RECOMMENDATION ITU-R P

Transcription

1 Rec. ITU-R P RECOMMENDATION ITU-R P Precton proceure for the evaluaton of mcrowave nterference between statons on the surface of the Earth at frequences above about 0.7 GHz * (Queston ITU-R 208/3) The ITU Raocommuncaton Assembly, ( ) conserng a) that ue to congeston of the rao spectrum, frequency bans must be share between fferent terrestral servces, between systems n the same servce an between systems n the terrestral an Earth-space servces; b) that for the satsfactory coexstence of systems sharng the same frequency bans, nterference propagaton precton proceures are neee that are accurate an relable n operaton an acceptable to all partes concerne; c) that nterference propagaton prectons are requre to meet worst-month performance an avalablty objectves; ) that precton methos are requre for applcaton to all types of path n all areas of the worl, recommens 1 that the mcrowave nterference precton proceure gven n Annex 1 be use for the evaluaton of the avalable propagaton loss n nterference calculatons between statons on the surface of the Earth for frequences above about 0.7 GHz. Annex 1 1 Introucton Congeston of the rao-frequency spectrum has mae necessary the sharng of many frequency bans between fferent rao servces, an between the fferent operators of smlar rao servces. In orer to ensure the satsfactory coexstence of the terrestral an Earth-space systems nvolve, t s mportant to be able to prect wth reasonable accuracy the nterference potental between them, usng precton proceures an moels whch are acceptable to all partes concerne, an whch have emonstrate accuracy an relablty. * Computer programs (REC452 an SCAT) assocate wth precton proceures escrbe n ths Recommenaton are avalable from that part of the ITU-R webste ealng wth Raocommuncaton Stuy Group 3.

2 2 Rec. ITU-R P Many types an combnatons of nterference path may exst between statons on the surface of the Earth, an between these statons an statons n space, an precton methos are requre for each stuaton. Ths Annex aresses one of the more mportant sets of nterference problems,.e. those stuatons where there s a potental for nterference between mcrowave rao statons locate on the surface of the Earth. The precton proceure s approprate to rao statons operatng n the frequency range of about 0.7 GHz to 30 GHz. The metho nclues a complementary set of propagaton moels whch ensure that the prectons embrace all the sgnfcant nterference propagaton mechansms that can arse. Methos for analysng the rao-meteorologcal an topographcal features of the path are prove so that prectons can be prepare for any practcal nterference path fallng wthn the scope of the proceure up to a stance lmt of km. 2 Interference propagaton mechansms Mcrowave nterference may arse through a range of propagaton mechansms whose nvual omnance epens on clmate, rao frequency, tme percentage of nterest, stance an path topography. At any one tme a sngle mechansm or more than one may be present. The prncpal nterference propagaton mechansms are as follows: Lne-of-sght (Fg. 1): The most straghtforwar nterference propagaton stuaton s when a lne-of-sght transmsson path exsts uner normal (.e. well-mxe) atmospherc contons. However, an atonal complexty can come nto play when subpath ffracton causes a slght ncrease n sgnal level above that normally expecte. Also, on all but the shortest paths (.e. paths longer than about 5 km) sgnal levels can often be sgnfcantly enhance for short peros of tme by multpath an focusng effects resultng from atmospherc stratfcaton (see Fg. 2). Dffracton (Fg. 1): Beyon lne-of-sght an uner normal contons, ffracton effects generally omnate wherever sgnfcant sgnal levels are to be foun. For servces where anomalous short-term problems are not mportant, the accuracy to whch ffracton can be moelle generally etermnes the ensty of systems that can be acheve. The ffracton precton capablty must have suffcent utlty to cover smooth-earth, screte obstacle an rregular (unstructure) terran stuatons. Tropospherc scatter (Fg. 1): Ths mechansm efnes the backgroun nterference level for longer paths (e.g. more than km) where the ffracton fel becomes very weak. However, except for a few specal cases nvolvng senstve earth statons or very hgh power nterferers (e.g. raar systems), nterference va troposcatter wll be at too low a level to be sgnfcant. Surface uctng (Fg. 2): Ths s the most mportant short-term nterference mechansm over water an n flat coastal lan areas, an can gve rse to hgh sgnal levels over long stances (more than 500 km over the sea). Such sgnals can excee the equvalent free-space level uner certan contons.

3 Rec. ITU-R P FIGURE 1 Long-term nterference propagaton mechansms Tropospherc scatter Dffracton Lne-of-sght Elevate layer reflecton an refracton (Fg. 2): The treatment of reflecton an/or refracton from layers at heghts up to a few hunre metres s of major mportance as these mechansms enable sgnals to overcome the ffracton loss of the terran very effectvely uner favourable path geometry stuatons. Agan the mpact can be sgnfcant over qute long stances (up to km). Hyrometeor scatter (Fg. 2): Hyrometeor scatter can be a potental source of nterference between terrestral lnk transmtters an earth statons because t may act vrtually omnrectonally, an can therefore have an mpact off the great-crcle nterference path. However, the nterferng sgnal levels are qute low an o not usually represent a sgnfcant problem. A basc problem n nterference precton (whch s nee common to all tropospherc precton proceures) s the ffculty of provng a unfe consstent set of practcal methos coverng a we range of stances an tme percentages;.e. for the real atmosphere n whch the statstcs of omnance by one mechansm merge graually nto another as meteorologcal an/or path contons change. Especally n these transtonal regons, a gven level of sgnal may occur for a total tme percentage whch s the sum of those n fferent mechansms. The approach n ths proceure has been elberately to keep separate the precton of nterference levels from the fferent propagaton mechansms up to the pont where they can be combne nto an overall precton for the path. Ths overall precton s mae usng a blenng technque that ensures for any gven path stance an tme percentage that the sgnal enhancement n the equvalent notonal lne-of-sght moel s the hghest attanable.

4 4 Rec. ITU-R P FIGURE 2 Anomalous (short-term) nterference propagaton mechansms Hyrometeor scatter Elevate layer reflecton/refracton Ductng Lne-of-sght wth multpath enhancements Clear-ar nterference precton 3.1 General comments The proceure uses fve propagaton moels to eal wth the clear-ar propagaton mechansms escrbe n 2. These moels are as follows: lne-of-sght (nclung sgnal enhancements ue to multpath an focusng effects); ffracton (embracng smooth-earth, rregular terran an sub-path cases); tropospherc scatter; anomalous propagaton (uctng an layer reflecton/refracton); heght-gan varaton n clutter (where relevant). Depenng on the type of path, as etermne by a path profle analyss, one or more of these moels are exercse n orer to prove the requre precton of basc transmsson loss. 3.2 Dervng a precton Outlne of the proceure The steps requre to acheve a precton are as follows: Step 1: Input ata The basc nput ata requre for the proceure s gven n Table 1. All other nformaton requre s erve from these basc ata urng the executon of the proceure.

