A path-specific propagation prediction method for point-to-area terrestrial services in the VHF and UHF bands

Transcription

1 Recommenaton ITU-R P.8- (0/0) A pat-specfc propagaton precton meto for pont-to-area terrestral servces n te VHF an UHF bans P Seres Raowave propagaton

2 Rec. ITU-R P.8- Forewor Te role of te Raocommuncaton Sector s to ensure te ratonal, equtable, effcent an economcal use of te rao-frequency spectrum by all raocommuncaton servces, nclung satellte servces, an carry out stues wtout lmt of frequency range on te bass of wc Recommenatons are aopte. Te regulatory an polcy functons of te Raocommuncaton Sector are performe by Worl an Regonal Raocommuncaton Conferences an Raocommuncaton Assembles supporte by Stuy Groups. Polcy on Intellectual Property Rgt (IPR) ITU-R polcy on IPR s escrbe n te Common Patent Polcy for ITU-T/ITU-R/ISO/IEC reference n Annex of Resoluton ITU-R. Forms to be use for te submsson of patent statements an lcensng eclaratons by patent olers are avalable from ttp:// were te Guelnes for Implementaton of te Common Patent Polcy for ITU-T/ITU-R/ISO/IEC an te ITU-R patent nformaton atabase can also be foun. Seres of ITU-R Recommenatons (Also avalable onlne at ttp:// Seres BO BR BS BT F M P RA RS S SA SF SM SNG TF V Ttle Satellte elvery Recorng for proucton, arcval an play-out; flm for televson Broacastng servce (soun) Broacastng servce (televson) Fxe servce Moble, raoetermnaton, amateur an relate satellte servces Raowave propagaton Rao astronomy Remote sensng systems Fxe-satellte servce Space applcatons an meteorology Frequency sarng an coornaton between fxe-satellte an fxe servce systems Spectrum management Satellte news gaterng Tme sgnals an frequency stanars emssons Vocabulary an relate subjects Note: Ts ITU-R Recommenaton was approve n Engls uner te proceure etale n Resoluton ITU-R. Electronc Publcaton Geneva, 0 ITU 0 All rgts reserve. No part of ts publcaton may be reprouce, by any means watsoever, wtout wrtten permsson of ITU.

3 Rec. ITU-R P.8- RECOMMENDATION ITU-R P.8- A pat-specfc propagaton precton meto for pont-to-area terrestral servces n te VHF an UHF bans (Queston ITU-R 03/3) ( ) Scope Ts Recommenaton escrbes a propagaton precton meto sutable for terrestral pont-to-area servces n te frequency range 30 MHz to 3 GHz. It prects sgnal levels at te mean of te multpat strbuton exceee for a gven percentage of tme, p%, n te range % p 50% an a gven percentage of locatons, p L, n te range % p L 99%. Te meto proves etale analyss base on te terran profle. Te meto s sutable for prectons for raocommuncaton systems utlzng terrestral crcuts avng pat lengts from 0.5 km up to about km stance, wt bot termnals wtn approxmately 3 km egt above groun. It s not sutable for propagaton prectons on eter ar-groun or space-eart rao crcuts. Ts Recommenaton complements Recommenaton ITU-R P.546. Te ITU Raocommuncaton Assembly, conserng a) tat tere s a nee to gve guance to engneers n te plannng of terrestral raocommuncaton servces n te VHF an UHF bans; b) tat, for statons workng n te same or ajacent frequency cannels, te etermnaton of te mnmum geograpcal stance of separaton requre to avo unacceptable nterference ue to long-stance terrestral propagaton s a matter of great mportance, notng a) tat Recommenaton ITU-R P.58 proves guance on te precton of pont-to-area pat loss for te aeronautcal moble servce for te frequency range 5 MHz to 30 GHz an te stance range up to 800 km; b) tat Recommenaton ITU-R P.45 proves guance on te etale evaluaton of mcrowave nterference between statons on te surface of te Eart at frequences above about 0.7 GHz; c) tat Recommenaton ITU-R P.67 proves guance on te precton of pont-to-pont (P-P) pat loss for trans-orzon rao-relay systems for te frequency range above 30 MHz an for te stance range 00 to 000 km; ) tat Recommenaton ITU-R P.4 proves guance on precton for sort-range (up to km) outoor servces; e) tat Recommenaton ITU-R P.530 proves guance on te precton of P-P pat loss for terrestral LoS systems;

