Evaluation progresion path loss model

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Evaluation progresion path loss model

  1. 1. 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 t o The F a c u l t y of t h e College of Engineering and Technology Ohio U n i v e r s i t y I n Partial F u l f i l l m e n t of t h e Requirements f o r t h e Degree Master of Science Richard Ma. November 1983
  2. 2. I INTRODUCTION The work p r e s e n t e d i n t h i s paper was funded by S o u t h e a s t e r n Conference f o r E l e c t r i c a l Engineering Education under 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 of employing Geometrical Theory of D i f f r a c t i o n f o r modeling e l e c t r o m a g n e t i c wave propagat i o n path l o s s over i r r e g u l a r t e r r a i n . The GTD 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 can 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 of 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 and/or d i f f r a c t i o n p o i n t s l i e , and a mathematical p r o c e s s of e v a l u a t i n g t h e magnitude and phase of t h e corresponding e l e c t r i c f i e l d at 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 ray-types a r e considered 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 parameters 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 antennas, frequency, 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 not 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 determine t h e Instrument Landing System ( I L s ) g l i d e s l o p e performance. For t h a t
  3. 3. a p p l i c a t i o n , t h e wavelength is 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 ground 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 roughness. However, t o p r o v i d e more meaningful 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 modified 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 roughness 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 is 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 . Although 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 models, 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 ) model, 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 re- r a d i a t e d by ground 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 computation t i m e . I t s performance i s a l s o l i m i t e d by 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 between l i n e a r segments c o m p r i s i n g t h e p r o f i l e . Another model, developed by Longley-Rice, which is 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 where 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) data 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 , and h a s been 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
  4. 4. s h o r t c o m i n g s of e x i s t i n g models l e d t o t h e developments o f t h e GTD model 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 were compared a g a i n s t measured 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 . These comparisons, which were made o v e r a r a n g e of d i s t a n c e s and 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 .
  5. 5. I I GTD 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 phase 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 from 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 Geometric 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 its o r i g i n i n a mathematical 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 mathematics of 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 changes 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 of Sommerfeld'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, it 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 developed t h e Geometrical 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 workers and is s t i l l undergoing changes 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 expansions were used 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 immediate v i c i n i t y o f t h e shadow and 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 modified Keller's work t o a uniform 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 everywhere; t h i s r e v i s e d
  6. 6. t h e o r y i s t h e Uniform Theory o f D i f f r a c t i o n (UTD). The method addressed 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 of UTD. S i n c e UTD i s an e x t e n s i o n of GTD c o n c e p t , i t is commonly r e f e r r e d t o as GTD. Geometrical O p t i c s (GO) Geometrical 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 developed 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 not be c o n s i d e r e d . GO t h e o r y assumes 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 between two p o i n t s i n s p a c e c a n b e viewed 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 hence 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 fundamental r a y t y p e s a r e c o n s i d e r e d i n GO. 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 ray 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 between 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 of ( * ) 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 because 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 be t o o weak t o be s i g n i f i c a n t .
  7. 7. 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 assumed t o b e small compared 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 is 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 assumed t o e m i n a t e from 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 of reflect i o n . Also, G e o m e t r i c a l O p t i c s assumes t h e p h a s e o f t h e d i r e c t and 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 from a r e f e r e n c e p o i n t , where t h e p h a s e is d e f i n e d t o b e z e r o . The 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 of c o n s e r v a t i o n of 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 below. Throughout 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 , and 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 form 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 , high-frequency s o l u t i o n o f Maxwell's e q u a t i o n 161. The 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 and i n c u r s a phase v a r i a t i o n o f e-1 BR, where R i s t h e p a t h d i s t a n c e measured from 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 , and 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 and t h e method f o r c a l c u l a t i n g its 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, which
  8. 8. d e p i c t s t h e d i r e c t and r e f l e c t e d r a y s , and 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 and r e f l e c t e d r a y s a r e eminated from 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 above a f l a t ground 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 , and 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 ground p l a n e is removed, and a n image s o u r c e i s added a t a d i s t a n c e -h from w h e r e t h e ground 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 and is 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 and o u t of 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 e2-3. The distanse 2, S e t w e e n t h e o b s e r v e r and t h e i n a g e s o u r c e i s e q u a l t o : where h i s t h e h e i g h t o f t h e a n t e n n a from t h e ground. 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 and 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 and s u r f a c e roughness. 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 by t h e complex 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 and -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 which 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 above 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
  9. 9. 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 is 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 phase v a r i a t i o n of e-jBRd ,where R d is t h e p a t h d i s t a n c e from 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 composite 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 by 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 of 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 cause 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
  10. 10. 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 it 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 example, 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 edge 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 are 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 as 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 and below t h e r e f l e c t i o n boundary b e c a u s e t h e p o i n t of r e f l e c t i o n migrates beyond t h e edge. C o n s e q u e n t l y , GO 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 boundary. A l s o , c o n s i d e r t h e immediate v i c i n i t y oi ?he shadzw 3oundsry where t h e d i r e c t r a y i s b l o c k e d by t h e t i p of t h e edge; 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 shadow boundary 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 Geometric-Optics 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 and 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 and 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 GO. 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 development 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 Keller 181, h a v e c e r t a i n p r o p e r t i e s : 1 . The 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 on t h e boundary s u r f a c e . T h e s e r a y
  11. 11. p a t h s obey t h e p r i n c i p l e of Fermat, a l s o known as t h e p r i n c i p l e of t h e s h o r t e s t o p t i c a l path. 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 ray p a t h s o t h a t t h e energy 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 at h i g h f r e q u e n c i e s . That is, 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 immediate neighborhood of t h e p o i n t of d i f f r a c t i o n . Contemporary GTD t h e o r y can be used t o c a l c u l a t e d i f f r a c t i o n from cones, curve s u r f a c e s , and wedges 131. However, t h e work addressed 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 segments; hence only wedge d i f f r a c t ion 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 encountered where o t h e r t y p e s of d i f f r a c t i o n may provide more meaningful 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 at 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 by 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 determined by t h e geometry i n t h e immediate neighborhood of t h e p o i n t of d i f f r a c t i o n .