5 Rec. ITU-R P TABLE 1 Basc nput ata Parameter Preferre resoluton Descrpton f 0.01 Frequency (GHz) p Requre tme percentage(s) for whch the calculate basc transmsson loss s not exceee ϕ t, ϕ r Lattue of staton (egrees) ψ t, ψ r Longtue of staton (egrees) h tg, h rg 1 Antenna centre heght above groun level (m) h ts, h rs 1 Antenna centre heght above mean sea level (m) G t, G r 0.1 Antenna gan n the recton of the horzon along the great-crcle nterference path (B) NOTE 1 For the nterferng an nterfere-wth statons: t : nterferer r : nterfere-wth staton. Step 2: Selectng average year or worst-month precton The choce of annual or worst-month prectons s generally ctate by the qualty (.e. performance an avalablty) objectves of the nterfere-wth rao system at the recevng en of the nterference path. As nterference s often a brectonal problem, two such sets of qualty objectves may nee to be evaluate n orer to etermne the worst-case recton upon whch the mnmum permssble basc transmsson loss nees to be base. In the majorty of cases the qualty objectves wll be couche n terms of a percentage of any month, an hence worstmonth ata wll be neee. The propagaton precton moels prect the annual strbuton of basc transmsson loss. For average year prectons the percentages of tme p, for whch partcular values of basc transmsson loss are not exceee, are use rectly n the precton proceure. If average worst-month prectons are requre, the annual equvalent tme percentage, p, of the worst-month tme percentage, p w, must be calculate for the path centre lattue ϕ usng: log( p ) log( ) ω w + G L ω 10 + p = % (1) ω : fracton of the path over water (see Table 3). G L = cos 2 ϕ cos 2 ϕ for for ϕ ϕ 45 > 45 (1a)

6 6 Rec. ITU-R P If necessary the value of p must be lmte such that 12 p p w. Note that the lattue ϕ (egrees) s eeme to be postve n the Northern Hemsphere. The calculate result wll then represent the basc transmsson loss for the requre worst-month tme percentage, p w %. Step 3: Raometeorologcal ata The precton proceure employs three rao-meteorologcal parameters to escrbe the varablty of backgroun an anomalous propagaton contons at the fferent locatons aroun the worl. N (N-unts/km), the average rao-refractve nex lapse-rate through the lowest 1 km of the atmosphere, proves the ata upon whch the approprate effectve Earth raus can be calculate for path profle an ffracton obstacle analyss. Fgures 4 an 5, respectvely, prove worl maps of average annual N values an maxmum monthly mean values for worst-month prectons. Note that N s a postve quantty n ths proceure. β 0 (%), the tme percentage for whch refractve nex lapse-rates exceeng 100 N-unts/km can be expecte n the frst 100 m of the lower atmosphere, s use to estmate the relatve ncence of fully evelope anomalous propagaton at the lattue uner conseraton. The value of β 0 to be use s that approprate to the path centre lattue. N 0 (N-unts), the sea-level surface refractvty, s use only by the troposcatter moel as a measure of locaton varablty of the troposcatter scatter mechansm. Fgure 6 proves annual values of N 0. As the scatter path calculaton s base on a path geometry etermne by annual or worst-month values of N, there s no atonal nee for worst-month values of N 0. The correct values of N an N 0 are gven by the path-centre values as erve from the approprate maps. Pont ncence of anomalous propagaton, β 0 (%), for the path centre locaton s etermne usng: ϕ µ µ % for ϕ 70 β = (2) 4.17µ 1 µ 4 % for ϕ > 70 ϕ : path centre lattue (egrees). The parameter µ 1 epens on the egree to whch the path s over lan (nlan an/or coastal) an water, an s gven by: tm τ µ 1 = ( τ) [ ] (3) where the value of µ 1 shall be lmte to µ 1 1,

7 Rec. ITU-R P wth: τ 1 e ( ) = lm (3a) tm : lm : longest contnuous lan (nlan + coastal) secton of the great-crcle path (km) longest contnuous nlan secton of the great-crcle path (km). The raoclmatc zones to be use for the ervaton of tm an lm are efne n Table 2. ( ϕ ) log µ 1 10 for ϕ 70 µ 4 = (4) 0.3 log µ 10 1 for ϕ > 70 TABLE 2 Rao-clmatc zones Zone type Coe Defnton Coastal lan A1 Coastal lan an shore areas,.e. lan ajacent to the sea up to an alttue of 100 m relatve to mean sea or water level, but lmte to a stance of 50 km from the nearest sea area. Where precse 100 m ata are not avalable an approxmate value,.e. 300 ft, may be use Inlan A2 All lan, other than coastal an shore areas efne as coastal lan above Sea B Seas, oceans an other large boes of water (.e. coverng a crcle of at least 100 km n ameter) Large boes of nlan water A large boy of nlan water, to be consere as lyng n Zone B, s efne as one havng an area of at least km 2, but exclung the area of rvers. Islans wthn such boes of water are to be nclue as water wthn the calculaton of ths area f they have elevatons lower than 100 m above the mean water level for more than 90% of ther area. Islans that o not meet these crtera shoul be classfe as lan for the purposes of the water area calculaton.

