a r i a t i o n s , s o t h a t r e f l e c t i o n i s c o n s i d e r e d t o

b e a l o c a l phenomenon. C o n s e q u e n t l y , r e f l e c t i o n i s a s s u m e d

t o e m i n a t e f rom a p o i n t r a t h e r t h a n a n area. T h a t p o i n t i s

commonly c a l l e d p o i n t o f r e f l e c t i o n .

A l s o , G e o m e t r i c a l O p t i c s a s s u m e s t h e p h a s e o f t h e d i r e c t

a n d r e f l e c t e d r a y t o b e p r o p o r t i o n a l t o t h e t o t a l o p t i c a l

p a t h l e n g t h o f t h e r a y f r o m a r e f e r e n c e p o i n t , w h e r e t h e

p h a s e i s d e f i n e d t o b e z e r o . T h e a m p l i t u d e v a r i e s a c c o r d i n g

t a t h e p r i n c i p l e o f c o n s e r v a t i o n o f e n e r g y ; t h u s f i e l d

i z t e n s i t y d e c r e a s e s w i t h i n c r e a s i n g d i s t a n c e as d e s c r i b e d

b e l o w .

T h r o u g h o u t t h i s t h e s i s , t h e r e c e i v i n g p o i n t i s l o c a t e d i n

t h e f a r f i e l d o f t h e a n t e n n a , a n d h e n c e , a r a y i s c o n s i d e r e d

t o b e i n t h e f o r m o f p l a n e wave a t t h e p o i n t o f r e f l e c t i o n .

F o r a f a r - f i e l d a p p l i c a t i o n , a GO f i e l d s u c h as t h e d i r e c t

r a y c a n b e o b t a i n e d b y c o n s i d e r i n g o n l y t h e l e a d i n g term i n

t h e a s y m p t o t i c , h i g h - f r e q u e n c y s o l u t i o n o f Maxwell's

e q u a t i o n 16 1. T h e s o l u t i o n t h u s o b t a i n e d i n d i c a t e s t h a t

f i e l d i n t e n s i t y d e c r e a s e s i n v e r s e l y w i t h d i s t a n c e a n d i n c u r s

a p h a s e v a r i a t i o n o f e-1 BR, w h e r e R i s t h e p a t h d i s t a n c e

measured f r o m t h e t r a n s m i t t i n g a n t e n n a t o t h e r e c e i v i n g

a n t e n n a , a n d B=2n/X i s t h e p h a s e c o n s t a n t o f t h e wave.

To i l l u s t r a t e t h e r e f l e c t e d r a y a n d t h e method f o r

c a l c u l a t i n g i ts c o n t r i b u t i o n , r e f e r t o F i g u r e 2-2 , w h i c h

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d e p i c t s t h e d i r e c t a n d r e f l e c t e d r a y s , a n d a n image

r e p r e s e n t a t i o n o f t h e s o u r c e . B o t h t h e d i r e c t a n d r e f l e c t e d

r a y s a r e e m i n a t e d f rom t h e s o u r c e a n t e n n a r a d i a t i n g a t a

h e i g h t h a b o v e a f l a t g r o u n d p l a n e , a s s u m i n g p e r f e c t

c o n d u c t i v i t y . The o b s e r v a t i o n p o i n t i s l o c a t e d as i n d i c a t e d

i n t h e f i g u r e , a n d i s i n t h e f a r - f i e l d r e g i o n o f t h e

a n t e n n a . Image t h e o r y 171 s t a t e s t h a t a n e q u i v a l e n t

c o n f i g u r a t i o n w i l l r e s u l t i f t h e g r o u n d p l a n e is removed ,

a n d a n image s o u r c e i s a d d e d a t a d i s t a n c e -h f r o m w h e r e t h e

g r o u n d p l a n e had b e e n , as i n d i c a t e d i n t h e f i g u r e . The

a n p i i t u d e o f tze imge mirre.~ L - a q u a 1 t o t h e a m p l i t u d e of

t h e d i r e c t s o u r c e a n d i s i n p h a s e f o r v e r t i c a l p o l a r i z a t i o n

a n d o u t o f p h a s e f o r h o r i z o n t a l 2 o l a r i z a t i o n as i s shown i n

F i g ~ r e 2-3. The distanse 2, S e t w e e n t h e o b s e r v e r a n d t h e

i n a g e s o u r c e i s e q u a l t o :

w h e r e h i s t h e h e i g h t o f t h e a n t e n n a f r o m t h e g r o u n d . F o r

p r a c t i c a l a p p l i c a t i o n s , t h e r e f l e c t i n g s u r f a c e w i l l

i n t r o d u c e l o s s e s a n d p h a s e s h i f t t o t h e i n c i d e n t f i e l d d u e

t o i m p e r f e c t c o n d u c t i v i t y a n d s u r f a c e r o u g h n e s s . T h e s e

e f f e c t s a r e a c c o u n t e d f o r b y t h e c o m p l e x v a l u e d r e f l e c t i o n

c o e f f i c i e n t ( r ) . I n case of p e r f e c t c o n d u c t i v i t y , ( r )

r e d u c e s t o +1 f o r v e r t i c a l p o l a r i z a t i o n a n d -1 f o r

h o r i z o n t a l p o l a r i z a t i o n , b o t h o f w h i c h i n d i c a t e s i n c i d e n t

f i e l d i s t o t a l l y r e f l e c t e d t o t h e o b s e r v a t i o n p o i n t . G i v e n

t h e a b o v e i n f o r m a t i o n a b o u t t h e p h a s e s h i f t and l o s s e s

i n c u r r e d by t h e e a r t h s u r f a c e , t h e r e f l e c t e d r a y

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c o n t r i b u t i o n c a n b e w r i t t e n as:

where Eo i s a c o n s t a n t r e p r e s e n t i n g t h e f i e l d i n t e n s i t y a t

t h e r e f e r e n c e p o i n t .

The d i r e c t f i e l d which t r a v e l s a l o n g t h e l i n e j o i n i n g t h e

s o u r c e and o b s e r v a t i o n p o i n t and i s similar t o r e f l e c t e d

r a y ; t h e e n e r g y d e n s i t y d e c r e a s e s i n v e r s e l y w i t h d i s t a n c e

and a p h a s e v a r i a t i o n o f e-jBRd , where R d i s t h e p a t h

d i s t a n c e f rom t h e s o u r c e a n t e n n a t o t h e o b s e r v a t i o n p o i n t

The c o m p o s i t e s i g n a l r e c e i v e d a t t h e o b s e r v a t i o n c a n be

c a l c u l a t e d b y summing t h e d i r e c t f i e l d and r e f l e c t e d f i e l d

as f o l l o w s :

where Er i s t h e r e c e i v e d f i e l d a t t h e o b s e r v a t i o n p o i n t .

Knowing t h e e l e c t r i c a l p r o p e r t i e s o f t h e r e f l e c t i o n s u r f a c e ,

which d e t e r m i n e s t h e v a l u e o f t h e r e f l e c t i o n c o e f f i c i e n t ,

and t h e l o c a t i o n o f t h e o b s e r v a t i o n p o i n t , s i g n a l c a n b e

r e a d i l y d e t e r m i n e d .

D e f i c i e n c y o f G e o m e t r i c a l O p t i c s

The r e f l e c t e d r a y and d i r e c t r a y c o n f i g u r a t i o n c o n s i d e r e d

i n SO c a n c a u s e a s e r i o u s d e f i c i e n c y i f u s e d i n VHF wave

Page 14: Evaluation progresion path loss model

p r o p a g a t i o n m o d e l l i n g o v e r i r r e g u l a r t e r r a i n b e c a u s e i t

f a i l s t o a c c o u n t f o r d i f f r a c t i o n . F o r e x a m p l e , c o n s i d e r a

two d i m e n s i o n a l c o n d u c t i n g e d g e as i l l u s t r a t e d i n F i g u r e

2-4. If o b s e r v a t i o n s a re made on a c i r c l e o f c o n s t a n t r a d i u s

a s i l l u s t r a t e d , s t a r t i n g i n r e g i o n I , moving c l o c k w i s e t o

r e g i o n 11, t h e f o l l o w i n g w i l l b e o b s e r v e d . F i r s t , t h e

r e f l e c t e d r a y d i s a p p e a r s at a n d b e l o w t h e r e f l e c t i o n

b o u n d a r y b e c a u s e t h e p o i n t o f r e f l e c t i o n migrates b e y o n d t h e

e d g e . C o n s e q u e n t l y , G O p r e d i c t s a f i e l d d i s c o n t i n u i t y a t t h e

r e f l e c t i o n b o u n d a r y . A l s o , c o n s i d e r t h e i m m e d i a t e v i c i n i t y

oi ?he shadzw 3 o u n d s r y w h e r e t h e d i r e c t r a y i s b l o c k e d b y

t h e t i p of t h e e d g e ; GO a g a i n p r e d i c t s a f i e l d d i s c o n t i n u i t y

st t h e s h a d o w b o u n d a r y d u e t o t h e l o s s o f t h e d i r e c t r a y .

S i n c e G e o m e t r i c - O p t i c s f a i l s t o a c c o u n t f o r t h e phenomena

o f d i f f r a c t i o n , a b r u p t a n d u n r e a l i s t i c f i e l d d i s c o n t i n u i t i e s

a c r o s s t h e shadow a n d r e f l e c t i o n b o u n d a r i e s a r e p r e d i c t e d b y

G O . I n a d d i t i o n , r e g i o n I11 (shadow r e g i o n ) w i l l b e

d e t e r m i n e d by GO t o h a v e z e r o f i e l d i n t e n s i t y , a g a i n a n

u n r e a l i s t i c c a l c u l a t i o n . T h e s e d e f i c i e n c i e s l e d t o t h e

d e v e l o p m e n t o f GTD.

D i f f r a c t i o n

D i f f r a c t e d r a y s , a c c o r d i n g t o Kel le r 18 1 , h a v e c e r t a i n

p r o p e r t i e s :

1 . T h e d i f f r a c t e d f i e l d p r o p a g a t e s a l o n g r a y p a t h s

t h a t i n c l u d e p o i n t s o n t h e b o u n d a r y s u r f a c e . T h e s e r a y

Page 15: Evaluation progresion path loss model
Page 16: Evaluation progresion path loss model

p a t h s obey t h e p r i n c i p l e o f Fe rma t , a l s o known as t h e

p r i n c i p l e o f t h e s h o r t e s t o p t i c a l p a t h .

2 . A d i f f r a c t e d wave p r o p a g a t e s a l o n g i t s r a y p a t h s o

t h a t t h e e n e r g y d e n s i t y d e c r e a s e s i n v e r s e l y w i t h

i n c r e a s i n g i n d i s t a n c e , and t h e phase d e l a y e q u a l s t h e

wave number t i m e s t h e d i s t a n c e a l o n g t h e r a y p a t h .

3 . D i f f r a c t i o n , l i k e r e f l e c t i o n and t r a n s m i s s i o n , i s a

l o c a l phenomenon a t h i g h f r e q u e n c i e s . T h a t i s , i t

depends o n l y on t h e n a t u r e of t h e boundary s u r f a c e and

t h e i n c i d e n t f i e l d i n t h e immedia te ne ighborhood o f

t h e p o i n t o f d i f f r a c t i o n .

Contemporary GTD t h e o r y c a n b e u s e d t o c a l c u l a t e d i f f r a c t i o n

from c o n e s , c u r v e s u r f a c e s , and wedges 131. However, t h e

work a d d r e s s e d h e r e models t e r r a i n as + U W U - u ~ ~ ~ ~ C I L O A U L L ~ L , ---'---'

p i e c e w i s e - l i n e a r segment s ; hence o n l y wedge d i f f r a c t i o n is

c o n s i d e r e d , a l t h o u g h it i s l i k e l y t h a t p r o p z g a t i o n p a t h s may

b e e n c o u n t e r e d where o t h e r t y p e s of d i f f r a c t i o n may p r o v i d e

more mean ingfu l r e s u l t s .

The v a l u e o f a d i f f r a c t e d r a y i s c a l c u l a t e d by t h e v a l u e

o f t h e i n c i d e n t p l a n e wave a t t h e p o i n t of d i f f r a c t i o n

m u l t i p l i e d b y a d i f f r a c t i o n c o e f f i c i e n t . T h i s is s i m i l a r t o

t h e r e f l e c t e d r a y , which i s o b t a i n e d by m u l t i p l y i n g t h e

i n c i d e n t r a y by a r e f l e c t i o n c o e f f i c i e n t . The d i f f r a c t i o n

c o e f f i c i e n t f o r a wedge c o n f i g u r a t i o n is de te rmined by t h e

geometry i n t h e immediate ne ighborhood of t h e p o i n t of

d i f f r a c t i o n .