  12. 12. 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 and 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 on a two-dimensional edge as i l l u s t r a t e d i n F i g u r e 2-5. GTD employs 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 where Dd' and D, are t h e v e r t i c a l and 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 terzas f o r t h e edge f a c e s o and n r e s p e c t i v e l y . These f o u r terms are u s e d t o c a m n ~ n a a t er ---- 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 and r e f l e c t i o n boundary f o r t h e two f a c e s of t h e wedge. For i n s t a n c e , t h e terms o f t h e form ( @ - @ I ) are t o compensate 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 boundary; t h o s e of t h e form + a r e t o compensate f o r t h e l o s s of t h e r e f l e c t e d r a y at r e f l e c t i o n b o u n d a r y . Thus, t h e GTD 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 of 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 of 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:
  13. 13. 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 from d i f f r a c t i o n is 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 edge, 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 have been performed, 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 .
  14. 14. 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 and S u r f a c e Roughness I n t h e e a r l y development o f GTD, t h e t h e o r y assumed 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 . Because 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 from 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 , GTD 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 match 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.. tlmmi+$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 . These o b j e c t i v e s were met, and 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 and 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 had 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 of 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 on wave r e f l e c t i o n , which is 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 imposed 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 .
  15. 15. 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 water 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 magnitude of t h e r e f l e c t ion c o e f f i c i e n t approaches u n i t y . I n such 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 , approaches -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 occur 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 due t o s u r f a c e i r r e g u l a r i t i e s . One of 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 of a smooth s u r f a c e and a rough s u r f a c e is 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 dimensions) 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 energy d i f f u s e l y . The d e g r e e of roughness depends upon t h e wavelength and angle of i n c i d e n c e . To account f o r s u r f a c e
  16. 16. INCIDENTRNGLE d In P-- m LL u D 00 In-- rn lL u oI U) N 0 0 Figure3-1Amplitudeofreflectioncoefficientasafunctionofincidentangle horizontaL -- conductivity=0.012O/m relativepermittivity=15.0 frequency=300MHz -- II1----- I1I 1 18.0036.0054.0072.0090
  17. 17. conductivity=0.012U/m relativepermittivity=15.0 frequency=300MHz 0 0verticalpolarization rn 0 0 Wo -Id=co-- ZI a WZ cnrn a0 nI 0 0 rn 0 00 d I horizontalpolarization 1 I 1 I 1 I 1 II 0.0018.0036.0054.0072.0090.00 INCIDENTANGLEFigure3-2Phaseofreflectioncoefficientasafunctionofincidentangle
  18. 18. roughness, a f a c t o r is u s e d t o modify 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 modified r e f l e c t i o n c o e f f i c i e n t is d e f i n e d by 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 from a rough 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 smooth 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 of rough 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 . According t o C e n t r a l L i m i t Theorem 11 21, random 2-dimensional t e r r a i n roughness w i l l converge 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 of terms i n t h e sum i s l a r g e (The 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 from 0.5 k i l o m e t e r t o 120 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 is d e f i n e d by 1131 : A + i s t h e phase s h i f t between 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 of h e i g h t Ah a t a grazing
  19. 19. a n g l e Y . The p a t h d i f f e r e n c e between t h e two r a y s i s : A r = 2 A h s i n y and hence t h e p h a s e d i f f e r e n c e is: 4rAh -s i n y where Ah is 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 and 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 , however, t h e model 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 phase d i f f e r e n c e is small, t h e two r a y s w i l l b e a i r n o s t i n phase as t h e y are i n t h e case o f a p e r f e c t l y smooth 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 1141 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 .
  20. 20. 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 is 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 on 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 dimensional 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 expressed as 1151: I A I1 II I I II I1 + AoDo ( @ + @ ' I + A,D,(++@') f i iII I where Lo , 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 boundary 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 Chapter 2 , these fozr cz;.sta~"~ts a r e e q u a l t o 1 I II II u n i t y . The terms L o and 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 phase and a m p l i t u d e due t o d i f f e r e n c e s between f i n i t e l y conducting wedges and p e r f e c t l y c o n d u c t i n g wedges at 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 ; rfw h i l e A! and 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 between 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 energy 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 accounted f o r by t h e c o n s t a n t s L! and L, . For high-frequency t e r r a i n modeling, r a y t r a n s m i t t e d t h r o u g h ;i 4h i l l s and mountains is n e g l i g i b l e , t h u s L o =Ln = l .