8 8 Rec. ITU-R P Large nlan lake or wet-lan areas Large nlan areas of greater than km 2 whch contan many small lakes or a rver network shoul be eclare as coastal Zone A1 by amnstratons f the area comprses more than 50% water, an more than 90% of the lan s less than 100 m above the mean water level. Clmatc regons pertanng to Zone A1, large nlan boes of water an large nlan lake an wetlan regons, are ffcult to etermne unambguously. Therefore amnstratons are nvte to regster wth the ITU Raocommuncaton Bureau (BR) those regons wthn ther terrtoral bounares that they wsh entfe as belongng to one of these categores. In the absence of regstere nformaton to the contrary, all lan areas wll be consere to pertan to clmate Zone A2. For maxmum consstency of results between amnstratons t s strongly recommene that the calculatons of ths proceure be base on the ITU-R Dgtze Worl Map (IDWM) whch s avalable from the BR for manframe or personal computer envronments Effectve Earth raus The mean effectve Earth raus factor k 50 for the path s etermne usng: 157 k50 = (5) 157 N Assumng a true Earth raus of km, the mean value of effectve Earth raus a e can be etermne from: Step 4: Path profle analyss a e = k 50 km (6) Values for a number of path-relate parameters necessary for the calculatons, as ncate n Table 3, must be erve va an ntal analyss of the path profle base on the value of a e gven by equaton (6). Informaton on the ervaton, constructon an analyss of the path profle s gven n Appenx 2. Havng thus analyse the profle, the path wll also have been classfe nto one of the three geometrcal categores ncate n Table 4. NOTE 1 The etermnaton of values for atonal profle-relate parameters requre specfcally for ffracton calculatons s escrbe n Recommenaton ITU-R P.526. Step 5: Calculaton of propagaton prectons Table 4 ncates, for each type of path, the propagaton moels that are approprate. The necessary equatons for these nvual propagaton mechansm prectons are to be foun n the text sectons ncate n the Table. In orer to bul an overall precton, the nvual propagaton mechansm prectons must be calculate an combne n the manner shown n 4.7. For trans-horzon paths, elements from both the lne-of-sght an ffracton moels are reuse wthn the combnng process. Once ths has been acheve for each of the requre tme percentages, the precton s complete. It shoul be note that equaton (8c) use for the combnaton s a mathematcal blen to prevent abrupt slope changes an not the lnear aton of electrcal powers.

9 Rec. ITU-R P TABLE 3 Parameter values to be erve from the path profle analyss Path type Parameter Descrpton Trans-horzon Great-crcle path stance (km) Trans-horzon lt, lr Dstance from the transmt an receve antennas to ther respectve horzons (km) Trans-horzon θ t, θ r Transmt an receve horzon elevaton angles respectvely (mra) Trans-horzon θ Path angular stance (mra) All h ts, h rs Antenna centre heght above mean sea level (m) Trans-horzon h te, h re Effectve heghts of antennas above the terran (m) (see Appenx 2 for efntons) All (1) b Aggregate length of the path sectons over water (km) All ω (1) Fracton of the total path over water: ω = b / (7) where s the great-crcle stance (km) calculate usng equaton (42). For totally overlan paths: ω = 0 Trans-horzon ct (1) Trans-horzon cr (1) Dstance from the frst termnal (the nterference source) to the coast along the great-crcle nterference path (km) Corresponng stance for the secon (nterfere-wth) staton (km) (1) These parameters are only requre when the path has one or more sectons over water. The exact values of ct an cr are only of mportance f ct an cr 5 km. If, n ether or both cases, the stances are obvously n excess of 5 km, then t s only necessary to note the > 5 km conton. Few nterference paths wll n fact nee etale evaluaton of these two parameters. TABLE 4 Interference path classfcatons an propagaton moel requrements Classfcaton Lne-of-sght wth frst Fresnel zone clearance Lne-of-sght wth sub-path ffracton,.e. terran ncurson nto the frst Fresnel zone Trans-horzon Moels requre Lne-of-sght ( 4.2) Clutter loss ( 4.5, where approprate) Lne-of-sght ( 4.2) Dffracton ( 4.3) Clutter loss ( 4.3, where approprate) Dffracton ( 4.3 for 200 km) Ductng/layer reflecton ( 4.5) Troposcatter ( 4.4) Clutter loss ( 4.6, where approprate)

10 10 Rec. ITU-R P TABLE 5 Methos of ervng overall prectons Lne-of-sght Path type Lne-of-sght wth sub-path ffracton Trans-horzon Acton requre The precton s obtane by summng the losses gven by the lne-of-sght an clutter loss moels,.e.: L b ( p) = L b0 ( p) + A ht + A hr B (8a) L b0 ( p) : precte basc transmsson loss not exceee for p% of tme gven by the lne-of-sght moel A ht, A hr : approprate atonal losses ue to heght-gan effects n local clutter The precton s obtane by summng the losses gven by the lne-of-sght an (sub-path) ffracton moels an clutter moels,.e.: L b ( p) = L b0 ( p) + L s ( p) + A ht + A hr B (8b) L s ( p): precton for p% of tme gven by the sub-path ffracton loss element of the ffracton moel The overall precton s obtane n two stages: The mofe uctng/layer reflecton moel loss, L ( p), s foun by ba applcaton of the algorthm n The overall precton can then be obtane by applyng the followng ancllary algorthm: L b ( p) = 5 log (10 0.2L bs L b L ba ) + Aht + A hr B (8c) where L bs ( p) an L b ( p): nvual precte basc transmsson loss for p% of tme gven by the troposcatter an ffracton propagaton moels respectvely. NOTE 1 Where a moel has not been propose for a path (because the contons gven n Table 4 were not met), the approprate term shoul be omtte from equaton (8c). 4 Clear-ar propagaton moels 4.1 General The proceure gven above nvokes one or more separate propagaton moels to prove the components of the overall precton. These propagaton moels are prove n ths secton. 4.2 Lne-of-sght propagaton (nclung short-term effects) The basc transmsson loss L b0 ( p) not exceee for tme percentage, p%, ue to lne-of-sght propagaton s gven by: E s ( p) : L b0 ( p) = log f + 20 log + E s ( p) + A g B (9) correcton for multpath an focusng effects: E s ( p) = 2.6 (1 e / 10 ) log ( p / 50) B (10)

11 Rec. ITU-R P A g : total gaseous absorpton (B): [ γ γ (ρ)] B Ag = o + w (11) γ o, γ w (ρ) : ρ : specfc attenuaton ue to ry ar an water vapour, respectvely, an are foun from the equatons n Recommenaton ITU-R P.676 water vapour ensty: ρ = ω g/m 3 (11a) ω : fracton of the total path over water. 4.3 Dffracton The tme varablty of the excess loss ue to the ffracton mechansm s assume to be the result of changes n bulk atmospherc rao refractvty lapse rate,.e. as the tme percentage p reuces, the effectve Earth raus factor k ( p) s assume to ncrease. Ths process s consere val for β 0 p 50%. For tme percentages less than β 0 sgnal levels are omnate by anomalous propagaton mechansms rather than by the bulk refractvty characterstcs of the atmosphere. Thus for values of p less than β 0 the value of k ( p) has the value k(β 0 ). The value of effectve Earth raus to use n ffracton calculatons s gven by: p : may take the values 50 or β 0 k (50%): s gven by equaton (5) k (β 0 ) = 3. a( p) = k( p) km (12) The excess ffracton loss L ( p) s compute by the metho escrbe n Recommenaton ITU-R P , combne wth a log-normal strbuton of loss between 50% an β 0 as follows: for p = 50%, L (50%) s compute usng the metho escrbe n Recommenaton ITU-R P.526 for the mean effectve Earth raus a (50%); for p β 0, L (β 0 ) s compute usng the metho escrbe n Recommenaton ITU-R P.526 for effectve Earth raus a (β 0 ), usng the knfe eges entfe for the 50% (mean) case; for β 0 < p < 50% L ( p) s gven by: [ L (50%) L ( β )] L ( p) = L (50%) F ( p) 0 (13) F : nterpolaton factor base on a log-normal strbuton of ffracton loss over the range β 0 % < p < 50% gven by: F = I( p/100) / I(β 0 /100) (13a) where I(x) s the nverse cumulatve normal functon. A sutable approxmaton for I(x) whch may be use wth confence for x < 0.5 s gven n Appenx 4.

