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Analysis of multipath fading observations in British Columbia, Canada Lee, Edwin Kam-lun 1983

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ANALYSIS OF MULTIPATH FADING OBSERVATIONS IN BRITISH B.A.Sc, U n i v e r s i t y Of B r i t i s h Columbia, 1981 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES Department Of E l e c t r i c a l E n g i n e e r i n g We accept t h i s t h e s i s as conforming to the r e q u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA COLUMBIA,CANADA by LEE KAM-LUN, EDWIN A p r i l 1983 © Lee Kam-lun, Edwin, 1983 In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y available for reference and study. I further agree that permission for extensive copying of t h i s thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. I t i s understood that copying or publication of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of (z^c.cjfj^.Ce^L^ ^\-P>^KlXh-n e-The University of B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 Date DE-6 f . v s n i i A b s t r a c t A n a l y s i s of the data measured i n twelve s e l e c t e d microwave l i n k s i n the Province of B r i t i s h Columbia, Canada, between July'79 to October'82 has been c a r r i e d out. These l i n k s are r e p r e s e n t a t i v e of about 90% of the microwave l i n k s d i s t r i b u t e d i n three of the f i v e main t o p o g r a p h i c - c l i m a t i c regions of the P r o v i n c e . The o b s e r v a t i o n s are given i n terms of worst-month m u l t i p a t h f a d i n g p r o b a b i l i t y as a f u n c t i o n of fade depth, the number of f a d i n g events, the average fade d u r a t i o n , and the v a r i a t i o n of monthly f a d i n g time over the measurement p e r i o d . The d i u r n a l f a d i n g c h a r a c t e r i s t i c s of s e v e r a l paths are a l s o shown. The a n a l y s i s i n v o l v e s : (1) comparisons of c e r t a i n parameters d e r i v e d from the o b s e r v a t i o n s with those given i n the l i t e r a t u r e and g e n e r a l i z e d i n the CCIR formula which d e s c r i b e s m u l t i p a t h f a d i n g p r o b a b i l i t y , (2) f i n d i n g of the exponent values i n the e x p r e s s i o n s c o n c e r n i n g the number of f a d i n g events and the average fade d u r a t i o n , and (3) f i n d i n g of the y e a r l y to worst month f a d i n g r a t i o . I t i s found that the M o r i t a parameters, of the CCIR formula, are most a p p r o p r i a t e f o r a p p l i c a t i o n to microwave l i n k s i n B r i t i s h Columbia. The exponent v a l u e s i n the expressions concerning the number of fa d i n g events and the average fade d u r a t i o n are a,=0.67 and a 2=0.33, r e s p e c t i v e l y . The y e a r l y to worst month f a d i n g r a t i o can be assumed to be 2.0 f o r most l i n k s . Moreover, the o b s e r v a t i o n s show t h a t the most a c t i v e m u l t i p a t h f a d i n g months are J u l y to October. The peak of the d i u r n a l m u l t i p a t h f a d i n g f o r l i n k s over, and perhaps a l o n g , a water body i s around afternoon and at sunset. For p l a t e a u l i n k s , the f a d i n g s occur mostly around s u n r i s e and f o r most mountain l i n k s , no g e n e r a l p a t t e r n can be observed. Furthermore, d i f f e r e n t types of m u l t i p a t h fading mechanisms s p e c i f i c to v a r i o u s t o p o g r a p h i c - c l i m a t i c r e g i o n s are i n v e s t i g a t e d . The dominant m u l t i p a t h mechanisms f o r c o a s t a l r e g i o n are sea breeze, o f f s h o r e streaming, and a d v e c t i o n of n o c t u r n a l l y - c o o l e d a i r . For p l a t e a u r e g i o n , the dominant mechanism i s r a d i a t i o n i n v e r s i o n and f o r mountain r e g i o n , m u l t i p a t h f a d i n g i s most l i k e l y caused by trapped r a d i a t i o n fog i n the v a l l e y s with c l e a r a i r above. Table of Contents A b s t r a c t i i L i s t of Tables v i L i s t of F i g u r e s v i i Acknowledgements v i i i I. INTRODUCTION 1 1. MULTI PATH PROPAGATION 2 1.1 R e f r a c t i v i t y 3 1.1.1 R e f r a c t i v e Index 3 1.1.2 R e f r a c t i v i t y P r o f i l e s 4 1.1.3 R e f r a c t i v i t y Gradient 5 1.1.4 R e f r a c t i v e Layer And M u l t i p a t h Propagation ....7 1.2 A n a l y t i c a l Models For M u l t i p a t h Propagation 9 1.2.1 R u t h r o f f ' s Model 9 1.2.2 CNR Model 10 1.2.3 Webster's Model 14 1.2.4 Other Models 16 1.3 S t a t i s t i c a l Approach To M u l t i p a t h Propagation ..16 2. OTHER REFRACTIVITY-RELATED PHENOMENA 18 2.1 O b s t r u c t i o n Fading 18 2.2 Ducting 18 2.3 Blackout Fading 19 3. NON-REFRACTIVITY-RELATED PHENOMENA 19 3.1 Rain A t t e n u a t i o n 19 3.2 Fog A t t e n u a t i o n 19 3.3 Snow A t t e n u a t i o n And M e l t i n g - l a y e r Fading 19 3.4 Gaseous Ab s o r p t i o n s 20 4. THE LAYOUT OF THE THESIS 20 I I . REGIONS AND MICROWAVE LINKS CONSIDERED 22 1. THE TOPOGRAPHIC-CLIMATIC REGIONS OF B.C 22 1.1 The C o a s t a l Mountains And I s l a n d s 23 1.2 The I n t e r i o r P l a t e a u 25 1.3 The Columbia Mountains And Southern Rockies ....25 1.4 The Northern And C e n t r a l P l a t e a u And Mountains .25 1.5 The Great P l a i n s 26 2. MICROWAVE LINKS CONSIDERED 27 I I I . DATA ACQUISITION 28 1. TYPES OF RECORD 28 2. CHART ESTIMATION 29 IV. OBSERVATIONS AND ANALYSIS 31 1. PROBABILITY OF FADING 31 2. NUMBER OF EVENTS AND AVERAGE FADE DURATION 36 3. MONTHLY VARIATION OF FADING 38 4. DIURNAL VARIATION OF FADING 39 V. TYPES OF MULTIPATH FADING OBSERVED 42 1. COASTAL LINKS 42 2. PLATEAU LINKS 47 3. MOUNTAIN LINKS 53 VI. OTHER PHENOMENA OBSERVED 54 1. MULTIPATH-LIKE RAIN-INDUCED FADING 54 2. MELTING-LAYER FADING 55 3. QUASI-PERIODIC SIGNAL VARIATION 55 V V I I . CONCLUSION 57 1. SUMMARY OF RESULTS 57 2. DIRECTIONS OF FURTHER RESEARCH 58 BIBLIOGRAPHY ' 60 APPENDIX A - PATH PROFILES OF LINKS INVESTIGATED 67 APPENDIX B - SAMPLE CALCULATION OF REFRACTIVITY GRADIENT .73 APPENDIX C - MAIN POINTS OF RUTHROFF*S MODEL 77 1. PHASE DIFFERENCE - GENERAL CASE 78 2. PHASE DIFFERENCE - WORST CASE OF INTERFERENCE ...80 3. FADING PROBABILITY - FREQUENCY AND PATH LENGTH DEPENDENCE 81 4. FADING PROBABILITY - SIGNAL POWER LEVEL RATIO DEPENDENCE ....82 APPENDIX D - MAIN POINTS OF THE CNR MODEL 84 1. SIGNAL POWER RATIO OF TWO RAYS - GENERAL EXPRESSION 84 2. RELATIVE DELAY BETWEEN TWO RAYS - GENERAL EXPRESSION 86 3. SIGNAL POWER RATIOS & RELATIVE DELAYS BETWEEN TWO RAYS - SPECIAL CONDITION 87 3.1 Case I 87 3.2 Case II 88 APPENDIX E - MAIN POINTS OF WEBSTER'S MODEL 89 1. VARIATION IN ANOMALY INTENSITY 90 2. VARIATION IN PATH LENGTH 90 3. VARIATION IN ANOMALY THICKNESS 90 4. VARIATION IN ANOMALY HEIGHT 92 v i L i s t of Tables I. Atmospheric and propagation c o n d i t i o n s v s . r e f r a c t i v i t y g r a d i e n t 8 I I . S a l i e n t f e a t u r e s of l i n k s measured 26 I I I . E s t i m a t o r 29 IV. Comparison of Exact and Estimated data 30 V. Comparison of parameters f o r Eq.4.1 32 VI. Worst month f a d i n g p r o b a b i l i t y vs. fade depth 33 V I I . Number of events i n the worst month vs. fade depth .35 V I I I . Average fade d u r a t i o n i n worst month vs.fade depth .36 IX. Parameters f o r Eqs. 4.2 & 4.3 37 X. The value d i s t r i b u t i o n of a? 38 XI. Monthly v a r i a t i o n of f a d i n g and y e a r l y to worst month f a d i n g p r o b a b i l i t y r a t i o 39 X I I . S a t u r a t e d vapour pressure v s. temperature 74 X I I I . Data f o r r e f r a c t i v i t y c a l c u l a t i o n - 0400 PST 21st Sep.'82 at P r i n c e George 74 v i i L i s t of F i g u r e s 1. C r o s s - s e c t i o n of t o p o g r a p h i c - c l i m a t i c r e g i o n s i n southern B.C 22 2. D i s t r i b u t i o n of microwave l i n k s i n v e s t i g a t e d 24 3. Worst month f a d i n g p r o b a b i l i t y - p r e d i c t e d vs. measured 34 4. D i u r n a l v a r i a t i o n of f a d i n g 40 5. Sea breeze 42 6. O f f s h o r e streaming 43 7. Advection of n o c t u r n a l l y - c o o l e d a i r 44 8. The geography along l i n k C 45 9. Rapid f a d i n g on a c o a s t a l l i n k 46 10. R a d i a t i o n i n v e r s i o n 47 11. Rapid and slow fad i n g on a p l a t e a u l i n k 48 12. Rapid deep f a d i n g and shallow s c i n t i l l a t i o n s on a p l a t e a u l i n k 49 13. O b s t r u c t i o n f a d i n g coupled with m u l t i p a t h f a d i n g on a p l a t e a u l i n k 50 14. C l e a r sky above trapped mountain fog 51 15. Fading on a mountain l i n k i n the presence of fog 52 16. M u l t i p a t h - l i k e r a i n - i n d u c e d f a d i n g 54 17. M e l t i n g - l a y e r f a d i n g 55 18. Q u a s i - p e r i o d i c v a r i a t i o n preceding m u l t i p a t h f a d i n g ..56 19. Path p r o f i l e of l i n k s A & B 67 20. Path p r o f i l e of l i n k C 68 21. Path p r o f i l e of l i n k D 68 22. Path p r o f i l e of l i n k E 69 23. Path p r o f i l e of l i n k F 69 24. Path p r o f i l e of l i n k G 70 25. Path p r o f i l e of l i n k H 70 26. Path p r o f i l e of l i n k I 71 27. Path p r o f i l e of l i n k J 71 28. Path p r o f i l e of l i n k K 72 29. Path p r o f i l e of l i n k L 72 30. Radiosonde data on tephigram 73 31. R e f r a c t i v i t y p r o f i l e - 0400 PST 21st Sep.'82 at P r i n c e George 75 32. R e f r a c t i o n from a s i n g l e l a y e r 77 33. S i n g l e - l a y e r r e f r a c t i o n with a ray r i s i n g above the l a y e r 78 34. Region of i n t e g r a t i o n f o r f a d i n g p r o b a b i l i t y 82 35. S i n g l e - l a y e r above t e r m i n a l s 84 36. Geometry of ray bundle from t r a n s m i t t e r to r e c e i v e r ..85 37. R e f r a c t i v i t y p r o f i l e proposed by Webster 89 38. R e l a t i o n s between the ray t r a j e c t o r i e s and r e f r a c t i v i t y p r o f i l e 89 39. Changes i n s i g n a l amplitudes, r e l a t i v e d e l a y s and angles of a r r i v a l w.r.t. anomly i n t e n s i t y , path l e n g t h , anomaly t h i c k n e s s and anomaly height 91 v i i i A c k n o w l e d g e m e n t I w o u l d l i k e t o t h a n k my t h e s i s s u p e r v i s o r , D r . M . M . Z . K h a r a d l y , f o r h i s s u p e r v i s i o n a n d a d v i c e t h r o u g h o u t my r e s e a r c h . I w o u l d a l s o l i k e t o t h a n k M r . N . O w e n f o r h i s h e l p f u l d i s c u s s i o n s a n d r e s o u r c e f u l i d e a s , e s p e c i a l l y on t h e p a r t o f d a t a a n a l y s i s . M o r e o v e r , my t h a n k s a r e e x t e n d e d t o t h e B r i t i s h C o l u m b i a T e l e p h o n e Company f o r s u p p l y i n g t h e p r o p a g a t i o n d a t a a s w e l l a s p a r t o f t h e d a t a a n a l y s i s o f l i n k s A , B , t o t h e P a c i f i c W e a t h e r C e n t r e f o r t h e r a d i o s o n d e d a t a , a n d t o t h e O f f i c e o f t h e A t m o s p h e r i c E n v i r o n m e n t S e r v i c e f o r t h e c l i m a t i c d a t a . My r e s e a r c h was f i n a n c i a l l y s u p p o r t e d by t h e N a t i o n a l R e s e a r c h C o u n c i l r e s e a r c h g r a n t A-3344, t h e c o n t r a c t s o f t h e C o m m u n i c a t i o n s R e s e a r c h C e n t r e , O t t a w a , a n d t h e B r i t i s h C o l u m b i a T e l e p h o n e C o m p a n y , a s w e l l a s t h e U n i v e r s i t y G r a d u a t e F e l l o w s h i p o f t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a . I am g r a t e f u l t o my p a r e n t s who s u p p o r t e d me o v e r t h e p a s t y e a r s , a n d my h e a v e n l y F a t h e r whose g r a c e s u s t a i n s me. T o H i m be t h e h o n o u r a n d g l o r y ! 1 I . INTRODUCTION The troposphere, which l i e s between the e a r t h s u r f a c e and the tropopause at about 10km above s e a - l e v e l , has i n t e r e s t e d m e t e o r o l o g i s t s and r a d i o engineers a l i k e f o r i t s great v a r i a b i l i t y . From an e n g i n e e r i n g viewpoint, s t u d i e s of the troposphere are important because v a r i o u s m e t e o r o l o g i c a l phenomena can s e r i o u s l y a f f e c t radiowave propagation (Ref.1). In d e s i g n i n g 1 i n e - o f - s i g h t microwave l i n k s , one of the major c o n s i d e r a t i o n s i s e s t i m a t i n g the p r o b a b i l i t y of m u l t i p a t h f a d i n g (Ref.2). In Canada, a t y p i c a l design f o r a l i n k , using analogue frequency modulation, i n v o l v e s f i r s t e n s u r i n g an adequate f r e e - s p a c e s i g n a l such that the noise i s w i t h i n a p r e s c r i b e d l i m i t . Then the c a l c u l a t i o n i s made of the small percentage of the year d u r i n g which deep f a d i n g i s t o l e r a t e d . I t i s t h i s c a l c u l a t i o n that r e q u i r e s knowledge of f a d i n g , p a r t i c u l a r l y m u l t i p a t h f a d i n g . In B r i t i s h Columbia (B.C.), we found t h a t when modern r a d i o equipment and c a r e f u l l i n k designs are used, the d e s i g n p o i n t around the free-space l e v e l has been dominant, n e g l e c t i n g i n t e r f e r e n c e c o n s i d e r a t i o n s . In the past few years, microwave l i n k s that use d i g i t a l modulation have been widely used. For d i g i t a l modulation, B i t E r r o r Rate (BER) i s of major concern. The fade depth which corresponds to an a c c e p t a b l e BER i s about 25dB. T h i s fade depth i s s u b s t a n t i a l l y s m a l l e r than that of analogue modulation which guarantees a c c e p t a b l e performance. Hence l i n k s u s i n g d i g i t a l modulation are more s u s c e p t i b l e to m u l t i p a t h f a d i n g . To take 2 t h i s shallow f a d i n g i n t o account i n design r e q u i r e s knowledge of the p r o b a b i l i t y of f a d i n g . I t i s a l s o expected that f u r t h e r i n f o r m a t i o n , such as the number and d u r a t i o n of f a d i n g events, w i l l be r e q u i r e d as d i g i t a l designs e v o l v e . From a s c i e n t i f i c viewpoint, i t i s important to understand the p h y s i c s of the propagation phenomena. In understanding the mechanisms of r e f r a c t i v e l a y e r formation, one may be a b l e to o b t a i n i n s i g h t to combat m u l t i p a t h propagation problems in designs or, at l e a s t , to know the c r i t e r i a f o r choosing s u i t a b l e t e r m i n a l s i t e s . 