  21. 21. The r e f l e c t e d f i e l d which is modified 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 at t h e r e f l e c t i o n boundary; 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 compensate 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 boundary s o t h a t t h e t o t a l high-f requency f i e l d i s c o n t i n u o u s everywhere. 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 edge I iss 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 modified 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 demonstrate t h a t t h e above changes 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 performed. The r e s u l t s of 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 comparison w i t h measured
  22. 22. I V Measured and Modeled Data Comparisions The GTD model modified 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 been 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 model's performance, 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 of employing 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 from 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 . 116 J and were reduced t o d i g i t a l f 3 r m a t t o s f f o r d comparison w i t h modeled d a t a . ~h~ referenced 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 from p r o p a g a t i o n measurements o v e r i r r e g u l a r t e r r a i n i n Colorado 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 seven f r e q u e n c i e s i n t h e 230- t o 9200-MHz range. These reduced d a t a c o n s i s t p r i m a r i l y of 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 from t h e measurement of each 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 photographs, 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 of 230, 410, 751, 910, 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 .
  23. 23. To adopt t h e McQuatels 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 GTD model, t h e p r o f i l e was f i r s t approximated by p i e c e w i s e - l i n e a r segments 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 proceed i n a s t r a i g h t f o r w a r d manner, i f t h e predominant 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 peaks and l a r g e i r r e g u l a r roughness. 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' - , - : : - ~ + 3 r , , - i = --- --- " - * - " , f i 2 i.r- + n =, ." t h e u s e r , based o n h i s uwn e x p e r i z n c e , ,a i a ~ e r - i n e whether an 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 merely a s o u r c e of l o c a l s u r f a c e roughness. Thus, t h e r e i s no well- d e f i c e d methodology 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 it 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 cumulative 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 of 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 approximation. rn, ,,,.-: A, A u V V L U ~ a "vnchiiiark f o r t h e GTD model performance, modeled d a t a from t h e Longley-Rice Point-to-Point model L17 , I 81 is 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 developed a t t h e I n s t i t u t e f o r Telecommunication 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 GTD and ITS 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 of ITS
  24. 24. 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 its 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 of d a t a are 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 is 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 beyond 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 , and where a p p r o p r i a t e , comments on t h e b e h a v i o r o f GTD modeled 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 redrawn from 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 by d o t t e d l i n e s s u p e r i m p o s e d on t h e t e r r a i n p r o f i l e . The 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 Appendix 3. A . DATA REDUCTION A l l t e r r a i n i n f o r m a t i o n and measured p r o p a g a t i o n p a t h l o s s d a t a were o b t a i n e d from a h a r d copy 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 from 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 and 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
  25. 25. 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 computer 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 of 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 increment 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 of 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 of 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 of 13 meters. By f o l l o w i n g a p r e d e f i n e d procedure 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 seven 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 McQuate'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 dewlett-Packard 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 viewer was employed f o r t h i s e f f o r t ( t h e optical viewer is loaded 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 connected 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 an ADM-3A CRT t e r m i n a l . The computer t o which t h i s hardware was connected was a n IBX 4341 running under -$%/SP CMS t i m e s h a r e mode. To p r o v i d e p r o p e r handshaking f o r d a t a t r a n s f e r between t h e h o s t computer and 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 can 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 hard 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 of 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 contaminated by photocopy d i s t o r t i o n e r r o r s . Evidence of such e r r o r s a p p e a r as s l i g h t l y curved a x e s , non-squareness,
  26. 26. and d i s t o r t i o n . To compensate f o r s u c h e r r o r s , t h e end p o i n t s of t h e a x e s were e n t e r e d , from 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 from 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 were 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 , which 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 , were 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 one p l o t f o r e a c h f r e q u e n c y . The ITS modeled and GTD modeled d a t a a r e a l s o p l o t t e d on 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 model 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 .
  27. 27. B. P r e s e n t a t i o n of 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 ground 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 development stage o f t h e GTD model 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 second 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 was 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 and 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 arises from t h e i n t e r f e r e n c e between 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 one d i s c u s s e d h e r e , t h e GTD model 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 model s i n c e t h e r e a r e no d i f f r a c t i v e edges. Thus, GTD model estimates o f p a t h l o s s are based e x c l u s i v e l y on a s i n g l y - r e f l e c t e d r a y and 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 are 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
  28. 28. c o n s t a n t s used 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 ground p l a n e w e r e v a r i e d o v e r a wide r a n g e of 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 . The 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 is 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 ground p l a n e s . However, t h i s r e s u l t would 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 were i n v e s t i g a t e d t o d e t e r m i n e its e f f e c t o n t h e modeled data. G e n e r a l l y , t h e model 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 modeled 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 %he modeled 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 of a l t e r n a t i n g s t r i p s o f plowed ground and wheat 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 from 6-1 8 i n c h e s were u s e d , which i s r e a s o n a b l e based upon 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 . Those v a l u e s p r o v i d e d good r e s u l t s i n t h e modeled d a t a , a l t h o u g h g r e a t e s t agreement b e t w e e n modeled and measured 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 . Hence, 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 modeled 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
  29. 29. n o t p r o m i n e n t , and t h e modeled 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 measured 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 becoming more n o t i c e a b l e w i t h t h e s i z e and 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 good a g r e e m e n t f o r b o t h measured and modeled d a t a . I n some i n s t a n c e s , t h e modeled 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 measured 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 between t h e measured and modeled d a t a . However, t h i s s e p a r a t i o n is 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 .