12 12 Rec. ITU-R P NOTE 1 Recommenaton ITU-R P can be use for the calculaton of ffracton loss over ether a lne-of-sght path wth sub-path obstructon, or a trans-horzon path. The basc transmsson loss not exceee for p% tme for a ffracton path s then gven by: L b ( p) = log f + 20 log + L ( p) + E s ( p) + A g B (14) E s ( p) : correcton for multpath effects between the antennas an the horzon obstacles: ( ( + )/ 10 p E ( p) = e lt lr s ) log B (14a) 50 A g : gaseous absorpton etermne usng equatons (11) an (11a). 4.4 Tropospherc scatter (Notes 1 an 2) NOTE 1 At tme percentages much below 50%, t s ffcult to separate the true tropospherc scatter moe from other seconary propagaton phenomena whch gve rse to smlar propagaton effects. The tropospherc scatter moel aopte n ths Recommenaton s therefore an emprcal generalzaton of the concept of tropospherc scatter whch also embraces these seconary propagaton effects. Ths allows a contnuous consstent precton of basc transmsson loss over the range of tme percentages p from 0.001% to 50%, thus lnkng the uctng an layer reflecton moel at the small tme percentages wth the true scatter moe approprate to the weak resual fel exceee for the largest tme percentage. NOTE 2 Ths troposcatter precton moel has been erve for nterference precton purposes an s not approprate for the calculaton of propagaton contons above 50% of tme affectng the performance aspects of trans-horzon rao-relay systems. The basc transmsson loss ue to troposcatter, L bs ( p) (B) not exceee for any tme percentage, p, below 50%, s gven by: L 0. 7 [ log ( / 50 ] bs ( p) Lf + 20 log θ 0.15 N0 + Lc + Ag 10.1 p ) = B (15) L f : frequency epenent loss: L f = 25 log f 2.5 [log ( f / 2)] 2 B (15a) L c : aperture to meum couplng loss (B): L c 0.055( G t + G ) = e r B (15b) N 0 : path centre sea-level surface refractvty erve from Fg. 6 A g : gaseous absorpton erve from equaton (11) usng ρ = 3 g/m 3 for the whole path length.

13 Rec. ITU-R P Ductng/layer reflecton The precton of the basc transmsson loss, L ba ( p) (B) occurrng urng peros of anomalous propagaton (uctng an layer reflecton) s base on the followng functon: L ba ( p) = A f + A ( p) + A g B (16) A f : total of fxe couplng losses (except for local clutter losses) between the antennas an the anomalous propagaton structure wthn the atmosphere: A f = log f + 20 log ( lt + lr ) + A st + A sr + A ct + A cr B (17) A st, A sr : ste-shelng ffracton losses for the nterferng an nterfere-wth statons respectvely: [ θ ( f ) 1/ ] θ 1/ 3 20log t, r lt,lr t, r f B for θ t, r > 0 mra A st, sr = (18) 0 B for θ 0 mra t, r θ = θ 0.1 mra (18a) t, r t,r lt,lr A ct, A cr : over-sea surface uct couplng correctons for the nterferng an nterferewth statons respectvely: = 3 e ct,cr Act,cr 1 + tanh (0.07(50 hts,rs )) B for ω 0.75 ct,cr lt,lr (19) ct,cr 5 km A ct, cr = 0 B for all other contons (19a) It s useful to note the lmte set of contons uner whch equaton (19) s neee. A ( p) : tme percentage an angular-stance epenent losses wthn the anomalous propagaton mechansm: A ( p) = γ θ + A ( p) B (20) γ : specfc attenuaton: γ = a e f 1/3 B/mra (21)

14 14 Rec. ITU-R P θ : angular stance (correcte where approprate (va equaton (22a)) to allow for the applcaton of the ste shelng moel n equaton (18)): 10 3 θ = + θ t + θ r mra (22) a e θ t, r = θt,r 0.1 lt,lr mra mra for for θ θ t,r t,r 0.1 > 0.1 lt,lr lt,lr mra mra (22a) A( p) : tme percentage varablty (cumulatve strbuton): 3 p p A ( p) = 12 + ( ) log + 12 B (23) β β ( log β) ( log β (log β) ) e Γ = (23a) β = β 0 µ 2 µ 3 % (24) µ 2 : correcton for path geometry: Γ µ = ae 2 ( h + h ) te re 2 α (25) The value of µ 2 shall not excee 1. α = 0.6 ε τ (25a) ε = 3.5 τ : s efne n equaton (3a) an the value of α shall not be allowe to reuce below 3.4 µ 3 : correcton for terran roughness: µ 3 1 = exp 5 [ ( h 10) ( )] m for for hm hm 10 m > 10 m (26) = mn ( lt lr, 40) km (26a) A g : total gaseous absorpton etermne from equatons (11) an (11a). The remanng terms have been efne n Tables 1 an 2 an Appenx 2.