Page 17: Evaluation progresion path loss model

To i l l u s t r a t e how f i e l d c o n t i n u i t y n e a r t h e shadow a n d

r e f l e c t i o n b o u n d a r i e s is p r e s e r v e d as a r e s u l t of t h e

d i f f r a c t e d - r a y c o n t r i b u t i o n , c o n s i d e r a r a y i n c i d e n t o n a

t w o - d i m e n s i o n a l e d g e as i l l u s t r a t e d i n F i g u r e 2-5. G T D

e m p l o y s t h e f o l l o w i n g e x p r e s s i o n t o d e s c r i b e t h e f i e l d

b e h a v i o r of d i f f r a c t i o n [ I 0 1 :

I I I I i'i D ( @ , @ ' I = ~ d ' ( @ - $ ' ) + Dn ( @ - @ I )

I I II

w h e r e Dd' a n d D, a re t h e v e r t i c a l a n d h o r i z o n t a l

p o l a r i z a t i o n d i f f r a c t i o n c o e f f i c i e n t t e rzas f o r t h e e d g e

f a c e s o a n d n r e s p e c t i v e l y .

T h e s e f o u r terms a re u s e d t o c a m n ~ n a a t e r - --- f o r t h e

d i s c o n t i n u i t y i n t h e g e o m e t r i c a l - o p t i c s f i e l d a t a shadow

a n d r e f l e c t i o n b o u n d a r y f o r t h e two f a c e s o f t h e wedge. F o r

i n s t a n c e , t h e terms o f t h e f o r m ( @ - @ I ) a re t o c o m p e n s a t e f o r

t h e l o s s o f t h e d i r e c t r a y a t t h e shadow b o u n d a r y ; t h o s e o f

t h e fo rm + a r e t o c o m p e n s a t e f o r t h e l o s s o f t h e

r e f l e c t e d r a y a t r e f l e c t i o n b o u n d a r y . T h u s , t h e G T D

d i f f r a c t i o n c o e f f i c i e n t e n a b l e s a r e a l i s t i c f i e l d t o b e

c a l c u l a t e d r e g a r d l e s s of t h e l o c a t i o n o f t h e o b s e r v a t i o n

p o i n t .

The o v e r a l l e l e c t r i c f i e l d i n a n y o f t h e t h r e e r e g i o n i n

s p a c e c a n now b e w r i t t e n as:

Page 18: Evaluation progresion path loss model
Page 19: Evaluation progresion path loss model

where t h e e l e c t r i c f i e l d c o n t r i b u t i o n f rom d i f f r a c t i o n i s

o b t a i n e d b y GTD method. While t h e above e q u a t i o n a p p l i e s

o n l y t o a p e r f e c t l y c o n d u c t i n g e d g e , m o d i f i c a t i o n f o r f i n i t e

c o n d u c t i v i t y a p p l i c a t i o n s h a v e b e e n p e r f o r m e d , and i s

d e s c r i b e d i n t h e n e x t c h a p t e r .

Page 20: Evaluation progresion path loss model

I I I GTD M o d i f i e d f o r F i n i t e C o n d u c t i v i t y a n d S u r f a c e

R o u g h n e s s

I n t h e e a r l y d e v e l o p m e n t o f G T D , t h e t h e o r y a s s u m e d t h a t

d i f f r a c t i v e e d g e s w e r e p e r f e c t l y c o n d u c t i n g , w h i c h

s i m p l i f i e d t h e d i f f r a c t i o n c o e f f i c i e n t e x p r e s s i o n . B e c a u s e

p r o p a g a t i o n m o d e l i n g i n v o l v e s d i f f r a c t i o n f r o m i m p e r f e c t l y -

c o n d u c t i n g s u r f a c e s , G T D t h e o r y was m o d i f i e d i n o r d e r t o

p r o v i d e more m e a n i n g f u l r e s u l t s when e s t i m a t i n g t e r r a i n

d i f f r a c t i o n . The o b j e c t i v e s s o u g h t i n i m p l e m e n t i n g t h e

m o d i f i c a t i o n were t o m a t c h t h e r e f l e c t e d Tay : o n t r i b u t i o n a t

t h e r e f l e c t i o n b o u n d a r y , a n 2 "LA.. t lmmi+$e.2 r a Y

c o n t r i b u t i o n a t t h e shadow b o u n d a r y . T h e s e o b j e c t i v e s w e r e

met, a n d s u b s e q u e n t c o n t i n u i t y c h e c k s a t t h e shadow a n d

r e f l e c t i o n b o u n d a r i e s i n d i c a t e d t h a t c o n t i n u i t y h a d n o t b e e n

v i o l a t e d b y t h e m o d i f i c a t i o n .

I n o r d e r t o p r o v i d e i n s i g h t i n t o wave i n t e r a c t i o n w i t h

t e r r a i n , t h i s c h a p t e r b e g i n s w i t h a d i s c u s s i o n o f t h e

e f f e c t s o f f i n i t e l y - c o n d u c t i n g a n d l o c a l l y - r o u g h t e r r a i n o n

wave r e f l e c t i o n , w h i c h i s t h e n e x t e n d e d t o d e f i n i n g t h o s e

c o n s t r a i n t s i m p o s e d by t h e e f f e c t s o n t h e d i f f r a c t i o n

c o e f f i c i e n t .

Page 21: Evaluation progresion path loss model

F i n i t e C o n d u c t i v i t y R e f l e c t i o n C o e f f i c i e n t

The b e h a v i o r of t h e v e r t i c a l and h o r i z o n t a l r e f l e c t i o n

c o e f f i c i e n t f o r f i n i t e c o n d u c t i v i t y i s i l l u s t r a t e d i n F i g u r e

3-1, where t h e p e r c e n t a g e of r e f l e c t i o n i s p l o t t e d a g a i n s t

t h e i n c i d e n c e a n g l e f o r f r e s h w a t e r and commonly-encountered

e a r t h s u r f a c e s . The c o n d u c t i v i t y and p e r m i t t i v i t y o f t h e

medium a r e shown i n t h e f i g u r e .

I n F i g u r e 3-1, i t is s e e n t h a t as t h e i n c i d e n c e a n g l e

changes t o 90 d e g r e e s ( i . e . g r a z i n g a n g l e ) , t h e magn i tude of

t h e r e f l e c t i o n c o e f f i c i e n t a p p r o a c h e s u n i t y . I n s u c h c a s e ,

t h e phase a n g l e of t h e r e f l e c t i o n c o e f f i c i e n t , a p p r o a c h e s

-180 d e g r e e s as d e p i c t e d i n F i g u r e 3-2. A s a r e s u l t , a

r e f l e c t i o n c o e f f i c i e n t of -1 w i l l o c c u r a t g r a z i n g zr ,gle

f o r a l l common ground p l a n e s .

Rough S u r f a c e s

The laws of r e f l e c t i o n by a p e r f e c t l y smooth s u r f a c e

c a n n o t , i n g e n e r a l , b e d i r e c t l y a p p l i e d t o t e r r a i n d u e t o

s u r f a c e i r r e g u l a r i t i e s . One o f t h e major d i f f e r e n c e i n t h e

c h a r a c t e r i s t i c s o f a smooth s u r f a c e and a rough s u r f a c e i s

t h a t a smooth p l a n e ( o f s u f f i c i e n t l y l a r g e d i m e n s i o n s ) w i l l

r e f l e c t t h e i n c i d e n t wave s p e c u l a r l y , o r i n a s i n g l e

d i r e c t i o n , w h i l e a rough s u r f a c e w i l l s c a t t e r e n e r g y

d i f f u s e l y . The d e g r e e of r o u g h n e s s depends upon t h e

wave leng th and a n g l e o f i n c i d e n c e . To a c c o u n t f o r s u r f a c e

Page 22: Evaluation progresion path loss model

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Page 23: Evaluation progresion path loss model

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Page 24: Evaluation progresion path loss model

r o u g h n e s s , a f a c t o r is u s e d t o mod i fy t h e r e f l e c t i o n

c o e f f i c i e n t . T h i s m o d i f i e d r e f l e c t i o n c o e f f i c i e n t i s

d e f i n e d b y L I I ] :

where 4' is t h e plane-wave r e f l e c t i o n c o e f f i c i e n t f o r L

s p e c u l a r r e f l e c t i o n f rom a r o u g h s u r f a c e , Ro II i s t h e

plane-wave r e f l e c t i o n c o e f f i c i e n t f o r a f l a t s m o o t h s u r f a c e

( R' is f o r h o r i z o n t a l p o l a r i z a t i o n , and R " i s f o r

v e r t i c a l p o l a r i z a t i o n ) , and 6 s i s t h e s u r f a c e r o u g h n e s s

f a c t o r .

The t h e o r y d e s c r i b i n g t h e e f f e c t s o f r o u g h s u r f a c e s o n

t h e r e f l e c t i o n assume t h a t t e r r a i n e l e v a t i o n a r e G a u s s i a n l y

d i s t r i b u t e d w i t h r e s p e c t t o t h e mean e l e v a t i o n . A c c o r d i n g

t o C e n t r a l L i m i t Theorem 11 2 1 , random 2 - d i m e n s i o n a l t e r r a i n

r o u g h n e s s w i l l c o n v e r g e t o a G a u s s i a n d i s t r i b u t i o n as t h e

number o f t e r m s i n t h e sum i s l a r g e ( T h e t e r r a i n

i n v e s t i g a t e d i n t h i s p a p e r r a n g e s f r o m 0 .5 k i l o m e t e r t o 1 2 0

k i l o m e t e r s w i t h v a r i o u s s h a p e s and f e a t u r e s s o t h a t t h e

number of t e r m s are c o n s i d e r e d l a r g e ) . F o r a G a u s s i a n

Model , 6 s i s d e f i n e d b y 11 31 :

A + i s t h e phase s h i f t b e t w e e n t h e s h o r t e s t and t h e l o n g e s t

r e f l e c t e d p a t h . C o n s i d e r r a y s 1 and 2 ( F i g u r e 3-3) i n c i d e n t

on a s u r f a c e w i t h i r r e g u l a r i t i e s o f h e i g h t Ah a t a grazing

Page 25: Evaluation progresion path loss model
Page 26: Evaluation progresion path loss model

a n g l e Y . The p a t h d i f f e r e n c e b e t w e e n t h e two r a y s i s :

A r = 2 A h s i n y

a n d h e n c e t h e p h a s e d i f f e r e n c e is:

4rAh - s i n y

w h e r e Ah i s t h e s t a n d a r d d e v i a t i o n o f t h e t e r r a i n

e l e v a t i o n a l o n g e a c h p i e c e w i s e - 1 i n e a r s e c t i o n o f t h e t e r r a i n

. . d e f i n i n g t h e p r o f i l e a n d X t h e w a v e l e n g t h . The vai1~ -n

i s assumed t o b e c o n s t a n t t h r o u g h o u t t h e e n t i r e p r o p a g a t i o n

p a t h , h o w e v e r , t h e m o d e l c o u l d b e m o d i f i e d t o a c c e p t

d i f f e r e n t v a l u e s f o r d i f f e r e n t p a r t s o f t h e p r o f i l e . I f A @ ,

t h e p h a s e d i f f e r e n c e i s small, t h e two r a y s w i l l b e a i r n o s t

i n p h a s e as t h e y are i n t h e case o f a p e r f e c t l y s m o o t h

s u r f a c e . T h i s A @ i s t h e same v a r i a b l e as is u s e d i n t h e

R a y l e i g h c r i t e r i o n 11 41 i n d e t e r m i n i n g w h e t h e r t h e s u r f a c e

i s smooth f o r a g i v e n f r e q u e n c y .

Page 27: Evaluation progresion path loss model

F i n i t e C o n d u c t i v i t y D i f f r a c t i o n C o e f f i c i e n t

To i l l u s t r a t e t h e edge d i f f r a c t i o n c o e f f i c i e n t s f o r two

d i e l e c t r i c p l a t e s and t o show how f i e l d c o n t i n u i t y n e a r

shadow and r e f l e c t i o n b o u n d a r i e s i s p r e s e r v e d , c o n s i d e r a

r a y i n c i d e n t o n a d i e l e c t r i c edge as d e p i c t e d i n F i g u r e 3-4.