1. MULTIPATH PROPAGATION In microwave t r a n s m i s s i o n at the frequency range below 10GHz, the most pronounced f a d i n g i s due to m u l t i p a t h p r o p a g a t i o n . M u l t i p a t h propagation or m u l t i p a t h t r a n s m i s s i o n i s d e f i n e d i n Ref.3 as "The propagation phenomenon that r e s u l t s i n s i g n a l r e a c h i n g the r e c e i v i n g antenna by two or more paths." The e x i s t e n c e of m u l t i p a t h propagation was confirmed by i n v e s t i g a t o r s l i k e F r i i s (Ref.4) using a n g l e - o f - a r r i v a l measurement. The propagation channel can be modelled by the t r a n s f e r f u n c t i o n M H(f) = Z a e x p ( - j 2 i r f T ) (1.1) m= 1 m m where, a : the amplitude of the mth s i g n a l component m f the c a r r i e r frequency 3 T : the propagation delay of the mth s i g n a l component m M : the t o t a l number of s i g n a l components. The parameters i n Eq.1.1 can be determined e i t h e r d i r e c t l y by the pulsed s i g n a l technique i n time domain or i n d i r e c t l y by the swept frequency technique i n frequency domain. I f the .second technique i s used, computer r e c o n s t r u c t i o n of the s i g n a l p a t t e r n i s necessary i n order to obtain the received s i g n a l amplitudes and r e l a t i v e delays of d i f f e r e n t s i g n a l components (Ref.5). M u l t i p a t h fading can be c l a s s i f i e d i n t o antenna-selective and non-antenna-selective types (Ref.6). The f i r s t type includes d i s c r e t e r e f l e c t i o n s from mountains and b u i l d i n g s as w e l l as surface r e f l e c t i o n and s c a t t e r i n g from ground. This type of f a d i n g can be g r e a t l y reduced by good antenna and system designs. The second type includes volume s c a t t e r i n g due to atmospheric turbulence as w e l l as fading due to r e f r a c t i v e l a y e r s . Volume s c a t t e r i n g becomes i n s i g n i f i c a n t when compared wit h fading due to r e f r a c t i v e l a y e r s . The major concern of t h i s t h e s i s i s , t h e r e f o r e , m u l t i p a t h fading due to r e f r a c t i v e l a y e r s . 1.1 R e f r a c t i v i t y 1.1.1 R e f r a c t i v e Index Since the r e f r a c t i v e index, n, of the troposphere i s very c l o s e to 1, t h e r e f o r e , i n order to accentuate i t s changes, r e f r a c t i v i t y i s used i n s t e a d . I t i s defined as N = ( n - 1 ) x ! 0 6 4 In a d d i t i o n , N can be expressed as a f u n c t i o n of temperature T(K), pressure P(mb) and vapour pressure e(mb) as f o l l o w s The f i r s t and second terms are o f t e n r e f e r r e d to as the dry and wet terms, r e s p e c t i v e l y . 1.1.2 R e f r a c t i v i t y P r o f i l e s Because the troposphere i s non-uniform, t h e r e f o r e , we expect N to vary with h e i g h t . N expressed as a f u n c t i o n of height i s c a l l e d r e f r a c t i v i t y p r o f i l e . R e f r a c t i v i t y p r o f i l e can be obtained e i t h e r d i r e c t l y from a i r b o r n e refTactometer or i n d i r e c t l y from c a l c u l a t i o n u s i n g Eg.1.2 (Appendix B) basing on captured b a l l o o n radiosonde data which c o n s i s t of temperature, dew p o i n t and pr e s s u r e i n f o r m a t i o n at d i f f e r e n t a l t i t u d e s . B esides, many i d e a l i z e d p r o f i l e s have a l s o been proposed i n order to f a c i l i t a t e a n a l y t i c a l i n v e s t i g a t i o n s . Two very good surveys are given i n Refs.8 and 9. The l i n e a r p r o f i l e s , the power-law p r o f i l e s , the l i n e a r - e x p o n e n t i a l p r o f i l e s , the l i n e a r -piecewise p r o f i l e and the b i - e x p o n e n t i a l p r o f i l e are commonly used. The two p r o f i l e s adopted by the N a t i o n a l Bureau of Standards are the CRPL r e f e r e n c e r e f r a c t i v i t y p r o f i l e and the CRPL e x p o n e n t i a l r e f e r e n c e p r o f i l e . The former i s a combination of l i n e a r and e x p o n e n t i a l p r o f i l e s at d i f f e r e n t a l t i t u d e s expressed as ( R e f . 7 ) (1.2) 5 r N 0 - ( h - h 0 ) ( N 0 - N , ) , h 0 < h < h 0+ 1 k m N = + N r 1 N , exp - ( In ) (h-ho-1 ) L 8 - h 0 105 ,h 0+1km < h < 9km L l 0 5 e x p [ - 0 . 1 4 2 4 ( h - 9 ) ] , h Z 9km where, N 0 : the s u r f a c e r e f r a c t i v i t y N , : the r e f r a c t i v i t y at 1km a l t i t u d e h 0 : the s u r f a c e a l t i t u d e h : the a l t i t u d e i n q u e s t i o n . The l a t t e r i s an e x p o n e n t i a l p r o f i l e e x p r e s s e d as N = N 0 e x p [ C e ( h - h 0 ) ] Ce : the l o c a t i o n p a r a m e t e r . 1.1.3 R e f r a c t i v i t y G r a d i e n t Because e l e c t r o m a g n e t i c wave t r a v e l s f a s t e r i n a medium of s m a l l e r N , ray bending o c c u r s when the r a t e of change of N w . r . t . h e i g h t h ( d N / d h ) , commonly c a l l e d r e f r a c t i v i t y g r a d i e n t , i s n o n - z e r o . T h e r e f o r e , in p r o p a g a t i o n prob lems , r e f r a c t i v i t y g r a d i e n t i s an important q u a n t i t y . Other e q u i v a l e n t systems used to express t h i s r a t e of change are the m o d i f i e d r e f r a c t i v i t y g r a d i e n t (dM/dh) i n M u n i t s per km, . the m o d i f i e d r a d i u s of c u r v a t u r e of the ray t r a j e c t o r y (Rmod) i n km, and the e f f e c t i v e e a r t h r a d i u s f a c t o r ( k ) . The f i r s t two q u a n t i t i e s are o b t a i n e d from the F l a t t e n e d where, 6 E a r t h C o o r d i n a t e T r a n s f o r m a t i o n ( R e f . 6 ) . The r e l a t i o n between M and N i s as f o l l o w s : and hence , dM dN 10 6 dh dh a where a i s the e a r t h r a d i u s (6400km). The e x p r e s s i o n Rmod i s g i v e n as -1 Rmod = . (dn/dh) + d / a ) The l a s t q u a n t i t y k i s g i v e n as R r dN/dh-, -1 where R i s the r a d i u s of c u r v a t u r e of the ray t r a j e c t o r y . For a s t a n d a r d atmosphere , 7 dN — = -40 Nu/km , dh dM — = +116 Mu/km , dh Rmod = -8600 km , and k = 4/3 . R e f r a c t i v i t y g r a d i e n t has g r e a t e r v a r i a t i o n at lower a l t i t u d e . I t s s e a s o n a l v a r i a t i o n i s maximum i n summer and i t s d i u r n a l v a r i a t i o n i s maximum a t n i g h t (Re f s . 10 ,1 1 ) . For 60% of the t i m e , the r a t e of change of r e f r a c t i v i t y g r a d i e n t w . r . t . t ime i s g r e a t e r than 1 Nu/km/min ( R e f . 1 0 ) . For d i f f e r e n t v a l u e s of r e f r a c t i v i t y g r a d i e n t , the c o r r e s p o n d i n g a tmospher ic and microwave p r o p a g a t i o n c o n d i t i o n s were t a b u l a t e d i n R e f . 1 2 and the t a b l e i s reproduced here (Tab le I ) . 1 .1.4 R e f r a c t i v e Layer And M u l t i p a t h P r o p a g a t i o n Because the t r o p o s p h e r e i s not u n i f o r m , r e g i o n s of s teep n e g a t i v e r e f r a c t i v i t y g r a d i e n t of l e s s than - l57Nu/km may e x i s t due to s teep h u m i d i t y a n d / o r temperature i n v e r s i o n s . These r e g i o n s , commonly c a l l e d r e f r a c t i v e l a y e r s , are r e s p o n s i b l e for r e f r a c t i v e m u l t i p a t h p r o p a g a t i o n . R e f r a c t i v e l a y e r f o r m a t i o n may be a t t r i b u t e d to d i f f e r e n t mechanisms such as h e a t i n g from below, r a d i a t i o n i n v e r s i o n , subs idence i n v e r s i o n , f r o n t a l i n v e r s i o n , sea b r e e z e , o f f s h o r e 8 T a b l e I - Atmospher ic and p r o p a g a t i o n c o n d i t i o n s v s . r e f r a c t i v i t y g r a d i e n t k dN dh ATMOSPHERIC CONDITION MICROWAVE PROPAGATION 5/12 + 220 HUMIDITY INVERSION EXTREME EARTH BULGE (LARGE POSITIVE GRADIENT) (DIFFRACTION FADE) 1/2 + 1 57 MODERATELY SUBREFRACTIVE MODERATE EARTH BULGE 2/3 + 80 SLIGHTLY SUBREFRACTIVE SLIGHT EARTH BULGE 1 , 0 HOMOGENEOUS NO REFRACTION 1 .25 -30 DRY ATMOSPHERE STANDARD (MOUNTAINOUS) 4/3 -40 STANDARD ATMOSPHERE STANDARD 1 .6 -58 HUMID ATMOSPHERE STANDARD (COASTAL) OO -157 MODERATE NEGATIVE GRADIENT FLAT EARTH -1 -314 STEEP GRADIENT POSSIBLE BLACKOUT - 0 . 5 -470 EXTREME GRADIENT BLACKOUT s t r e a m i n g , a d v e c t i o n of n o c t u r n a l l y - c o o l e d a i r , and warm dry a i r o v e r l a y i n g t r a p p e d mountain fog ( R e f s . 6 , 1 3 - 1 6 ) . The l a y e r t h i c k n e s s ranges from 40m to 400m but f o r 90% of the t i m e , i t i s l e s s than 100m ( R e f . 1 7 ) . I t s mean t h i c k n e s s i s r e c o r d e d as 66m i n the A r c t i c r e g i o n , 97m i n the Temperate r e g i o n and 106m i n the T r o p i c a l r e g i o n ( R e f . 8 ) . Under normal c o n d i t i o n s , the l a y e r can be assumed to be h o r i z o n t a l . However, i n the case of f r o n t a l i n v e r s i o n or i n the presence of wind s h e e r , the l a y e r may be t i l t e d up to 2 . 3 ° ( R e f . 1 6 ) . A l though m u l t i p a t h f a d i n g i s u n l i k e l y to occur on s l a n t e d paths when the l a y e r i s h o r i z o n t a l , ye t i t can occur when the l a y e r i s t i l t e d 9 ( R e f . 1 8 ) . D y n a m i c a l l y , r e f r a c t i v e l a y e r can a t t a i n v e r t i c a l v e l o c i t y of a few c e n t i m e t e r s per second ( R e f . 1 9 ) . M o r e o v e r , because the d e n s i t y of r e f r a c t i v e l a y e r i s c o n s i d e r a b l y h i g h e r than those of i t s s u r r o u n d i n g s , i n t e r n a l g r a v i t y wave (or l e v i t y wave) may e x i s t ( R e f s . 1 7 , 2 0 , 2 1 ) . There i s a l s o ev idence t h a t r e f r a c t i v e l a y e r o s c i l l a t e s w i th a p e r i o d of one to two hours i n the h e i g h t range of about 0-300m ( R e f . 2 2 ) . 1.2 A n a l y t i c a l Models F o r M u l t i p a t h P r o p a g a t i o n R a y - t r a c i n g , or G e o m e t r i c a l o p t i c s , t e c h n i q u e i s mos t ly used i n a n a l y z i n g m u l t i p a t h phenomena. S ince R u t h r o f f ' s n o v e l attempt (Ref .23 ) to produce a model that agrees w i t h B a r n e t t ' s r e s u l t of s t a t i s t i c a l a n a l y s i s of m u l t i p a t h f a d i n g o b s e r v a t i o n s ( R e f . 2 4 ) , the CNR group ( R e f s . 6 , 1 8 , 2 5 , 2 6 ) and Webster ( R e f s . 2 7 -29) f o l l o w e d h i s a p p r o a c h . 1.2.1 R u t h r o f f ' s Model R u t h r o f f assumed a l i n e a r - p i e c e w i s e r e f r a c t i v i t y p r o f i l e r e p r e s e n t i n g a h o r i z o n t a l r e f r a c t i v e l a y e r w i t h c o n s t a n t r e f r a c t i v i t y g r a d i e n t . T h i s l a y e r was a l s o assumed to be h o r i z o n t a l l y above the equa l h e i g h t t r a n s m i t t i n g and r e c e i v i n g antennas ( F i g u r e s 3 2 , 3 3 ) . R u t h r o f f showed tha t the maximum number of ray p a t h s , i n c l u d i n g the d i r e c t p a t h , i n r e f r a c t i v e m u l t i p a t h p r o p a g a t i o n i s t h r e e , and the fade depth of the s i g n a l a m p l i t u d e i s l e s s than 3db i f the p a t h l e n g t h i s s h o r t e r than a c r i t i c a l v a l u e d 0 . ( e . g . d 0 i s 8.2km for 6GHz t r a n s m i s s i o n . ) Moreover , he showed t h a t the m u l t i p a t h f a d i n g p r o b a b i l i t y i n the worst case of i n t e r f e r e n c e , when one of the r e f r a c t e d r a y s i s 10 about 1 8 0 ° out of phase w i t h the d i r e c t r a y , i s a f u n c t i o n of f ' . d 3 (Appendix C , S e c t i o n 3) as found by B a r n e t t (Tab le V ) . F u r t h e r m o r e , f or l o n g paths where the phase d i f f e r e n c e can be assumed to have c o n s t a n t d i s t r i b u t i o n over the 0 to 2ir range , the deep m u l t i p a t h f a d i n g p r o b a b i l i t y was shown to be p r o p o r t i o n a l to the r a t i o of the f a d i n g s i g n a l power l e v e l to the f r e e space power l e v e l W/Wo (Appendix C , S e c t i o n 4) as found i n Chapter I V , E q . 4 . 1 . 1.2.2 CNR Model The CNR group assumed a l i n e a r - p i e c e w i s e m o d i f i e d r e f r a c t i v i t y p r o f i l e . ( i . e . F l a t t e n e d E a r t h C o o r d i n a t e T r a n s f o r m a t i o n was u s e d . ) In the CNR mode l , the case when the t r a n s m i t t i n g and r e c e i v i n g antennas are of d i f f e r e n t h e i g h t s was c o n s i d e r e d ( F i g u r e 35 ) . Moreover , the treatment a l s o i n c l u d e d the cases when the r e f r a c t i v e l a y e r i s above , below and between the a n t e n n a s . When the l a y e r i s between the antennas , i t was deduced t h a t no m u l t i p a t h p r o p a g a t i o n can o c c u r . B e s i d e s , the r a t i o of the r e c e i v e d s i g n a l to the t r a n s m i t t e d s i g n a l power i n t e n s i t y was d e r i v e d . The r a t i o i s a p p r o x i m a t e l y i n v e r s e l y p r o p o r t i o n a l to the a n g l e of a r r i v a l (Appendix D, S e c t i o n 1 ) . For the s p e c i a l case when the l a y e r i s above the t r a n s m i t t i n g and r e c e i v i n g antennas of the same h e i g h t , there are two p o s s i b l e ways tha t t h r e e ray pa ths can e x i s t . In the f i r s t c a s e , the s i g n a l s of the two r e f r a c t e d rays have the same a m p l i t u d e and d e l a y wheras i n the second c a s e , t h e i r a m p l i t u d e s and d e l a y s are d i f f e r e n t (Appendix D , S e c t i o n 3 ) . The p o i n t of i n t e r e s t i s t h a t , i n both c a s e s , a t l e a s t one of the r e f r a c t e d 11 rays has g r e a t e r s i g n a l a m p l i t u d e than tha t of the d i r e c t r a y . Only i n the c r i t i c a l s i t u a t i o n when the l a y e r h e i g h t ( i . e . the h e i g h t of the l a y e r base) i s the same as the h e i g h t of the antennas would the d i r e c t ray s i g n a l a m p l i t u d e e q u a l those of the r e f r a c t e d r a y s . The g e n e r a l c o n d i t i o n s for r e f r a c t i v e m u l t i p a t h p r o p a g a t i o n were d e r i v e d as f o l l o w s : (1) the maximum l a y e r h e i g h t above the mean h e i g h t of the t r a n s m i t t i n g and r e c e i v i n g antennas 8h = min{2.2w } max 8R(p+2) (2) the maximum angle of d e p a r t u r e r w 2( — «- R ho-h ) 1/2 s i n 0 max -Ro (3) the maximum angle of a r r i v a l 12 (4) the minimum angle of a r r i v a l r 2 ( h 2 - h 1 ) -,1/2 s i n 0 2 | = L -Ro J m i n (5) the maximum he ight d i f f e r e n c e between the t r a n s m i t t i n g and r e c e i v i n g antennas w ( h 2 - h , ) = , max p (6) the minimum l a y e r t h i c k n e s s h , + h 2 w = p(ho - ) , min 2 (7) the maximum number of e x t r a o s c i l l a t i o n s of a r e f r a c t e d ray t r a j e c t o r y ( F i g u r e 35) TJ = In t max 1+-1/2 - 4 R o ( 2 h o - h 1 - h 2 H 1+p . -1 13 (8) the minimum path l e n g t h L = v/4R(p+2) (2ho-h,-h 2) ,and min (9) the minimum lapse r a t e 0.62139x10 s 1/2 + 156.78 LL 8RfAJ -I 0.62139x10 s Rf l 1 / 2 - ( ^ l ) l LL 8RfA-l J , V = o + 156.78 , T? £ 1 where, 6h : the l a y e r height above the mean antenna height ('min' i s a f u n c t i o n which g i v e s the minimum value of the q u a n t i t i e s w i t h i n the b r a c k e t s . ) w : the l a y e r t h i c k n e s s R : the r a d i u s of c u r v a t u r e of the ray t r a j e c t o r y i n s i d e the l a y e r -Ro: the r a d i u s of c u r v a t u r e of the ray t r a j e c t o r y o u t s i d e the l a y e r Rf : the r a d i u s of c u r v a t u r e of the ray t r a j e c t o r y i n a standard atmosphere p : the r a t i o of R to -Ro ho : the l a y e r height 14 h , : the t r a n s m i t t i n g antenna h e i g h t h 2 : the r e c e i v i n g antenna h e i g h t 0, : the ang le of d e p a r t u r e 62 i the ang le of a r r i v a l T? : the number of e x t r a o s c i l l a t i o n s of a r e f r a c t e d ray t r a j e c t o r y ( ' I n t ' i s a f u n c t i o n which g i v e s the i n t e g e r v a l u e of the q u a n t i t y w i t h i n the b r a c k e t s . ) L : the p a t h l e n g t h L : the l a p s e r a t e (the same as r e f r a c t i v i t y g r a d i e n t but wi thout s i g n ) . In the 1977 v e r s i o n of the CNR model , the case when the r e c e i v i n g ( t r a n s m i t t i n g ) antenna i s i n s i d e the l a y e r wh i l e the t r a n s m i t t i n g ( r e c e i v i n g ) antenna i s o u t s i d e has a l s o been c o n s i d e r e d . 