15 Rec. ITU-R P Atonal clutter losses General Conserable beneft, n terms of protecton from nterference, can be erve from the atonal ffracton losses avalable to antennas whch are mbee n local groun clutter (bulngs, vegetaton etc.). Ths proceure allows for the aton of such clutter losses at ether or both ens of the path n stuatons where the clutter scenaro s known. Where there are oubts as to the certanty of the clutter envronment ths atonal loss shoul not be nclue. The clutter losses are esgnate as A ht (B) an A hr (B) for the nterferer an nterfere-wth statons respectvely. The atonal protecton avalable s heght epenent, an s therefore moelle by a heght-gan functon normalze to the nomnal heght of the clutter. Approprate nomnal heghts are avalable for a range of clutter types. The correcton apples to all clear-ar prectons n ths Recommenaton,.e. for all propagaton moes an tme percentages Clutter categores Table 6 ncates the clutter (or groun cover) categores as efne n Recommenaton ITU-R P.1058 for whch the heght-gan correcton can be apple. The nomnal clutter heght, h a (m) an stance from the antenna, k (km) are eeme to be average values most representatve of the clutter type. However, the correcton moel has been mae conservatve n recognton of the uncertantes over the actual heght that are approprate n nvual stuatons. Where the clutter parameters are more accurately known they can be rectly substtute for the values taken from Table 6. The nomnal heghts an stances gven n Table 6 approxmate to the characterstc heght H c an gap-wth G c efne n Recommenaton ITU-R P However the moel use here to estmate the atonal losses ue to shelng by clutter (groun cover) s ntene to be conservatve The heght-gan moel The atonal loss ue to protecton from local clutter s gven by the expresson: e 1 tanh h A = k h 0.33 (27) ha k : stance (km) from nomnal clutter pont to the antenna (see Fg. 3) h : h a : antenna heght (m) above local groun level nomnal clutter heght (m) above local groun level.

16 16 Rec. ITU-R P Clutter (groun-cover) category TABLE 6 Nomnal clutter heghts an stances Nomnal heght, h a (m) Nomnal stance, k (km) Hgh crop fels Park lan Irregularly space sparse trees Orchar (regularly space) Sparse houses Vllage centre Decuous trees (rregularly space) Decuous trees (regularly space) Mxe tree forest Conferous trees (rregularly space) Conferous trees (regularly space) Tropcal ran forest Suburban Dense suburban Urban Dense urban Inustral zone Atonal losses ue to shelng by clutter (groun cover) shoul not be clame for categores not appearng n Table 6. FIGURE 3 Metho of applyng heght-gan correcton, A ht or A hr "Ste shelng" obstacle * Nomnal clutter heght, h (m) a h Nomnal groun heght, h (m) g Path length, (km) s (km) L k Assume clutter stance(s), s an k (km) Nomnal clutter locaton

17 Rec. ITU-R P Metho of applcaton The metho of applyng the heght-gan correcton, A ht or A hr (B) s straghtforwar, an s shown n Fg. 3. The steps to be ae to the basc precton proceure are as follows: Step 1: where the clutter type s known or can be safely assume, the man proceure s use to calculate the basc transmsson loss to the nomnal heght, h a, for the approprate clutter type, as selecte from Table 6. The path length to be use s k (km). However where >> k ths mnor correcton for k can safely be gnore. Step 2: where there s a ste-shelng obstacle that wll prove protecton to the termnal ths shoul stll be nclue n the basc calculaton, but the shelng loss (A st or A sr (B)) shoul be calculate to the heght h a at stance s, rather than to h at L as woul otherwse be the case. Step 3: once the man proceure s complete, the heght gan correcton from equaton (27) can be ae, as ncate n Table 5. Step 4: where nformaton on the clutter s not avalable, the basc calculaton shoul be unertaken usng stances an L (f approprate) an heght h. NOTE 1 Clutter heght-gan correctons shoul be ae to both ens of the path where ths s approprate. NOTE 2 Where both the lan heght-gan correcton an the sea uct couplng correcton (A ct or A cr (B)) are requre (.e. the antenna s close to the sea but there s ntervenng clutter), the two correctons can be use together as they are complementary an compatble. NOTE 3 If s not sgnfcantly greater than k ths moel s not sutable. 4.7 The overall precton Table 5 gves the actons requre to bul the overall precton for each classfcaton of path type. For paths classfe as lne-of-sght or lne-of-sght wth sub-path ffracton, no further pre-processng of the nvual moel results are requre before applyng the requre acton from the Table Trans-horzon paths In the case of trans-horzon paths, although the lne-of-sght moel s not a requre moel, use s mae of the equvalent notonal lne-of-sght moel loss n the combnng process. The overall precton s base upon calculaton of a mofe uctng/layer reflecton loss, L ba ( p), from the followng functon pror to the applcaton of equaton (8c) n Table 5: Lba p) = Lba( p) + ( Lmnb ( p) Lba( p)) Fj ( 0 (28) Lb ( p) for Lmnba ( p) > Lb ( p) Lba ( p) = (29) Lmnba ( p) + ( Lb ( p) Lmnba ( p)) Fk for Lmnba ( p) Lb ( p) L b ( p): ffracton loss evaluate at p% tme from equaton (14).

18 18 Rec. ITU-R P F k : nterpolaton factor whch blens the uctng/layer reflecton nto the ffracton loss wth stance: κ F k = tanh 3.0 ( sw ) (30) sw : great crcle path length efne n Table 3 sw : fxe parameter etermnng the stance range of the transton; set to 20 κ : fxe parameter etermnng the approach slope at the ens of the range; set to 0.5 Lmn ba ( p): mofe uctng/layer reflecton loss: ( ) ( ) Lmn ( p) = η ln exp ba p + exp b0 p ba η η (31) L ba ( p): uctng/layer reflecton loss from equaton (16) L b0 ( p): notonal lne-of-sght loss for the path evaluate from equaton (16) η = 2.5 Lmn b0 ( p): notonal mnmum propagaton loss that the mofe uctng/layer reflecton loss can attan: Lb0 ( p) for p < β0 Lmnb 0 ( p) = (32) Lb50 ( Lb50 Lb0β ) F for p β0 L b0β : notonal lne-of-sght loss evaluate at β 0 % tme from equaton (9): L b 0 β = Lb 0 ( β 0 %) (33) L b50 : ffracton loss evaluate at 50% tme from equaton (14): L b50 = Lb (50%) (34) F : nterpolaton factor base on a log-normal strbuton of ffracton loss efne n equaton (13c) F j : nterpolaton factor whch blens the mofe uctng/layer reflecton nto the notonal lne-of-sght loss: ξ F j = tanh 3.0 ( θ Θ) (35) Θ Θ = 0.3 ξ = 0.8 θ : path angular stance efne n Table 7.