4 Rec. ITU-R P.8- f) tat Recommenaton ITU-R P.546 proves guance on te precton of pont-to-area fel strengts n te VHF an UHF bans base prncpally on statstcal analyses of expermental ata, recommens tat te proceure gven n Annex soul be use for te etale evaluaton of pont-toarea sgnal levels n connecton wt tese servces. Annex Introucton Te propagaton precton meto escrbe n ts Annex s recommene for te etale evaluaton of sgnal levels sutable for use n connecton wt terrestral pont-to-area servces n te VHF an UHF bans. It prects te sgnal level (.e. electrc fel strengt) exceee for a gven percentage, p%, of an average year n te range % p 50% an p L % locatons n te range % p L 99%. Terefore, ts meto may be use to prect bot te servce area an avalablty for a esre sgnal level (coverage), an te reuctons n ts servce area an avalablty ue to unesre, co- an/or ajacent-cannel sgnals (nterference). Te propagaton moel of ts meto s symmetrc n te sense tat t treats bot rao termnals n te same manner. From te moel s perspectve, t oes not matter wc termnal s te transmtter an wc s te recever. However, for convenence n te moel s escrpton, te terms transmtter an recever are use to enote te termnals at te start an en of te rao pat, respectvely. Te meto s frst escrbe n terms of calculatng basc transmsson loss (B) not exceee for p% tme for te mean value of locatons. Te locaton varablty an bulng entry loss elements are ten caracterze statstcally wt respect to recever locatons. A proceure s ten gven for convertng to electrc fel strengt (B(μV/m)) for an effectve raate power of kw. Ts meto s ntene prmarly for use wt systems usng low-gan antennas. However, te cange n accuracy wen g-gan antennas are use only affects te troposcatter element of te overall meto, an te cange n te prectons s small. For example, even wt 40 B antennas at bot ens of te lnk te over-estmaton of troposcatter sgnals wll amount to only about B. Te meto s sutable for prectons for raocommuncaton systems utlzng terrestral crcuts avng pat lengts from 0.5 km up to about km stance, wt bot termnals wtn approxmately 3 km egt above groun. It s not sutable for propagaton prectons on eter ar-groun or space-eart rao crcuts. Te propagaton precton meto n ts Annex s pat-specfc. Pont-to-area prectons usng ts meto consst of seres of many P-P (.e. transmtter-pont-to-recever-multpont) prectons, unformly strbute over notonal servce areas. Te number of ponts soul be large enoug to ensure tat te precte values of basc transmsson losses or fel strengts tus obtane are reasonable estmates of te mean values, wt respect to locatons, of te corresponng quanttes for te elemental areas tat tey represent. In consequence, t s assume tat users of ts Recommenaton are able to specfy etale terran profles (.e. elevatons above mean sea level) as functons of stance along te great crcle pats (.e. geoesc curves) between te termnals, for many fferent termnal locatons (recever-ponts).