I n t h e two d i m e n s i o n a l c a s e t h e d i f f r a c t i o n c o e f f i c i e n t is

e x p r e s s e d as 1151:

I A I1 I I

I I II I1

+ AoDo ( @ + @ ' I + A,D,(++@') f i i II I

where L o , L, , A, , A: are f i n i t e c o n d u c t i v i t y c o r r e c t i o n

c o n s t a n t s n e c e s s a r y t o p r e s e r v e f i e l d c o n t i n u i t y a t t h e

r e f l e c t i o n bounda ry and shadow boundary f o r t h e d i e l e c t r i c

wedge. I n t h e c a s e of the p e r f e c t l y c o n d u c t i n g edge

d i s c u s s e d i n C h a p t e r 2 , these fozr c z ; . s t a ~ " ~ t s a r e e q u a l t o 1 I I I I I u n i t y . The t e r m s L o a n d Ln a r e c o r r e c t i o n terms t o a c c o u n t

f o r v a r i a t i o n s i n p h a s e and a m p l i t u d e d u e t o d i f f e r e n c e s

be tween f i n i t e l y c o n d u c t i n g wedges and p e r f e c t l y c o n d u c t i n g

wedges a t t h e shadow boundary f o r t h e d i e l e c t r i c p l a t e o and I

n r e s p e c t i v e l y ; rf w h i l e A! a n d An a c c o u n t f o r s u c h

d i f f e r e n c e s a t t h e r e f l e c t i o n boundary . A t shadow

b o u n d a r i e s , t h e d i f f e r e n c e be tween f i n i t e and p e r f e c t

c o n d u c t i v i t y i s t h a t e n e r g y may b e t r a n s m i t t e d t h r o u g h t h e

f i n i t e l y - c o n d u c t i n g medium. If t r a n s m i s s i o n d o e s o c c u r s , I I

I I t h i s must b e a c c o u n t e d f o r by t h e c o n s t a n t s L! a n d L, . For

h igh - f r equency t e r r a i n m o d e l i n g , r a y t r a n s m i t t e d t h r o u g h

;i 4 h i l l s and moun ta ins is n e g l i g i b l e , t h u s L o =Ln = l .

Page 28: Evaluation progresion path loss model
Page 29: Evaluation progresion path loss model

The r e f l e c t e d f i e l d which i s m o d i f i e d by t h e r e f l e c t i o n

c o e f f i c i e n t v a n i s h e s a t t h e r e f l e c t i o n bounda ry ; as a

r e s u l t , t h e d i f f r a c t e d f i e l d is r e q u i r e d t o i n c r e a s e i n

a m p l i t u d e t o compensa t e f o r t h e r e f l e c t e d r a y l o s s a t t h e

r e f l e c t i o n bounda ry s o t h a t t h e t o t a l h igh- f r e q u e n c y f i e l d

i s c o n t i n u o u s eve rywhere . I n t h i s a p p l i c a t i o n , A, and A,

a r e s e t t o e q u a l t o t h e r e f l e c t i o n c o e f f i c i e n t s of t h e e d g e I is s u r f a c e s 0 and n , r e s p e c t i v e l y . T h e r e f o r e , A! = Rg f o r t h e

L

two d i m e n s i o n a l c a s e . 4 i s e q u a l t o t h e m o d i f i e d

r e f l e c t i o n c o e f f i c i e n t f o r rough s u r f a c e s a p p l i c a t i o n as

d e s c r i b e d e a r l i e r .

To d e m o n s t r a t e t h a t t h e above c h a n g e s t o t h e d i f f r a c t i o n

c o e f f i c i e n t s do n o t v i o l a t e c o n t i n u i t y c o n s t r a i n t s ,

c o n t i n u i t y t e s t s were p e r f o r m e d . The r e s u l t s o f t h e s e t e s t s

p r e s e n t e d i n Appendix A show t h a t t h e m o d i f i c a t i o n s zbcxre d s

n o t v i o l a t e any GTD c o n c e p t s . The f o l l o w i n g c h a p t e r w i l l

p r e s e n t s a model e v a l u a t i o n by compar i son w i t h measured

Page 30: Evaluation progresion path loss model

I V Measured and Modeled Data C o m p a r i s i o n s

The GTD model m o d i f i e d f o r rough s u r f a c e s and f i n i t e

c o n d u c t i v i t y h a s b e e n used t o p r e d i c t p r o p a g a t i o n p a t h l o s s

f o r a v a r i e t y o f t e r r a i n p r o f i l e s . T h i s c h a p t e r p r e s e n t s

t h o s e r e s u l t s a l o n g w i t h measured d a t a f o r t e r r a i n p r o f i l e s

o f d i f f e r e n t l e n g t h s and c o n t o u r s . These r e s u l t s e n a b l e a

r e a l i s t i c e v a l u a t i o n o f t h e m o d e l ' s p e r f o r m a n c e , which i n

t u r n d e t e r m i n e s t h e f e a s i b i l i t y o f employ ing t h e model i n

g e n e r a l p r o p a g a t i o n p a t h l o s s p r e d i c t i o n .

Yeaauzsd d a t a were o b t a i n e d f rom a p r o p a g a t i o n

e x p e r i a e n t r e p o r t by McQuate , e t . a l . 11 6 J and w e r e r educed

t o d i g i t a l f 3 r m a t t o s f f o r d c o m p a r i s o n w i t h modeled d a t a .

~h~ r e f e r enced r e p o r t c o n t a i n s t a b u l a t i o n s 0 f

e l e c t r o m a g n e t i c p r o p a g a t i o n l o s s d a t a r e s u l t i n g f rom

p r o p a g a t i o n measu remen t s o v e r i r r e g u l a r t e r r a i n i n C o l o r a d o

w i t h p a t h l e n g t h s r a n g i n g from 0 . 5 t o 120 km a t s e v e n

f r e q u e n c i e s i n t h e 230- t o 9200-MHz r a n g e . T h e s e r e d u c e d

d a t a c o n s i s t p r i m a r i l y o f g r a p h s showing b a s i c t r a n s m i s s i o n

l o s s v s . r e c e i v i n g a n t e n n a h e i g h t d e r i v e d f rom t h e

measurement o f e a c h p a t h . I n f o r m a t i o n a b o u t t h e p r o p a g a t i o n

p a t h a r e g i v e n by p h o t o g r a p h s , a t e r r a i n p r o f i l e , and a

d e s c r i p t i o n o f v e g e t a t i o n c o v e r . All t r a n s m i s s i o n s were

c o n t i n u o u s wave and f r e q u e n c i e s o f 230, 4 1 0 , 751 , 9 1 0 , 1846 ,

4595 , and 9190 MHz were used w i t h h o r i z o n t a l p o l a r i z a t i o n

o n l y .

Page 31: Evaluation progresion path loss model

To a d o p t t h e M c Q u a t e l s t e r r a i n p r o f i l e as i n p u t d a t a t o

t h e G T D model , t h e p r o f i l e was f i r s t a p p r o x i m a t e d by

p i e c e w i s e - l i n e a r s e g m e n t s which r e p r e s e n t t h e o r i g i n a l p a t h .

I n some c a s e s , t h i s p r o c e s s c a n p roceed i n a

s t r a i g h t f o r w a r d manner , i f t h e p redominan t s l o p e s and

d i f f r a c t i v e e d g e s a r e w e l l d e f i n e d . However, i n o t h e r

c a s e s , t h e p r o c e s s i s n o t s o s t r a i g h t f o r w a r d , p a r t i c u l a r l y

t h o s e p r o f i l e s i n v o l v i n g m u l t i p l e p e a k s and l a r g e i r r e g u l a r

r o u g h n e s s . O f t e n , a p r o f i l e c a n b e r e p r e s e n t e d by more t h a n

one p i e c e w i s e - l i n e a r i z e d a p p r o x i m a t i o n . Under t h i s

r' - , -::-~+3r,,- i= - - - --- "-* - " , f i 2 i . r - + n

=, ." t h e u s e r , ba sed o n h i s uwn

e x p e r i z n c e , ,a i a ~ e r - i n e w h e t h e r a n edge c o n s t i t u t e s

d i f f r a c t i o n o r r e f l e c t i a n ; o r i f t h e edge i s m e r e l y a

s o u r c e o f l o c a l s u r f a c e r o u g h n e s s . Thus , t h e r e i s no w e l l -

d e f i c e d me thodo logy e s t a b l i s h e d t o a i d i n t h e l i n e a r i z a t i o n

p r o c e s s , a i t h o u g n i t is known t h a t t h e number o f e d g e s

d e f i n i n g t h e t e r r a i n s h o u l d b e k e p t t o a minimum due t o t h e

c u m u l a t i v e e f f e c t of computer e r r o r s . These f a c t o r s a r e

d i s c u s s e d where a p p l i c a b l e a l o n g w i t h t h e p r e s e n t a t i o n o f

t e r r a i n p r o f i l e and p i e c e w i s e - l i n e a r a p p r o x i m a t i o n .

r n , ,,,.-: A, A u V V L U ~ a "vnchiiiark f o r t h e G T D model p e r f o r m a n c e ,

modeled d a t a f rom t h e Long ley -Rice P o i n t - t o - P o i n t model

L17 , I 81 i s a l s o p l o t t e d a l o n g w i t h GTD-modeled r e s u l t s and

measured d a t a . The Longley-Rice model was d e v e l o p e d a t t h e

I n s t i t u t e f o r Te lecommunica t ion S c i e n c e , and i s r e f e r r e d t o

h e r e as t h e ITS model. I n p u t d a t a r e q u i r e d by b o t h t h e G T D

and I T S models a r e i d e n t i c a l . S i n c e t h e i n c l u s i o n o f ITS

Page 32: Evaluation progresion path loss model

modeled d a t a s e r v e s o n l y as b a s e l i n e i n f o r m a t i o n , a

d i s c u s s i o n of i t s p e r f o r m a n c e is n o t i n c l u d e d .

The p r e s e n t a t i o n o f d a t a a r e a r r a n g e d a c c o r d i n g t o t h e

p a t h l e n g t h , s t a r t i n g w i t h t h e s h o r t e s t p a t h ; i n a l l ,

e l e v e n p a t h s a r e p r e s e n t e d . P r e c e e d i n g e a c h o f t h e p a t h s

i n v e s t i g a t e d , a b r i e f d e s c r i p t i o n i s o f f e r e d o n t h e s a l i e n t

c h a r a c t e r i s t i c s o f t h e p a t h (e .g. w h e t h e r i t i s w i t h i n l i n e

o f s i g h t o r b e y o n d l i n e o f s i g h t ) , a s s u m p t i o n s made i n t h e

l i n e a r i z a t i o n p r o c e s s , a n d w h e r e a p p r o p r i a t e , comments o n

t h e b e h a v i o r o f G T D m o d e l e d r e s u l t s . The t e r r a i n p r o f i l e

i t s e l f is a r e d r a w n f r o m M c Q u a t e ' s r e p o r t , a l o n g w i t h t h e

p i e c e w i s e l i n e a r a p p r o x i m a t i o n o f t h e p r o f i l e , r e p r e s e n t e d

b y d o t t e d l i n e s s u p e r i m p o s e d o n t h e t e r r a i n p r o f i l e . T h e

i n p u t d a t a f i l e s f o r t h o s e e l e v e n p r o f i l e s can b e f o u n d i n

A p p e n d i x 3.

A . D A T A REDUCTION

A l l t e r r a i n i n f o r m a t i o n a n d m e a s u r e d p r o p a g a t i o n p a t h

l o s s d a t a w e r e o b t a i n e d f r o m a h a r d c o p y o f t h e McQuate

r e p o r t . To r e t r i e v e t h o s e d a t a f r o m g r a p h s i n t h e r e p o r t ,

a n e l e c t r o n i c d i g i t i z e r was u s e d t o f a c i l i t a t e t h e p r o c e s s .

A s i n g l e d a t a p o i n t was o b t a i n e d b y moving a n o p t i c a l v i e w e r

( u s i n g t h e f r o n t p a n e l c o n t r o l s ) o v e r t h e d e s i r e d l o c a t i o n

o n t h e curve and t h e n p r e s s i n g a b u t t o n on t h e d i g i t i z e r .

The c o - o r d i n a t e o f t h a t p o i n t was a u t o m a t i c a l l y s c a l e d a n d

t r a n s l a t e d i n t o t h e a p p r o p r i a t e v a l u e s as a p p e a r e d i n t h e

Page 33: Evaluation progresion path loss model

r e p o r t , which was s t o r e d d i s c r e t e l y i n compu te r d i s k

s t o r a g e . The o n l y d a t a t h a t t h e o p e r a t o r had t o e n t e r d u r i n g

t h e p r o c e s s was: f o r t h e c a s e o f P a t h l o s s d a t a , t h e d e c i b e l

p a t h l o s s s c a l e i n c r e m e n t on t h e Y-axis ; and f o r t h e t e r r a i n

p r o f i l e , t h e l e n g t h and h e i g h t o f t h e p a t h .

P a t h l o s s d a t a were sampled a t t h e i n t e r v a l o f e v e r y 1 / 2

meter o v e r t h e e n t i r e a n t e n n a h e i g h t movement r a n g e o f 1 3

m e t e r s . By f o l l o w i n g a p r e d e f i n e d p r o c e d u r e o f d i g i t i z i n g

t h e p a t h l o s s d a t a , t h e s e v e n c u r v e s c o r r e s p o n d i n g t o t h e

s e v e n d i f f e r e n t f r e q u e n c i e s i n t h e McQua te ' s r e p o r t were

o r g a n i z e d i n t o a n a t r i x f i l e .