1 .2 .3 W e b s t e r ' s Model Webster t a c k l e d the problem s l i g h t l y d i f f e r e n t l y by assuming , i n s t e a d of a l i n e a r - p i e c e w i s e r e f r a c t i v i t y p r o f i l e , a smooth p r o f i l e ( F i g u r e 37) expres sed as f o l l o w s : AN • a r c t a n and the r e f r a c t i v i t y g r a d i e n t e x p r e s s i o n i s 1 5 dN AN l 2 . 6 3 A h — = k 0 + dh TT A h 2 + [ 12 .63(h-ho) ] 2 where, N 0 . the s u r f a c e r e f r a c t i v i t y AN , the anomaly i n t e n s i t y k 0 the r e f r a c t i v i t y g r a d i e n t i n a s t a n d a r d atmosphere h the h e i g h t in q u e s t i o n ho • the anomaly h e i g h t Ah the anomaly t h i c k n e s s . By u s i n g a smooth p r o f i l e , Webster hopes to a v o i d the d i s c o n t i n u i t i e s o c c u r r e d i n the ray p r o p e r t i e s a t the r e c e i v i n g end caused by the abrupt p r o f i l e changes i f a l i n e a r - p i e c e w i s e p r o f i l e were u s e d . V a r i a t i o n s i n s i g n a l a m p l i t u d e s , r e l a t i v e d e l a y s and a n g l e of a r r i v a l w . r . t . changes i n AN, A h , ho and p a t h l e n g t h were s t u d i e d (Appendix E ) . I t was found t h a t m u l t i p a t h p r o p a g a t i o n cannot occur when the l a y e r i s below both the t r a n s m i t t i n g and r e c e i v i n g antennas . ( T h i s c o n c l u s i o n i s p r o b a b l y due to the f l a t e a r t h assumption which w i l l be mentioned l a t e r . ) One of the r e f r a c t e d rays has s i g n a l a m p l i t u d e of about 4dB above that of the d i r e c t r a y , wheras the o ther r e f r a c t e d ray has s i g n a l a m p l i t u d e of about 1OdB below tha t of the d i r e c t r a y . The major drawback of W e b s t e r ' s model i s t h a t , i n s t e a d of u s i n g the F l a t t e n e d E a r t h C o o r d i n a t e T r a n s f o r m a t i o n , f l a t e a r t h was assumed i n which case the r e l a t i v e c u r v a t u r e s of the ray t r a j e c t o r i e s w . r . t . the c u r v a t u r e of the e a r t h cannot be p r e s e r v e d . 16 1-2.4 Other Models Other works i n v o l v i n g R u t h r o f f ' s approach are shown in R e f s . 3 0 - 3 3 . U n l i k e R u t h r o f f ' s a p p r o a c h , Shkarof sky and N i c k e r s o n ( R e f s . 3 4 , 3 5 ) used r a y - t r a c i n g t e c h n i q u e f o r a n a l y s i s by s o l v i n g systems of d i f f e r e n t i a l e q u a t i o n s . 1.3 S t a t i s t i c a l Approach To M u l t i p a t h P r o p a g a t i o n A very good survey was w r i t t e n by Stephansen (Ref .36) on which t h i s s e c t i o n i s based . D i f f e r e n t s t a t i s t i c a l d i s t r i b u t i o n f u n c t i o n s of r e c e i v e d s i g n a l a m p l i t u d e c h a r a c t e r i z i n g the p r o p a g a t i o n phenomena have been p r o p o s e d . The more common ones a r e the R a y l e i g h d i s t r i b u t i o n (Ref .37) which assumes l a r g e number of independent s i g n a l components, and the Rice-Nakagami d i s t r i b u t i o n ( R e f s . 3 7 , 3 8 ) which assumes a c o n s t a n t s i g n a l t o g e t h e r w i t h a R a y l e i g h d i s t r i b u t e d random s i g n a l . M o r e o v e r , m u l t i p a t h f a d i n g p r o b a b i l i t y e x p r e s s i o n s have a l s o been proposed by v a r i o u s i n v e s t i g a t o r s ( R e f s . 2 4 , 3 9 - 4 2 ) which were g e n e r a l i z e d i n the CCIR r e p o r t (Ref .43 ) as a f u n c t i o n of c l i m a t i c c o n d i t i o n , t e r r a i n roughness , c a r r i e r f r e q u e n c y , p a t h l e n g t h and fade depth as d e t a i l e d i n Chapter I V . F u r t h e r m o r e , Wheeler (Ref .44) at tempted to harmonize the d i f f e r e n c e s of v a r i o u s s e t s of da ta c o l l e c t e d from v a r i o u s p l a c e s by i n t r o d u c i n g a p a t h c l e a r a n c e f a c t o r . Other than the m u l t i p a t h f a d i n g p r o b a b i l i t y , o ther q u a n t i t i e s l i k e the average fade d u r a t i o n , the number of f a d i n g events and the r a t e of change of s i g n a l l e v e l ( R e f s . 1 9 , 2 4 , 4 0 , 4 5 - 5 0 ) are a l s o important to d e s i g n e n g i n e e r s . 17 M u l t i p a t h p r o p a g a t i o n has d i f f e r e n t impacts on d i f f e r e n t modula t ion schemes. For analogue frequency m o d u l a t i o n , the major concern i s the drop of the s i g n a l to no i se r a t i o . The i n t e r m o d u l a t i o n n o i s e i s i n s i g n i f i c a n t for paths s h o r t e r than 100km and w i t h bandwidth l e s s than 12MHz ( R e f . 5 1 ) . For d i g i t a l m o d u l a t i o n , the i n - b a n d a m p l i t u d e and phase d i s t o r t i o n s have most s e r i o u s e f f e c t s . ~ The f e a s i b i l i t y of d i f f e r e n t d i g i t a l modu la t ion schemes has been e v a l u a t e d ( R e f s . 5 2 , 5 3 ) . I t i s found t h a t the s i g n a l a m p l i t u d e s l o p e p r o v i d e s a much b e t t e r measure f o r the BER than the average s i g n a l power l e v e l can p r o v i d e ( R e f s . 5 4 - 5 9 ) . For the convenience of e s t i m a t i n g the BER's for d i f f e r e n t d i g i t a l l i n k s , s i m p l i f i e d s t a t i s t i c a l models were p r o p o s e d . E q . 1 . 1 i s used in these models by assuming reasonab le parameter v a l u e s . The s i m p l e s t of a l l these models i s a two-ray model ( R e f s . 3 1 , 3 2 , 6 0 - 6 3 ) . More s o p h i s t i c a t e d than t h i s i s a t h r e e - r a y model (Ref s .64 -69 ) based on the s i m p l i f i e d t r a n s f e r f u n c t i o n H( f ) = a { l - b - e x p [ - j 2 7 r ( f - f o ) 8 r ] } where, a : the s c a l e parameter b : the shape parameter fo : the f requency of the minimum s i g n a l l e v e l f : the frequency i n q u e s t i o n 6r : the r e l a t i v e d e l a y of the r e f r a c t e d ray w . r . t . the d i r e c t r a y . 18 There i s another model which i s , i n f a c t , a s e r i e s expans ion of E q . 1 . 1 ( R e f s . 6 9 , 7 0 ) . I t was r e p o r t e d t h a t the f i r s t order expans ion i s good enough f o r a p p l i c a t i o n when the o p e r a t i n g frequency i s below 15GHz. 2. OTHER REFRACTIVITY-RELATED PHENOMENA 2.1 O b s t r u c t i o n F a d i n g O b s t r u c t i o n f a d i n g , or e a r t h bulge f a d i n g , o c c u r s when the s i g n a l i s t r a n s m i t t e d through a s u b r e f r a c t i v e t r o p o s p h e r e i n a low c l e a r a n c e p a t h . As a r e s u l t , the s i g n a l p a t h i s b l o c k e d by the ground and o n l y the d i f f r a c t e d wave can r e a c h the r e c e i v e r . T h i s w i l l p r o d u c e , at the r e c e i v i n g end , a g e n e r a l power l e v e l d e p r e s s i o n of about 1OdB below the f r e e space l e v e l . S u b r e f r a c t i v e c o n d i t i o n i s u s u a l l y a s s o c i a t e d w i t h c o l d fog (Ref .12) and l a r g e s c a l e a d v e c t i o n of mois t a i r ( R e f . 7 1 ) . 2.2 D u c t i n g D u c t i n g o c c u r s when radiowave i s t r a p p e d i n a t r o p o s p h e r i c waveguide , which can be e l e v a t e d or ground b a s e d . The t r o p o s p h e r i c waveguide i s bounded above by r e f r a c t i v e l a y e r and bounded below e i t h e r by g r o u n d , water or by a i r l a y e r w i t h l e s s n e g a t i v e r e f r a c t i v i t y g r a d i e n t . S i g n a l enhancement up to 20dB or more above f ree space l e v e l (Ref .12) i s o f t en a s s o c i a t e d wi th d u c t i n g . Low l o s s i n l o n g d i s t a n c e d u c t i n g p r o p a g a t i o n o f t en l e a d s to c o - c h a n n e l i n t e r f e r e n c e . 19 2.3 B l a c k o u t F a d i n g B l a c k o u t f a d i n g o c c u r s when the s i g n a l t r a j e c t o r y bends toward the e a r t h under extreme s u p e r r e f r a c t i v e c o n d i t i o n (about -470Nu/km) so tha t the r e c e i v e r cannot be i l l u m i n a t e d by the s i g n a l . Such extreme s u p e r r e f r a c t i v e c o n d i t i o n may be produced i n the presence of warm water a n d / o r steam fog beneath the p a t h . Severe f a d i n g of 40dB or more can l a s t up to 24 hours ( R e f . 1 2 ) . 3. NON-REFRACTTVITY-RELATED PHENOMENA 3.1 R a i n A t t e n u a t i o n R a i n a t t e n u a t i o n , which i s due to a b s o r p t i o n and s c a t t e r i n g of s i g n a l power by r a i n d r o p s w i t h r a d i i from 0.05cm to 0.7cm, i s most pronounced above 10GHz. The a t t e n u a t i o n i n c r e a s e s w i t h f requency and r a i n r a t e ( R e f . 7 2 ) . V e r t i c a l p o l a r i z a t i o n seems to be l e s s s u s c e p t i b l e to r a i n a t t e n u a t i o n ( R e f . 7 3 ) . 3.2 Fog A t t e n u a t i o n Fog a t t e n u a t i o n i s due to a b s o r p t i o n of s i g n a l power by p a r t i c l e s w i t h r a d i i s m a l l e r than 0.01cm. The a t t e n u a t i o n i n c r e a s e s w i t h frequency and decreases w i t h temperature ( R e f s . 7 4 , 7 5 ) . 3.3 Snow A t t e n u a t i o n And M e l t i n g - l a y e r F a d i n g Dry snow has l i t t l e e f f e c t on microwave at 10GHz or below d e s p i t e the s n o w f a l l r a t e ( R e f . 7 6 ) . However, the a t t e n u a t i o n due to wet snow i s h i g h . In f a c t , when snowflakes f a l l through a m e l t i n g l a y e r , the s c a t t e r i n g of s i g n a l power due to m e l t i n g snow causes e x c e s s i v e a t t e n u a t i o n , which i s 6 to 15 t imes of t h a t p r e d i c t e d by r a i n model ( R e f . 7 7 ) . The e x c e s s i v e a t t e n u a t i o n i s most pronounced at 4 to 7GHz. 20 3.4 Gaseous A b s o r p t i o n s The maximum a b s o r p t i o n of s i g n a l power due to water vapour occurs at 22, 183 and 323GHz wheras t h a t due to oxygen occurs at 60 and 119GHz. These a b s o r p t i o n s , which decrease w i t h h e i g h t , a r e caused by the i n t e r a c t i o n s between the e l e c t r o m a g n e t i c wave and the e l e c t r i c d i p o l e s i n water vapour m o l e c u l e s as w e l l as the magnetic moments of oxygen molecu le s ( R e f . 7 5 ) . 4. THE LAYOUT OF THE THESIS The sequence of the c h a p t e r s i s as f o l l o w s : Chapter I i s an i n t r o d u c t i o n to the s u b j e c t o f m u l t i p a t h p r o p a g a t i o n and the r a t i o n a l e f o r c o n d u c t i n g t h i s r e s e a r c h p r o j e c t . C h a p t e r II g i v e s a survey of the f i v e main t o p o g r a p h i c - c l i m a t i c r e g i o n s of the P r o v i n c e of B . C . Chapter I II shows d i f f e r e n t da ta a c q u i s i t i o n methods used and the method of c h a r t e s t i m a t i o n which h e l p s to improve the a c c u r a c y i n c h a r t data a n a l y s i s . Chapter IV p r e s e n t s the o b s e r v a t i o n s i n terms of p r o b a b i l i t y of f a d i n g , the number of f a d e s , the average fade d u r a t i o n , the monthly v a r i a t i o n and the d i u r n a l v a r i a t i o n of m u l t i p a t h f a d i n g . Chapter V shows the dominant mechanisms of r e f r a c t i v e l a y e r f o r m a t i o n i n d i f f e r e n t t o p o g r a p h i c - c l i m a t i c r e g i o n s . Some i n t e r e s t i n g phenomena o b s e r v e d , o t h e r than r e f r a c t i v e m u l t i p a t h f a d i n g , a r e i n c l u d e d i n Chapter V I . Chapter VII i s a c o n c l u s i o n and summary of the r e s u l t s of t h i s a n a l y s i s w i t h some sugges t ions for f u t u r e r e s e a r c h d i r e c t i o n s . Appendix A shows the path p r o f i l e s and ray t r a j e c t o r i e s under v a r i o u s r e f r a c t i v i t y c o n d i t i o n s . Appendix B g i v e s d e t a i l s of r e f r a c t i v i t y g r a d i e n t c a l c u l a t i o n u s i n g 21 rad iosonde d a t a . F i n a l l y , Appendices C , D & E are p r e s e n t i n g the h i g h l i g h t s of R u t h r o f f ' s model , the CNR model and W e b s t e r ' s model , r e s p e c t i v e l y . 22 I I . REGIONS AND MICROWAVE LINKS CONSIDERED 1. THE TOPOGRAPHIC-CLIMATIC REGIONS OF B . C . The topography of B . C . i s d i f f e r e n t from those of the o ther Canadian p r o v i n c e s . I t i s c h a r a c t e r i z e d by mountain ranges r u n n i n g from n o r t h to s o u t h . F u r t h e r m o r e , because the P r o v i n c e i s s i t u a t e d on the east coas t of the P a c i f i c Ocean, the c l i m a t e i s ma in ly governed by the eastward f l o w i n g a i r from the P a c i f i c . Most of the p r e c i p i t a t i o n f a l l s on the western s l o p e s of the mountain ranges l e a v i n g d r i e r weather on the o ther s i d e ' ( R e f s . 7 8 , 7 9 ) . PHYSIOGRAPHIC REGIONS 3000 2700 2400 2100 1800 1500 (0 0) « e o n > o Ui COAST MOUNTAINS AND ISLANDS V i c t o r i a A i r p o r t V a n c o u v e r A i r p o r t T o f i n o A i r p o r t Comox A i r p o r t P o r t H a r d y A i r p o r t B e l l a C o o l a S a n d s p i t A i r p o r t P r i n c e R u p e r t NORTH-NORTHERN AND CENTRAL PLATEAUS AND MOUNTAINS Smi t h e r s CDA Germansen L a n d i n g Dease L a k e A t l i n SOUTH-INTERIOR PLATEAU S u m n e r l a n d K a m l o o p s A i r p o r t W i l l i a m s L a k e A i r p o r t P r i n c e G e o r g e A i r p o r t NORTH-THE GREAT PLAINS F o r t S t . J o h n A i r p o r t F o r t N e l s o n A i r p o r t SOUTH-COLUMBIA MOUNTAINS AND SOUTHERN ROCKY MNTS. G r a n d F o r k s C r a n b r o o k A i r p o r t R e v e l s t o k e V a l e m o u n t 127° 126° 125" 124° 123' 121° 120° 119° 118° 117° 1 l e - ns0 F i g u r e 1 - C r o s s - s e c t i o n of t o p o g r a p h i c - c l i m a t i c r e g i o n s i n southern B . C . 