5 Rec. ITU-R P.8-3 For most practcal applcatons of ts meto to pont-to-area coverage an nterference prectons, ts assumpton mples te avalablty of a gtal terran elevaton atabase, reference to lattue an longtue wt respect to a consstent geoetc atum, from wc te terran profles may be extracte by automate means. If tese etale terran profles are not avalable, ten Recommenaton ITU-R P.546 soul nstea be use for prectons. In vew of te foregong, te locaton varablty an bulng entry loss moel elements of ts Recommenaton are caracterze va te statstcs of lognormal strbutons wt respect to recever locatons. Altoug ts statstcal caracterzaton of te pont-to-area propagaton problem woul appear to make te overall moel unsymmetrcal (.e. non-recprocal), users of ts Recommenaton soul note tat te locaton varablty coul, n prncple, be apple at eter en of te pat (.e. eter termnal), or even bot (.e. te transmtter an te recever). However, te locaton varablty correcton s only meanngful n stuatons wen exact locaton of a gven termnal s unknown an a statstcal representaton over tat termnal s potental locatons s requre. Tere are unlkely to be many stuatons were ts coul meanngfully be apple to te transmtter locaton. If te locatons of bot termnals are known exactly an ts proceure s beng use n P-P moe, ten ts Recommenaton s only applcable wt p L = 50%. A smlar pont s true regarng bulng entry losses. Te argument s slgtly more complcate tan for locaton varablty owng to te fact tat te mean entry loss correcton s non-zero. At te transmtter en, users soul also a te bulng entry loss to te basc transmsson loss f te transmtter s nse a bulng, but users must also be aware tat te mean loss values n Table 6 may be msleang f te transmtter s not n a mean locaton. Moel elements of te propagaton precton meto Ts propagaton precton meto takes account of te followng moel elements: lne-of-sgt (LoS) ffracton (embracng smoot-eart, rregular terran an sub-pat cases) troposperc scatter anomalous propagaton (uctng an layer reflecton/refracton) egt-gan varaton n clutter locaton varablty bulng entry losses. 3 Input parameters 3. Basc nput ata Table escrbes te basc nput ata, wc efnes te rao termnals, te frequency, an te percentage tme an locatons for wc a precton s requre. Te lattue an longtue of te two statons are state as basc nputs on te bass tat tey are neee to obtan te pat profle. Rao-meteorologcal parameters must be obtane for a sngle locaton assocate wt te rao pat, an for a long pat te pat-centre soul be selecte. It s approprate to obtan te rao-meteorologcal parameters for te transmtter locaton wen prectng ts coverage area.

6 4 Rec. ITU-R P.8- TABLE Basc nput ata Parameter Unts Mnmum Maxmum Descrpton f GHz Frequency (GHz) p % Percentage of average year for wc te calculate sgnal level s exceee p L % 99 Percentage of locatons for wc te calculate sgnal level s exceee φ t, φ r egrees Lattue of transmtter, recever ψ t, ψ r egrees Longtue of transmtter, recever (postve = East of Greenwc) tg, rg m Antenna centre egt above groun level 3. Terran profle A terran profle for te rao pat s requre for te applcaton of te propagaton precton meto. In prncple, ts conssts of tree arrays eac avng te same number of values, n, as follows: : stance from transmtter of -t proflepont (km) : egt of -t proflepont above sealevel (m) g = + representatve clutter egt of -t proflepont (m) :,, 3... n = nex of te profle pont n: number of profle ponts. Note tat te frst profle pont s at te transmtter. Tus s zero an s te terran egt at te transmtter n metres above sea level. Smlarly, te n-t profle pont s at te recever. Tus n s te pat lengt n km, an n te terran egt at te recever n metres above sea level. No specfc stance between profle ponts s gven. Assumng tat profles are extracte from a gtal terran elevaton moel, a sutable spacng wll typcally be smlar to te pont spacng of te source ata. Te profle ponts are not requre to be equally-space, but t s esrable tat tey are at a smlar spacng for te wole profle. It s esrable to ave nformaton on groun cover (clutter) along te pat. It s convenent to store clutter categores n an atonal array of n ponts to matc te profle egt ata. Te representatve clutter egt referre to n equaton (c) concerns groun cover, suc as vegetaton an bulngs. Ang clutter egts to a profle s base on te assumpton tat te egts represent te bare surface of te Eart. If te rao pat passes over woolan or urbanzaton were ffracton or sub-pat obstructon occurs, n general te effectve profle egt wll be ger because te rao sgnal wll travel over te clutter. Tus a more accurate representaton of te profle can be obtane by ang egts to account for te clutter. Te approprate aton s not necessarly pyscal, suc as rooftop egts n te case of bulngs. Were gaps exst between clutter objects, as seen by te rao wave, some energy may travel between rater tan over tem. In ts stuaton te presence of clutter s expecte to ncrease ffracton loss, but not by as muc as rasng te profle to te pyscal clutter egt. (a) (b) (c)