  30. 30. 7 :&" O C 0
  31. 31. 2 a Fi aJ 4 Q , a a J Q u a g 2 gffl P a m b Q , b U X H
  32. 32. m G 0- ZR 0) 0) C C m 2 0 a er U a 'ti k 3 LO 4 L?-Y - 0 0 1 : I I I o-OOI- oo-ori- oo-oai- oo-osi- oo-oni- [BQI SSOl Hltfd
  33. 33. '(I 0) a d 0) d Q , ' ( I a l a 0 ) m g 2 gLO P a r / ] E aJ E-r W E H
  34. 34. 2 . P a t h R1-5-T6A (4.6 km., Mixed P a t h w i t h Double 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 figure. 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 is 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 which h a s its shadow boundary 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 is 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 ht 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 , and is below 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 of 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 of 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 GTD 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 GTD h a s a r e g i o n i n which 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 would 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 one 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 measured and modeled 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 above. 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 model r e s p o n s e and is 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
  35. 35. modeling. 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 of 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 . Although t h e d i s c o n t i n u i t i e s may s t i l l be p r e s e n t , t h e y a r e a p p a r e n t l y bypassed i n t h e s a m p l i n g scheme used 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 agreement is demonstrated between t h e modeled d a t a and t h e measured 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 119 ) g a i n e d -l r o s ~ r o p a g a t i o nmodeling, 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 model, 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 .
  36. 36. 0 0 a > I +X - - - - - ! OO'OL- 00 08- 00 08- 00'
  37. 37. 0 0 m )8 1P a I M 8 X l O X j a X a X 8 X I- 8 X a X a 0 8 [f Q > 8 0 8 8 I 8 X + -- '+.- A"ooqor- 00-od- 00-od- 00-oor- oo 011- oo 021- oo orr- 00-ohi- oo.0~1-- (90)S S Q ~H L ~ M
  38. 38. 0 0 ex B# ex I T~ I I ex 8 X 8 X 1'e X 8 X I 8 X 1::0 X 8 X 8 X ee xx 1;;r-a8 X 8 X 8 X 8 8 8 0 8 i"" a X i" oo-ooi-- oo*oz;- OO.DO;-
  39. 39. 0 L Q - a3 r n . 2 2 s 3 2 5C 0 -4 U a 0 '+I k 7 II K' ;2S 'Z
  40. 40. 3. P a t h R1-5-T5A (5.0 Km., 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 drawing 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 approximated by 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 lower 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 between 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 due 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 observed w i t h t h e p r e v i o u s p a t h .
  41. 41. xxxxxGTDModeled -Measured QDBOQITSModeled LocalSurfaceRoughness(one sic~ma)=9inches(0.2286meters) Frequency=910MHz Conductivity=0.012U/m RelativePermittivity=15.0 Figure4-21.Pathlossvs.receiving antennaheightforProfileR1-5-T5A, Figure4-17.Transmitterheightisat 7.3meters. 'r.oos;005;007:00B;001i.0019.00 RCVR.ANT.HT.[MI
  42. 42. 4. P a t h RI -10-T2A (9.8 Km. , 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 shown i n F i g u r e 4-24. The p a t h i s beyond l i n e of 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 edges a r e used as i n p u t d a t a . The measured and modeled d a t a a r e shown i n F i g u r e s 4-25 through 4-31; c l o s e agreement between 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 measured d a t a d o n o t s u f f e r t h e high-frequency 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 of t r e e s a l o n g t h e p a t h .
  43. 43. 5. P a t h R1-10-T3 (9.6 Km., Line 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 approximation does 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 experiment t o i n v e s t i g a t e its 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 roughness v a l u e s of .2286 meter and 2 meters were used. The GTD 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 parameters. 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. GTD 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 , except at 751 MHz. A t 751 LVIHZ, a n anomaly i s obvious 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 is i n c o n s i s t e n t with t h e r e p o r t e d l o s s e s at h i g h e r o r lower f r e q u e n c i e s ; hence comments on GTD modeled performance a t t h a t frequency a r e not o f f e r e d . A t 1846 MHz, GTD over 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 . Secondly, t h e roughness f a c t o r w a s a d j u s t e d over a wide range of v a l u e s . I t was found t h a t by i n c r e a s i n g t h e roughness f a c t o r t o 2 m e t e r s , t h e d e p t h of 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 not i c e a b l e e f f e c t
  44. 44. o n f r e q u e n c i e s lower 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 from 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 upon t h e s i z e and t h e d e p t h o f t h e l o b e , and 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 .