23 In w i n t e r , h e a v i e r r a i n and s n o w f a l l s occur because of the passage of the f requent P a c i f i c s t o r m s . Moreover , there i s a secondary a i r flow o r i g i n a t i n g from the A r c t i c . T h i s a i r flow i s much c o l d e r and d r i e r a n d , t h e r e f o r e , l e a d s to o c c a s i o n a l l ong p e r i o d s of c o l d and dry d a y s . In summer, there are fewer f r o n t s moving a c r o s s the P r o v i n c e because the west to east upper a i r flow i s weakened and t h e r e i s a p e r s i s t e n t h i g h p r e s s u r e r e g i o n o f f the c o a s t . C o n s e q u e n t l y , the summer i n the P r o v i n c e i s u s u a l l y d r i e r . Owing to the h i g h l y mountainous topography i n the P r o v i n c e , t h e r e are many s m a l l l o c a l c l i m a t i c r e g i o n s . B u t , e s s e n t i a l l y , one can d i v i d e B . C . i n t o f i v e main t o p o g r a p h i c - c l i m a t i c r e g i o n s ( F i g u r e s 1 , 2 ) 1 as f o l l o w s : 1.1 The C o a s t a l Mountains And I s l a n d s T h i s r e g i o n i s c h a r a c t e r i z e d by heavy p r e c i p i t a t i o n , mos t ly i n autumn and w i n t e r , m i l d w i n t e r s and c o m p a r a t i v e l y c o o l summers. B e s i d e s , there i s not much s u n s h i n e , and long p e r i o d s of n o n - f r e e z i n g temperature are common. The l eeward s i d e of Vancouver I s l a n d , where V i c t o r i a and Vancouver a r e s i t u a t e d , i s more p r o t e c t e d from the P a c i f i c a i r f low, and ye t there i s s t i l l a c o n s i d e r a b l e amount of p r e c i p i t a t i o n . I t has r e l a t i v e l y more sunshine and g r e a t e r s e a s o n a l v a r i a t i o n than the windward s i d e of the r e g i o n . 1 F i g u r e 1 i s r eproduced from R e f . 7 8 . 2 4 1 C O S T A L M T N S . & I S L A N D S 2 I N T E R I O R P L A T E A U 3 C O L U M B I A M T N S . & S O U T H E R N R O C K I E S F i g u r e 2 - D i s t r i b u t i o n of microwave l i n k s i n v e s t i g a t e d 25 1.2 The I n t e r i o r P l a t e a u S i n c e most of the p r e c i p i t a t i o n o c c u r s i n the c o a s t a l r e g i o n , the a i r p a s s i n g t hrough the mountain b a r r i e r s e n t e r i n g the I n t e r i o r P l a t e a u r e g i o n i s much d r i e r . F u r t h e r m o r e , g r e a t e r s easona l and d i u r n a l v a r i a t i o n s can be o b s e r v e d . Summers are warmer and d r i e r wh i l e w i n t e r s are c o l d e r and l e s s m o i s t . The n o r t h e r n p a r t of the r e g i o n , where P r i n c e George i s s i t u a t e d , t ends to be c o l d e r and wetter than the southern p a r t , e s p e c i a l l y i n w i n t e r . The amount of p r e c i p i t a t i o n i s q u i t e e v e n l y d i s t r i b u t e d throughout the year i n the I n t e r i o r P l a t e a u r e g i o n . 1.3 The Co lumbia Mountains And Southern R o c k i e s There a r e three mountain ranges i n t h i s r e g i o n , namely, the Monashee, the S e l k i r k and the P u r c e l l M o u n t a i n s . The a i r flow from the west b r i n g s p r e c i p i t a t i o n and c o l d temperature to the windward s l o p e s l e a v i n g the v a l l e y bottoms between the mountains s e m i - a r i d w i t h warmer summers and c o l d e r w i n t e r s . Most of the p r e c i p i t a t i o n o c c u r s i n w i n t e r . 1.4 The N o r t h e r n And C e n t r a l P l a t e a u And Mountains Due to the more f r e q u e n t i n f l u e n c e by the A r c t i c a i r flow than by the P a c i f i c moist a i r , t h i s r e g i o n has c o l d e r and d r i e r weather b o t h i n the summer and winter months when compared wi th the p r e v i o u s r e g i o n s . A g a i n , l i g h t p r e c i p i t a t i o n i s to be expected on . t h e western s l o p e s of the mountain ranges such as the Skeena, the Omineca and the Rocky M o u n t a i n s . The p r e c i p i t a t i o n d i s t r i b u t i o n i s even throughout the y e a r . 2 6 T a b l e I I - S a l i e n t f e a t u r e s o f l i n k s m e a s u r e d CLIMATIC REGION LINK LABEL SITE TX RX ANT.HT.(m) TX RX FREQ.(GHz) PATH LEN.(Km) TER.ROUGH. (m)+ MN.SLOPE (mrad) COVERAGE & TERRAIN DATA COLL. PERIOD REC. TYPE THE COASTAL MOUNTAINS & ISLANDS A Big Sicker 48° 51' 38" N 123° 45' 20" W Vancouver 49° 16' 52" N 123° 07' 02" W 740 105 4.2 66.1 428 (96) 9.6 60% water 40% trees Jul 79 Oct 79 CHT CST B Vancouver 49° 16' 52" N 123° 07' 02" W Big Sicker 48° 51' 38" N 123° 45' 20" W 99 740 8.2 66.1 428 (96) 9.6 60% water 40% trees Jul 80 Oct 80 CHT CST C Hope 49° 24' 35" N 121° 33' 28" W Chilllwack 49° 06' 52" N 121° 54' 07" W 1489 282 7.8 41.4 719 (313) 29.2 50% f i e l d s 50% trees on mtns. Feb 81 Oct 82 CHT D Blackwall 49° 06* 05" N 120° 45' 25" W Hope 49° 24' 35" N 121° 33' 28" W 2028 1474 3.8 67.6 705 (408) 8.2 trees on mtns. Feb 81 May 82 CHT THD THE INTERIOR PLATEAU (NORTH) E F i r t h 54° 48' 45" N 122° 46' 11" W Tabor 53° 54' 44" N 122° 27' 01" W 1050 1253 7.5 102.3 415 (95) 2.0 trees on r e l . f l a t t e r r a i n Jul 81 Oct 82 CHT THD F McEwan 54° 24' 11" N 122° 29' 45" W Tabor 53° 54' 44" N 122° 27' 01" W 1124 1262 3.8 45.7 463 (134) 2.4 trees on r e l . f l a t t e r r a i n Jul 81 Oct 82 CHT G Hixon 53° 28' 43" N 122° 38' 00" W Tabor 53° 54* 44" N 122° 27' 01" W 843 1306 3.9 49.8 223 (133) 9.3 trees on r e l . f l a t t e r r a i n Jul 81 Oct 82 CHT H Prince George 53° 54' 54" N 122° 44' 52" W Tabor 53° 54' 44" N 122° 27' 01" W 580 1274 11.5 19.6 229 (139) 35.9 trees on r e l . f l a t t e r r a i n Jul 81 Oct 82 CHT I Cluculz 53° 54' 15" N 123° 27' 25" W Fraser 54° 01' 51" N 124° 37' 21" W 955 1160 7.2 & 7.5 (Ch.l) (Ch.2) 77.8 303 (72) 2.6 trees on r e l . f l a t t e r r a i n Apr 80 May 81 CHT high r e s o l . THE COLUMBIA MOUNTAINS & SOUTHERN ROCKIES J Creston 49° 05' 35" N 116° 22' 45" W Salmo 49° 04' 18" N 117° 04" 56" W 2133 2179 4.1 51.4 1029 (541) 0.4 trees on mtns. Feb 82 Oct 82 CHT K Rossland 49° 05' 35" N 117° 47' 50" W Salmo 49° 04' 18" N 117° 04' 56" w 1280 2172 6.9 52.3 696 (415) 17.2 trees on mtns. Feb 82 Oct 82 CHT L Santa Rosa 49° 01' 27" N 118° 03' 31" W Salmo 49° 04' 18" N 117° 04' 56" W 1715 2182 4.1 71.6 878 (352) 6.6 trees on mtns. Feb 82 Oct 82 CHT THD +The figure without bracket i s the te r r a i n roughness defined as the standard deviation of te r r a i n elevation at 1 Km intervals about the mean slope of the path (excluding terminals) whereas the figure with brackets i s the terrain roughness defined as the standard deviation of te r r a i n elevations at 1 Km i n t e r v a l (excluding terminals) which w i l l be used i n the Extended Barnett parameters mentioned l a t e r (Ref.43). Quadrature p a r t i a l response s i g n a l l i n g (QPRS) modulation was used i n lin k s B,C, and FM modulation was used i n a l l other l i n k s . 1.5 T h e G r e a t P l a i n s T h i s r e g i o n i s p a r t o f t h e p l a i n e x t e n d i n g f r o m A l b e r t a t o M a n i t o b a . T h e m o u n t a i n s on t h e w e s t o f t h e r e g i o n b a r s o f f t h e P a c i f i c a i r f l o w a n d h e n c e c o n t i n e n t a l c l i m a t e s h o u l d be e x p e c t e d . C o n t i n e n t a l c l i m a t e i s c h a r a c t e r i z e d b y l o n g c o l d w i n t e r s a n d s h o r t warm s u m m e r s , much s u n s h i n e , b i g s e a s o n a l a n d 27 d i u r n a l temperature v a r i a t i o n s w i th p r e c i p i t a t i o n most ly o c c u r r i n g i n summer. 2. MICROWAVE LINKS CONSIDERED Out of the f i v e main t o p o g r a p h i c - c l i m a t i c r e g i o n s , about 90% of the microwave l i n k s i n B . C . a r e d i s t r i b u t e d i n t h r e e of them. -They are the C o a s t a l Mountains and I s l a n d s r e g i o n , the I n t e r i o r P l a t e a u r e g i o n , and the Columbia Mountains and Southern R o c k i e s r e g i o n . Data a c q u i s i t i o n systems were se t up on some of the e x i s t i n g l i n k s i n these r e g i o n s i n order to s tudy p r o p a g a t i o n phenomena. The g e o g r a p h i c a l d i s t r i b u t i o n of the l i n k s i n v e s t i g a t e d and t h e i r s a l i e n t f e a t u r e s are shown i n F i g u r e 2 and T a b l e I I , r e s p e c t i v e l y . Moreover , the p a t h p r o f i l e s showing ray t r a j e c t o r i e s under d i f f e r e n t r e f r a c t i v i t y c o n d i t i o n s are g i v e n i n Appendix A. 28 I I I . DATA ACQUISITION 1. TYPES OF RECORD The data r e p o r t e d are d e r i v e d from r e c o r d i n g s of the automat ic g a i n c o n t r o l s i g n a l ( A G O . The i n f o r m a t i o n o b t a i n e d c o n s i s t s of the t ime below a g i v e n fade depth ( r e l a t i v e to f r e e - s p a c e ) , the number of o c c u r r e n c e s and the time of day of m u l t i p a t h f a d i n g . Three data a c q u i s i t i o n methods have been used (Table I I ) . The one w i t h the best t ime r e s o l u t i o n (0.1 second) used magnetic tape c a s s e t t e s (CST) and computer r e c o n s t r u c t i o n of the d a t a . The second method used a v o l t a g e t h r e s h o l d d e t e c t o r (THD) w i t h four p r e - s e t t h r e s h o l d s and had a time r e s o l u t i o n of 1 second. The t h i r d method was by c h a r t r e c o r d i n g (CHT) and had a time r e s o l u t i o n of about 10 seconds except f o r l i n k I (h igh r e s o l u t i o n c h a r t ) . A l t h o u g h the a n a l y s i s of the data o b t a i n e d by the c h a r t r e c o r d i n g method was l a b o r i o u s , i t was c o n s i d e r e d i n v a l u a b l e i n d i s t i n g u i s h i n g f a d i n g c o n d i t i o n s from o ther e v e n t s . In o r d e r to o b t a i n the bes t p o s s i b l e a c c u r a c y from the c h a r t r e c o r d i n g s , however, a comparison was made w i t h the data c o l l e c t e d by a t h r e s h o l d d e t e c t o r as d e t a i l e d in the next s e c t i o n . The r e s u l t of t h i s comparison was u t i l i z e d i n the a n a l y s i s of l i n k s C , F , G , H , J , K . I t was a l s o p a r t i a l l y u t i l i z e d f o r l i n k E , as p a r t of the worst month t h r e s h o l d d e t e c t o r data of t h i s l i n k was l o s t . 29 2. CHART ESTIMATION Many of the c h a r t r e c o r d i n g s had low r e s o l u t i o n but p r e s e n t e d no problem i n a n a l y s i s of slow f a d i n g events where the down-stroke and u p - s t r o k e on the c h a r t are s e p a r a t e d by 1/2 mm which c o r r e s p o n d s to 1 m i n u t e . However, t h i s i s not the case f o r r a p i d m u l t i p a t h f a d i n g where one or more events are so c l o s e t o g e t h e r t h a t they appear as one v e r t i c a l l i n e . In such c a s e s , we e s t i m a t e d the d u r a t i o n by measuring the width of the l i n e and t h e n , d i v i d i n g t h i s width by an " E s t i m a t o r " . The E s t i m a t o r s c o r r e s p o n d i n g to d i f f e r e n t widths a r e shown i n T a b l e I I I . T a b l e I I I - E s t i m a t o r MEASURED (MIN.) ESTIMATOR 1 / 4 9 1 / 2 5 1 - 2 4 >3 3 The E s t i m a t o r s were o b t a i n e d by comparing the c h a r t and the t h r e s h o l d d e t e c t o r d a t a of l i n k E between 10th J u l y ' 8 1 and 11th A u g u s t ' 8 1 . The number of fade events c o r r e s p o n d i n g to one l i n e i s e s t i m a t e d to be 3. T h i s was a l s o o b t a i n e d from the comparison ment ioned . The exact and e s t i m a t e d da ta are shown i n T a b l e I V . From the E x a c t / E s t i m a t e d r a t i o (Tab le IV) f o r fade d u r a t i o n and hence f o r the p r o b a b i l i t y of m u l t i p a t h f a d i n g , the e r r o r i s e s t i m a t e d t o be from 0 . 5 t o 2 . 0 . The e r r o r bar i n F i g u r e 3 i s , 3 0 t h e r e f o r e , set a c c o r d i n g l y . T a b l e IV - Comparison of Exact and E s t i m a t e d data FADE DURATION ( S E C . ) NO. OF EVENTS FADE EXACT EXACT DEPTH PERIOD EXACT E S T I M . E S T I M . EXACT E S T I M . E S T I M . (dB) 2319 1125 2 . 0 6 214 132 1 . 6 2 - 1 8 1 0 t h J u l 8 2 -273 460 0 . 5 9 30 66 0 . 4 5 - 2 3 1 1 t h Aug 82 132 196 0 . 6 7 25 48 0 . 5 2 - 2 8 22 26 0 . 8 5 14 27 0 . 5 2 - 3 8 9 0 0 1335 0 . 6 7 143 189 0 . 7 6 - 1 5 22nd Sep 8 2 -301 530 0 . 5 7 74 105 0 . 7 0 - 2 0 2 7 t h Sep 82 31 I V . OBSERVATIONS AND ANALYSIS 1. PROBABILITY OF FADING D i f f e r e n t i n v e s t i g a t o r s ( R e f s . 2 4 , 3 9 - 4 2 ) have proposed d i f f e r e n t parameters f o r the CCIR formula f o r v a r i o u s t o p o g r a p h i c - c l i m a t i c r e g i o n s as shown i n T a b l e V reproduced from R e f . 4 3 . T h i s formula shown as E q . 4 . 1 , g i v e s the o v e r a l l p r o b a b i l i t y of t r o p o s p h e r i c f a d i n g on paths wi thout s i g n i f i c a n t r e f l e c t i o n s . W B C Pr(W) = Pm«K.Q - f «d (4 .1) Wo where, Pr (W): the o v e r a l l p r o b a b i l i t y of f a d i n g a t power l e v e l W Pm : the p r o b a b i l i t y tha t deep f a d i n g o c c u r s K : the c l i m a t i c f a c t o r Q : the t e r r a i n f a c t o r Wo : the f r e e - s p a c e power l e v e l f : the c a r r i e r frequency (GHz) d : the path l e n g t h (km) B , C : s u i t a b l e exponents . Attempt . has been made to draw from data c o l l e c t e d between J u l y ' 7 9 and O c t o b e r ' 8 2 the parameters a p p l i c a b l e to B . C . for the CCIR f o r m u l a . A summary of data i s g i v e n i n T a b l e VI which shows the worst c a l e n d a r month of m u l t i p a t h f a d i n g p r o b a b i l i t y v e r s u s fade d e p t h . The worst c a l e n d a r month i s de termined u s i n g a -15dB t h r e s h o l d f o r a l l l i n k s except A & B . F o r l i n k s A & B, a -20dB 3 2 T a b l e V - Comparison of parameters f o r E q . 4 . 1 Proposed f o r Japan* NW Europe United Kingdom United States USSR Reference M o r i t a , 1970, Blomqu-ist,1978 Doble, 1979 B a r n e t t , 1972 Nadenen-ko,1980 B 1.2 1.0 0.85 1.0 1 .5 C 3.5 3.5 3.5 3.0 2.0 Pm.K.Q f o r mari-time temperate mediterranean, c o a s t a l or hi g h -humidity-and-temperature c l i m a t i c regions -5 4.1x10 1.3 s , -5 2x10 Pm.K.Q f o r mari-time s u b t r o p i c a l c l i m a t i c regions -5 3.1x10 1 .3 s , Pm.K.Q f o r con-t i n e n t a l tem-perate c l i m a t e s or m i d - l a t i t u d e i n l a n d c l i m a t i c r egions w i t h average r o l l i n g t e r r a i n -9 10 -8 1 .4x10 -7 8.1x10 1 .4 s 2 to -6 4.1x10 1 .4 s 2 -5 2.1x10 1 .3 s , -6 4.1x10 Pm.K.Q f o r tem-perate c l i m a t e s , c o a s t a l regions w i t h f a i r l y f l a t t e r r a i n -8 9.9x10 •/h,+h2 -5 2.3x10 to -5 4.9x10 Pm.K.Q f o r high dry mountainous c l i m a t i c regions -10 3.9x10 -5 10 1.3 s , Pm.K.Q f o r tem-perate c l i m a t e s , i n l a n d regions with f a i r l y f l a t t e r r a i n -6 7.6x10 to -5 2x10 * The Japanese data a p p l i e s f o r the worst season. Note. - h, and h 2 are antenna h e i g h t s i n metres. S~J i s the t e r r a i n roughness measured i n metres by the standard d e v i a t i o n of t e r r a i n e l e v a t i o n s a t 1km i n t e r v a l s , 6m £ S, £ 42m. The height of the r a d i o s i t e s has t o be excluded. S 2 i s d e f i n e d as the rms value of the slopes ( i n m i l l i - r a d i a n s ) measured between p o i n t s separated by 1km along the path, but ex c l u d i n g the f i r s t and the l a s t complete km i n t e r v a l , 1 < S 2 < 80. I t i s p o s s i b l e t h a t some of these parameters may be d i s t o r t e d by the i n c l u s i o n of data from paths which experience surface r e f l e c t i o n problems and/or d i f f r a c t i o n f a d i n g . 