7 Rec. ITU-R P.8-5 Ts apples partcularly to g-rse urban areas. Categores suc as ense urban or g-rse urban ten to be assocate wt bulng egts of 30 metres or more. But some g-rse areas ave large spaces between te tall bulngs, an t s possble for low-loss pats to exst passng aroun tem, rater tan over te roofs. At te oter extreme, even n areas classfe as open or rural t s unusual for te groun to be completely bare, tat s, free of any objects wc mgt a to propagaton losses. Tus small values of R, rater tan zero, mgt be approprate n many cases. Tere s a separate use of clutter nformaton to estmate termnal clutter losses, as escrbe n 4.7. Te concept of representatve clutter egt, R, s retane, but may be nterprete fferently. Partcularly for urban categores te objectve s to entfy te egt over wc te sgnal must propagate for a termnal below clutter egt. In suc cases an estmate soul agan be mae as to wat extent, on a statstcal bass, te sgnal passes aroun rater tan over clutter objects. In te case of open, rural an water categores, R s essentally a scalng factor for equaton (54b). Tus representatve clutter egt R epens not only on te typcal pyscal egt of clutter objects but also on te orzontal spacng of objects an te gaps between tem. Tere s no accepte stanar as to wat a clutter category, suc as urban, represents n pyscal terms n fferent countres. Table suggests efault values for R wc may be use n te absence of more specfc nformaton approprate for te regon concerne. Clutter type TABLE Default nformaton for clutter-loss moellng Representatve clutter egt (m) A to profle equaton (c) Termnal clutter losses 4.7 Termnal clutter loss moel Water/sea 0 0 Equaton (64b) Open/rural 0 0 Equaton (64b) Suburban 0 0 Equaton (64a) Urban/trees/forest 5 5 Equaton (64a) Dense urban 0 0 Equaton (64a) 3.3 Rao-clmatc zones Informaton s also neee on wat lengts of te pat are n te rao-clmatc zones escrbe n Table 3. For maxmum consstency of results between amnstratons t s strongly recommene tat te calculatons of ts proceure be base on te ITU Dgtze Worl Map (IDWM) wc s avalable from te BR for manframe or personal computer envronments. If all ponts on te pat are at least 50 km from te sea or oter large boes of water, ten only te nlan category apples. If te zone nformaton s store n successve ponts along te rao pat, t soul be assume tat canges occur mway between ponts avng fferent zone coes.

8 6 Rec. ITU-R P.8- TABLE 3 Rao-clmatc zones Zone type Coe Defnton Coastal lan A Coastal lan an sore areas,.e. lan ajacent to te sea up to an alttue of 00 m relatve to mean sea or water level, but lmte to a stance of 50 km from te nearest sea area. Were precse 00 m ata are not avalable an approxmate value may be use Inlan A All lan, oter tan coastal an sore areas efne as coastal lan above Sea B Seas, oceans an oter large boes of water (.e. coverng a crcle of at least 00 km n ameter) 3.4 Termnal stances from te coast If te pat s over zone B two furter parameters are requre, ct, cr, gvng te stance of te transmtter an te recever from te coast (km), respectvely, n te recton of te oter termnal. For a termnal on a sp or sea platform te stance s zero. 3.5 Basc rao-meteorologcal parameters Te precton proceure requres two rao-meteorologcal parameters to escrbe te varablty of atmosperc refractvty. ΔN (N-unts/km), te average rao-refractve nex lapse-rate troug te lowest km of te atmospere, proves te ata upon wc te approprate effectve Eart raus can be calculate for pat profle an ffracton obstacle analyss. Note tat ΔN s a postve quantty n ts proceure. N 0 (N-unts), te sea-level surface refractvty, s use only by te troposcatter moel as a measure of varablty of te troposcatter mecansm. Appenx gves global maps of ΔN an N 0, an ata fles contanng te gtze maps are avalable from te Bureau. 3.6 Incence of uctng Te egree to wc sgnal levels wll be enance ue to anomalous propagaton, partcularly uctng, s quantfe by a parameter β 0 (%), te tme percentage for wc refractve nex lapserates exceeng 00 N-unts/km can be expecte n te frst 00 m of te lower atmospere. Te value of β 0 s calculate as follows. Calculate te parameter μ, wc epens on te egree to wc te pat s over lan (nlan an/or coastal) an water: tm μ = 0 τ + 0 were te value of μ sall be lmte to μ, 5 ( τ) 0. ()