19 Rec. ITU-R P Calculaton of transmsson loss The metho escrbe n 4.2 to 4.7 above proves the basc transmsson loss between the two statons. In orer to calculate the sgnal level at one staton ue to nterference from the other t s necessary to know the transmsson loss, whch takes account of the antenna gans of the two statons n the recton of the rao (.e. nterference) path between them. The followng proceure proves a metho for the calculaton of transmsson loss between two terrestral statons. As ntermeate steps n the metho, t also proves formulae for the calculaton of the great-crcle path length an angular stance base on the statons geographc coornates, as oppose to the ervatons of these quanttes from the path profle, as assume n Table 3. Calculate the path angular stance, θ, from the statons geographc coornates usng: θ = arccos(sn(ϕ t ) sn(ϕ r ) + cos(ϕ t ) cos(ϕ r ) cos(ψ t ψ r )) ra (36) The great crcle stance,, between the statons s: = θ km (37) Calculate the bearng (azmuthal recton clockwse from true North) from staton t to staton r usng: α tr = arccos({sn(ϕ r ) sn(ϕ t ) cos(θ)}/sn(θ) cos(ϕ t )) ra (38) Havng mplemente (38), f ψ t ψ r < 0 then: α tr = 2π α tr ra (39) Calculate the bearng from staton r to staton t, α rt, by symmetry from equatons (38) an (39). Next, assume that the man beam (boresght) recton of staton t s (ε t, α t ) n (elevaton, bearng), whle the man beam recton of staton r s (ε r, α r ). To obtan the elevaton angles of the rao (.e. nterference) path at statons t an r, ε pt an ε pr, respectvely, t s necessary to stngush between lne-of-sght an trans-horzon paths. For example, for lne-of-sght paths, an ε pt = [(h r h t )/] [/2a e ] ra (40a) ε pr = [(h t h r )/] [/2a e ] ra (40b) where h t an h r are the heghts of the statons above mean sea level (km), whle for trans-horzon paths, the elevaton angles are gven by ther respectve horzon angles, vz., an ε pt = θ t 10 3 ra (41a) ε pr = θ r 10 3 ra (41b) Be aware that the rao horzon angles, θ t an θ r, are efne n an 5.1.3, respectvely, of Appenx 1.

20 20 Rec. ITU-R P To calculate the off-boresght angles for statons t an r, χ t an χ r, respectvely, n the recton of the nterference path at statons t an r, t s recommene to use: χ t = arccos(cos(ε t ) cos(ε pt ) cos(α tr α t ) + sn(ε t ) sn(ε pt )) (42a) an χ r = arccos(cos(ε r ) cos(ε pr ) cos(α rt α r ) + sn(ε r ) sn(ε pr )) (42b) Usng ther respectve off-boresght angles, obtan the antenna gans for statons t an r, G t an G r, respectvely (B). If the actual antenna raaton patterns are not avalable, the varaton of gan wth off-boresght angle may be obtane from the nformaton n Recommenaton ITU-R S.465. To obtan the transmsson loss, L, use: L = L b0 ( p) G t G r B (43) For clear-ar nterference scenaros where rao propagaton s omnate by troposcatter, the elevaton angles wll be slghtly greater than the rao horzon angles, θ t an θ r. The use of these shoul ntrouce neglgble error, unless these also conce wth ther respectve statons boresght rectons. 5 Hyrometeor-scatter nterference precton In contrast wth the preceng clear-ar nterference precton methos escrbe above, the hyrometeor-scatter nterference precton metho escrbe below evelops an expresson for the transmsson loss rectly, owng to the fact that ths metho reles on some knowlege of the nterferng an nterfere-wth antenna gans. 5.1 Introucton Ths moel, for whch software (SCAT) s avalable from the BR, prects transmsson loss statstcs of an nterferng sgnal from ranfall rate statstcs. It s base on two funamental assumptons: scatterng occurs only wthn ran cells havng crcular cross-sectons whose ameters epen on the ranfall rates nse the cell. For any lnk geometry, one cell s assume to be n a fxe poston whch s ntene to represent the worst case. Wthn the ran cell, the ranfall rate, an hence the reflectvty, s constant up to a ran heght whose mean value epens on geographc lattue, but wth a specfc strbuton about ths mean that reflects the annual varaton n heght. Above the ran heght, a lnear ecrease of the reflectvty (B) s assume; attenuaton occurs nse as well as outse the cell, but only below the ran heght. Inse the cell, the well known epenence of specfc attenuaton on the ranfall rate s assume. The moel s able to compute nterference levels for both long-path (> 100 km) an short-path geometres (own to a few klometres) wth arbtrary elevaton angles at both termnals, as well as se scatter (non great-crcle) geometres, an se-lobe couplng. Because of the complexty of the path geometry, t s avalable n the form of an example computer mplementaton.

21 Rec. ITU-R P The physcal bass of the metho s gven n Appenx 3, where the ntersecton of a narrow beam (e.g., an earth staton), an a we beam (e.g., a terrestral staton) s assume. In comparatve testng aganst both rect an raar-erve measurements, the metho has yele goo results for a varety of frequences an geometres. 5.2 Transmsson loss formula The transmsson loss, L (B), ue to hyrometeor scatter, for a gven ranfall rate an ran heght may be expresse as follows: L = log ηe + 20 log T 20 log f 10 log zr + 10 log S + Ag 10 log C B (44) η E : antenna effcency (factor < 1) of the earth staton T : stance between statons va the scatterng volume (km) f : frequency (GHz) z R : unt volume ran scatter reflectvty factor below the (top of) ran heght (mm 6 /m 3 ): S : z R = 400 R( p) 1.4 mm 6 /m 3 (45) R( p) : pont ranfall rate exceee for tme percentage, p, of nterest (wth an ntegraton tme of 1 mn) allowance for the evaton from Raylegh law scatterng n ran at frequences above 10 GHz (assume S = 0 above the ran heght): cos ϕs 10 log S = R( p) 10 4 ( f 10) (46a) 2 A g : C : h mn, h max : g T0 : g T : + 5 ( f cos ϕs 10) B for f > 10 GHz 2 10 log S = 0 B for f 10 GHz (46b) ϕ s : scatter angle,.e. angle between the rectons of propagaton of the waves ncent on, an outgong from, the scatter volume (for example, ϕ s = 0 for forwar scatter, an ϕ s = 180 for back scatter) gaseous attenuaton by oxygen an water vapour, calculate usng the formulae of Recommenaton ITU-R P.676 an a water vapour ensty of 7.5 g/m 3 effectve scatter transfer functon: hmax 1 C = gt 0 gt ( h) ζ( h) AT ( h) AE ( h) sn ε h E h (47) mn mnmum an maxmum heghts for ntegraton on-axs antenna gan factor of the terrestral staton antenna rectvty (factor 1) of the terrestral staton n the recton towars the ntegraton pont (volume element) uner conseraton