  45. 45. 0 0 .e X e 5" x e X e X e x e x e X 0 X X . a X I +.---- AXooaoL- 00 08- oo 08- o 0 - oo.oci-oo.oni-oososr-@(gal SSO-I ~ l t i d
  46. 46. 0 0 B m 8L I 8( j I - 8 oo-0:- 00-00- 00-06- 00-001- o ~ * o ~ i -00-ozi~ oo'06i- 00-obi- (801 SSOl Hltfd
  47. 47. 4 4 a a a , a a , a g : i ?ffl C l a m E a I 3 W X H
  48. 48. 6 . P a t h R1-20-TI (27.7 Km., 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 approximation o n l y t e n d s t o i n c l u d e t h e major p e a k s and s l o p e s of t h e a c t u a l t e r r a i n . The approximation 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 . Because of v a r i a t i o n s of 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 approximation, a modeled l o c a l roughness p a r a m e t e r o f 2 meter was chosen. C a l c u l a t e d r e s u l t s from 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 from t h e s e figures, 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 caused by modeled- ---- ~ ~ i t ;rat'ri reflection from t h e c o m p a r a t i v e l y smooth segments used t o approximate t h e i r r e g u l a r t e r r a i n .
  49. 49. C, P - a C -4 m $ 4 .rl a J L J U O C a, CJ tn k I .4 4 a, . I r ; C ? a h .-I a, rn .4 4J r n u - i c , 0 0 .4 d k h W C 5 k l d l d O h h W B
  50. 50. rl d a 5 Q) a a l aO L I O E 2 5 : a r d r n E-1 s E-( W E H 0 0 X a x 0 X I . X a X a X a X a a rn X O X . X a X X .x .X .X X .X e x 8( a e x '--T-'-00-oat- 00 on- -m*mi- 00-osi- w-osi- oo*o~i- (80)SSOl Hltfd
  51. 51. XXXXXGTDModeled -Measured 8Qaec)ITSModeled 7-I 1.003.005.00:---+-------I---+-------I 7.008-0011-0013.00 RCVR.FINT.HT.(MI LocalSurfaceRoughness(one sigma)=2meters Frequency=1846MHz Conductivity=0.012U/m RelativePermittivity=15.0 Figure4-52.Pathlossvs.receiving antennaheightforProfileR1-20-Ti, Figure4-47.Transmitterheightisat 7.3meters.
  52. 52. 0 X a X '3X O I xm xe isXb X. xe * i:"Y C W r m X . X a X a X X X X X X X i"" X X Y 1 L < -AXoo.oo:- w - o t i - 00-ozi- ooosi- oonmi- oo*osi- h * o s i - 0 0 - o ~ i - ooos~-- (001SSQl Hltld
  53. 53. XXXXXGTDModeled ---Measured aQa@JQITSModeled LocalSurfaceRoughness(one sicpa)=2meters Frequency=9190MHz Conductivity=0.012U/m RelativePermittivity=15.0 Figure4-54.Pathlossvs.receiving I antennaheightforProfileRl-20-T1, grFigure4-47.Transmitterheightisat -_t___17.3meters. '1.003.005.007.008.0011.0019.00 RCVR.RNT.HT.(MI
  54. 54. 7. P a t h T I - 2 0 4 4 (20.7 Km., Beyond L i n e of S i g h t ) The l i n e a r i z e d approximation 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 of 6 edges 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 roughness f a c t o r of 2 meters was used f o r modeling. 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 through 4-61. As can be 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 similar t o t h a t of t h e p r e v i o u s przlf lie. ,7 .n7. A t f r e q u e n c i e s below 1 GZZ? ~ T L U modeled r e s u l t s show c l o s e agreement 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 red d a t a ,
  55. 55. 0 X B X 8 X e X . i"0 X X X X X X X X X X X X X X X X X X i'" X X , Y l oo*oo:- 00-01i- 00-ozi- oo9osi- oo*mi.- 00*bi- OO-mi- 0 0 - o ~ i - (90)SSOl Hltfd
  56. 56. 8 . 49.0 K m . , Beyond L i n e of S i g h t Path. 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. Because of 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 approximations 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 between 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 roughness parameter. 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 edges, i s shown by 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 , hence, a roughness p a r a m e t e r of 9 i n c h e s is used. 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 givan iz P i g u r e 4-63 through 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 , evidence 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 observed 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 edge approximation, a l o c a l t e r r a i n roughness f a c t o r of 2 meter 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 through 4-77. These f i g u r e s show GTD 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 employing s m a l l e r s u r f a c e roughness 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 important 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-
  57. 57. p r o f i l e i n v e s t i g a t i o n presented above. The accuracy o f t h e GTD model does n o t s o l e l y depend on t h e accuracy 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 combinations of 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 roughness f a c t o r a r e necessary f o r model accuracy. The r u l e s f o r d e t e r m i n i n g what combination c o n s t i t u t e s a n optimum combination would r e q u i r e a n in-depth s t u d y which is beyond t h e scope 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 .