9 Rec. ITU-R P.8-7 an 4.4 ( 4. 0 ) τ = e lm (3) tm : longest contnuous lan (nlan + coastal) secton of te great-crcle pat (km) lm : longest contnuous nlan secton of te great-crcle pat (km). Te rao-clmatc zones to be use for te ervaton of tm an lm are efne n Table 3. If all ponts on te pat are at least 50 km from te sea or oter large boes of water, ten only te nlan category apples an tm an lm are equal to te pat lengt,. Calculate te parameter μ 4, wc epens on μ an te lattue of te pat centre n egrees: Calculate β 0 : μ μ 4 4 = μ = μ ( ϕ ) 0.3 φ: pat centre lattue (egrees). for ϕ 70 for ϕ > ϕ μ μ % for ϕ 70 β = 4 0 (5) 4.7μ μ4 % for ϕ > Effectve Eart raus Te mean effectve Eart raus factor k 50 for te pat s gven by: 57 k50 = (6) 57 ΔN Te value of te average rao-refractvty lapse-rate, ΔN, may be obtane from Fg., usng te lattue an longtue of te pat centre as representatve for te entre pat. Te mean value of effectve Eart raus a e s gven by: a e = 6 37 k km (7a) 50 (4) Te effectve Eart raus exceee for β 0 tme, a β, s gven by: a = 6 37 k km (7b) β β were k β = 3.0 s an estmate of te effectve Eart-raus factor exceee for β 0 tme. 3.8 Parameters erve from te pat profle analyss Values for a number of pat-relate parameters necessary for te calculatons, as ncate n Table 4, must be erve va an ntal analyss of te pat profle base on te value of a e gven by equaton (7a). Informaton on te ervaton, constructon an analyss of te pat profle s gven n Appenx of ts Annex.

10 8 Rec. ITU-R P.8-4 Te precton proceure 4. General Te overall precton proceure s escrbe n ts secton. Frst, te basc transmsson loss, L b (B), not exceee for te requre annual percentage tme, p%, an 50% locatons s evaluate as escrbe n (.e. te basc transmsson losses ue to LoS propagaton, propagaton by ffracton, propagaton by troposperc scatter, propagaton by uctng/layer reflecton an te combnaton of tese propagaton mecansms to prect te basc transmsson loss, respectvely). In , metos to account for te ncluson of termnal clutter effects, te effects of locaton varablty an bulng entry loss are escrbe. Fnally, 4. gves expressons tat relate te basc transmsson loss to te fel strengt (B μv/m) for kw effectve raate power. TABLE 4 Parameter values to be erve from te pat profle analyss Parameter lt, lr θ t, θ r θ ts, rs tc, rc te, re b ω Great-crcle pat stance (km) Descrpton Dstance from te transmt an receve antennas to ter respectve orzons (km) Transmt an receve orzon elevaton angles respectvely (mra) Pat angular stance (mra) Antenna centre egt above mean sea level (m) max( ts, g ) an max( rs, g n ) respectvely Effectve egts of antennas above te terran (m) Aggregate lengt of te pat sectons over water (km) Fracton of te total pat over water: ω = b / were s te great-crcle stance (km) calculate usng equaton (73). For totally overlan pats: ω = 0 4. Lne-of-sgt propagaton (nclung sort-term effects) Te followng soul all be evaluate for bot LoS an trans-orzon pats. Te basc transmsson loss ue to free-space propagaton s gven by: L bfs = log f + 0 log B (8) Correctons for multpat an focusng effects at p an β 0 percentage tmes, respectvely, are gven by: + lt lr =.6 e 0 p Esp log B (9a) 50 + lt lr β0 E β =.6 e 0 s log B (9b) 50