33 T a b l e VI - Worst month f a d i n g p r o b a b i l i t y v s . fade depth L I N K FADE PROB. - 1 0 - 1 5 ( X I O - 6 ) V S . FADE DEPTH ( d B ) - 2 0 - 2 5 - 3 0 - 3 5 - 4 0 WORST MONTH A 961 155 15 O c t 79 B 3 5 2 78 21 4 0 . 7 J u l 80 C 45 12 2 2 J u l 82 D 38 8 Dec 81 E 1 9 7 3 490 200 19 Sep 82 F 386 77 6 Sep 82 G 515 65 11 2 0 . 7 0 . 7 Sep 82 H 409 236 45 37 11 7 J u l 82 I C h . l 7675 553 119 29 J u l 80 C h . 2 2449 548 85 29 Sep 80 J 28 9 6 6 2 F e b 82 K 59 22 6 O c t 82 L 604 105 27 9 O c t 82 t h r e s h o l d was used . F i g u r e 3 compares the r e s u l t s from the measured da ta wi th those from v a r i o u s p r e d i c t i o n s f o r the worst c a l e n d a r months. In p l o t t i n g F i g u r e 3, a s l o p e of - l O d B per decade of p r o b a b i l i t y f o r the measured data i s assumed as i n the CCIR f o r m u l a . In cases where there was a s c a t t e r of data p o i n t s , the -15dB p o i n t was p i c k e d as a r e f e r e n c e through which the - l O d B per decade l i n e was p a s s e d . The p r e d i c t e d r e s u l t s were o b t a i n e d by employing parameters proposed by B a r n e t t ( R e f s . 2 4 , 4 3 ) and M o r i t a ( R e f s . 3 9 , 4 3 ) . S i n c e the t e r r a i n roughness , as used by B a r n e t t , has an upper bound of 34 10" ** I O - 3 10" 2 10" 1 1.0 M E A S U R E D P R O B A B I L I T Y F i g u r e 3 - Worst month f a d i n g p r o b a b i l i t y - p r e d i c t e d v s . measured 42m, and t h i s i s exceeded by a l l our l i n k s , the upper bound has been i n c r e a s e d t o i n f i n i t y and the parameter thus o b t a i n e d was c a l l e d the Extended B a r n e t t parameter , as i n d i c a t e d i n the f o o t n o t e of T a b l e I I . In F i g u r e 3, i f the measured and the p r e d i c t e d p r o b a b i l i t i e s are the same, the p o i n t w i l l f a l l on the 4 5 ° . l i n e . 35 As we can see , the M o r i t a p r e d i c t i o n i s neares t to the l i n e , the Extended B a r n e t t p r e d i c t i o n i s somewhat c o n s e r v a t i v e whereas the B a r n e t t p r e d i c t i o n i s o v e r l y c o n s e r v a t i v e . E r r o r bars are a p p l i e d to the data p o i n t s of the l i n k s i n v o l v i n g c h a r t e s t i m a t i o n (Chapter I I I , S e c t i o n 2 ) . The abnormal ly heavy f a d i n g i n l i n k H was due to heavy thundershower a t t e n u a t i o n , as d i s c u s s e d i n Chapter V I , S e c t i o n 1. T a b l e VII - Number of events in the worst month v s . fade depth L I N K - 1 0 NO. OF - 1 5 EVENTS - 2 0 V S . FADE DEPTH ( d B ) - 2 5 - 3 0 - 3 5 - 4 0 A 248 84 21 B+ 117 48 16 5 C 24 9 3 3 D 3 2 E 329 173 84 10 F 74 10 3 G 63 21 6 3 3 3 I C h . l 117 37 14 7 C h . 2 57 30 16 8 J 15 3 3 3 3 K 15 6 3 L 33 6 6 5 + I n c o m p l e t e m o n t h 36 Because the p r e d i c t i o n s of Doble ( R e f . 4 1 ) , B lomquis t ( R e f . 4 0 ) , and Nadenenko (Ref .42 ) do not cover a l l the t h r e e t o p o g r a p h i c - c l i m a t i c r e g i o n s mentioned i n Chapter I I , S e c t i o n 2, t h e r e f o r e , they were not i n c l u d e d in F i g u r e 3. G e n e r a l l y s p e a k i n g , f o r the l i n k s i n the I n t e r i o r P l a t e a u r e g i o n , the Doble p r e d i c t i o n i s more c o n s e r v a t i v e than the M o r i t a p r e d i c t i o n , wheras the B lomqui s t and Nadenenko p r e d i c t i o n s are more c o n s e r v a t i v e than the B a r n e t t p r e d i c t i o n . T a b l e V I I I - Average fade d u r a t i o n in worst month v s . f a d e depth L I N K AVERAGE FADE - 1 0 - 1 5 DURATION - 2 0 ( S E C . ) - 2 5 V S . FADE DEPTH ( d B ) - 3 0 - 3 5 - 4 0 A 1 0 . 4 4 . 9 1 . 9 B+ 4 . 9 2 . 8 1 . 9 1 . 6 D 3 4 . 3 1 0 . 5 I C h . l 1 7 5 . 7 4 0 . 1 2 2 . 7 1 1 . 1 C h . 2 1 1 1 . 3 4 7 . 3 1 3 . 8 9 . 4 L 4 9 . 0 4 7 . 0 1 2 . 0 4 . 8 + I n c o m p l e t e m o n t h 2. NUMBER OF EVENTS AND AVERAGE FADE DURATION B e s i d e s i n v e s t i g a t i n g the worst month f a d i n g p r o b a b i l i t y , w e have a t tempted to deduce from our measured data (Tables V I I , V I I I ) the a p p r o p r i a t e v a l u e of a , i n E q . 4 . 2 which g i v e s the number of events and t h a t of a2 i n E q . 4 . 3 which g i v e s the average fade d u r a t i o n . E q s . 4.2 and 4.3 are g i v e n below ( R e f . 4 3 ) . 37 N* = C 1 W WO-a, 01 •f (4 .2) r w 1^2 02 L WO-J (4 .3 ) where, N* : the number of events at power l e v e l W in the worst month f : the average fade d u r a t i o n a t power l e v e l W C 1 f C 2 : the p r o p o r t i o n a l i t y c o n s t a n t s Wo : the f r e e - s p a c e power l e v e l f : the c a r r i e r f requency (GHz) a , , a 2 : the exponent parameters for power r a t i o W/Wo /3 1 r j3 2 : the exponent parameters f o r frequency f . T a b l e IX - Parameters f o r E q s . 4.2 & 4.3 L o c a t i o n a. a 2 0i 02 01+02 Ci c 2 F r a n c e 0.5 0.5 1.4 -1 0.4 - -Denmark 0.67 0.33 - - - 0.7* -U n i t e d S t a t e s 0.5 0.5 1 .32 - 0 . 5 0 0.82 5 6 . 6 / d S w i t z e r l a n d 0.41 0.59 1 .38 -1 .38 0.0 - -*Based on an assumed va lue 0! of 1.4. D i f f e r e n t v a l u e s of the parameters in E q s . 4 . 2 and 4.3 have a l s o been proposed from d i f f e r e n t c o u n t r i e s . They are t a b u l a t e d i n the CCIR r e p o r t and the t a b l e i s reproduced here (Tab le I X ) . 38 T a b l e X - The va lue d i s t r i b u t i o n of a , DATA TYPE a l 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Direct Direct Estimates Indirect 1 2 1 1 1 1 3 1 1 1 2 3 The parameter a , , can be o b t a i n e d d i r e c t l y from E q . 4 . 2 or i n d i r e c t l y from E q . 4 . 3 through the r e l a t i o n s h i p a , = 1 - a 2 . We r e f e r to data as " d i r e c t " when they are o b t a i n e d from the l i n k s i n v o l v i n g no c h a r t e s t i m a t i o n ( A , B , D , I , L ) and as " d i r e c t e s t imates" when they i n v o l v e c h a r t e s t i m a t i o n ( C , E , F , G , J , K ) and as " i n d i r e c t " when they are o b t a i n e d from f, of l i n k s ( A , B , D , I , L ) u s i n g the r e l a t i o n s h i p . The v a l u e s f o r a t c o n c e n t r a t e d i n the 0.6 s l o t ( 0 . 6 - 0 . 6 9 ) as shown i n T a b l e X f o r these d i f f e r e n t types of d a t a . I t thus seems r e a s o n a b l e to suggest tha t a , = 0.67 and hence a2 = 0.33 would be a p p r o p r i a t e f o r a p p l i c a t i o n i n B . C . These va lues are a l s o the v a l u e s a p p l i c a b l e to Denmark (Table I X ) . 3. MONTHLY VARIATION OF FADING T a b l e XI g i v e s the i n f o r m a t i o n c o n c e r n i n g monthly v a r i a t i o n of f a d i n g . I t i s observed t h a t the most a c t i v e f a d i n g months are J u l y to O c t o b e r . The y e a r - t o - y e a r f a d i n g i n f o r m a t i o n i s l a c k i n g and i t i s d i f f i c u l t to r e c o g n i z e any p a t t e r n . However, t h e r e i s a tendency f o r fades to occur i n the same p e r i o d each y e a r . Other than on l i n k s A , B and I , the y e a r l y to worst f a d i n g month f a d i n g p r o b a b i l i t y r a t i o s (Tab le XI) l i e between 1.0 and 39 T a b l e XI - Monthly v a r i a t i o n of f a d i n g and y e a r l y to worst month f a d i n g p r o b a b i l i t y r a t i o FADE PROBABILITY (X 10 _6) IN MONTHLY VARIATION LINK J F M A M J J A S 0 N D YR. YEARLY TO WORST MONTH YEAR PERIOD A 132 218 161 993 79 ? Jul 79 - Oct 79 B 352 204 246 318 80 ? Jul 80 - Oct 80 C 0 0 0 0 0 0 0 0 0 0 0.7 0 12 11 0 0 0 0 0 0 0 81 82 1.1 Oct 81 - Sep 82 D 0 0 0 0 0 0 0 15 0 0 0 0 0 0 0 40 81 82 1.4 Feb 81 - Jan 82 E 0 433 17 0 'o 21 820 287 161 213 19 1900 72 38 37 213 81 82 1.5 Nov 81 - Oct 82 F 0 0 (0) 0 0 0 6 39 0 0 0 75 0 5 0 0 81 82 1.6 Nov 81 - Oct 82 G 0 0 (0) 0 6 0 0 6 0 0 0 65 0 0 0 0 81 82 1.2 Nov 81 - Oct 82 H 0 0 (0) 0 0 0 0 243 29 6 6 0 0 12 0 0 81 82 1.1 Nov 81 - Oct 82 ICh.l 233 ' 0 0 161 32 9 21 72 572 (520) 310 284 4 0 80 81 3.8 Apr 80 - Mar 81 Ch.2 417 0 0 233 54 56 54 67 468 (520) 530 214 4 0 80 81 4.6 Apr 80 - Mar 81 J 6 0 0 0 0 0 0 0 4 62 1.7 Feb 82 - Oct 82 K 0 0 0 0 0 0 6 0 23 82 1.3 Feb 82 - Oct 82 L 0 0 0 0.8 0 11 0 0 (283) 82 1.0 Feb 82 - Oct 82 ( ) : The data within brackets were obtained by interpolation. Link C: The results exclude fading due to melting-layer conditions. Link H: A l l the fading i s probably precipitation-induced. 1.7. (We assume t h a t November to January are i n a c t i v e months f o r l i n k s J , K , L . ) T h i s seems to suggest tha t for most l i n k s , we can t a k e , c o n s e r v a t i v e l y , t h i s r a t i o to be 2 . 0 . 4. DIURNAL VARIATION OF FADING F i g u r e 4 shows the d i u r n a l v a r i a t i o n of f a d i n g . One can r e c o g n i z e two d i s t i n c t i v e p a t t e r n s . The l i n k s a c r o s s dry and r e l a t i v e l y f l a t t e r r a i n ( E , F , G , I ) have f a d i n g m o s t l y around 40 100 • Q O M cc a cu o z M Q < < Z M ac H CO H z cu > u o a ca £ D Z CU 33 H 6u O u S3 H Z Cd CJ oc w 50« Link C at -lOdB Aug-Sep 81 J u l 82 Link I at -15dB J u l 80 Link B at -20dB Jul-Oct 80 0000 0800 1600 2400 T I M E O F D A Y ( P S T H R S . ) F i g u r e 4 - D i u r n a l v a r i a t i o n of f a d i n g s u n r i s e (0000-0800) 2 as r e p r e s e n t e d by l i n k I . The l i n k s a c r o s s water (A,B) or may be even a l o n g a water body (C) have f a d i n g 2 The number between b r a c k e t s i n d i c a t e s P a c i f i c S t a n d a r d Time ( P S T ) . 41 most ly around sunset (1600-2400) as r e p r e s e n t e d by l i n k s B and C . The l i n k s a c r o s s dry and mountainous t e r r a i n ( D , J , K , L ) have no g e n e r a l p a t t e r n . 42 V . TYPES OF MULTIPATH FADING OBSERVED M u l t i p a t h f a d i n g observed may be a t t r i b u t e d to r e f l e c t i o n or r e f r a c t i o n from e l e v a t e d or ground r e f r a c t i v e l a y e r s , r e f l e c t i o n from ground, from water or from atmospher ic sheets ( s m a l l r e f r a c t i v e l a y e r s i n the a t m o s p h e r e ) . In some c a s e s , m u l t i p a t h f a d i n g i s a s s o c i a t e d w i t h fog which produces temperature i n v e r s i o n and h u m i d i t y i n v e r s i o n at the i n t e r f a c e between fog below and dry c l e a r a i r above . The c o n d i t i o n s tha t produce m u l t i p a t h f a d i n g i n v a r i o u s r e g i o n s are d i s c u s s e d below i n more d e t a i l s . F i g u r e 5 - Sea breeze 1 . COASTAL LINKS The c o a s t a l l i n k s A & B e x p e r i e n c e d frequent m u l t i p a t h f a d i n g d u r i n g the m o n i t o r i n g p e r i o d s . S ince any i n t e r f e r i n g s i g n a l due to water r e f l e c t i o n was b l o c k e d by the i n t e r v e n i n g t e r r a i n , the o c c u r r e n c e s of f a d i n g were due e x c l u s i v e l y to r e f r a c t i v e l a y e r ( s ) . The t h r e e dominant mechanisms which c o u l d r e s u l t i n a r e f r a c t i v e l a y e r are sea breeze (1300-1900), o f f s h o r e s t reaming 43 (1700-0100) and a d v e c t i o n of n o c t u r n a l l y - c o o l e d a i r (2400-0900) as d i s c u s s e d i n R e f s . 13 and 14, and summarized below. Sea breeze ( F i g u r e 5) o c c u r s d u r i n g the a f t e r n o o n a l o n g the c o a s t when the l a n d temperature i s more than a few degrees h i g h e r than t h a t of the s ea . The warmer and d r i e r a i r on l a n d ^ r i s e s wh i l e the onshore breeze b r i n g s the c o o l e r and more humid a i r from s e a , u n d e r c u t t i n g the l a n d a i r mass. Temperature i n v e r s i o n and humid i ty i n v e r s i o n w i l l then produce a r e f r a c t i v e l a y e r at the a i r mass boundary . Under f a v o u r a b l e c o n d i t i o n s , the system can p e r s i s t f or s e v e r a l d a y s . warm,dry offs h o r e „ wind 7777777777777777777777777777 F i g u r e 6 - O f f s h o r e s t reaming O f f s h o r e s t reaming ( F i g u r e 6) o c c u r s around even ing when warm and dry a i r passes from l a n d to the s l i g h t l y c o o l e r s ea . The heat i n the warm a i r i s conducted downwards to the lower a i r l a y e r in c o n t a c t w i t h the sea w h i l e the m o i s t u r e d i f f u s e s upwards from the sea s u r f a c e to the l a y e r . Hence temperature and h u m i d i t y i n v e r s i o n s e x i s t between the bottom and the upper a i r l a y e r s . A s u r f a c e duct can then be formed e x t e n d i n g some temperature and humidity in v e r s i o n s cool,moist 44 d i s t a n c e above the s e a . A d v e c t i o n of n o c t u r n a l l y - c o o l e d a i r ( F i g u r e 7) o c c u r s around s u n r i s e when the warmer sea and the c o o l e r ground set up an o f f s h o r e w ind . T h i s w i l l c a r r y the r a d i a t i o n i n v e r s i o n , and hence the r e f r a c t i v e l a y e r formed i n the l a n d a i r mass, to the . s e a . T h i s r a d i a t i o n i n v e r s i o n ( F i g u r e 10) i s e s t a b l i s h e d when the heat absorbed by the ground d u r i n g the day i s a l l o w e d to r a d i a t e to the outer space through a c l e a r sky , thus c o o l i n g the advection * r a d i a t i o n i n v e r s i o n l a y e r t r a n s p o r t e d out t o sea 77777777777777777777777777777 F i g u r e 7 - A d v e c t i o n of n o c t u r n a l l y - c o o l e d a i r a i r l a y e r near the ground w h i l e the upper a i r temperature remains a lmost unchanged. However, once a t sea , t h i s t emperature i n v e r s i o n w i l l be upset s i n c e the warmer sea q u i c k l y m o d i f i e s the temperature of the lower a i r l a y e r . From our o b s e r v a t i o n s shown i n F i g u r e 4, sea breeze and o f f s h o r e s t reaming appears to be most pronounced i n l i n k s A & B . L i n k C a l s o d i s p l a y s s i m i l a r d i u r n a l v a r i a t i o n c h a r a c t e r i s t i c s , ye t to a much l e s s e r ex tent in terms of frequency of o c c u r r e n c e and fade d e p t h . N o t i n g t h a t 50% of the t e r r a i n of l i n k C 4 5 F i g u r e 8 - The geography a l o n g l i n k C 46 c o n s i s t s of f i e l d s c l o s e to the F r a s e r R i v e r ( F i g u r e 8, T a b l e I I ) , one may expect tha t the l o c a l c l i m a t i c c o n d i t i o n s to be s i m i l a r to those of the c o a s t but on a s m a l l e r s c a l e . R a p i d f a d i n g o c c u r r e d on l i n k s A , B ( F i g u r e 9 ) . T h i s i s thought to be due to m u l t i p l e rays a s s o c i a t e d w i t h s l i g h t L i n k B 2200 2100 2000 1900 1800 1700 TIME OF DAY (PST HRS.) F i g u r e 9 - R a p i d f a d i n g on a c o a s t a l l i n k changes i n duct parameters i f a duct i s formed ( R e f . 