A d e w l e t t - P a c k a r d 7225A G r a p h i c s P l o t t e r equipped v i t h a

o p t i c a l v i e w e r was employed f o r t h i s e f f o r t ( t h e optical

v iewer is l o a d e d l i k e a pen f o r v i e w i n g ) .

The p l o t t e r was c o n n e c t e d i n a p a r a l l e l c o n f i g u r a t i o n

w i t h a n ADM-3A C R T t e r m i n a l . The computer t o which t h i s

hardware was c o n n e c t e d was a n IBX 4341 r u n n i n g u n d e r -$%/SP

C M S t i m e s h a r e mode. To p r o v i d e p r o p e r h a n d s h a k i n g f o r d a t a

t r a n s f e r be tween t h e h o s t computer a n d p l o t t e r , a n ASSEMBLER

r o u t i n e was w r i t t e n . P l o t t e r ~zsolutlon i n b o t h a x e s

exceeds 0.001 i n c h , i n d i c a t i n g t h a t q u a n t i z a t i o n and

t r u n c a t i o n e r r o r s c a n be c o n s i d e r e d i n s i g n i f i c a n t . The h a r d

copy r e p o r t from which t h e s e d a t a were t a k e n was a Xerox

copy o f t h e o r i g i n a l r e p o r t . Thus , d a t a were l i k e l y

c o n t a m i n a t e d by pho tocopy d i s t o r t i o n e r r o r s . E v i d e n c e of

s u c h e r r o r s a p p e a r as s l i g h t l y c u r v e d a x e s , n o n - s q u a r e n e s s ,

Page 34: Evaluation progresion path loss model

a n d d i s t o r t i o n . To c o m p e n s a t e f o r s u c h e r r o r s , t h e e n d

p o i n t s o f t h e a x e s were e n t e r e d , f r o m t h e p l o t t e r , t o t h e

s o f t w a r e ; t h i s i n f o r m a t i o n was t h e n u s e d t o c o r r e c t

s u b s e q u e n t d a t a f r o m t h e p l o t t e r v i a a l i n e a r i n t e r p o l a t i o n

method . A l l d a t a f i l e s t h u s o b t a i n e d w e r e c h e c k e d a g a i n s t

t h e o r i g i n a l d a t a ; any e r r o r s , w h i c h were u s u a l l y o b v i o u s

when t h e y e x i s t e d , w e r e c o r r e c t e d by e d i t i n g t h e a s s o c i a t e d

d a t a f i l e .

i ' leasured p a t h l o s s d a t a a r e p l o t t e d v e r s u s r e c e i v e r

a n t e n n a h e i g h t , w i t h o n e p l o t f o r e a c h f r e q u e n c y . The I T S

mode led a n d GTD m o d e l e d d a t a a r e a l s o p l o t t e d o n t h e same

g r a p h t o e n a b l e a d i r e c t p e r f o r m a n c e e v a l u a t i o n t o b e made;

t h e s e mode l r e s u l t s r e p r e s e n t a b s o l u t e p a t h l o s s , r a t h e r

t h a n r e l a t i v e l o s s .

Page 35: Evaluation progresion path loss model

B. P r e s e n t a t i o n o f d a t a

1 . P a t h R1-0.5-TI (0.5~n., f l a t , w i t h i n l i n e o f s i g h t )

T h i s t e r r a i n p r o f i l e is shown i n F i g u r e 4-1. A s c a n be

s e e n , t h e p r o f i l e i s made u p o f f l a t g r o u n d s l o p i n g down

t o w a r d s t h e t r a n s m i t t i n g a n t e n n a . B e c a u s e o f p r o f i l e

s i m p l i c i t y , t h e l i n e a r i z a t i o n p r o c e s s was s t r a i g h t f o r w a r d ,

r e s u l t i n g i n a modeled p r o f i l e d e f i n e d s o l e l y b y t h e

e n d p o i n t s .

T h i s p r o f i l e was t h e f i r s t o n e t o b e c h o s e n i n t h e

d e v e l o p m e n t s t age o f t h e GTD m o d e l t o v e r i f y t h a t no g r o s s

e r r o r s e x i s t e d .

The s e c o n d r e a s o n i n s e l e c t i n g t h i s p r o f i l e w a s t o s t u d y

t h e l o c a l s u r f a c e r o u g h n e s s f a c t o r a n d i t s e f f e c t s o n t h e

v e r t i c a l l o b e s t r u c t u r e which a r i ses f r o m t h e i n t e r f e r e n c e

b e t w e e n t h e d i r e c t r a y and r e f l e c t e d r a y s . F o r a f l a t g r o u n d

p l a n e , s u c h as t h e o n e d i s c u s s e d h e r e , t h e G T D mode l

o p e r a t e s as a G e o m e t r i c a l O p t i c s mode l s i n c e t h e r e a r e n o

d i f f r a c t i v e e d g e s . Thus , G T D m o d e l es t imates o f p a t h l o s s

are b a s e d e x c l u s i v e l y o n a s i n g l y - r e f l e c t e d r a y a n d d i r e c t

r a y F o r s u c h a c o n f i g u r a t i o n , t h e b e h a v i o r o f t h e m o d i f i e d

r e f l e c t i o n c o e f f i c i e n t f o r l o c a l s u r f a c e r o u g h n e s s c a n b e

s t u d y e x p l i c i t l y .

Measured and Modeled d a t a f o r t h i s t e r r a i n p r o f i l e a re

p l o t t e d i n F i g u r e s 4-2 t h r o u g h 4-8, w i t h t h e g r o u n d e l e c t r i c

Page 36: Evaluation progresion path loss model

c o n s t a n t s u s e d as shown i n t h e f i g u r e . D u r i n g t h e

i n v e s t i g a t i o n o f t h i s p r o f i l e , t h e e l e c t r i c a l c o n s t a n t s o f

t h e g r o u n d p l a n e w e r e v a r i e d o v e r a w i d e r a n g e o f v a l u e s t o

d e t e r m i n e i t s e f f e c t s o n t h e r e c e i v e d f i e l d . T h e r e s u l t o f

t h i s e x p e r i m e n t showed t h a t f i e l d s t r e n g t h d i d n o t c h a n g e

a p p r e c i a b l y . T h i s i s a n e x p e c t e d r e s u l t f o r h o r i z o n t a l

p o l a r i z a t i o n b e c a u s e i t s p r o p e r t i e s a t low a n g l e s o f

i n c i d e n c e a r e similar t o p e r f e c t l y c o n d u c t i n g g r o u n d p l a n e s .

However , t h i s r e s u l t w o u l d n o t b e e x p e c t e d f o r v e r t i c a l

p o l a r i z a t i o n o r f o r p a t h s i n v o l v i n g h i g h i n c i d e n c e a n g l e s .

A d d i t i o n a l l y , a r a n g e o f l o c a l s u r f a c e r o u g h n e s s

-,~-.F\-a+I..c. , s i Y 1 * 1 - 3 w e r e i n v e s t i g a t e d t o d e t e r m i n e i t s e f f e c t o n t h e

mode led data. G e n e r a l l y , t h e m o d e l i s s e n s i t i v e t o t h e l o c a l

s u r f a c e r o u g h n e s s ; t h e l a r g e r t h e mode led s u r f a c e r o u g h n e s s ,

t h e s m a l l e r % h e m o d e l e d l o b i n g d e p t h . The a c t u a l p r o f i l e

f o r e g r o u n d c o n s i s t s o f a l t e r n a t i n g s t r i p s o f p l o w e d g r o u n d

a n d w h e a t s t u b b l e ; t h e r e f o r e a r a n g e o f s u r f a c e r o u g h n e s s

v a l u e s f r o m 6-1 8 i n c h e s were u s e d , w h i c h i s r e a s o n a b l e b a s e d

u p o n t h e d e s c r i p t i o n o f t h e p r o f i l e . T h o s e v a l u e s p r o v i d e d

g o o d r e s u l t s i n t h e m o d e l e d d a t a , a l t h o u g h g r e a t e s t

a g r e e m e n t b e t w e e n mode led a n d m e a s u r e d r e s u l t s were o b t a i n e d

u s i n g a r o u g h n e s s v a l u e e q u a l t o 9 i n c h e s . H e n c e , 9 i n c h e s

o f l o c a l s u r f a c e r o u g h n e s s is u s e d f o r a l l s u b s e q u e n t

mode led d a t a f o r t h i s p r o f i l e .

F o r t h e f i r s t t h r e e l o w e r f r e q u e n c i e s p l o t s u s i n g t h e 9

i n c h e s l o c a l s u r f a c e r o u g h n e s s f a c t o r , t h e l o b i n g e f f e c t is

Page 37: Evaluation progresion path loss model

n o t p r o m i n e n t , a n d t h e mode led d a t a i s i n c l o s e a g r e e m e n t

w i t h t h e m e a s u r e d d a t a . A t h i g h e r f r e q u e n c i e s , v e r t i c a l

l o b i n g d o e s b e c o m i n g more n o t i c e a b l e w i t h t h e s i z e a n d t h e

d e p t h o f t h e l o b e n u l l s , and as w e l l as t h e s p a c i n g b e t w e e n

t h o s e n u l l s b e i n g i n g o o d a g r e e m e n t f o r b o t h m e a s u r e d a n d

modeled d a t a . I n some i n s t a n c e s , t h e mode led l o b i n g o c c u r s

a t d i f f e r e n t r e c e i v e r a n t e n n a h e i g h t s t h a n d o e s t h e m e a s u r e d

l o b i n g , c a u s i n g a n a p p a r e n t d i v e r g e n c e b e t w e e n t h e m e a s u r e d

a n d mode led d a t a . However , t h i s s e p a r a t i o n i s c o n s i d e r e d t o

b e c a u s e d b y e r r o r s i n t e r r a i n p r o f i l e d e f i n i t i o n o r

a n t e n c a h e l g A t hats rstfier t:sn >"> - 3 d e l i n g e r r o r .

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7 : & " O C

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2 a Fi

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Page 40: Evaluation progresion path loss model

m G 0 - ZR 0) 0) C C m 2 0 a er U a 'ti k 3

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'(I 0)

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2 . P a t h R1-5-T6A ( 4 . 6 km., Mixed P a t h w i t h D o u b l e

D i f f r a c t i v e E d g e s )

T h i s t e r r a i n p r o f i l e , shown i n F i g u r e 4-9, i s made u p o f

r o l l i n g h i l l s . The p i e c e w i s e l i n e a r a p p r o x i m a t i o n p r o c e s s

was s t r a i g h t f o r w a r d , r e s u l t i n g i n t h e s e v e n e d g e s

r e p r e s e n t e d b y t h e d o t t e d l i n e i n t h e f i gu re . O f p r i m a r y

i n t e r e s t i n t h i s p r o f i l e i s t h e d o u b l y - d i f f r a c t i v e e d g e s

w h i c h h a s i t s s h a d o w b o u n d a r y c o r r e s p o n d i n g t o a r e c e i v i n g

a n t e n n a h e i g h t of 9 meter. A t t h a t h e i g h t , t h e r e c e i v i n g

a n t e n n a i s i n a s t r a i g h t l i n e a l o n g t h e two d i f f r a c t i v e

e d g e s ~ d i t h t h e t r a n s m i t t i n g a n t e n n a . Below t h i s h e i g h t , t h e

p a t n is b l o c k e d , a n d i s be low l i n e o f s i g h t . Above t h e 9

m e t e r a n t e n n a h e i g h t , t h e p a t h i s w i t h i n l i n e o f s i g h t .

T h i s t y p e o f c o n f i g u r a t i o n i s o f c o n s i d e r a b l e i n t e r e s t w i t h

r e g a r d s t o G T D m o d e l i n g t h e o r y b e c a u s e i t i n v o l v e s

c a i c u l a t i o n s of two r a p i d l y v a r y i n g f i e l d s n e a r t h e

t r a n s i t i o n r e g i o n ; i f G T D h a s a r e g i o n i n w h i c h t h e t h e o r y

i s n o t s t r i c t l y a p p l i c a b l e , i t w o u l d b e i n a t r a n s i t i o n

r e g i o n s u c h as t h e o n e p r e s e n t e d i n t h i s p r o f i l e .