  58. 58. u D - a E: ..I m 3 d' .r( -4 a 5' 4J U O C Q a D k I .r( rl 0) * d C m 0 X 9 X 0 X . X 0 X . X . X . X . X . X . X 0 e '--T+-00'001- 0 0 0 t r - 0 0 . 0 ~ i - 00*06i i- r n o o e i - (80) SSQl Hltfd
  59. 59. '8 a rl d Q ) a Q) a Q) a 2 9 gcn C l a m B Q ) E U X H
  60. 60. X s - . : , L - -A:!M*M:- w-oti- 00-ozi- oo-osi- oo'mi- oo-ost- oo-wi- o o * o ~ i - m*oet-- (901SSBl Hltfd
  61. 61. (I) (I) aJ C J2
  62. 62. a9) rl 2rl aJ $ % a O k O z ; x C l a m B a l E U E H
  63. 63. 9- P a t h TI-50-TI (52.5 Km., 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 can b e s e e n , t h e p a t h is unblocked and a t o t a l o f of f i v e edges a r e u s e d i n t h e l i n e a r approximation, w i t h a modeled s u r f a c e roughness f a c t o r of 2 meters. Measured and modeled d a t a a r e shown i n F i g u r e s 4-79 through 4-84. GTD modeled r e s u l t s do n o t show t h e d e g r e e of v e r t i c a l l o b i n g as is 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 roughness parameter a n d / o r improper placement of t e r r a i n p r o f i l e edges. S i n c e t h e p r o f i l e does n o t c o n s i s t d i f f r a c t i v e edge, t h e l i m i t o f GTD model'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 cannot be determined.
  64. 64. I $ i'" 8 X - +--y-t---oo.oo:- on-o~i- oo-oai- no-ori- &*mi- oo*osi- ^oo-wt- OOOLI- (001SSOl Hltfd
  65. 65. 0 0 j4 tl%g 0 . C x X 8 i"" +--Ft- - i'JsooWoor- w otr- w-ozi- on*oei- OO-mi-w b * ~ ~ i -m-osi- OO*OL~- on*o~r-~ [aa) S S Q ~H L U ~
  66. 66. ;s f-; 1 -i soo*w!- o o * o ~ i - oo*ozi- w*ori- oo-mi- %-mi- oo-ow- ooocr- ~ * o s r - ~ (001SSQ1 Hltfd
  67. 67. 4J g - a 0 0 X X X T" X I X X X X 0 X X X X X 0 X x a X e X a x a X x a x a x a X i"" X - " . Y m.oor- watt- ao=ozi- oagoci- m*lai- w-mi- w-OQI- an-o~i- (801SSQl Hltfd
  68. 68. 10. P a t h R3-80-T3 (80 Km., 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 l o n g p a t h i s shown i n F i g u r e 4-86. Again, 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 edges, The l i n e a r approximation f o r GTD i n p u t u s e s 12 edges as i s shown i n t h e Figure. 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 through 4-91. GTD 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 , perhaps due t o t r o p o s p h e r i c e f f e c t s not considered by 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 appear u n r e a i i s t i c . iiowever, i t shouid be noted 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 determine GTD a o d e l performance 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 account 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 provided 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 edges; u n f o r t u n a t e l y , such a p a t h i s n o t g i v e n i n McQuate, e t . a l .
  69. 69. 0 x X X X X X X X X X X x X X X X X X X X X X X I"" X - Y 1 + ' 00-oor- 00-011- oo-ozi- oo.osi- ao-mi- w0osr- wmosi- OO*OL~- (00)SSOl Hltfd
  70. 70. > a & d a, V) .rl 4J c n u u 0 8 -4 d 5C S k ,( d O k Q ' H h
  71. 71. 1 1 . P a t h R2-120-TI ( 1 1 5 km., L i n e of 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 does n o t i n c l u d e any d i f f r a c t i v e edges, s o t h a t t h e p o t e n t i a l performance of GTD on l o n g p a t h s can n o t b e e v a l u a t e d . Measured and 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. GTD 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 can be decreased by r a i s i n g t h e s u r f a c e roughness f a c t o r , t h e b i a s e r r o r between 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 considered t o be due 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 McQuatels and hence comparisons cannot be made.
  72. 72. aal a 4 al 4 . a aJ a al a a g a a a v ) B a J B U x H
  73. 73. V RECOMMENDATIONS While undergoing t h e GTD model performance e v a l u a t i o n on propagation 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 recommendations. 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 be 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 determine t h e a c t u a l mechanism of s c a t t e r i n g from t h e t e r r a i n edges, and hence e l i m i n a t e t h e p r e s e n t u s e r dependent f a c t o r . 2. The v a l u e of l o c a l t e r r a i n roughness f a c t o r s h o u l d b e obtained 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 chosen 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 vary g r o s s l y over d i f f e r e n t p a t h segments, GTD model s h o u l d be 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 segments. 3. GTD model does 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 been demonstrated t h a t t h e s e e f f e c t s can be e s t i m a t e d a c c u r a t e l y 1191. Consequently, GTD model s h o u l d be modified 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 expose f u r t h e r c a p a b i l i t i e s of t h e GTD 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
  74. 74. d i f f r a c t i v e edges 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 obliquely-angled edges 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 of 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 by nonhomogeneous atmosphere; a b s o r b t i o n by oxygen and water vapor molecules, 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.
  75. 75. V I C o n c l u s i o n A computer model 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 Theory 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 . Based upon comparisons of GTD modeled d a t a w i t h measured 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 . GTD 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 from 0.5 t o 80 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 ; b o t h w i t h i n and beyond l i n e of 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 used 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 does 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 and n e a r t h e v i c i n i t y o f t h e shadow and 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 of 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 minor 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 are 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 depends upon on 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. GTD 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 ,
  76. 76. a p p a r e n t l y due 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 not accounted 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.