11 Rec. ITU-R P.8-9 Calculate te basc transmsson loss not exceee for tme percentage, p%, ue to LoS propagaton (regarless of weter or not te pat s actually LoS), as gven by: L = L + E b0 p bfs sp B (0) Calculate te basc transmsson loss not exceee for tme percentage, β 0 %, ue to LoS propagaton (regarless of weter or not te pat s actually LoS), as gven by: L 0 B () b β = Lbfs + Esβ 4.3 Propagaton by ffracton Dffracton loss s calculate by te combnaton of a meto base on te Bullngton constructon an spercal-eart ffracton. Te Bullngton part of te meto s an expanson of te basc Bullngton constructon to control te transton between free-space an obstructe contons. Ts part of te meto s use twce: for te actual pat profle, an for a zero-egt smoot profle wt mofe antenna egts referre to as effectve antenna egts. Te same effectve antenna egts are also use to calculate spercal-eart ffracton loss. Te fnal result s obtane as a combnaton of tree losses calculate as above. For a perfectly smoot pat te fnal ffracton loss wll be te output of te spercal-eart moel. Ts meto proves an estmate of ffracton loss for all types of pat, nclung over-sea or over-nlan or coastal lan, an rrespectve of weter te pat s smoot or roug, an weter LoS or transorzon. Ts ffracton meto s always use for mean effectve Eart raus. If an overall precton s requre for p = 50%, no furter ffracton calculaton s necessary. In te general case were p < 50%, te ffracton calculaton must be performe a secon tme for an effectve Eart-raus factor equal to 3. Ts secon calculaton gves an estmate of ffracton loss not exceee for β 0 % tme, were β 0 s gven by equaton (5). Te ffracton loss not exceee for p% tme, for % p 50%, s ten calculate usng a lmtng or nterpolaton proceure escrbe n Te meto uses an approxmaton to te sngle knfe-ege ffracton loss as a functon of te mensonless parameter, ν, gven by: J ( ν) = log ( ) ν ν 0. () Note tat J( 0.78) 0, an ts efnes te lower lmt at wc ts approxmaton soul be use. J(ν) s set to zero for ν Te overall ffracton calculaton s escrbe n sub-sectons as follows: Secton 4.3. escrbes te Bullngton part of te ffracton meto. For eac ffracton calculaton for a gven effectve Eart raus ts s use twce. On te secon occason te antenna egts are mofe an all profle egts are zero. Secton 4.3. escrbes te spercal-eart part of te ffracton moel. Ts s use wt te same antenna egts as for te secon use of te Bullngton part n 4.3..

12 0 Rec. ITU-R P.8- Secton escrbes ow te metos n 4.3. an 4.3. are use n combnaton to perform te complete ffracton calculaton for a gven effectve Eart raus. Due to te manner n wc te Bullngton an spercal-eart parts are use, te complete calculaton as come to be known as te elta-bullngton moel. Secton escrbes te complete calculaton for ffracton loss not exceee for a gven percentage tme p% Te Bullngton part of te ffracton calculaton In te followng equatons slopes are calculate n m/km relatve to te baselne jonng sea level at te transmtter to sea level at te recever. Te stance an egt of te -t profle pont are klometres an metres above sea level respectvely, takes values from to n were n s te number of profle ponts, an te complete pat lengt s klometres. For convenence te termnals at te start an en of te profle are referre to as transmtter an recever, wt egts n metres above sea level ts an rs, respectvely. Effectve Eart curvature C e km s gven by /a e were a e s effectve eart raus n klometres. Wavelengt n metres s represente by λ. Fn te ntermeate profle pont wt te gest slope of te lne from te transmtter to te pont. S tm + 500Ce ( ) tc [ ] = max m/km (3) were te profle nex takes values from to n-. Calculate te slope of te lne from transmtter to recever assumng a LoS pat: Two cases must now be consere. Case. Pat s LoS S tr rc tc = m/km (4) If S tm < S tr te pat s LoS. Fn te ntermeate profle pont wt te gest ffracton parameter ν: { } tc ( ) + rc 0. [ + Ce ( ) ] ( ) 00 ν max = 500 λ max (5) were te profle nex takes values from to n-. In ts case, te knfe-ege loss for te Bullngton pont s gven by: ( ) L uc = J B (6) ν max were te functon J s gven by equaton () for ν b greater tan -0.78, an s zero oterwse. Case. Pat s transorzon If S tm S tr te pat s transorzon. Fn te ntermeate profle pont wt te gest slope of te lne from te recever to te pont. Srm + 500Ce ( ) rc [ ] = max m/km (7)