F i g u r e s 4-10 t h r o u g h 4-1 6 p r e s e n t p l o t s o f m e a s u r e d

a n d mode led r e s u l t s . R e f e r r i n g t o t h e 230 MHz p l o t i n F i g u r e

4 -10 , a f i e l d d i s c o n t i n u i t y o f a b o u t 5 d e c i b e l s s e e n a t t h e

t r a n s i t i o n r e g i o n d i s c r i b e d a b o v e . T h i s d i s c o n t i n u i t y i s t h e

l a r g e s t o b s e r v e d i n mode l r e s p o n s e a n d i s n o t c o n s i d e r e d t o

b e s i g n i f i c a n t l y d e t r e m e n t e l w i t h r e g a r d s t o p r o p a g a t i o n

Page 47: Evaluation progresion path loss model

mode l ing . A s t h e f r e q u e n c y becomes h i g h e r , t h e d i s c o n t i n u i t y

v a n i s h e s as is s e e n i n t h e f i g u r e . The r e a s o n f o r t h i s

b e h a v i o r i s t h a t t h e a r e a o f t h e t r a n s i t i o n r e g i o n d e f i n i n g

t h e r a p i d l y - v a r y i n g f i e l d s d e c r e a s e s w i t h i n c r e a s i n g

f r e q u e n c y . A l t h o u g h t h e d i s c o n t i n u i t i e s may s t i l l b e

p r e s e n t , t h e y a r e a p p a r e n t l y b y p a s s e d i n t h e s a m p l i n g scheme

u s e d f o r d a t a r e t r i e v a l .

G e n e r a l l y good a g r e e m e n t is d e m o n s t r a t e d b e t w e e n t h e

modeled d a t a and t h e measu red d a t a a l t h o u g h t h e r e i s a b i a s

e r r o r t h a t t e n d s t o i n c r e a s e w i t h f r e q u e n c y . T h i s i n c r e a s i n g - . o i a a e r r o r , a c c o r d i n g t o p r e v i o u s e x p e r i e n c e 11 9 ) g a i n e d

- l r o s ~ r o p a g a t i o n m o d e l i n g , i s l i k e l y d u e t o t r e e s w i t h i n t h e

p a t h t h a t a r e n o t t a k e n i n t o a c c o u n t by t h e mode l , whose

a b s o r p t i v e e f f e c t s i n c r e a s e w i t h f r e q u e n c y .

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+ -- '+.- A" ooqor- 00-od- 00-od- 00-oor- oo 011- oo 021- oo orr- 00-ohi- oo.0~1--

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Page 53: Evaluation progresion path loss model

0 0

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Page 55: Evaluation progresion path loss model

0 L Q - a3

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Page 56: Evaluation progresion path loss model

3. P a t h R1-5-T5A ( 5 . 0 K m . , beyond L i n e o f s i g h t )

R e f e r i n g t o t h e d r a w i n g of t h e t e r r a i n p r o f i l e i n F i g u r e

4-7, i t is s e e n t h a t t h e d i r e c t p a t h is b l o c k e d f o r a l l

a n t e n n a h e i g h t . The p i e c e w i s e - l i n e a r i z e d model i s

a p p r o x i m a t e d b y 3 p l a t e s .

GTD c a l c u l a t e d r e s u l t s f r o m t h i s p i e c e w i s e l i n e a r

t e r r a i n model f o r t h e l o w e r f r e q u e n c i e s a r e e x t r e m e l y c l o s e

t o t h e measured d a t a as c a n b e s e e n f r o m P i g u r e s 4-18

t h r o u g h 4-23. A s f r e q u e n c y becomes h i g h e r , d i s c r e p a n c i e s

be tween measured and modeled d a t a i n c r e a s e s . The r e a s o n may

b e d u e t o l o s s e s caused by t r e e s o r o t h e r i n t e r v e n i n g

o b j e c t s as was o b s e r v e d w i t h t h e p r e v i o u s p a t h .

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x x

x x x

GTD Modeled

- Measured

QD

BO

Q

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

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4. P a t h RI -10-T2A ( 9 . 8 Km. , Beyond L i n e o f S i g h t )

The t e r r a i n p r o f i l e a l o n g w i t h t h e p i e c e w i s e l i n e a r

a p p r o x i m a t i o n a r e shown i n F i g u r e 4-24. The p a t h i s beyond

l i n e o f s i g h t , w i t h t h e d i r e c t r a y b l o c k e d b y a h i l l . A

t o t a l o f 7 e d g e s a r e u s e d as i n p u t d a t a .

The measu red and modeled d a t a a r e shown i n F i g u r e s 4-25

t h r o u g h 4-31; c l o s e a g r e e m e n t b e t w e e n t h e two w e r e o b t a i n e d

f o r a l l f r e q u e n c i e s . A l s o , t h e measu red d a t a d o n o t s u f f e r

t h e h i g h - f r e q u e n c y e r r o r s e v i d e n t i n t h e p r e v i o u s two

p r o f i l e s ; zne r e a s o n may b e d u e t o t h e a b s e n c e o f t r e e s

a l o n g t h e p a t h .

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5 . P a t h R1-10-T3 ( 9 . 6 K m . , L i n e of S i g h t )

- .-- The t e r r a i n p r o f i l e f o r t h i s p a t h i s shown i n F i g u r e 4-32

Because t h e p i e c e w i s e - l i n e a r a p p r o x i m a t i o n d o e s n o t f i t t h e

a c t u a l t e r r a i n p r o f i l e as c l o s e l y as t h e p r e v i o u s p r o f i l e s ,

t h e l o c a l t e r r a i n roughness f a c t o r was a d j u s t e d d u r i n g t h e

e x p e r i m e n t t o i n v e s t i g a t e i ts e f f e c t s . I n t h i s e f f o r t ,

l o c a l t e r r a i n r o u g h n e s s v a l u e s o f .2286 m e t e r and 2 m e t e r s

were u s e d . The G T D program was r u n w i t h t h e same l i n e a r i z e d

t e r r a i n p r o f i l e u s i n g t h e s e d i f f e r e n t l o c a l s u r f a c e

roughness p a r a m e t e r s .

The f i r s t s e t of c a l c u l a t e d r e s u l t s u s i n g 9 i n c h e s l o c a l

s u r f a c e roughness a r e shown from F i g u r e s 4-33 t h r o u g h 4-39.

G T D modeled r e s u l t s a r e i n c l o s e a g r e e n e n t with t h e measured

d a t a , e x c e p t a t 751 MHz. A t 751 LVIHZ, a n anomaly i s o b v i o u s

i n t h e measured d a t a , where t h e p a t h l o s s a t 751 MHz i s

i n c o n s i s t e n t w i t h t h e r e p o r t e d l o s s e s a t h i g h e r o r lower

f r e q u e n c i e s ; hence comments on G T D modeled pe r fo rmance a t

t h a t f r e q u e n c y a r e n o t o f f e r e d . A t 1846 MHz, G T D o v e r

e s t i m a t e s t h e d e p t h of t h e v e r t i c a l l o b e .

S e c o n d l y , t h e r o u g h n e s s f a c t o r w a s a d j u s t e d o v e r a wide

r a n g e o f v a l u e s . I t was f o u n d t h a t by i n c r e a s i n g t h e

r o u g h n e s s f a c t o r t o 2 m e t e r s , t h e d e p t h o f t h e l o b i n g was

c l o s e r t o t h e measured d a t a . The new p a t h l o s s e s t i m a t e f o r

1846 31Hz i s p l o t t e d on F i g u r e 4-44; and o t h e r f r e q u e n c i e s

a r e shown i n F i g u r e s 4-40 t h r o u g h 4-46. G e n e r a l l y , t h e l o c a l

t e r r a i n roughness f a c t o r d o e s n o t i n c u r a n o t i c e a b l e e f f e c t

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o n f r e q u e n c i e s l o w e r t h a n 1 G H z . O t h e r v a l u e s o f t e r r a i n

r o u g h n e s s f a c t o r r a n g i n g f r o m 0.5 t o 5 m e t e r s were

a t t e m p t e d , b u t b a s e d u p o n t h e s i z e a n d t h e d e p t h o f t h e

l o b e , a n d t a k i n g i n t o c o n s i d e r a t i o n t h e v a r i a t i o n o f t h e o f

t h e l i n e a r i z e d p r o f i l e with r e s p e c t t o t h e a c t u a l t e r r a i n

p r o f i l e , a f i n a l v a l u e o f 2 m e t e r was s e l e c t e d .

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0 0 .

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0 0

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4 4 a a a , a a , a

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6 . P a t h R1-20-TI (27.7 K m . , Beyond L i n e of s i g h t )

The t e r r a i n p r o f i l e a l o n g w i t h t h e p i e c e w i s e - l i n e a r

a p p r o x i m a t i o n a r e p r e s e n t e d i n F i g u r e 4-47. The

a p p r o x i m a t i o n o n l y t e n d s t o i n c l u d e t h e m a j o r p e a k s and

s l o p e s o f t h e a c t u a l t e r r a i n . The a p p r o x i m a t i o n c o n s i s t s of

5 e d g e s as s e e n i n t h e f i g u r e . B e c a u s e of v a r i a t i o n s o f

t h e a c t u a l t e r r a i n w i t h r e s p e c t t o t h e l i n e a r a p p r o x i m a t i o n ,

a modeled l o c a l r o u g h n e s s p a r a m e t e r o f 2 m e t e r was chosen .

C a l c u l a t e d r e s u l t s f rom GTD modeled and measured d a t a a r e

. - . a i i o % - ~ i i i 4-48 t h r o u g h 4-54. A s a a s n f rom t h e s e

f i gu res , 223 r e s u l t s show a l a r g e r l o s s t h a n t h e measured

d a t a a s t h e f r e q u e n c y i n c r e a s e s , e s p e c i a l l y t h o s e above 910

MU?., These e x c e s s i v e v a r i a t i o n s may b e c a u s e d by modeled - ----

~ ~ i t ; r\at'ri reflection from t h e c o m p a r a t i v e l y smooth s e g m e n t s

u s e d t o a p p r o x i m a t e t h e i r r e g u l a r t e r r a i n .

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C, P - a C -4 m $ 4 .rl a J L J U O C a, CJ tn k I .4

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rl d a 5 Q) a a l a O L I O E 2 5 : a r d r n E-1 s E-( W E H

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Page 96: Evaluation progresion path loss model

X X

X

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T. HT.

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Local Surface Roughness (one

sigma) =

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Frequency =

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Conductivity =

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Relative Permittivity

= 15.0

Figure 4-52 . P

ath loss vs. receiving

antenna height for Profile R1-20-Ti ,

Figure 4-47 . T

ransmitter height is at

7.3

meters.

Page 97: Evaluation progresion path loss model

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7 . P a t h T I - 2 0 4 4 (20.7 K m . , Beyond L i n e o f S i g h t )

The l i n e a r i z e d a p p r o x i m a t i o n and t e r r a i n p r o f i l e f o r t h i s

p a t h a r e shown i n F i g u r e 4-55. The l i n e a r i z e d model

c o n s i s t s o f 6 e d g e s which f o l l o w o n l y t h e m a j o r t e r r a i n

f e a t u r e s ; a g a i n , a l o c a l t e r r a i n r o u g h n e s s f a c t o r of 2

m e t e r s was u s e d f o r model ing .

The modeled and measured d a t a f o r t h i s p r o f i l e a r e shown

i n F i g u r e s 4-45 t h r o u g h 4-61. As c a n b e s e e n from t h e

F i g u r e s , t h e p l o t s a r e s imilar t o t h a t o f t h e p r e v i o u s

przlf lie. ,7 .n 7. A t f r e q u e n c i e s be low 1 GZZ? ~ T L U m o d e l e d r e s u l t s

show c l o s e a g r e e m e n t w i t h meaanred d a t a ; vhilz above t h a t

f r e q u e n c y , GTD c o n s i s t e n t l y g i v e s a h i g h e r v a l u e t h a n t h e

r n e ~ q u r ed d a t a ,

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8 . 49.0 K m . , Beyond L i n e of S i g h t P a t h .

The t e r r a i n p r o f i l e f o r t h i s p r o f i l e i s shown i n F i g u r e

6-62. B e c a u s e o f t h e c o m p l e x i t y o f t h i s p r o f i l e , two

p i e c e w i s e - l i n e a r a p p r o x i m a t i o n s were u s e d . The p u r p o s e of

i n v e s t i g a t i n g b o t h a p p r o x i m a t i o n s is t o d e t e r m i n e t h e

r e l a t i o n s h i p be tween modeled t e r r a i n v a r i a t i o n and t h e l o c a l

s u r f a c e r o u g h n e s s p a r a m e t e r . The f i r s t a p p r o x i m a t i o n ,

c o n s i s t i n g of 17 e d g e s , i s shown b y t h e d o t t e d l i n e i n

F i g u r e 4-62. T h i s model d e f i n e s more a c c u r a t e l y t h e t e r r a i n

p r o f i l e , h e n c e , a r o u g h n e s s p a r a m e t e r of 9 i n c h e s is u s e d .

P4eas:ired and GTD modeled d a t a f o r t h e 17 edge p r o f i l e are

g i v a n iz P i g u r e 4-63 t h r o u g h F i g u r e 4-69. A s s e e n i n t h e s e

f i g u r e s , e v i d e n c e o f e x c e s s i v e v e r t i c a l l o b i n g i s o b s e r v e d

f o r f r e q u e n c i e s above 410 MHz.