1 4 ) . T h i s i s e s s e n t i a l l y the same as s a y i n g t h a t i t i s due to r e f l e c t i o n a n d / o r r e f r a c t i o n from one or more u n s t a b l e r e f r a c t i v e l a y e r s . Frequent s teep n e g a t i v e r e f r a c t i v i t y g r a d i e n t s e x i s t around the area where l i n k s A , B are s i t u a t e d . I t i s worth n o t i n g tha t r e f r a c t i v i t y g r a d i e n t of l e s s than -300Nu/km for 0.1% of the time has been observed a t Q u i l l a y u t e about 150km south-west of the l i n k s ( R e f . 8 0 ) . 4 7 2. PLATEAU LINKS For the I n t e r i o r P l a t e a u r e g i o n , i t appears t h a t the dominant mechanism for r e f r a c t i v e l a y e r format ion i s r a d i a t i o n i n v e r s i o n ( F i g u r e 10), as suggested i n R e f s . 13 and 14, which o c c u r s around s u n r i s e (0000-0800). R e f r a c t i v e l a y e r i n f o r m a t i o n was d e r i v e d from d a i l y (0400) rad iosonde data at P r i n c e George (15 km west of the Tabor r e c e i v e s i t e ) . C a l c u l a t i o n s of the c l e a r sky s t a b l e temperature and humidity temperature i n v e r s i o n heat l o s t by r a d i a t i o n at night c o o l e r ground  heat absorbed by ground d u r i n g daytime F i g u r e 10 - R a d i a t i o n i n v e r s i o n r e f r a c t i v i t y g r a d i e n t , i n N u n i t s per km, around the mean t e r m i n a l h e i g h t f o r the t h i r t e e n f a d i n g e v e n t s , which o c c u r r e d at the same time when the rad iosonde i n f o r m a t i o n was c o l l e c t e d , show the g r a d i e n t s to be more n e g a t i v e than -350 i n two e v e n t s , between -350 and -160 i n t h r e e e v e n t s , between -160 and -125 i n two events and between -125 and -90 i n f o u r e v e n t s . We have assumed i n t h i s a n a l y s i s , t h a t the l a y e r f o l l o w e d the g e n e r a l c o n t o u r of the p a t h t e r r a i n . I t i s noteworthy t h a t temperature i n v e r s i o n i s common i n 48 t h i s a r e a . As an example, the rad iosonde data showed that 85% of the J u l y ' 8 1 days had temperature i n v e r s i o n s a t a l t i t u d e s QQ T3 DC H O, w Q W Q < CL, - 1 5 -20 - 2 5 H -35H L i n k E 2 3 r d S e p 8 2 R a p i d f a d i n g S l o w f a d i n g 1 2 0 0 i 1 1 0 0 — I 1 0 0 0 — I — 0900 1 0 8 0 0 0700 T I M E OF D A Y ( P S T H R S . ) F i g u r e 11 - Rapid and slow f a d i n g on a p l a t e a u l i n k between 800 and 1500m. T h i s i s the range of the t r a n s m i t t e r and r e c e i v e r antenna h e i g h t s and thus m u l t i p a t h f a d i n g i s more l i k e l y to o c c u r on such d a y s . M o r e o v e r , the d i u r n a l v a r i a t i o n p a t t e r n ( F i g u r e 4) c o n f i r m s the t ime of o c c u r r e n c e of r a d i a t i o n 49 CD •D EE H P-i W Q Cd Q < - 3 5 S h a l l o w s c i n t i l l a t i o n s R a p i d d e e p f a d i n g L i n k E 2 3 r d S e p 8 2 2 1 0 0 2 0 0 0 1 9 0 0 i 1 8 0 0 1 7 0 0 1 6 0 0 T I M E OF D A Y ( P S T H R S . ) F i g u r e 12 - R a p i d deep f a d i n g and shal low s c i n t i l l a t i o n s on a p l a t e a u l i n k i n v e r s i o n . Slow m u l t i p a t h f a d i n g was sometimes observed ( F i g u r e 11) and i s thought t o be caused by r e f l e c t i o n or r e f r a c t i o n from r e l a t i v e l y s t a b l e r e f r a c t i v e l a y e r s . I t has a l s o been suggested t h a t t h i s type of slow f a d i n g i s due to d e f o c u s s i n g , and hence 50 CO H CH U Q W Q < 2300 T I M E O F D A Y ( P S T . H R S . ) F i g u r e 13 - O b s t r u c t i o n f a d i n g c o u p l e d w i t h m u l t i p a t h f a d i n g on a p l a t e a u l i n k i t i s n o n - f r e q u e n c y - s e l e c t i v e , when the l a y e r i s j u s t below the t r a n s m i t t i n g and r e c e i v i n g antennas ( R e f s . 2 7 , 2 9 , Appendix E ) . However, r a p i d ( m u l t i - r a y ) f a d i n g was more frequent and may be a t t r i b u t e d to r e f l e c t i o n a n d / o r r e f r a c t i o n from r e f r a c t i v e l a y e r s and a tmospher ic sheets above the t e r m i n a l s 51 ( F i g u r e s 11 ,12 ) . Futhermore , r a p i d s c i n t i l l a t i o n s (about 5 dB ampl i tude ) a l s o o c c u r r e d wi thout the presence of deep f a d i n g ( F i g u r e 12) . These are thought to be due to r e f l e c t i o n s from , , , temperature and c l e a r sky warm,dry humidity i n v e r s i o n s A fog cool,moist F i g u r e 14 - C l e a r sky above t r a p p e d mountain fog a t m o s p h e r i c shee t s ( R e f . 1 2 ) . S c i n t i l l a t i o n s b e g i n a t about 1000 PST and l a s t e d f o r s e v e r a l h o u r s . I t was observed t h a t temperature i n v e r s i o n a l s o s t a r t e d to break up at t h i s t i m e . F i g u r e 13 shows a g e n e r a l d e p r e s s i o n of the s i g n a l c o u p l e d w i t h m u l t i p a t h f a d i n g . D u r i n g t h i s p e r i o d , ground fog patches were o b s e r v e d . S i m i l a r o b s e r v a t i o n s were p r e v i o u s l y r e p o r t e d ( R e f . 1 2 ) . A p o s s i b l e phenomenon which c o u l d e x p l a i n t h i s type of f a d i n g i s d i s c u s s e d i n R e f . 1 4 . B r i e f l y , r a d i a t i o n fog i s formed beneath the r a d i a t i o n i n v e r s i o n (Ref .81) and d u r i n g the fog f o r m a t i o n , the water vapour i s condensed on the n u c l e i . T h i s p r o c e s s reduces or even r e v e r s e s the h u m i d i t y g r a d i e n t which c o u l d i n t u r n r e s u l t i n s u b r e f r a c t i o n and p o s s i b l y g i v e s 52 r i s e to o b s t r u c t i o n f a d i n g . The r e f r a c t i v i t y da ta taken at P r i n c e George ( F i g u r e 31) a p p r o x i m a t e l y 6 hours a f t e r the event shown i n F i g u r e 13 shows that s u b r e f r a c t i v i t y e x i s t e d . The r e f r a c t i v i t y g r a d i e n t was c a l c u l a t e d to be +67Nu/km. One can note from F i g u r e 22 tha t o b s t r u c t i o n f a d i n g w i l l occur i n l i n k E when the r e f r a c t i v i t y g r a d i e n t i s about +78Nu/km ( i . e . k=2/3) . 5 1 m x U a W Q < En 1 - i o H -15 -20 -25 -30 -35H L i n k L 14th Oct 82 2300 — I — 2200 — I — " 2100 — I — 2000 — I — 1900 1800 TIME OF DAY (PST HRS.) F i g u r e 15 - F a d i n g on a mountain l i n k i n the presence of fog 53 3. MOUNTAIN LINKS The o b s e r v a t i o n s shown in F i g u r e 3 i n d i c a t e tha t the m u l t i p a t h f a d i n g p r o b a b i l i t y f o r mountain l i n k s i s comparable to tha t for p l a t e a u l i n k s . There i s , however, no d i u r n a l v a r i a t i o n p a t t e r n (except for l i n k C ) . One of the p o s s i b l e r e f r a c t i v e l a y e r f o r m a t i o n mechanisms i n t h i s r e g i o n would be due to temperature and h u m i d i t y i n v e r s i o n s a c r o s s the i n t e r f a c e between the upper c l e a r a i r and the r a d i a t i o n fog t r a p p e d i n the v a l l e y s ( F i g u r e 14) . T h i s was the case i n at l e a s t three f a d i n g events which o c c u r r e d on l i n k s J , K and L d u r i n g O c t o b e r ' 8 2 ( F i g u r e 15). R a p i d s c i n t i l l a t i o n s were a l s o observed on the Columbia Mounta ins and Southern R o c k i e s l i n k s ( J , K , L ) . 5 4 V I . OTHER PHENOMENA OBSERVED 1. MULTI PATH-LIKE RAIN-INDUCED FADING A phenomenon, which resembles m u l t i p a t h f a d i n g ( F i g u r e 16), was observed on a very s h o r t l i n k ( l i n k H , 19.6km). Deep m u l t i p a t h - fad ing i s u n l i k e l y at 11GHz on t h i s l i n k and t h i s event was 0 n QQ T 3 ac H Cu ta a a : Q < - 1 0 - 1 5 - 2 0 - 2 5 - 3 0 - 3 5 - 4 0 - 5 0 L i n k H 1 3 t h J u l 8 2 1 8 0 0 — I — 1 7 0 0 — I 1 6 0 0 1 5 0 0 1 4 0 0 1 3 0 0 T I M E OF D A Y ( P S T H R S . ) F i g u r e 16 - M u l t i p a t h - l i k e r a i n - i n d u c e d f a d i n g c o n f i r m e d to be due to a heavy thundershower w i t h a r a i n r a t e of 59mm per h o u r . R a i n of such i n t e n s i t y occurs once every two y e a r s i n t h a t a r e a . 55 2. MELTING-LAYER FADING A l t h o u g h r e f r a c t i v e m u l t i p a t h f a d i n g i s not a problem on l i n k C , m e l t i n g - l a y e r f a d i n g poses a severe problem ( R e f s . 7 7 , 8 2 ) . The 04 0-- 1 0 -- 1 5 - V - 2 0 - L i n k C "I - 2 5 - 15th Nov 81 -30 -i 2400 2300 2200 2100 2000 1900 TIME OF DAY (PST. HRS.) F i g u r e 17 - M e l t i n g - l a y e r f a d i n g worst month f a d i n g p r o b a b i l i t y i n 1982 was 0.86% (to -15dB) and was a l l due to m e l t i n g - l a y e r c o n d i t i o n s . F i g u r e 17 shows one of the events r e c o r d e d i n 1981. I t has been suggested tha t m e l t i n g - l a y e r f a d i n g may i n v o l v e some k i n d of m u l t i p a t h f a d i n g due to m e l t i n g snow s t r a t a ( R e f . 8 2 ) . 3 . QUASI-PERIODIC SIGNAL VARIATION Sometimes, w a v e - l i k e v a r i a t i o n wi th p e r i o d of about 5 to 20 minutes can be observed on the AGC r e c o r d i n g on some l i n k s , e s p e c i a l l y the p l a t e a u l i n k s . Some of these o c c u r r e n c e s e i t h e r preceded ( F i g u r e 18) or f o l l o w e d m u l t i p a t h f a d i n g . I t has been suggested t h a t v a r i a t i o n of t h i s n a t u r e may be due to t r o p o s p h e r i c i n t e r n a l g r a v i t y wave ( R e f s . 1 7 , 2 0 , 2 1 ) . However, 56 -25 4 , 1 l I I 1 100 1000 0900 0800 0700 0600 ' TIME OF DAY (PST. HRS. ) F i g u r e 18 - Q u a s i - p e r i o d i c v a r i a t i o n p r e c e d i n g m u l t i p a t h f a d i n g t h i s type of v a r i a t i o n may a l s o be due to d e f o c u s s i n g when the r e f r a c t i v e l a y e r i s immediate ly below the t e r m i n a l s (Appendix E , S e c t i o n 4 ) . In f a c t , a c c o r d i n g to the P r i n c e George rad iosonde da ta r e c o r d e d at 0400 PST on 7th Aug . '81 ( c f . F i g u r e 18) , i t was observed tha t a l a y e r of r e f r a c t i v i t y g r a d i e n t a t -145Nu/km e x i s t e d below the t e r m i n a l s . 57 V I I . CONCLUSION 1. SUMMARY OF RESULTS S e v e r a l m u l t i p a t h f a d i n g s t a t i s t i c s for twelve microwave l i n k s i n B r i t i s h Columbia have been a n a l y z e d and p r e s e n t e d . Our c o n c l u s i o n s can be summarized as f o l l o w s : (1) The M o r i t a p a r a m e t e r s , of the CCIR formula which d e s c r i b e s m u l t i p a t h f a d i n g , are most a p p r o p r i a t e f o r a p p l i c a t i o n to microwave l i n k s i n B . C . The Extended B a r n e t t parameters a r e more c o n s e r v a t i v e and the B a r n e t t parameters are o v e r l y c o n s e r v a t i v e . (2) The exponent v a l u e s i n the e x p r e s s i o n s c o n c e r n i n g the number of f a d i n g o c c u r r e n c e s , N * , and the average fade d u r a t i o n , f , are a ^ O . 6 7 and a 2 = 0 .33 , r e s p e c t i v e l y . (3) The most a c t i v e f a d i n g p e r i o d f o r m u l t i p a t h f a d i n g i s J u l y to October and the y e a r l y to worst month f a d i n g r a t i o can be r e a s o n a b l y assumed as 2.0 f o r most l i n k s . (4) The peak of the d i u r n a l m u l t i p a t h f a d i n g f o r l i n k s o v e r , and perhaps a l o n g , a body of water i s around a f t e r n o o n and at s u n s e t . For l i n k s on p l a t e a u (or f l a t t e r r a i n ) , f requent f a d i n g s occur around s u n r i s e and f o r most mountain l i n k s , t h e r e i s no g e n e r a l p a t t e r n . 58 (5) The dominant m u l t i p a t h mechanisms are (a) sea b r e e z e , o f f s h o r e s t reaming and a d v e c t i o n of n o c t u r n a l l y - c o o l e d a i r for c o a s t a l l i n k s , (b) r a d i a t i o n i n v e r s i o n for p l a t e a u l i n k s , and (c) ,most l i k e l y , t r a p p e d r a d i a t i o n fog i n the v a l l e y s a s s o c i a t e d wi th upper , c l e a r a i r f o r mountain l i n k s . •2. DIRECTIONS OF FURTHER RESEARCH There are s e v e r a l a r e a s i n which f u r t h e r r e s e a r c h i s needed: (1) S i n c e most of the e x i s t i n g analogue l i n k s u s i n g frequency m o d u l a t i o n w i l l p r o b a b l y be c o n v e r t e d to d i g i t a l modu la t ion i n the f u t u r e , i t w i l l be an important c o n t r i b u t i o n i f means can be found to e s t i m a t e BER r e a s o n a b l y a c c u r a t e l y by use of AGC i n f o r m a t i o n . P r e s e n t l y , the i n v e s t i g a t i o n of the r e l a t i o n between BER and AGC i n f o r m a t i o n i s s t i l l at an e a r l y s t a g e . (2) I t has been suggested that the c l e a r a n c e f a c t o r (Chapter I , S e c t i o n 1.3) p o s s i b l y p l a y s an important r o l e in m u l t i p a t h f a d i n g o c c u r r e n c e s and f u r t h e r r e s e a r c h i s needed to c o n f i r m t h i s s u g g e s t i o n . (3) The 20th S e p . ' 8 2 event on l i n k E ( F i g u r e 13) may be caused by slow motion of the i n t e r f a c e between a s u p e r r e f r a c t i v e l a y e r on top and a s u b r e f r a c t i v e l a y e r beneath ( F i g u r e 31 ) . But f u r t h e r u n d e r s t a n d i n g of the mechanisms of t h i s and other types of m u l t i p a t h f a d i n g r e q u i r e s r e f r a c t i v i t y p r o f i l e data a l o n g the path of i n v e s t i g a t i o n d u r i n g the e v e n t . T h e r e f o r e , i t would be d e s i r a b l e to c o l l e c t the r e f r a c t i v i t y p r o f i l e da ta toge ther w i t h 5 9 the f a d i n g data in the f u t u r e work i f t h i s proves to be e c o n o m i c a l l y f e a s i b l e . (4) Improved a n a l y t i c a l models are needed to d e s c r i b e m u l t i p a t h f a d i n g more a c c u r a t e l y . F l a t t e n e d E a r t h C o o r d i n a t e T r a n s f o r m a t i o n shou ld be a p p l i e d to W e b s t e r ' s mode l . 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Rummler ,W.D. , 1979, A new s e l e c t i v e f a d i n g model; a p p l i c a t i o n to p r o p a g a t i o n d a t a , B S T J , v o l . 5 8 , n . 5 , pp .1037-1071 . 66. Rummler ,W.D. , 1979, E x t e n s i o n s of the m u l t i p a t h f a d i n g c h a n n e l model , I C C 79, I E E E , B o s t o n , p p . 3 2 . 2 . 1 - 3 2 . 2 . 5 . 