  77. 77. 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. Kent Chamberlin 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. Luebbers and D r . V i c h a t e Unguichian, who developed t h e b a s i c GTD model. Thanks a l s o t o Wong Sheung Shun f o r t e c h n i c a l drawings.
  78. 78. VIII REFERENCE 11 1 Sommerfeld, A . "Mathematische Theorie d e r D i f f r a k t i o n , " Math. Ann., vol. 47, pp. 317-374, 1896. 121 K e l l e r , J. B., "The Geometrical Theory o f D i f f r a c t i o n , " Symposium on Microwave O p t i c s , McGill U n i v e r s i t y , Montreal, Canada; June 1953. L3J K e l l e r , J. B., " The Geometrical 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. 141 K e l l e r , J. B , "Geometrical Theory o f D i f f r a c t i o n , " J. Opt. Soc. Am., 52, pp.116-130, February 1962. 151 Robert C . Hansen, E d i t o r , "Geometric 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 Asymptotic S o l u t i o n of Maxwell's Zquations" published i n "The Theory o f Electromagnetic- * 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, "Electromagnetic 2hzo.q and Geometerical O p t i c s , " p u b l i s h e d i n "Electromagnetic Waves" by L.E. Langer; U n i v e r i s t y o f i J 4n l u b v l L u ; L rm n nv,n -m P r e s s , Madison; 1962. i 7 j Weeks, W.L., "Antenna EngineeringH, McGraw-Hi 11 P u b l i s h i n g Company LTD, New York, N.Y., pp 39-40, 1968. 131 K e l l e r , J. B . , "Geometrical Theory of 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 . , Robert C . Hansen, pp. 83-218. L101 Kouyoumjian, R. G . , "A Uniform Geometrical 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 Conducting S u r f a c e " , Proc. IEE, v o l . 62, 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,Chapter 12. 1121 Larson, H. and Shubert. 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 , John Wiley & ~ o n n c . , New 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 Rayleigh, Lord, "On The L i g h t Dispersed 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 Transmitted by Very Narrow S l i t s , " P h i l . Mag. 1 4 , pp. 350-359, 1907.
  79. 79. 1151 Rojas-Teran, R. G . , and Burnside, W. D . , "GTD A n a l y s i s o f Airborne Antenna i n t h e Presence of Lossy D i e l e c t r i c Layers", 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 Laboratory Report. 1161 McQuate, P. L. e t a l , "Tabulations of 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 Report ERL-65-ITS-58, U. S. Department of Commerce, March 1968. 1171 Longley, A. G. and R i c e , P. L. " P r e d i c t i o n of Tropospheric Radio Transmission Loss Over I r r e g u l a r T e r r a i n " , ESSA Report ERL79-ITS-67, U.S. Department of Commerce, 1968. 1181 R i c e , P. L. e t a l , "Transmission Loss P r e d i c t i o n s f o r Tropospheric Communication C i r c u i t s " , Volume I , Report AD-687-820, U. S. Department of Commerce, J a n u a r y , 1967. 1131 Chamberlin, K. A . " I n v e s t i g a t i o n and Development of VHF Ground-Air Propagation Nodeling INncluding t h e A t t e n u a t i n g E f f e c t s of F o r e s t e d Areas f o r Within-Line- of-Sight Propagation Paths", Ohio U n i v e r s i t y Avionics Engineering C e n t e r , March 1982.
  80. 80. 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 Boundaries 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 have 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 modified d i f f r a c t i o n c o e f f i c i e n t does not v i o l a t e t h e b a s i c t h e o r y of t h e GTD fundamentals. I n t o t a l , t h r e e s e t s of edges a r e s t u d i e d ; t h e y a r e : a t t h e shadow boundary f o r a s i n g l y - d i f f r a c t e d r a y geometry; a t t h e r e f l e c t i o n boundary 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 higher-order r a y s . V e r i f i c a t i o n of 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 lower-order ray t y p e s and 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 considered s u f f i c i e n t proof 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 checks. I n a d d i t i o n , c o n t i n u i t y check 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 modified 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 check 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 .
  81. 81. 1 . R e f l e c t i o n Boundary Check The geometry used 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 13 meter 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 allowed t o e l e v a t e from 1 meter t o 81 meter h e i g h t and i s l o c a t e d at t h e v e r t i c a l c o o r d i n a t e . Three 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 by t h e s p e c i a l c o n f i g u r a t i o n of t h i s edge, 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 range. 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 at 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 at 1 1 meters of t h e a n t e n n a h e i g h t f o r t h e geometry shown. The purpose of 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 amplitude t o compensate 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 ray 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 at 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 occured. 'dith 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 of 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 geometry of 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 ,
  82. 82. c a l c u l a t e d f i e l d s a r e continuous at t h e r e f l e c t ion boundary as is expected, because GTD model o p e r a t e s a c c o r d i n g t o t h e conventional GTD b e f o r e modification. 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 ground 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 Figure. 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 ray 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 meter r e c e i v e r antenna 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 provided by t h e d i f f r a c t e d and d i r e c t rays. 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 be seen i n t h e Figure, 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 higher 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 case of F i g u r e A-2. The smooth f i e l d t r a n s i t ion 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 GTD r e f l e c t i o n boundary o p e r a t i o n f o r lower o r d e r r a y s .