A l e s s - a c c u r a t e l y d e f i n e d l i n e a r i z e d p r o f i l e f o r t h e same

p a t h i s shown i n F i g u r e 4-70. S i n c e t h i s modeled p r o f i l e

h a s a g r e a t e r v a r i a t i o n w i t h r e s p e c t t o t h e a c t u a l p r o f i l e

t h a n t h e 17 e d g e a p p r o x i m a t i o n , a l o c a l t e r r a i n r o u g h n e s s

f a c t o r o f 2 m e t e r is u s e d . GTD modeled and measured d a t a f o r

t h i s l i n e a r i z e d p r o f i l e are p r e s e n t e d i n F i g u r e s 4-71

t h r o u g h 4-77. T h e s e f i g u r e s show G T D e s t i m a t e d p a t h l o s s and

v e r t i c a l l o b i n g are i n c l o s e r a g r e e m e n t s w i t h t h e measured

d a t a t h a n p r e v i o u s model employ ing s m a l l e r s u r f a c e r o u g h n e s s

f a c t o r , e s p e c i a l l y a t f r e q u e n c i e s o f 751 MHz and above .

An i m p o r t a n t o b s e r v a t i o n is p r o v i d e d by t h e s i m p l e two-

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p r o f i l e i n v e s t i g a t i o n p r e s e n t e d above . The a c c u r a c y o f t h e

G T D model d o e s n o t s o l e l y depend on t h e a c c u r a c y o f t h e

i n p u t l i n e a r i z e d t e r r a i n p r o f i l e ; some c o m b i n a t i o n s o f

p r o f i l e d e f i n i t i o n and l o c a l s u r f a c e r o u g h n e s s f a c t o r a r e

n e c e s s a r y f o r model a c c u r a c y . The r u l e s f o r d e t e r m i n i n g what

c o m b i n a t i o n c o n s t i t u t e s a n optimum c o m b i n a t i o n would r e q u i r e

a n i n - d e p t h s t u d y which is beyond t h e s c o p e of t h e

f e a s i b i l i t y s t u d y o f f e r e d i n t h i s t h e s i s .

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u D - a E: ..I m 3 d' .r( -4 a 5' 4J U O C Q a D k I .r(

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9- P a t h TI-50-TI (52.5 K m . , L i n e of S i & t )

The t e r r a i n p r o f i l e , a l o n g w i t h l i n e a r i z e d model are

g i v e n i n F i g u r e 4-78. As c a n b e s e e n , t h e p a t h i s u n b l o c k e d

and a t o t a l o f o f f i v e e d g e s a r e u s e d i n t h e l i n e a r

a p p r o x i m a t i o n , w i t h a modeled s u r f a c e r o u g h n e s s f a c t o r o f 2

m e t e r s .

Measured and modeled d a t a a r e shown i n F i g u r e s 4-79

t h r o u g h 4-84. G T D modeled r e s u l t s do n o t show t h e d e g r e e o f

v e r t i c a l l o b i n g as i s e v i d e n t i n t h e measured d a t a . The

r e a s o n may b e due t o an e x c e s s i v e l o c a l s u r f a c e r o u g h n e s s

p a r a m e t e r a n d / o r imprope r p l acemen t of t e r r a i n p r o f i l e

e d g e s . S i n c e t h e p r o f i l e d o e s n o t c o n s i s t d i f f r a c t i v e e d g e ,

t h e l i m i t o f G T D m o d e l ' s c a p a b i l i t y i n p r e d i c t i n g l o n g p a t h s

c a n n o t b e d e t e r m i n e d .

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Page 131: Evaluation progresion path loss model

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Page 133: Evaluation progresion path loss model

10. P a t h R3-80-T3 (80 K m . , L i n e o f S i g h t )

The t e r r a i n p r o f i l e f o r t h i s l o n g p a t h i s shown i n F i g u r e

4-86. Aga in , t h e p a t h is w i t h i n l i n e of s i g h t . c o n s i s t s no

n a j o r d i f f r a c t i v e e d g e s , The l i n e a r a p p r o x i m a t i o n f o r G T D

i n p u t u s e s 1 2 e d g e s as i s shown i n t h e F i g u r e .

The measured and modeled d a t a a r e o f f e r e d i n F i g u r e s 4-86

t h r o u g h 4-91. G T D modeled d a t a h a s a b i a s e d e r r o r on a l l

f r e q u e n c i e s , p e r h a p s due t o t r o p o s p h e r i c e f f e c t s no t

c o n s i d e r e d b y t h e computer model; t h u s t h i s f r e e - s p a c e l o s s

e s t i m a t e does n o t a p p e a r u n r e a i i s t i c . iiowever, i t s h o u i d b e

n o t e d t h a t t h i s p a t h can not c o n c l u s i v e l y d e t e r m i n e G T D

a o d e l pe r fo rmance l i m i t s due t o t r o p o s p h e r i c e f f e c t s n o t

b e i n g t a k e n i n t o a c c o u n t by t h e model. A more

r e p r e s e n t a t i v e e v a l u a t i o n of GTD model f o r l o n g e r ~ a t h s

would be p r o v i d e d by a p a t h c o n t a i n i n g pronuounced

d i f f r a c t i v e e d g e s ; u n f o r t u n a t e l y , s u c h a p a t h i s n o t g i v e n

i n McQuate, e t . a l .

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1 1 . P a t h R2-120-TI ( 1 1 5 km., L i n e o f S i g h t )

A s s e e n i n F i g u r e 4-92, t h i s t e r r a i n p r o f i l e is t h e

l o n g e s t i n v e s t i g a t e d i n t h i s t h e s i s . Again , i t d o e s n o t

i n c l u d e a n y d i f f r a c t i v e e d g e s , s o t h a t t h e p o t e n t i a l

pe r fo rmance of GTD o n l o n g p a t h s c a n n o t b e e v a l u a t e d .

Measured a n d GTD modeled d a t a f o r t h i s p a t h are shown i n

F i g u r e 4-93 t h r o u g h 4-95. G T D modeled d a t a shows

u n r e a l i s t i c a l l y large v e r t i c a l l o b i n g , which a l t h o u g h c a n b e

d e c r e a s e d b y r a i s i n g t h e s u r f a c e r o u g h n e s s f a c t o r , t h e b i a s

e r r o r be tween measured and modeled r e s u l t s as e x i s t e d i n the

p r e v i o u s model w i l l n o t d e c r e a s e . T h i s b i a s e r r o r i s a g a i n

c o n s i d e r e d t o b e d u e t o t r o p o s p h e r i c e f f e c t . Higher

f r e q u e n c i e s d a t a a r e n o t a v a i l a b l e from t h e M c Q u a t e l s and

h e n c e c o m p a r i s o n s c a n n o t b e made.

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a al

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V RECOMMENDATIONS

Whi le u n d e r g o i n g t h e GTD model p e r f o r m a n c e e v a l u a t i o n on

p r o p a g a t i o n p a t h l o s s , c e r t a i n s u g g e s t i o n s and o b s e r v a t i o n s

l e d t o t h e f o l l o w i n g recommendat ions .

1 . The t e r r a i n l i n e a r i z a t i o n p r o c e s s s h o u l d b e c a l c u l a t e d

a n a l y t i c a l l y by computer a l g o r i t h m t o d e t e r m i n e t h e a c t u a l

mechanism of s c a t t e r i n g f rom t h e t e r r a i n e d g e s , a n d h e n c e

e l i m i n a t e t h e p r e s e n t u s e r d e p e n d e n t f a c t o r .

2 . The v a l u e o f l o c a l t e r r a i n r o u g h n e s s f a c t o r s h o u l d b e

o b t a i n e d by t h e a c t u a l g a u s s i a n a v e r a g e o f t h e t e r r a i n

i r r e g u l a r i t i e s i n a d d i t i o n t o t h e two v a l u e s b e i n g c h o s e n

i n t h i s t h e s i s . However, i f i r r e g u l a r i t i e s v a r y g r o s s l y

o v e r d i f f e r e n t p a t h s e g m e n t s , G T D model s h o u l d b e c a p a b l e t o

a s s i g n v a r i a b l e v a l u e s t o d i f f e r e n t edge s e g m e n t s .

3. G T D model d o e s n o t i n c l u d e t h e e f f e c t s o f f o r e s t e d

a r e a s i n p r e d i c t i n g p a t h l o s s a l t h o u g h i t h a s b e e n

d e m o n s t r a t e d t h a t t h e s e e f f e c t s c a n b e e s t i m a t e d a c c u r a t e l y

11 91. C o n s e q u e n t l y , GTD model s h o u l d b e m o d i f i e d t o i n c l u d e

t h e known e f f e c t s of f o r e s t e d a r e a s .

4 . I n t h i s s t u d y , o n l y t h e h o r i z o n t a l p o l a r i z e d f i e l d was

i n v e s t i g a t e d . S i m i l i a r s t u d i e s s h o u l d b e u n d e r t a k e n f o r

v e r t i c a l and c i r c u l a r p o l a r i z e d wave s o as t o e x p o s e f u r t h e r

c a p a b i l i t i e s of t h e G T D model.

5 . A s p r e s e n t l y c o n f i g u r e d , G T D model c a n o n l y c a l c u l a t e

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d i f f r a c t i v e e d g e s t h a t a r e p e r p e n d i c u l a r t o t h e p r o p a g a t i o n

p a t h . M o d i f i c a t i o n of GTD model t o a c c o u n t f o r d i f f r a c t i o n

from o b l i q u e l y - a n g l e d e d g e s would improve p r e d i c t i o n

a c c u r a c y f o r c e r t a i n p r o f i l e s .

6 . E f f e c t s o f t r o p o s p h e r e s u c h as: r e f r a c t i o n ( b e n d i n g )

o f wave b y nonhomogeneous a t m o s p h e r e ; a b s o r b t i o n b y oxygen

a n d w a t e r v a p o r m o l e c u l e s , a b s o r b t i o n and s c a t t e r i n g b y

p r e c i p i t a t i o n o f c l o u d s t h a t a r e n o t i n c l u d e d a t p r e s e n t

s h o u l d be implemented i n f u t u r e work.

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V I C o n c l u s i o n

A c o m p u t e r mode l h a s b e e n d e v e l o p e d t o e s t i m a t e

e l e c t r o m a g n e t i c wave p r o p a g a t i o n o v e r i r r e g u l a r t e r r a i n

u s i n g t h e G e o m e t r i c a l T h e o r y o f D i f f r a c t i o n (GTD) m o d i f i e d

t o a c c o u n t f o r f i n i t e c o n d u c t i v i t y and l o c a l g r o u n d s u r f a c e

r o u g h n e s s . B a s e d u p o n c o m p a r i s o n s o f G T D m o d e l e d d a t a w i t h

m e a s u r e d d a t a , t h e f o l l o w i n g c o n c l u s i o n s a r e o f f e r e d :

1 . G T D p r o v i d e s a c c u r a t e p r e d i c t i o n c a p a b i l i t i e s f o r

i r r e g u l a r t e r r a i n w i t h p a t h l e n g t h s f r o m 0 .5 t o 80 K m . , a t

s e v e n f r e q u e n c i e s i n t h e 230- t o 9200- MHz r a n g e ; b o t h

w i t h i n a n d beyond l i n e o f s i g h t p a t h s f o r h o r i z o n t a l l y -

p o l a r i z e d wave.

2. The m o d i f i e d d i f f r a c t i o n c o e f f i c i e n t u s e d t o a c c o u n t

f o r f i n i t e c o n d u c t i v i t y and l o c a l s u r f a c e r o u g h n e s s d o e s n o t

a f f e c t f i e l d c o n t i n u i t y a t a n d n e a r t h e v i c i n i t y o f t h e

shadow a n d r e f l e c t i o n b o u n d a r i e s .

3. The p r e s e n c e o f d o u b l e d i f f r a c t e d e d g e s w i t h i n t h e

f i e l d t r a n s i t i o n r e g i o n c a u s e d m i n o r f i e l d d i s c o n t i n u i t i e s ,

a l t h o u g h t h e s e e f f e c t s a re n o t c o n s i d e r e d d e t r e m e n t a l t o

p r e d i c t i o n a c c u r a c y .

4. G T D a c c u r a c y d e p e n d s u p o n o n a n o p t i m i z e d c o m b i n a t i o n

o f b o t h t h e l o c a l s u r f a c e r o u g h n e s s p a r a m e t e r and t h e

p i e c e w i s e - l i n e a r i z e d t e r r a i n d a t a .

5. G T D a c c u r a c y d e c r e a s e s f o r l o n g e r p a t h s i n v e s t i g a t e d ,

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a p p a r e n t l y d u e t o t r o p o s p h e r i c a t t e n u a t i o n e f f e c t s n o t

accoun ted f o r by t h e model.

b . T h e v a l u e of t h e l o c a l s u r f a c e roughness f a c t o r

n e c e s s a r y f o r r e a l i s t i c v e r t i c a l l o b e e s t i m a t e s t e n d s t o

i n c r e a s e w i t h p a t h l e n g t h , and t h u s t h e s i z e of t h e F r e s n e l

Zone.