22 22 Rec. ITU-R P ε Ε : ζ(h) : elevaton angle of earth staton beam reflectvty functon n the scatter volume, normalze to z R (the value below the ran heght): ζ ( h ) = 1 for h ran heght (48a) 0.65( h hr) ζ( h ) = 10 for h > ran heght (48b) h R : mean ran heght as gven n Recommenaton ITU-R P.839 (see Appenx 3) A T, A E : ran attenuaton (factors 1) for the paths from the terrestral staton to the ntegraton pont an from there to the earth staton, respectvely. Informaton gven n Appenx 3 s necessary for the calculaton of A T an A E. Equaton (44) assumes the worst case (maxmum) polarzaton couplng. For less than ths eal couplng, atonal loss wll occur (see Appenx 3). To calculate the overall transmsson loss, the ntegraton of equaton (47) has to be performe along the part of the earth staton s antenna beam that s ether, wthn the ran cell, or wthn the antenna beam of the terrestral staton (shown ark on Fg. 9). The antenna beam of the terrestral staton s assume to have a Gaussan shape. The ntegraton s extene to the _ 18 B ponts of the antenna pattern, relatve to the maxmum gan foun along the narrow beam. To erve an analytcal expresson for the ntegral, the rectvty pattern of the antenna of T s approxmate by a Gaussan functon as follows: 2 h h g = 0 T ( h) exp 4 ln 2 (49) h1/2 where h 1/2 s the fference of the heghts of those two ponts on the antenna axs of the earth staton where the rectvty functon of the antenna of the terrestral staton falls to 0.5 ( 3 B ponts). 5.3 Cumulatve strbuton of transmsson loss The (annual) cumulatve strbuton of transmsson loss ue to hyrometeor scatter s evaluate n two steps. Frstly, for each combnaton of ranfall rate an ran heght, the transmsson loss s calculate as f there were a etermnstc epenence on these parameters. It s assume that ths value of transmsson loss happens wth the same probablty as the corresponng combnaton of ranfall rate an ran heght, assumng statstcal nepenence of these two parameters. Seconly, the probabltes of all ranfall-rate/ran-heght combnatons leang to the same transmsson loss values are summe to yel the total probablty for that transmsson loss. The resultng cumulatve strbuton s taken as the precte strbuton although there s no one-to-one correlaton between the nvual ranfall-rate/ran-heght combnatons an the transmsson loss.

23 Rec. ITU-R P Worst-month prectons Worst-month scalng factors, Q, for hyrometeor scatter have been foun to be about 3 at 1% tme, 4.5 at 0.01% tme an about 7 at 0.001% tme n Europe. These are base on a lmte amount of ata at frequences of 11 GHz an above, an shoul be use pruently. It was foun that the mean values were very close to the European ranfall rate factors. Therefore, n the absence of measure Q values for precptaton scatter, t s suggeste that the Q values for ranfall rate be use nstea (see Recommenaton ITU-R P.841 for tables of Q values). As an example, base on results for an 11 GHz path of 131 km n the Unte Kngom, a transmsson loss of 141 B was exceee for all but 0.01% of tme on an annual bass. Usng a Q factor of 4.5, the transmsson loss exceee for all but 0.002% of the annual strbuton, B, woul occur for 0.01% of the worst-month, a ecrease n loss of 1.7 B. In prncple, these worst-month factors shoul take complete account of the meltng layer, but moel calculatons have suggeste that the nterference effect of ths layer may be sgnfcant f t s centre on the common volume of the ntersectng man beams for a sgnfcant pero of tme urng, for example, a worst-month. The effect s frequency epenent, beng more sgnfcant at lower frequences, such as 4-6 GHz, an less so at hgh frequences. The effect was observe on measurements on a 131 km path at 11.2 GHz (composte ran clmate C, D, E) whch ncate that the presence of the meltng layer n the summer ncrease the nterference level by about 2-3 B at percentages of tme between 0.1% an 0.01%, relatve to the expecte enhancement n the seasonal statstcs n the absence of the meltng layer. At 5 GHz, the scale nterference enhancement ue to the presence of the meltng layer woul be 3-4 B. Worst-month enhancements n nterference resultng from the presence of the meltng layer woul be slghtly larger than these worst-season enhancements. Appenx 1 to Annex 1 Rao-meteorologcal ata requre for the clear-ar precton proceure 1 Introucton The clear-ar precton proceures rely on rao-meteorologcal ata to prove the basc locaton varablty for the prectons. These ata are prove n the form of maps whch are contane n ths Appenx.

24 24 Rec. ITU-R P Maps of vertcal varaton of rao refractvty ata For the global proceure, the clear-ar rao-meteorology of the path s characterze for the contnuous (long-term) nterference mechansms by the average annual value of N (the refractve nex lapse-rate over the frst 1 km of the atmosphere) an for the anomalous (short-term) mechansms by the tme percentage, β 0 %, for whch the refractve graent of the lower atmosphere s below 100 N-unts/km. These parameters prove a reasonable bass upon whch to moel the clear-ar propagaton mechansms escrbe n 2 of Annex 1. For some of these quanttes, ata are prove n ths Appenx for annual an worst-month calculatons: Fgure 4 proves average year N ata; Fgure 5 proves the assocate maxmum monthly mean N contours. FIGURE 4 Average annual values of N Lattue (egrees) Longtue (egrees)

25 Rec. ITU-R P FIGURE 5 Maxmum monthly mean values of N (for worst-month precton) Lattue (egrees) Longtue (egrees) Map of surface refractvty, N 0 Fgure 6 proves a map of average sea-level surface refractvty, N 0, for the troposcatter moel. 4 Implementaton of maps n computer atabase form For computer mplementaton of the proceures, t s convenent to capture these maps n gtal form an to convert them nto smple atabases that can be accesse by the software. For the global refractve nex maps, t s suggeste that the contours be converte nto two-mensonal arrays of lattue an longtue. To avo scontnutes n the precton wth small changes n locaton or stance the values for each array cell shoul be erve by nterpolaton between the contours.