67. L u n d g r e n , C . W . , 1979, A methodology for p r e d i c t i n g non-d i v e r s i t y outage of h i g h c a p a c i t y d i g i t a l r a d i o systems, I C C 7 9 , I E E E , B o s t o n , pp . 32 . 3 . 1-32 . 3 . 6 . 68. L u n d g r e n , C . W . and Rummler ,W.D. , 1979, D i g i t a l r a d i o due to s e l e c t i v e f a d i n g - O b s e r v a t i o n vs p r e d i c t i o n from l a b o r a t o r y s i m u l a t i o n , B S T J , v o l . 5 8 , n . 5 , pp .1073-1100 . 69. G r e e n s t e i n , L . J . , 1978, A m u l t i p a t h f a d i n g c h a n n e l model f o r t e r r e s t r i a l d i g i t a l r a d i o systems, IEEE T r a n . C o m m . , COM-26(8) , 1247-1250. 70. G r e e n s t e i n , L . J . and C z e k a j , B . A . , 1979, A s t a t i s t i c a l model f o r m u l t i p a t h f a d i n g channe l r e s p o n s e s , I C C ' 7 9 ,  I E E E , B o s t o n , p p . 3 2 . 1 . 1 - 3 2 . 1 . 5 . 71. S c h i a v o n e , J . A * , 1981, P r e d i c t i o n of p o s i t i v e r e f r a c t i v i t y g r a d i e n t s for l i n e - o f - s i g h t microwave r a d i o p a t h s , B S T J , v o l . 6 0 , n . 6 , pp .803-822 . 72. G u n n , K . L . S . and E a s t , T . W . R . , 1954, The microwave p r o p e r t i e s of p r e c i p i t a t i o n p a r t i c l e s , J . R o y . M e t e o . S o c . , v o l . 8 0 , pp .552 -545 . 73. S e m p l a k , R . A . , 1970, E f f e c t of O b l a t e r a i n d r o p s on a t t e n u a t i o n at 30 .9GHz, Radio S c . , v o l . 5 , n . 2 , pp .559-564 . 74. B e a c h , J . B . , 1979, Atmospher ic e f f e c t s on r a d i o wave p r o p a g a t i o n , P t . I , Defence E l e c t r . T e c h . , v o l . 1 1 , n . 1 2 , p p . 9 5 - 9 8 . 75. M i l l m a n , G . H . , 1971, T r o p o s p h e r i c e f f e c t s on space communicat ions , T r o p o s p h e r i c Radio^Wave P r o p a g a t i o n , P t . I ,  AGARD C o n f . P r o c . N o . 7 0 , AGARD A v i o n i c Pane l T e c h n i c a l Symposium, D u s s e l d o r f , F . R . G e r m a n y . 76. A t l a s , D . , et a l . , 1952, Weather e f f e c t s on r a d a r , G e o p h . R e s . D i r e c t o r a t e , A i r F o r c e Survey i n G e o p h y s i c s , n . 2 3 . 77. Vander S t a r , J . and K h a r a d l y , M . , 1981, Measurements of c o p o l a r a t t e n u a t i o n through the b r i g h t band at 4 & 7GHz, 66 Anna les des Telecommun. , v o l . 3 6 , n . 1 - 2 . 78. C h i l t o n , R . R . H . , 1981, A summary of c l i m a t i c regimes of  B r i t i s h C o l u m b i a , M i n i s t r y of E n v i r o n . , Assessment and P l a n n i n g D i v i s i o n . 79. M u r d o c h , D . F . , 1966, Annual temperature and p r e c i p i t a t i o n  t r e n d s i n the B r i t i s h Columbia I n t e r i o r , B . A . ( h o n . ) Graduate T h e s i s , G e o g . , U n i v . of B . C . 80. S e g a l , B . and B a r r i n g t o n , R . E . , 1977, The r a d i o c l i m a t o l o g y  of Canada - T r o p o s p h e r i c r e f r a c t i v i t y a t l a s f o r Canada, Commun. Res . C e n t r e , Dept . of Commun., Canada . 81. A n d e r s o n , B . R . , 1975, Weather i n the West, Am. West P u b l . C o . , pp .137 -143 . 82. K h a r a d l y , M . , et a l . , 1983, O b s e r v a t i o n s of abnormal microwave p r o p a g a t i o n phenomena d u r i n g m e l t i n g l a y e r c o n d i t i o n s , 3rd I n t l . C o n f . o n Ant .& P r o p . I C A P 83, Norwich , UK, 12-15 A p r i l , 1 9 8 3 . 83. F l o c k , W . L . , 1979, E l e c t r o m a g n e t i c s and the environment:  remote s e n s i n g and t e l e c o m m u n i c a t i o n , P r e n t i c e H a l l , p p . 3 2 5 . 84. R o g e r s , R . R . , 1979, A s h o r t course in C l o u d P h y s i c s , 2nd e d . , I n t ' l S e r . i n N a t . P h i l . , v o l . 9 6 , Pergamon P r e s s . 85. N e l k o n , M . and P a r k e r , P . , 1970, Advanced l e v e l P h y s i c s , 3rd e d . , Heinemann E d u c a t i o n a l Books L t d . , London . 86. N o r m a n , R . B . , 1945, N u m e r i c a l and g r a p h i c a l d a t a , Handbook  of m e t e o r o l o g y , McGraw H i l l , p p . 2 - 1 2 1 . 87. D e s c h a m p s , G . A . , 1972, Ray t echn iques in e l e c t r o m a g n e t i c s , IEEE P r o c . , v o l . 6 0 , n . 9 , pp.1022-1035. 6 7 APPENDIX A - PATH PROFILES OF LINKS INVESTIGATED A l l p a t h p r o f i l e s , except those of l i n k s D, H and K, are p r o v i d e d by B r i t i s h Columbia Telephone Company. A l though some of the antenna h e i g h t s on the p r o f i l e s are d i f f e r e n t from those quoted i n T a b l e I I , the s l i g h t d i f f e r e n c e s do not change the ray t r a j e c t o r i e s i n the p r o f i l e s s i g n i f i c a n t l y . The d e t a i l s of ray t r a j e c t o r y t r a c i n g f o r d i f f e r e n t v a l u e s of k ( e f f e c t i v e e a r t h r a d i u s f a c t o r ) are g i v e n in R e f . 8 3 . BIG SICKER ANT.15m ELEV.716m (DISTANCE IN km) F i g u r e 19 - Path p r o f i l e of l i n k s A & B 6 8 HOPE ANT.26m ELEV.1463m 1 1 I 1 1 I I ~' 0 6 12 18 24 30 36 41.36 (DISTANCE IN km) F i g u r e 20 - Path p r o f i l e of l i n k C BLACKWALL ANT.18m ELEV.2010m (DISTANCE IN km) F i g u r e 21 - Path p r o f i l e of l i n k D 69 TABOR ANT.6m ELEV.1247m (DISTANCE IN km) F i g u r e 22 - Path p r o f i l e of l i n k E TABOR ANT.9m ELEV.1247m 600 I , i i I I I 1 0 B 16 24 32 40 48 54.54 (DISTANCE IN km) F i g u r e 23 - Path p r o f i l e of l i n k F 7 0 TABOR ANT. 57m ELEV.1245m ' 680 , , , • , . 1 1 1 1 1 r-l 600 0 4 8 12 16 20 24 28 32 36 40 44 48 49.57 (DISTANCE IN km) F i g u r e 24 - Path p r o f i l e of l i n k G TABOR ANT.27m ELEV.1247m I , , , 1 500 0 5 10 15 19.55 (DISTANCE IN km) F i g u r e 25 - Path p r o f i l e of l i n k H 71 CLUCULZ ANT.27m ELEV.92Bm (DISTANCE IN km) FRASER MTN. ANT.15m ELEV.1145m 1G80 h 680 72 77.73 F i g u r e 26 - Pa th p r o f i l e of l i n k I SALMO ANT.15m ELEV.2164m 2000 A k-4/3 CRESTON ANT. 15m ELEV.2118m 16 24 32 (DISTANCE IN km) F i g u r e 27 - Pa th p r o f i l e of l i n k J 7 2 SALMO ANT.6m ELEV.2164m (DISTANCE IN km) F i g u r e 28 - Path p r o f i l e of l i n k K SANTA ROSA ANT. 14m ELEV.1701m (DISTANCE IN km) t- 1400 _ 1000 -800 71.45 F i g u r e 29 - Path p r o f i l e of l i n k L 73 APPENDIX B - SAMPLE CALCULATION OF REFRACTIVITY GRADIENT The rad iosonde data o b t a i n e d from the P a c i f i c Weather Centre in Vancouver are r e c o r d e d on tephigrams (Ref .84) as shown in F i g u r e 30. (In order to a v o i d c o n f u s i o n , o n l y i s o b a r s and i so therms are shown.) The i s o b a r s are the n e a r l y h o r i z o n t a l l i n e s and the i so therms are the l i n e s s l a n t e d at about 5 0 ° . P r i n c e George 21st Sep 82 0400 PST Dew Pt, Temp. 6 E ( A O CS) 1-1 800 Z [1949] B50 [1457] 900 .CS88] 950 [540] TEMPERATURE/DEW POINT C O F i g u r e 30 - Radiosonde data on t eph igram Atmospher ic p r e s s u r e , i n m i l l i b a r u n i t s (mb), decreases w i t h h e i g h t , and hence i t i s used as a c o r r e s p o n d i n g measure f o r a l t i t u d e . Moreover , temperature and dew p o i n t , as a form of h u m i d i t y measure, are r e c o r d e d in degree C e l c i u s ( ° C ) at d i f f e r e n t a l t i t u d e s . In order to c a l c u l a t e r e f r a c t i v i t y , E q . 1 . 2 i s u sed . N = 77 .6^ J +3 . 73x 1 0 5 | ^ — - j . (1 .2) where, N : the r e f r a c t i v i t y (Nu) P : the a tmospher ic p r e s s u r e (mb) T : the temperature ( ° K ) e : the p a r t i a l vapour p r e s s u r e (mb) . A l t h o u g h the p r e s s u r e i n f o r m a t i o n i s r e a d i l y u s a b l e , a c o n s t a n t v a l u e of 273 has to be added to a l l temperature r e a d i n g s r e c o r d e d in degree C e l c i u s for c o n v e r s i o n i n t o degree K e l v i n . S i n c e the dew p o i n t i s d e f i n e d as "the temperature at which the s a t u r a t e d vapour p r e s s u r e of water i s e q u a l to the 74 T a b l e XII - S a t u r a t e d vapour p r e s s u r e v s . temperature Temp. ( ° C ) S . V . P . (mb) Temp. ( ° C ) S . V . P . (mb) Temp. ( ° C ) S . V . P . (mb) Temp. ( ° C ) S . V . P . (mb) 20 23.37 10 12.28 0 6.105 -10 2.86 18 20.61 8 10.73 -2 5.27 "12 2.44 16 18.16 6 9.35 -4 4.54 -14 2.07 14 15.98 4 8.13 -6 3.90 -16 1 .75 12 14.03 2 7.05 -8 3.34 -18 1 .48 T a b l e XII I - Data for r e f r a c t i v i t y c a l c u l a t i o n - 0400 PST 21st S e p . ' 8 2 a t P r i n c e George h t . h(m) temp. T ( ° C ) p r e s s . P(mb) dew p t . T d ( ° C ) v a p . p r e s s . e (mb) r e f r . N(Nu) r e f r . g r a d . dN/dh(Nu/km) 674 6.0 935 6.0 9.4 305 + 44 719 7.5 930 7.5 10.4 307 + 22 809 10.0 920 10.0 12.3 309 + 67 898 13.0 910 13.0 15.0 315 + 44 943 14.0 905 14.0 16.0 317 -1 33 988 14.5 900 13.0 15.0 31 1 -128 1082 15.0 890 11.0 13.2 299 -128 1 1 29 15.5 885 10.0 12.3 293 -85 1 176 16.0 880 9.5 12.0 289 -54 1269 15.0 870 8.5 11.1 284 -53 1363 14.5 860 7.5 10.4 279 -53 1457 14.0 850 6.5 9.7 274 7 5 F i g u r e 31 - R e f r a c t i v i t y p r o f i l e - 0400 PST 21st S e p . ' 8 2 P r i n c e George 76 p a r t i a l p r e s s u r e of the water vapour p r e s e n t i n the atmosphere" ( R e f . 8 5 ) , t h e r e f o r e , the p a r t i a l vapour p r e s s u r e can r e a d i l y be o b t a i n e d from a t a b l e r e c o r d i n g s a t u r a t e d vapour p r e s s u r e ( S . V . P . ) v e r s u s temperature as shown i n R e f . 8 6 . A p o r t i o n of t h i s t a b l e i s reproduced here (Table X I I ) . A f t e r s u b s t i t u t i o n of the a p p r o p r i a t e v a l u e s for a tmospher ic p r e s s u r e , t emperature , and p a r t i a l vapour p r e s s u r e i n t o E g . 1 . 2 , i t w i l l y i e l d the r e f r a c t i v i t y at the a l t i t u d e that -those q u a n t i t i e s are measured. Hence the r e f r a c t i v i t y p r o f i l e and the r e f r a c t i v i t y g r a d i e n t s a t d i f f e r e n t h e i g h t s can be o b t a i n e d . A sample c a l c u l a t i o n i s done on the r a d i o s o n d e data r e c o r d e d at 0400 PST on 21st S e p . ' 8 2 (Table X I I I ) 3 at P r i n c e George ( 5 3 ° 53' N , 1 2 2 ° 40' W, 676.0 m) . The r e f r a c t i v i t y p r o f i l e o b t a i n e d ( F i g u r e 31) shows s u b r e f r a c t i v i t y up to +55Nu/km at lower a l t i t u d e and s u p e r r e f r a c t i v i t y up to 160Nu/km at h i g h e r a l t i t u d e . T h i s d a t a was r e c o r d e d 6 hours a f t e r the event shown i n F i g u r e 13 where o b s t r u c t i o n f a d i n g was c o u p l e d w i t h m u l t i p a t h f a d i n g . 3 I n t e r p o l a t i o n s were a p p l i e d to the v a l u e s of he ight and p a r t i a l vapour p r e s s u r e i n the c a l c u l a t i o n . 7 7 APPENDIX C ~ MAIN POINTS OF RUTHROFF'S MODEL In t h i s a p p e n d i x 4 , the e x p r e s s i o n s d e r i v e d are : (1) the phase d i f f e r e n c e between the r e f r a c t e d ray and the d i r e c t ray i n a g e n e r a l c a s e , (2) the phase d i f f e r e n c e between a r e f r a c t e d ray and the d i r e c t ray i n the worst case of i n t e r f e r e n c e ( i . e . when the two rays are n e a r l y 1 8 0 ° out of p h a s e ) , (3) the f a d i n g p r o b a b i l i t y on long paths shown as a f u n c t i o n of f ' . d 3 ( c f . B a r n e t t parameters i n T a b l e V ) , where f i s frequency and d i s pa th l e n g t h , and (4) the f a d i n g p r o b a b i l i t y on long paths d u r i n g heavy f a d i n g shown as p r o p o r t i o n a l to W/Wo ( c f . C h a p t e r I V , E q . 4 . 1 ) , the r a t i o of the f a d i n g s i g n a l power l e v e l to the f r e e - s p a c e s i g n a l power l e v e l . h REFRACTING F i g u r e 32 - R e f r a c t i o n from a s i n g l e l a y e r * A l l f i g u r e s i n t h i s append ix , except F i g u r e 34, are reproduced from R e f . 2 3 w i t h s l i g h t n o t a t i o n m o d i f i c a t i o n . 78 1. PHASE DIFFERENCE - GENERAL CASE By use of Ray T r a c i n g t e c h n i q u e ( R e f . 8 7 ) , one can show tha t the c u r v a t u r e of a r e f r a c t e d r a y , through a medium of cons tant r e f r a c t i v i t y g r a d i e n t , can be approx imated as 1 -1 =* , R d n / d h and the o p t i c a l l e n g t h of the ray p a t h i s 2n <t> = J nds ( C 1 ) X c where, n : the r e f r a c t i v e index h : the h e i g h t X : the f r e e - s p a c e wavelength c : the ray p a t h . F i g u r e 33 - S i n g l e - l a y e r r e f r a c t i o n w i t h a ray r i s i n g above the l a y e r 7 9 The r e f r a c t i v e index at d i f f e r e n t r e g i o n s , as shown i n F i g u r e 33, are n o - c o s 0 + c o s 0 , 0 , , ^ 0 < 6 n =* -f n 0-cosi/'+cos6' , e22 < * < e,, L n 0-cos7+cos? ,0 < y < 6 2 2 where, n 0 0i 0, 1 e 2 2 the r e f r a c t i v e index i n a s t a n d a r d atmosphere the ang le of d e p a r t u r e of a ray from the t r a n s m i t t e r the ang le of d e p a r t u r e of a r e f r a c t e d ray from the lower l a y e r boundary the ang le of d e p a r t u r e of a r e f r a c t e d ray from the upper l a y e r boundary . S u b s t i t u t i o n of these v a l u e s of n i n t o Eq.C1 w i l l y i e l d 2TT 4> -{2Ro[ (n 0 +cos9 , ) ( 0 , - 0 , , )-sin0,+51110, , ] +2R[ (n o +cos0 , ) ( 0 1 1 - 0 2 2 ) - s i n 0 1 1 + s i n 0 2 2 ] + 2 R o [ ( n o + c o s 0 1 ) 0 2 2 - s i n 0 2 2 ] } (C2) where, Ro : the r a d i u s of c u r v a t u r e of a ray o u t s i d e the l a y e r R : the r a d i u s of c u r v a t u r e of a r e f r a c t e d ray i n s i d e the l a y e r . Other g e o m e t r i c a l c o n s t r a i n t s y i e l d the f o l l o w i n g r e l a t i o n s : R o « s i n 0 , - ( R o - R ) ( s i n 0 , , - s i n 0 2 2 ) = L / 2 (C3) 0 < 0 2 2 < 0 , y < 6, (C4) (C5) 6h = h o - h ! = R o*cos0i1 - R o*cos0 w = h 3 - h o = R « c o s 0 2 2 - R « c o s 0 ! (C6) where, ho h , h 2 h 3 8h w the l a y e r h e i g h t the t r a n s m i t t e r h e i g h t the r e c e i v e r h e i g h t the h e i g h t of the l a y e r top the l a y e r h e i g h t r e l a t i v e t o the t e r m i n a l s the l a y e r t h i c k n e s s . In p r i n c i p l e , 0 1 f 0 1 t and 0 2 2 can be o b t a i n e d by s o l v i n g 80 E q s . C 3 , C 5 and C 6 . A f t e r s u b s t i t u t i o n of those v a l u e s i n t o E q . C 2 , i t w i l l y i e l d the r e f r a c t e d ray o p t i c a l l e n g t h , 4> . R I t i s noteworthy t h a t , i n f a c t , i f the r e f r a c t i v e l a y e r i s not f l a t , and i s assumed to f o l l o w the e a r t h ' s c u r v a t u r e , the r a y s which r i s e above the l a y e r cannot reach the r e c e i v e r . The d i r e c t ray o p t i c a l l e n g t h can be found by n o t i n g tha t - the d i r e c t ray does not en ter the l a y e r and hence 0 , , and 0 22 can be set to z e r o . B e s i d e s , 0, i s the same as a i n F i g u r e 32 which can be expressed as A f t e r s u b s t i t u t i o n of the v a l u e s f o r 0 , , 0 , , and 0 22 i n