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V I1 ACKNOWLEDGEMENTS

The a u t h o r is i n d e b t e d t o h i s a d v i s o r Dr. Ken t C h a m b e r l i n

who g e n e r o u s l y gave h i s t i m e , e n d l e s s p a t i e n c e , a n d g u i d a n c e

d u r i n g t h i s e f f o r t .

S p e c i a l g r a t i t u d e is due t o Dr. R.J. L u e b b e r s and D r .

V i c h a t e U n g u i c h i a n , who d e v e l o p e d t h e b a s i c G T D model .

Thanks a l s o t o Wong Sheung Shun f o r t e c h n i c a l drawings.

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VIII REFERENCE

1 1 1 Sommerfeld, A . "Mathematische T h e o r i e d e r D i f f r a k t i o n , " Math. Ann., v o l . 4 7 , pp. 317-374, 1896.

121 K e l l e r , J . B . , "The Geomet r i ca l Theory o f D i f f r a c t i o n , " Symposium o n Microwave O p t i c s , McGil l U n i v e r s i t y , M o n t r e a l , Canada; J u n e 1953.

L3J K e l l e r , J. B., " The G e o m e t r i c a l Theory o f D i f f r a c t i o n . " i n The C a l c u l u s of V a r i a t i o n s -- and Its ~ ~ ~ l i c a t i o n s , McGraw H i l l Book cK, I n c . , New York, N . Y . , 1958.

1 4 1 K e l l e r , J . B , "Geomet r i ca l Theory o f D i f f r a c t i o n , " J . Opt. Soc . A m . , 52 , pp.116-130, February 1962.

1 5 1 R o b e r t C . Hansen, E d i t o r , "Geometr ic Theory of D i f f r a c t i o n , " IEEE P r e s s , New York, N . Y . , 1981.

. - , --- I ? ! "!'"a - J ------- 7 Pi., t'An Asymptot ic S o l u t i o n o f Maxwell ' s Z q u a t i o n s " p u b l i s h e d i n "The Theory o f E l e c t r o m a g n e t i c - * Naves, " a Symposium, I n t e r s c i e n c e h b l i s h e r s , I n c . , New -- + , - - 3 . 1 1 . See a l s o M . KLi2e, " E l e c t r o m a g n e t i c 2hzo.q and G e o m e t e r i c a l O p t i c s , " p u b l i s h e d i n " E l e c t r o m a g n e t i c Waves" by L.E. Langer ; U n i v e r i s t y o f i J 4 n l u b v l L u ; L r m n nv,n - m P r e s s , Madison; 1962.

i 7 j Weeks, W.L., "Antenna E n g i n e e r i n g H , McGraw-Hi 11 P u b l i s h i n g Company L T D , New York, N . Y . , pp 39-40, 1968.

131 K e l l e r , J . B . , "Geomet r i ca l Theory o f D i f f r a c t i o n " J . Opt. Soc. Amer., v o l . 52 , pp. 116-130.

131 I b i d . , Rober t C . Hansen, pp. 83-218.

L101 Kouyoumjian, R . G . , "A Uniform G e o m e t r i c a l Theory o f D i f f r a c t i o n f o r an Edge i n a P e r f e c t l y Conduc t ing S u r f a c e " , Proc . IEE, v o l . 6 2 , pp. 1448-1461, Nov. 1974.

Ll 11 Beckmann, P. and S p i z z i c h i n o , A . The S c a t t e r i n 6 of E l e c t r o m a g n e t i c Waves from Rough S u r f a c e s , P e r g a m z P r e s s , New York, 1963, C h a p t e r 12.

11 21 L a r s o n , H . and S h u b e r t . B . , P r o b a b i l i s t i c Models i n E n g i n e e r i n g S c i e n c e s , v o l 1 , J o h n Wiley & ~ o n n c . , N e w York, pp 358, 1979.

L13j I b i d . , Bechmann, P. and S p i z z i c h i n o , A . S e c t . 5 .3.

114J R a y l e i g h , Lord , "On The L i g h t Dispe r sed from F i n e L i n e s Ruled upon R e f l e c t i n g S u r f a c e s o r T r a n s m i t t e d by Very Narrow S l i t s , " P h i l . Mag. 1 4 , pp. 350-359, 1907.

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11 51 Rojas-Teran , R . G . , and B u r n s i d e , W . D . , "GTD A n a l y s i s o f A i r b o r n e Antenna i n t h e P r e s e n c e o f Lossy D i e l e c t r i c L a y e r s " , Ohio S t a t e U n i v e r s i t y E l e c t r o - S c i e n c e L a b o r a t o r y Repor t .

1161 McQuate, P. L. e t a l , " T a b u l a t i o n s o f P r o p a g a t i o n Data o v e r I r r e g u l a r T e r r a i n i n t h e 230-920OMHz Fr equency Range", ESSA R e p o r t ERL-65-ITS-58, U . S . Depar tment o f Commerce, March 1968.

1171 Long ley , A . G. and R i c e , P. L. " P r e d i c t i o n of T r o p o s p h e r i c Radio T r a n s m i s s i o n L o s s Over I r r e g u l a r T e r r a i n " , ESSA R e p o r t ERL79-ITS-67, U.S. Depar tment o f Commerce, 1968.

1181 R i c e , P. L. e t a l , " T r a n s m i s s i o n L o s s P r e d i c t i o n s f o r T r o p o s p h e r i c Communication C i r c u i t s " , Volume I , R e p o r t AD-687-820, U . S. Department of Commerce, J a n u a r y , 1967.

1131 Chamber l in , K . A . " I n v e s t i g a t i o n and Development o f VHF Ground-Air P r o p a g a t i o n N o d e l i n g I N n c l u d i n g t h e A t t e n u a t i n g E f f e c t s o f F o r e s t e d A r e a s f o r Within-Line- o f - S i g h t P r o p a g a t i o n P a t h s " , Ohio U n i v e r s i t y A v i o n i c s E n g i n e e r i n g C e n t e r , March 1982 .

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X Appendix

A . D i f f r a c t i o n C o e f f i c i e n t B o u n d a r i e s C o n t i n u i t y Checks

S e v e r a l c r i t i c a l b o u n d a r i e s c o n t i n u i t y c h e c k s f o r

d i f f e r e n t r a y t y p e s h a v e b e e n d e v i s e d t o e n s u r e t h a t t h e

m o d i f i e d d i f f r a c t i o n c o e f f i c i e n t d o e s n o t v i o l a t e t h e b a s i c

t h e o r y o f t h e GTD f u n d a m e n t a l s . I n t o t a l , t h r e e s e t s o f

e d g e s a r e s t u d i e d ; t h e y a r e : a t t h e shadow bounda ry f o r a

s i n g l y - d i f f r a c t e d r a y geomet ry ; a t t h e r e f l e c t i o n bounda ry

f o r a d i r e c t , s i n g l y - r e f l e c t e d and s i n g l y - d i f f r a c t e d r a y ;

and at t n e r e f l e c t i o n boundar~? J A d - F n r t w s c a s e s i n v o l v i n g

h i g h e r - o r d e r r a y s .

V e r i f i c a t i o n o f f i e l d c o n t i n u i t y at t h o s e b o u n d a r i e s f o r

l ower -o rde r r a y t y p e s a n d as w e l l as h i g h e r - o r d e r r a y t y p e s

a r e c o n s i d e r e d s u f f i c i e n t p r o o f o f p r o p e r GTD o p e r a t i o n .

Both t h e h o r i z o n t a l and v e r t i c a l f i e l d p o l a r i z a t i o n a r e

i n v e s t i g a t e d i n t h e s e c h e c k s . I n a d d i t i o n , c o n t i n u i t y c h e c k

a r e c a r r i e d o u t i n p e r f e c t c o n d u c t i v i t y f o r t h e same p r o f i l e

which r e p r e s e n t t h e GTD model b e f o r e i t is m o d i f i e d s o as t o

p r o v i d e a b a s e l i n e i n f o r m a t i o n . A a o r e d e t a i l e d e x p l a n a t i o n

o f each o f t h e f i e l d c o n t i n u i t y c h e c k o p e r a t i o n a r e i n c l u d e d

i n t h e i r c o r r e s p o n d i n g s e c t i o n .

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1 . R e f l e c t i o n Boundary Check

The geometry u s e d f o r s i n g l y d i f f r a c t e d r a y c o n t i n u i t y

check a t r e f l e c t i o n boundary i s shown i n F i g u r e A-1 . The

p r o f i l e , which c o n s i s t s o f a t r a n s m i t t i n g a n t e n n a r a d i a t i n g

o v e r t h e h o r i z o n t a l ground p l a n e i s t r u n c a t e d a t 1 3 m e t e r

t o c r e a t e a r e f l e c t i o n boundary . The r e c e i v i n g a n t e n n a i s

a l l o w e d t o e l e v a t e from 1 m e t e r t o 81 m e t e r h e i g h t and i s

l o c a t e d a t t h e v e r t i c a l c o o r d i n a t e . T h r e e r a y t y p e s e x i s t :

d i r e c t r a y , s i n g l y r e f l e c t e d r a y and s i n g l e d i f f r a c t e d r a y ;

and s i n c e b y t h e s p e c i a l c o n f i g u r a t i o n o f t h i s e d g e , o t h e r

r a y t y p e s ' e x i s t e n c e is r u l e d o u t o v e r t h e e n t i r e r e c e i v i n g

a n t e n n a h e i g h t r a n g e . The r e f l e G i o n -:a7=dsA7, , i s l i n e d by

t h e p o i n t a t which t h e r e f l e c t e d r a y v a n i s h e s , o c c u r s a t 1 1

m e t e r s of t h e a n t e n n a h e i g h t f o r t h e geomet ry shown.

The purpose o f r e f l e c t i o n boundary c o n t i n u i t y check i s t o

e n s u r e a p r o p e r e l e c t r i c f i e l d t r a n s i t i o n a t t h e r e f l e c t i o n

boundary when t h e r e f l e c t i o n r a y v a n i s h e s . S i n c e f i e l d

i n t e n s i t y d e c r e a s e s , t h e d i f f r a c t e d r a y s h o u l d r i s e i n

a m p l i t u d e t o compensa te t h e l o s s of r e f l e c t e d r a y s o t h a t

f i e l d c o n t i n u i t y would be p r e s e r v e d . The d i f f r a c t e d r a y

a l s o p r o v i d e s f i e l d v a l u e a t t h e shadow r e g i o n . Any a b r u p t

changes a t t h e boundary i n d i c a t e s t h a t a n e r r o r i n t h e

d i f f r a c t e d f i e l d c a l c u l a t i o n h a s o c c u r e d .

' d i t h t h e above f a c t s , r e f e r t o F i g u r e A-2 which is a p l o t

o f t h e GTD e s t i m a t e d p a t h l o s s f o r t h e geomet ry o f F i g u r e

A-1 assuming p e r f e c t c o n d u c t i v i t y . A s s e e n i n t h i s F i g u r e ,

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c a l c u l a t e d f i e l d s a r e c o n t i n u o u s at t h e r e f l e c t i o n boundary

as is e x p e c t e d , b e c a u s e GTD model o p e r a t e s a c c o r d i n g t o t h e

c o n v e n t i o n a l GTD b e f o r e m o d i f i c a t i o n .

The f i n i t e c o n d u c t i v i t y p a t h l o s s f o r a s i n g l y r e f l e c t e d

r a y o f t h e same geometry i s p l o t t e d on F i g u r e A - 3 , w i t h t h e

g round e l e c t r i c c o n s t a n t s i n d i c a t e d i n t h e F i g u r e . S i n c e

o n l y t h e s i n g l y r e f l e c t e d r a y e x i s t s t h e f i e l d d i s a p p e a r s

below t h e r e f l e c t i o n boundary a t 1 1 m e t e r r e c e i v e r a n t e n n a

h e i g h t . F i e l d c o n t r i b u t i o n below t h e r e f l e c t i o n boundary i s

p r o v i d e d by t h e d i f f r a c t e d and d i r e c t r a y s . F i g u r e A-4 shows

t h i s c o n t r i b u t i o n i n t h e f i n i t e c o n d u c t i v i t y c a s e . And a l s o

can b e s e e n i n t h e F i g u r e , t h e f i e l d t r a n s i t i o n i s smooth

a c r o s s t h e r e f l e c t i o n boundary. The v e r t i c a l p o l a r i z a t i o n

r a y s u f f e r s a h i g h e r l o s s t h a n t h e p e r f e c t c o n d u c t i v i t y

c a s e ; and t h e h o r i z o n t a l p o l a r i z a t i o n f i e l d v a l u e f o r t h e

f i n i t e c o n d u c t i v i t y c a s e i s e s s e n t i a l l y unchanged from t h e

p e r f e c t c o n d u c t i v i t y c a s e of F i g u r e A - 2 . The smooth f i e l d

t r a n s i t i o n a c r o s s t h e r e f l e c t i o n boundary v e r i f i e s t h e G T D

r e f l e c t i o n boundary o p e r a t i o n f o r l o w e r o r d e r r a y s .