  83. 83. 2. Shadow Boundary Check The purpose o f t h i s shadow boundary c o n t i n u i t y check is 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 fundamental 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 geometry employed is shown i n F i g u r e A-5. A s one c a n s e e from 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 right-hand end of 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 , whereas 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 meters h e i g h t through twenty-f i v e meter. S i n c e the t r m i t t i x & ~ 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 the p r o f i l e , t h e shadow boundary 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 meter. 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 of t h e r e c e i v i n g antenna. A s a r e s u l t , i n t e r f e r e n c e from 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 ones does not 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 is 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 from 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 at t h e shadow boundary. T h i s is caused by t h e d i s a p p e a r a n c e of t h e
  84. 84. d i r e c t ray a t t h e boundary. 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 presvered 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 conducting case. F i n i t e c o n d u c t i v i t y p l o t of p a t h l o s s f o r t h e geometry 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 conducting edges 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 at t h e shadow boundary due t o t h e disapperance of t h e d i r e c t r a y . Refering 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 , it 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 modified d i f f r a c t i o n c o e f f i c i e n t is performing i n a f a s h i o n c o n s i s t a n t with GTD.
  85. 85. 3. R e f l e c t i o n Boundary check f o r Higher-order 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-10, which c o n s i s t s of seven 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 ray 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 ray i s l o c a t e d a t 1 1 meter of t h e r e c e i v i n g antenna height. The purpose of t h i s t e s t is t o check t h a t lower-order r a y s and higher-order r a y s compensate each another t o preserve 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 of 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 antenna 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 excess of 18 db can be observed a t t h e r e f l e c t i o n boundary. This i s due t o t h e f a c t t h a t lower o r d e r r a y s a r e absented ( 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 higher- o r d e r r e f l e c t e d ray l o s s e s at t h e boundary. T o t a l path l o s s f o r t h e geometry of F i g u r e A-10 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 expected, f i e l d i s again continuous w i t h t h e a d d i t i o n of lower-ordered ray t y p e s although t h e i n t e n s i t y is rapidly-varying due t o t h e number of 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 because o f p e r f e c t conductivity.
  86. 86. 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 edges 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 on F i g u r e A-13. 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 can be observed a t t h e r e f l e c t ion boundary 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 is h i g h e r t h a n t h e 18 db i n t h e p e r f e c t l y conducting edges is because f i e l d s are f u r t h e r a t t e n u a t e d by 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 with t h e c o n t r i b u t i o n s of 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, assuming t h e same ground 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 boundary a t 1 1 meter, 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 modified GTD t h e o r y i n t h e higher and lower ray t y p e s combinations is k e p t .
  87. 87. 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 read i n by t h e GTD 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 of t h e i n p u t d a t a format and its f u n c t i o n t o t h e GTD model is given. It is t h e n followed 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, ICON, YMIN, YMAX, EPSIR, SIGMA, DELTAG XN YN ZN FREQ1 --> RAY-TYPE CONTRGL PARAMZTERS
  88. 88. Where H E , ( 1 5 ) I C O N , ( 1 5 ) ICON = 1 ICON = 0 YMIN, ( F I O . 5 ) YMAX, ( F 1 0 . 5 ) E P S I R , ( F 1 0 . 5 ) SIGMA, ( F 1 0 . 5 ) DELTAG, ( 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 of 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 roughness f a c t o r i n meter Second r e c o r d t o t h e n-th record: X , Y , Z c o o r d i n a t e of t h e edge i n 32'10.5 format, where n is equal 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 parameters (Format = 1 3 1 1 ) J D I R DIRECT RAY J R E F SINGLY REFLECTED RAY J R R REFLECTED-REFLECTED RAY J R D REFLECTED-D IFFRACTED RAY J R R D REFLECTED-REFLECTED-DIFFRACTED RAY J R D R REFLECTED-D IFFRACTED-REFLECTED RAY J D I R SINGLY DIFFRACTED RAY J D R DIFFRACTED-REFLECTED RAY JDRD DIFFRACTED-REFLECTED-D IFFRACTED RAY J D D DOUBLY-D IFFRACT ED RAY
  89. 89. J D D R DIFFRACTED-D IFFRACTED-REFLECTED RAY JDRR DIFFRACTED-REFLECTED-REFLECT ED RAY J R D D REFLECTED-D IFFRACTED-DIFFRACTED RAY If any of t h e above parameter 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 ignored d u r i n g t h e computations. Other v a l u e s simply implied t h a t r a y t y p e is i n c l u d e d . Frequencies i n megahertz s h o u l d be e n t e r e d i n F10.3 format. 2. L i s t i n g s of Path P r o f i l e Data 1. Path R1-0.5-T1
  90. 90. 2. Path R 1 - 5 - T ~ A 3. Path R1-5-T5A
  91. 91. 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
  92. 92. 9. Path R1-50-T1
  93. 93. 11. Path R2-120-T1 11. 0-210.00000 -go.ooooo 15.00000 0.01200 0.22860 I? .? 9.0 2556.481

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