t o E q . C 2 , i t w i l l y i e l d the d i r e c t ray o p t i c a l l e n g t h shown as </> below. D <t> « L - . (C7) D X L 24Ro 2-l The phase d i f f e r e n c e ^ i n a g e n e r a l case i s , t h e r e f o r e , 0 = <t> ~<t> . R D 2. PHASE DIFFERENCE - WORST CASE OF INTERFERENCE When a r e f r a c t e d ray i s about 1 8 0 ° out of phase w i t h the d i r e c t r a y , the worst case of i n t e r f e r e n c e o c c u r s . R u t h r o f f s t a t e d wi thout p r o o f tha t t h i s i s c o r r e s p o n d i n g to the c o n d i t i o n when 0 2 2 = 0 ( i . e . when no r e f r a c t e d ray which r i s e s above the l a y e r w i l l a r r i v e a t the r e c e i v e r ) . F u r t h e r m o r e , by use of T a y l o r S e r i e s e x p a n s i o n , the f o l l o w i n g a p p r o x i m a t i o n s can be made KL 1 r KL n 3 2Ro 6 L 2Ro J 1 r KL -|2 cose?, « 1 -2 L 2Ro -J 81 L(K-1 ) 1 r L (K-1 )-, 3 ^ 1 1 - +  2(Ro-R) 6 L2(Ro-R) J where k i s d e f i n e d as 2Ro K = s i n e , , 1 < K < Ro/R . L (The c o n s t r a i n t s a r e d e r i v e d from Eq .C3 and I n e q . C 4 . ) A f t e r s u b s t i t u t i o n of 6y , 6 , , and 622 i n t o E q . C 2 , i t y i e l d s 2TT r L 3 r 2 ( K - 1 ) 3 <f> <* k + 2K 3 3K 2 . (C8) R X L 24Ro 2 L ( 1 - R / R o ) 2 J-" The phase d i f f e r e n c e , 0 , i n the worst case of i n t e r f e r e n c e , can be o b t a i n e d by s u b t r a c t i n g E q . C 7 from E q . C 8 , and hence 27T L 3 r 2 ( K - 1 ) 3 -. /3 * 2 K 3 - - 3K 2 + 1 . ( C 9 ) X 24Ro 2 L ( 1 - R / R o ) 2 J R u t h r o f f f u r t h e r a s s e r t e d t h a t the q u a n t i t y w i t h i n the square b r a c k e t s i n E q . C 9 i s a f u n c t i o n of r e f r a c t i v i t y g r a d i e n t , l a y e r h e i g h t r e l a t i v e t o the t e r m i n a l s , and l a y e r t h i c k n e s s a l o n e . Hence, 2VT L 3 0 ^ F ( d N / d h , 5 h , w ) . (C10) X 24Ro 2 3. FADING PROBABILITY - FREQUENCY AND PATH LENGTH DEPENDENCE If the r e c e i v e d s i g n a l ampl i tudes of a l l the r a y s are assumed to be n e a r l y e q u a l , t h e n , the two r a y i n t e r f e r e n c e i s much more p r o b a b l e than the three ray i n t e r f e r e n c e i n p r o d u c i n g deep m u l t i p a t h f a d i n g . Hence, the n o r m a l i z e d r e s u l t a n t r e c e i v e d s i g n a l ampl i tude f o r most of the deep fades can be expressed as E r / E o = 1 + ( E / E o ) e x p ( j/5) where, E r : the r e s u l t a n t r e c e i v e d s i g n a l a m p l i t u d e Eo : the d i r e c t ray r e c e i v e d s i g n a l a m p l i t u d e E : the r e f r a c t e d ray r e c e i v e d s i g n a l a m p l i t u d e . On long p a t h s , E / E o and 0 can be assumed to be s t a t i s t i c a l l y i n d e p e n d e n t . Then , the f a d i n g p r o b a b i l i t y of the s i g n a l below a c e r t a i n l e v e l Vo i s g i v e n as P ( | E r | / E o £ V o / E o ) = J / p , ( E / E o ) p 2 ( 0 ) d / 3 d ( E / E o ) R 82 w h e r e , R : t h e r e g i o n o f i n t e g r a t i o n ( F i g u r e 3 4 ) p , : t h e p r o b a b i l i t y d e n s i t y f u n c t i o n o f E / E o p 2 : t h e p r o b a b i l i t y d e n s i t y f u n c t i o n o f 0 . I f P i i s a s s u m e d t o b e a l m o s t c o n s t a n t w i t h i n t h e r a n g e 1 - V o / E o < E / E o ^ 1 + V o / E o , w h e r e V o < < E o , t h e n P ( | E r | / E o £ V o / E o ) * P ( 1 - V O / E O £ E / E O £ 1 + V o / E o ) • I P [ ( 2 m + 1 ) TT-VO/EO < 0 < ( 2 m + 1 ) TT+VO/EO ] m = 0 2 V o oo - p 1 (1 ) £ P [ ( 2 m + 1 )it-Vo/Eo < 0 < ( 2 m + 1 ) TT+VO/EO ] . E o m = 0 R u t h r o f f s t a t e d t h a t t h e p r o b a b i l i t y d e n s i t y f u n c t i o n o f F ( d N / d h , 6 h , w ) i n E q . C I O i s i n d e p e n d e n t o f f r e q u e n c y a n d p a t h l e n g t h . T h e r e f o r e , i t f o l l o w s t h a t t h e f a d i n g p r o b a b i l i t y i s a f u n c t i o n o f f 1 « d 3 , w h e r e d = L . 4 . F A D I N G P R O B A B I L I T Y - S I G N A L P O W E R L E V E L R A T I O D E P E N D E N C E D u r i n g p e r i o d s o f h e a v y f a d i n g o n l o n g p a t h s , /3 c a n b e a s s u m e d t o h a v e u n i f o r m p r o b a b i l i t y d e n s i t y d i s t r i b u t i o n o v e r t h e r a n g e 0 t o 2TT , t h e n t h e f a d i n g p r o b a b i l i t y c a n b e s h o w n a s p r o p o r t i o n a l t o t h e r a t i o o f t h e f a d i n g s i g n a l p o w e r l e v e l t o t h e f r e e - s p a c e s i g n a l p o w e r l e v e l . 83 2 P ( | E r | / E o < V o / E o ) oe p , (1 ) • (Vo/Eo) 2 7T CB W/WO where the s i g n a l power l e v e l r a t i o i s the square of the s i g n a l a m p l i t u d e r a t i o . 84 APPENDIX D - MAIN POINTS OF THE CNR MODEL Because the CNR group gave an ex tremely e x h a u s t i v e treatment on m u l t i p a t h p r o p a g a t i o n , i t i s v e r y hard to g i v e a f u l l l e n g t h summary on many a s p e c t s of the mode l . T h e r e f o r e , on ly the g e n e r a l e x p r e s s i o n f o r s i g n a l power r a t i o o f two r a y s i s d e r i v e d , and tha t f o r r e l a t i v e d e l a y i s s t a t e d . Moreover , f o r the s p e c i a l c o n d i t i o n when the l a y e r i s s i t u a t e d h o r i z o n t a l l y above the t r a n s m i t t i n g and r e c e i v i n g antennas of the same ' h e i g h t , the f i n a l forms of those two e x p r e s s i o n s a r e a l s o s t a t e d for the two p o s s i b l e cases mentioned i n Chapter 1, S e c t i o n 1 . 2 . 2 . The exact correspondence between the r e l a t i v e d e l a y i n one of those two cases and the phase d i f f e r e n c e , in the worst case of i n t e r f e r e n c e , i n R u t h r o f f ' s model (Appendix C , S e c t i o n 2) can be n o t e d 5 . F i g u r e 35 - S i n g l e - l a y e r above t e r m i n a l s 1. SIGNAL POWER RATIO OF TWO RAYS - GENERAL EXPRESSION In d e r i v i n g the s i g n a l power r a t i o ( F i g u r e 36 ) , the t r a n s m i t t e r i s assumed as a p o i n t source and the s i g n a l a r r i v e s at the r e c e i v e r i n a ray b u n d l e . By the Law of C o n s e r v a t i o n of E n e r g y , the f o l l o w i n g e q u a t i o n , a p p l y i n g to the ray b u n d l e , can be e s t a b l i s h e d . IdA = I dO L n where, . I : the i n t e n s i t y of the s i g n a l at L dA : the i n c r e m e n t a l a r e a normal to the r a y t r a j e c t o r y a t L L 5 A l l the f i g u r e s i n t h i s appendix are reproduced from R e f s . 6 & 18 w i t h n o t a t i o n m o d i f i c a t i o n . 8 5 I : the i n t e n s i t y of the s i g n a l on the u n i t sphere o dO : the a r e a that the ray bundle i n t e r c e p t s on the u n i t s p h e r e . F u r t h e r m o r e , Unit sphere around transmitter F i g u r e 36 - Geometry of ray bundle from t r a n s m i t t e r to r e c e i v e r dA = dA • s i n 62 L = L« sin6>2cl$clL and by assuming t h a t the ang le of d e p a r t u r e be ing s m a l l , dfl = cosd^dc^dS a*,d$ where, dA : the a r e a o f the ray bunaie a t L di : the a n g l e of a e p a r t u r e 82 : the a n g l e of a r r i v a l a$ : the a z i m u t h a l a i r e c t i o n L : the p a t h l e n g t h . 86 C o n s e q u e n t l y , I 1 d0 . I L • s i n 0 2 dL n T h e r e f o r e , the s i g n a l power r a t i o of two rays at L i s p< 1 > i ( i ) p( 2 ) J ( 2 ) s i n t 9 2 « 2 ) d 0 , ( 1 V d L (D1 ) s in0 2 < 1> de,< 2 >/dL 2. RELATIVE DELAY BETWEEN TWO RAYS - GENERAL EXPRESSION The approach of d e r i v i n g the r e l a t i v e d e l a y i s s i m i l a r to t h a t of d e r i v i n g the phase d i f f e r e n c e by R u t h r o f f except t h a t , i n the former c a s e , F l a t t e n e d E a r t h C o o r d i n a t e T r a n s f o r m a t i o n ( R e f . 6 ) , i n v o l v i n g m o d i f i e d r e f r a c t i v e i n d e x , i s u s e d . The e x p r e s s i o n d e r i v e d i s a p p l i c a b l e to s i t u a t i o n s when the t r a n s m i t t i n g and r e c e i v i n g antenna h e i g h t s are d i f f e r e n t . The p r o p a g a t i o n d e l a y of a r e f r a c t e d ray s i g n a l from t r a n s m i t t e r t o r e c e i v e r i s L L 3 r 3 K ( K , 2 + K 2 2 ) - ( K , 3 + K 2 3 ) T = — + R Co 24Ro 2 CoL 2 2 ( K - 1 ) 3 3 ( K , 2 + K 2 2 ) -, I (D2) (T?+1) 2 ( 1 - R / R o ) 2 where, 2Ro K , = s i n e , L 2RO K 2 = s i n 0 2 L 1 , , K = ( K , + K 2 ) < D 3 > 2 87 T? = 0, 1 ,2- • • (the number of e x t r a o s c i l l a t i o n s of a r e f r a c t e d ray t r a j e c t o r y ) . The p r o p a g a t i o n d e l a y of the d i r e c t ray s i g n a l from t r a n s m i t t e r to r e c e i v e r i s L L 3 r r n 2 _ h n 2 r 2 R o 2 T = 1+3 ( ) -1 (D4) L L J L s J- 1 D Co 24Ro 2 CoL   J   where, S = / L 2 + ( h 2 - h , ) 2 . T h e r e f o r e , the r e l a t i v e d e l a y i n a g e n e r a l case i s 6r = T - T R D 3. SIGNAL POWER RATIOS & RELATIVE DELAYS BETWEEN TWO RAYS - SPECIAL CONDITION For the s p e c i a l c o n d i t i o n when = h 2 (and hence the r e l a t i v e l a y e r h e i g h t above the antennas b e i n g 5h = h - h , = h - h 2 ) . 3.1 Case I T h i s i s the case when the two r e f r a c t e d rays c o i n c i d e . The r e l a t i o n s of the parameters are as f o l l o w s : K 2 = " K , , K = 0 . The r a t i o of the r e c e i v e d s i g n a l power of the d i r e c t ray to that of a r e f r a c t e d ray i s P D r L m 11 2 = 1-P L L R and the r e l a t i v e d e l a y of a r e f r a c t e d ray w . r . t . the d i r e c t ray i s L 3 r 8Ro5h L m , 2 -i 8T = 1+ : (1 ) 0 / I T > « 2 r - I r.m 2 T.2 J 2 4 R o 2 C o L L , where, 88 L m , 2 = -8RO(T?+1 ) 2 ( 1 - R / R o ) 2 5h . 3.2. Case II T h i s i s the case when the r e l a t i v e d e l a y i s c o r r e s p o n d i n g to the phase d i f f e r e n c e , i n the worst case of i n t e r f e r e n c e , d e r i v e d by R u t h r o f f . The r e l a t i o n s of the parameters a r e as f o l l o w s : K 2 = K , — K . The r a t i o s of the r e c e i v e d s i g n a l power of the d i r e c t ray to those of the r e f r a c t e d rays are P D ( L m 2 / L ) 2 = 1 -where, P 1+ y i - ( L m 2 / L ) */[ (77+1 ) ( 1 - R / R o ) ] R L m 2 2 = "8Ro[ U+1 ) 2 ( 1 - R / R o ) 2 - 1 ]6h and the r e l a t i v e d e l a y s of the r e f r a c t e d r a y s w . r . t . the d i r e c t ray can be o b t a i n e d by s u b t r a c t i n g Eq.D4 from E q . D 2 , and s e t t i n g K 2 s K, - K and h , = h 2 . The r e s u l t s are as f o l l o w s : L 3 r 2 ( K - 1 ) 3 -. 6r = 2K 3 - : - 3K 2 + 1 (D5) 24Ro 2Co<- (77+1 ) 2 ( 1 - R / R o ) 2 J where, -8Ro6h _ K = [ - 1 ± (17+1 ) (1-R/RO V l - ( L m 2 / L ) 2 ] . L m 2 2 I t can be noted t h a t i f t h e r e i s no e x t r a o s c i l l a t i o n i n the r e f r a c t e d ray t r a j e c t o r i e s ( i . e . 17 = 0 ) , then Eq.D5 i s e q u i v a l e n t to E q . C 9 (Appendix C ) . An a l t e r n a t e form of E q . D 5 i s L 3 r 16Ro6h-i 6r = (1-K) (1+K) - . 24Ro 2 Co L L 2 -I 89 APPENDIX E - MAIN POINTS OF WEBSTER'S MODEL F i g u r e 38 - R e l a t i o n s between the ray t r a j e c t o r i e s and r e f r a c t i v i t y p r o f i l e 9 0 A l t h o u g h Webster d i d not show h i s c a l c u l a t i o n s i n h i s r e p o r t (Ref .27 ) or paper ( R e f . 2 9 ) , he gave a g r a p h i c a l p r e s e n t a t i o n of the r e s u l t s o b t a i n e d from h i s model ( F i g u r e 39) . G e n e r a l l y s p e a k i n g , h i s model shows tha t (1) the r e c e i v e d s i g n a l a m p l i t u d e of ray 2 ( F i g u r e 38) i s the g r e a t e s t w h i l e t h a t of ray 3 i s the s m a l l e s t ; (2) the r e l a t i v e d e l a y of ray 2 w . r . t . ray 1 (the d i r e c t ray ) i s l onger than tha t of ray 3 w . r . t . ray 1; and (3) the a n g l e of a r r i v a l of ray 2 i s c l o s e to 0 ° w h i l e tha t of ray 3 i s p o s i t i v e and t h a t of ray 1 i s n e g a t i v e . The s t a n d a r d v a l u e s used i n W e b s t e r ' s model a r e as f o l l o w s 6 : N 0 : the s u r f a c e r e f r a c t i v i t y 300Nu k o ' the r e f r a c t i v i t y g r a d i e n t i n a -40Nu/km s t a n d a r d atmosphere -20Nu AN : the anomaly i n t e n s i t y Ah : the anomaly t h i c k n e s s 100m ho : the anomaly h e i g h t 1 50m h i : the t r a n s m i t t e r h e i g h t 1 00m h 2 : the r e c e i v e r h e i g h t 1 00m L : the p a t h l e n g t h 50m. 1. VARIATION IN ANOMALY INTENSITY An i n c r e a s e i n the magnitude of the anomaly i n t e n s i t y (AN) d e c r e a s e s the r e c e i v e d s i g n a l a m p l i t u d e , the r e l a t i v e d e l a y but i n c r e a s e s the ang le of a r r i v a l of ray 3 wheras a decrease i n the magnitude of AN r e v e r s e s the above changes u n t i l ray 3 c o a l e s c e s w i t h ray 2. B e s i d e s , r a y s 1 & 2 appear to be a lmost independent of the changes of AN. 2. VARIATION IN PATH LENGTH The changes i n s i g n a l a m p l i t u d e s , r e l a t i v e d e l a y s and ang le s of a r r i v a l of ray 3 w . r . t . pa th l e n g t h v a r i a t i o n are s i m i l a r to those changes w . r . t . anomaly i n t e n s i t y v a r i a t i o n , except t h a t , i n the former c a s e , rays 1 & 2 show g r e a t e r v a r i a b i l i t y . 3 . VARIATION IN ANOMALY THICKNESS Decrease i n the anomaly t h i c k n e s s (Ah) decreases the ampl i tude of ray 3 c o n s i d e r a b l y . M o r e o v e r , when Ah i s reduced to z e r o , t o t a l i n t e r n a l r e f l e c t i o n of the rays w i l l occur because of the abrupt change i n r e f r a c t i v e index a c r o s s the l a y e r boundary and because the a n g l e s of d e p a r t u r e of the rays are s m a l l . 6 A l l the f i g u r e s i n t h i s appendix a r e reproduced from R e f . 2 7 . Some n o t a t i o n s are s l i g h t l y m o d i f i e d . 91 H 1 I 1 I 30 40 SO 60 70 1 0 ' 2 0 " 3 0 PATH LENGTH, km. AN, NUNITS Ah, m ho> F i g u r e 39 - Changes i n s i g n a l a m p l i t u d e s , r e l a t i v e d e l a y s and ang les of a r r i v a l w . r . t . anomaly i n t e n s i t y , pa th l e n g t h , anomaly t h i c k n e s s and anomaly h e i g h t 92 4. VARIATION IN ANOMALY HEIGHT No m u l t i p a t h p r o p a g a t i o n can occur when the anomaly i s below both the t r a n s m i t t i n g and r e c e i v i n g antennas nor when i t i s above a c e r t a i n c r i t i c a l h e i g h t . However, when the anomaly i s below the an tennas , a -20dB d i p i n s i g n a l a m p l i t u d e , p r o b a b l y due to d e f o c u s s i n g , i s p o s s i b l e . On the o ther hand, the r e s u l t a n t r e c e i v e d s i g n a l ampl i tude of rays 1 & 2, as they c o a l e s c e , i n c r e a s e s to about +lOdB at the lower end of the anomaly h e i g h t range which p e r m i t s m u l t i p a t h p r o p a g a t i o n . . S i m i l a r s i g n a l enhancement o c c u r s at the upper end of t h i s range as rays 2 & 3 c o a l e s c e . 

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