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2 . Shadow Boundary Check

The p u r p o s e o f t h i s shadow b o u n d a r y c o n t i n u i t y check i s

t o e n s u r e t h a t f i e l d c o n t i n u i t y i s p r e s e r v e d a t t h e shadow

boundary s o t h a t GTD f u n d a m e n t a l i s n o t v i o l a t e d . The

t e s t i n g i n v o l v e s s i n g l y d i f f r a c t e d r a y and d i r e c t r a y . The

p r o f i l e geomet ry employed is shown i n F i g u r e A-5.

A s one c a n s e e f rom t h e f i g u r e , t h e t r a n s m i t t i n g a n t e n n a

i s l o c a t e d a t t h e r i g h t - h a n d end o f t h e two p l a t e s t h a t

c o n s t i t u t e t h e p r o f i l e , w h e r e a s t h e r e c e i v i n g a n t e n n a is

l o c a t e d st zne p c o o r d i n a t e as b e f o r e , b e i n g c a p a j l e o f

e l e v a t e d from one m e t e r s h e i g h t t h r o u g h twen ty - f i v e m e t e r .

S i n c e the t rmit t ix & ~ t e n n a h e i g h t is t h e s a n e as t h e

peak ~f t h e p r o f i l e , t h e shadow bounda ry becomes a s t r a i g h t

h o r i z o n t a l l i n e e x t e n d i n g from t h e peak t o t h e r e c e i v i n g

a n t e n n a o r d i n a t e at 15 m e t e r . The e x i s t e n c e of o t h e r r a y

t y p e s a r e n o t p o s s i b l e i n t h i s g e o m e t r i c a l c o n f i g u r a t i o n , as

t h e r e f l e c t e d r a y from t h e t r a n s m i t t i n g a n t e n n a o n t h e two

p l a t e s w i l l t r a v e l o u t s i d e t h e r a n g e o f t h e r e c e i v i n g

a n t e n n a . A s a r e s u l t , i n t e r f e r e n c e f rom r a y s o t h e r t h a n t h e

s i n g l y d i f f r a c t e d and d i r e c t o n e s d o e s n o t e x i s t .

The c a s e f o r p e r f e c t c o n d u c t i v i t y e d g e s which r e p r e s e n t s

GTD r e s u l t s b e f o r e m o d i f i c a t i o n is p r e s e n t e d f i r s t . F i g u r e

A-6 i s a p l o t of r e c e i v e r a n t e n n a h e i g h t v e r s u s p a t h l o s s

t h e s i n g l y d i f f r a c t e d r a y . As e v i d e n t f rom t h e f i g u r e ,

f i e l d d i s c o n t i n u i t y o c c u r s f o r b o t h p o l a r i z a t i o n s a t t h e

shadow bounda ry . T h i s is c a u s e d b y t h e d i s a p p e a r a n c e of t h e

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d i r e c t r a y a t t h e bounda ry . Thus, by t h e a d d i t i o n o f t h e

d i r e c t r a y s , c o n t i n u i t y i s a g a i n p r e s v e r e d a c r o s s t h e shadow

boundary as s e e n i n t h e p l o t o f F i g u r e A - 7 f o r t h e p e r f e c t l y

c o n d u c t i n g c a s e .

F i n i t e c o n d u c t i v i t y p l o t o f p a t h l o s s f o r t h e geomet ry o f

F i g u r e A - 5 is shown on F i g u r e A-7. Again, as i n t h e p r e v i o u s

c a s e o f p e r f e c t l y c o n d u c t i n g e d g e s d i f f r a c t e d r a y ,

d i s c o n t i n u i t y o c c u r s a t t h e shadow boundary d u e t o t h e

d i s a p p e r a n c e o f t h e d i r e c t r a y . R e f e r i n g t o F i g u r e A - 9 ,

which p l o t s t h e t o t a l f i e l d c o n t r i b u t i o n s o f t h e d i f f r a c t e d

and a l s o t h e d i r e c t r a y , i t is s e e n t h a t t h e f i e l d

c o n t i n u i t y i s win p s s z n e r l z% t h e shadow, p r o v i n g t h a t

t h e m o d i f i e d d i f f r a c t i o n c o e f f i c i e n t is p e r f o r m i n g i n a

f a s h i o n c o n s i s t a n t w i t h GTD.

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3. R e f l e c t i o n Boundary check f o r Higher -o rde r r a y s

The geometry used f o r t h i s t e s t i s shown on F i g u r e A - 1 0 ,

which c o n s i s t s of s e v e n edges . The r e f l e c t i o n boundary f o r

t h e r e f l e c t e d - d i f f r a c t e d - d i f f r a c t ed r a y and r e f l e c t e d -

d i f f r a c t e d - r e f l e c t e d r a y i s l o c a t e d a t 1 1 me te r o f t h e

r e c e i v i n g a n t e n n a h e i g h t . The p u r p o s e o f t h i s t e s t is t o

check t h a t lower -o rde r r a y s and h i g h e r - o r d e r r a y s compensate

e a c h a n o t h e r t o p r e s e r v e f i e l d 1 c o n t i n u i t y a t r e f l e c t i o n

boundary.

Assuming p e r f e c t con&uc-tivity edges , F i g u r e A-l l &ws a

p l o t o f t h e p a t h l o s s f o r t h e r e f l e c t e d - d i f f r a c t e d - r e f l e c t e d

and r e f l e c t e d - d i f f r a c t e d - d i f f r a c t e d r a y s as t h e r e c e i v i n g

a n t e n n a moves from t h e shadow r e g i o n t o t h e l i t e r e g i o n . P_

f i e l d d i s c o n t i n u i t y i n e x c e s s o f 18 db c a n be o b s e r v e d a t

t h e r e f l e c t i o n boundary . T h i s i s due t o t h e f a c t t h a t l o w e r

o r d e r r a y s a r e a b s e n t e d ( i . e . d i f f r a c t e d - r e f l e c t e d ,

d i f f r a c t e d , o r s i n g l y d i f f r a c t e d ) t o compensate t h e h i g h e r -

o r d e r r e f l e c t e d r a y l o s s e s a t t h e boundary . T o t a l p a t h l o s s

f o r t h e geometry of F i g u r e A - 1 0 i s p l o t t e d i n F i g u r e A-12

f o r t h e p e r f e c t c o n d u c t i v i t y c a s e ; and as e x p e c t e d , f i e l d i s

a g a i n c o n t i n u o u s w i t h t h e a d d i t i o n of lower -o rde red r a y

t y p e s a l t h o u g h t h e i n t e n s i t y is r a p i d l y - v a r y i n g due t o t h e

number o f r a y s i n t e r a c t i n g i n t h e v i n c i n i t y o f t h e boundary

and t h e i r r e l a t i v e l y s t r o n g l e v e l b e c a u s e o f p e r f e c t

c o n d u c t i v i t y .

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P a t h l o s s v e r s u s r e c e i v i n g a n t e n n a h e i g h t f o r t h e

f i n i t e l y c o n d u c t i n g e d g e s f o r t h e r e f l e c t e d - d i f f r a c t ed-

r e f l e c t e d r a y and t h e r e f l e c t e d - d i f f r a c t e d d i f f r a c t e d r a y i s

p l o t t e d o n F i g u r e A - 1 3 . Again , more t h a n 2 3 db of f i e l d

d i s c o n t i n u i t i e s c a n b e o b s e r v e d a t t h e r e f l e c t i o n bounda ry

a t 11 meters. The r e a s o n t h a t t h i s f i g u r e i s h i g h e r t h a n t h e

18 d b i n t h e p e r f e c t l y c o n d u c t i n g e d g e s is b e c a u s e f i e l d s

are f u r t h e r a t t e n u a t e d b y f i n i t e c o n d u c t i v i t y edges .

T o t a l p a t h l o s s e s w i t h t h e c o n t r i b u t i o n s o f a l l e x i s t i n g r a y

t y p e s is shown i n F i g u r e A-14, a s suming t h e same g r o u n d

e l e c t r i c a l p r o p e r t i e s as b e f o r e . Once a g a i n , t h e f i e i d

c o n t i n u i t y i s p r e s e r v e d a t t h e r e f l e c t i o n bounda ry a t 1 1

m e t e r , which s u f f i c i e n t l y i n d i c a t e s t h a t t h e m o d i f i e d G T D

t h e o r y i n t h e higher and l o w e r r a y t y p e s c o m b i n a t i o n s i s

k e p t .

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B. Modeled P a t h P r o f i l e

A l l t h e t e r r a i n p r o f i l e s i n p u t d a t a i n v e s t i g a t e d i n t h i s

t h e s i s a r e g i v e n i n t h i s s e c t i o n . These d a t a a r e i n t h e

o r i g i n a l form b e i n g r e a d i n b y t h e G T D model t o g e n e r a t e t h e

c a l c u l a t e d p a t h l o s s i n d e c i b e l s , which were s u b s e q u e n t l y

p l o t t e d v e r s u s r e c e i v i n g a n t e n n a h e i g h t . F i r s t , a n

e x p l a i n a t i o n o f t h e i n p u t d a t a f o r m a t and i t s f u n c t i o n t o

t h e GTD model i s g i v e n . I t is t h e n f o l l o w e d by t h e t e r r a i n

p r o f i l e f i l e s .

A t y p i c a l i n p u t d a t a f i l e w i l l l o o k l i k e t h e f o l l o w i n g :

NE, I C O N , Y M I N , YMAX, EPSIR, SIGMA, DELTAG

XN YN ZN

FREQ 1

--> RAY-TYPE CONTRGL PARAMZTERS

Page 175: Evaluation progresion path loss model

Where

H E , ( 1 5 )

I C O N , ( 1 5 )

I C O N = 1

I C O N = 0

Y M I N , ( F I O . 5 )

YMAX, ( F 1 0 . 5 )

E P S I R , ( F 1 0 . 5 )

S I G M A , ( F 1 0 . 5 )

D E L T A G , ( F 1 0 . 5 )

number of edges

i n f o r m a t i o n o u t p u t c o n t r o l

d e t a i l e d p r i n t o u t

b r i e f o u t p u t summary

min db v a l u e of p l o t a x i s

max db v a l u e o f p l o t a x i s

r e l a t i v e p e r m i t t i v i t y o f ground

ground c o n d u c t i v i t y i n MHO/METER

s u r f a c e r o u g h n e s s f a c t o r i n me te r

Second r e c o r d t o t h e n-th r e c o r d : X , Y , Z c o o r d i n a t e o f t h e

edge i n 3 2 ' 1 0 . 5 f o r m a t , where n is e q u a l t o N E (no. o f

e d g e s ) , i n t h e p r e v i o u s r e c o r d .

Ray-type c o n t r o l p a r a m e t e r s (Format = 1 3 1 1 )

J D I R D I R E C T RAY

J R E F S I N G L Y R E F L E C T E D RAY

J R R R E F L E C T E D - R E F L E C T E D RAY

J R D REFLECTED-D I F F R A C T E D RAY

J R R D R E F L E C T E D - R E F L E C T E D - D I F F R A C T E D RAY

J R D R REFLECTED-D I F F R A C T E D - R E F L E C T E D RAY

J D I R S I N G L Y D I F F R A C T E D RAY

J D R D I F F R A C T E D - R E F L E C T E D RAY

J DRD D I F F R A C T E D - R E F L E C T E D - D I F F R A C T E D RAY

J D D DOUBLY-D I F F R A C T ED RAY

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J D D R DIFFRACTED-D IFFRACT ED-REFLECTED RAY

J D R R DIFFRACTED-REFLECTED-REFLECT ED RAY

J R D D REFLECTED-D IFFRACTED-DIFFRACTED RAY

If any o f t h e above p a r a m e t e r is b e i n g s e t t o 1 , t h a t

s p e c i f i c r a y t y p e is i g n o r e d d u r i n g t h e c o m p u t a t i o n s . O t h e r

v a l u e s s imply i m p l i e d t h a t r a y t y p e is i n c l u d e d .

F r e q u e n c i e s i n megaher tz s h o u l d b e e n t e r e d i n F10.3 f o r m a t .

2 . L i s t i n g s of P a t h P r o f i l e Data

1. Path R1-0.5-T1

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2 . Path R 1 - 5 - T ~ A

3. Path R1-5-T5A

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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

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9. Path R1-50-T1

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11. Path R2-120-T1 11. 0-210.00000 -go.ooooo 15.00000 0.01200 0.22860

I? .? 9.0 2556.481