26 26 Rec. ITU-R P FIGURE 6 Sea-level surface refractvty, N0 N Lattue (egrees) S W E Longtue (egrees) Appenx 2 to Annex 1 Path profle analyss 1 Introucton For path profle analyss, a path profle of terran heghts above mean sea level s requre. The parameters that nee to be erve from the path profle analyss for the purposes of the propagaton moels are gven n Table 7. 2 Constructon of path profle Base on the geographcal coornates of the nterferng (ϕ t, ψ t ) an nterfere-wth (ϕ r, ψ r ) statons, terran heghts (above mean sea level) along the great-crcle path shoul be erve from a topographcal atabase or from approprate large-scale contour maps. The preferre stance resoluton of the profle s that gvng an nteger number of steps of approxmately 0.25 km. Other

27 Rec. ITU-R P stance ncrements can be use, up to a maxmum of about 1 km, wth some possble ecrease n precton accuracy. The profle shoul nclue the groun heghts at the nterferng an nterfere-wth staton locatons as the start an en ponts. To the heghts along the path shoul be ae the necessary Earth s curvature, base on the value of a e foun n equaton (6). Although equally-space profle ponts are consere preferable, t s possble to use the metho wth non-equally-space profle ponts. Ths may be useful when the profle s obtane from a gtal map of terran heght contours. However, t shoul be note that the Recommenaton has been evelope from testng usng equally-space profle ponts; nformaton s not avalable on the effect of non-equally-space ponts on accuracy. For the purposes of ths Recommenaton the pont of the path profle at the nterferer s consere as pont zero, an the pont at the nterfere-wth staton s consere as pont n. The path profle therefore conssts of n + 1 ponts. Fgure 7 gves an example of a path profle of terran heghts above mean sea level, showng the varous parameters relate to the actual terran. FIGURE 7 Example of a (trans-horzon) path profle -th terran pont θ Interferng staton (T) θ t h tg lt h l lr θr h ts h gt ae = k50 a Mean sea level Interfere-wth staton (R) h gr h rg h rs Note 1 The value of θ as rawn wll be negatve. t

28 28 Rec. ITU-R P Table 7 efnes parameters use or erve urng the path profle analyss. TABLE 7 Path profle parameter efntons Parameter a e f λ h ts h rs θ t θ r θ h st h sr h h m h te h re Effectve Earth s raus (km) Great-crcle path stance (km) Descrpton Great-crcle stance of the -th terran pont from the nterferer (km) Incremental stance for regular path profle ata (km) Frequency (GHz) Wavelength (m) Interferer antenna heght (m) above mean sea level (amsl) Interfere-wth antenna heght (m) (amsl) Horzon elevaton angle above local horzontal (mra), measure from the nterferng antenna Horzon elevaton angle above local horzontal (mra), measure from the nterfere-wth antenna Path angular stance (mra) Heght of the smooth-earth surface (amsl) at the nterferng staton locaton (m) Heght of the smooth-earth surface (amsl) at the nterfere-wth staton locaton (m) Heght of the -th terran pont amsl (m) h 0 : groun heght of nterferng staton h n : groun heght of nterfere-wth staton Terran roughness (m) Effectve heght of nterferng antenna (m) Effectve heght of nterfere-wth antenna (m) 3 Path length For general cases the path length, (km), can be foun from the path profle ata: = n = 1 however, for regularly-space path profle ata ths smplfes to: ( 1) km (50) = n km (51) where s the ncremental path stance (km).

29 Rec. ITU-R P Path classfcaton The path profle must next be use to classfy the path nto one of three geometrcal categores base on an effectve Earth s raus of a e. The nterference path classfcatons are as ncate n Table Classfcaton Step 1: Test for a trans-horzon path A path s trans-horzon f the physcal horzon elevaton angle as seen by the nterferng antenna (relatve to the local horzontal) s greater than the angle (agan relatve to the nterferer s local horzontal) subtene by the nterfere-wth antenna. The test for the trans-horzon path conton s thus: θ max > θ t mra (52) θmax n 1 = max ( θ ) = 1 mra (53) θ : elevaton angle to the - th terran pont h : h ts : : h hts 10 3 θ = mra (54) 2 a heght of the -th terran pont (m) amsl nterferer antenna heght (m) amsl stance from nterferer to the -th terran element (km) e hrs hts 10 3 θ t = 2 ae mra (55) h rs : nterfere-wth antenna heght (m) amsl : total great-crcle path stance (km) a e : mean effectve Earth s raus approprate to the path (equaton (6)). If the conton of equaton (52) s met, then the remanng path profle analyss requre for trans-horzon paths can be unertaken (see 5.1). Uner these contons Step 2 of the path classfcaton s not neee. If the conton of equaton (52) s not fulflle, the path s lne-of-sght, wth or wthout ncurson by the terran of the frst Fresnel zone. 4.2 Step 2: Test for lne-of-sght wth sub-path ffracton (.e. wthout full frst Fresnel zone clearance) A non trans-horzon path s lne-of-sght wth sub-path ffracton, f the elevaton angle over the physcal horzon, as seen by the nterferng antenna (relatve to the local horzontal), an allowng for clearance equal to the frst Fresnel ellpso raus at the horzon pont, s greater than the angle (agan relatve to the nterferer s local horzontal) subtene by the nterfere-wth antenna.

30 30 Rec. ITU-R P The path has sub-path ffracton f: θ fmax > θt mra (56) θfmax n 1 = max ( θf) = 1 (57) To complete ths test an extra term s therefore requre n equaton (54) to allow for the frst Fresnel ellpso. Recommenaton ITU-R P.526, 2, gves the raus of ths ellpso, R (m), at any pont along the path: R ( ) = m (58) f where f s the frequency (GHz). The approprate raus, R (m), s ae to each terran heght, h (m), n equaton (54) yelng equaton (59). Allowng for frst Fresnel zone clearance, θ f, the termnal antenna elevaton angle (ra) to the -th pont s obtane from the followng equaton: ( h + R ) hts f = ae θ mra (59) If the conton of equaton (56) s met, then the remanng path profle analyss requre for sub-path ffracton cases can be unertaken. If the conton of equaton (56) s not fulflle, the path s lne-of-sght an no further path profle analyss s neee. 5 Dervaton of parameters from the path profle 5.1 Trans-horzon paths The parameters to be erve from the path profle are those contane n Table Interferng antenna horzon elevaton angle, θ t The nterferng antenna s horzon elevaton angle s the maxmum antenna horzon elevaton angle when equaton (53) s apple to the n 1 terran profle heghts. wth θ max as etermne n equaton (53). θ t = θ max mra (60) Interferng antenna horzon stance, lt The horzon stance s the mnmum stance from the transmtter at whch the maxmum antenna horzon elevaton angle s calculate from equaton (53). lt = km for max (θ ) (61)