13 were te profle nex takes values from to n-. Calculate te stance of te Bullngton pont from te transmtter: Rec. ITU-R P.8- bp + S rc tc rm = km (8) Stm + Srm Calculate te ffracton parameter, ν b, for te Bullngton pont: ( ) + tc b rc bp νb = tc + Stmbp. 00 λb In ts case, te knfe-ege loss for te Bullngton pont s gven by: L uc ( ν ) b 0 (9) ( ) = J B (0) For L uc calculate usng eter equaton (6) or (0), Bullngton ffracton loss for te pat s now gven by: 4.3. Spercal-Eart ffracton loss [ exp( L / 6) ]( ) Lbull = Luc + uc 0 B () Te spercal-eart ffracton loss not exceee for p% tme for antenna egts te an re (m), L sp, s calculate as follows. Calculate te margnal LoS stance for a smoot pat: los p ( ) = a + 00 km () te If los calculate ffracton loss usng te meto n below for a ft = a p to gve L ft, an set L sp equal to L ft. No furter spercal-eart ffracton calculaton s necessary. Oterwse contnue as follows: Calculate te smallest clearance egt between te curve-eart pat an te ray between te antennas,, gven by: were se re se se te re 500 a p a p = m (3) se = ( + b) km (4a) = km (4b) se se m + π 3c 3m b = cos + arccos 3 (4c) 3m 3 3 ( m + ) bp

14 Rec. ITU-R P.8- were te arccos functon returns an angle n raans te c = (4) + p te te re re 50 m = (4e) a ( + ) Calculate te requre clearance for zero ffracton loss, req, gven by: re req se se λ m (5) = If > req te spercal-eart ffracton loss L sp s zero. No furter spercal-eart ffracton calculaton s necessary. Oterwse contnue as follows: Calculate te mofe effectve Eart raus, a em, wc gves margnal LoS at stance gven by: 500 a em = km (6) te + re Use te meto n for a ft = a em to gve L ft. If L ft s negatve, te spercal-eart ffracton loss L sp s zero, an no furter spercal-eart ffracton calculaton s necessary. Oterwse contnue as follows: Calculate te spercal-eart ffracton loss by nterpolaton: sp [ se req ] L ft L = / B (7) Frst-term part of spercal-eart ffracton loss Ts sub-secton gves te meto for calculatng spercal-eart ffracton usng only te frst term of te resue seres. It forms part of te overall ffracton meto escrbe n 4.3. above to gve te frst-term ffracton loss L ft for a gven value of effectve Eart raus a ft. Te value of a ft to use s gven n Set terran electrcal propertes typcal for lan, wt relatve permttvty ε r =.0 an conuctvty σ = S/m an calculate L ft usng equatons (9) to (36) an call te result L ftlan. Set terran electrcal propertes typcal for sea, wt relatve permttvty ε r = an conuctvty σ = 5.0 S/m an calculate L ft usng equatons (9) to (36) an call te result L ftsea. Frst-term spercal ffracton loss s now gven by: L = ωl + ( ω) L ft ftsea ftlan B (8)

15 Rec. ITU-R P.8-3 were ω s te fracton of te pat over sea. Start of calculaton to be performe twce, as escrbe above: Normalze factor for surface amttance for orzontal an vertcal polarzaton: an K /3 ( a f ) [( ε ) + (8 / ) ] = f (orzontal) (9a) H ft r σ Calculate te Eart groun/polarzaton parameter: were K s K H or K V accorng to polarzaton. Normalze stance: Normalze transmtter an recever egts: K V [ ] / ε + ( 8 σ/ f ) = K (vertcal) (9b) H r 4 /4 +.6K K β ft = (30) K +.53K X /3 f =.88 β ft (3) a ft Y t /3 f = β ft te (3a) a ft Yr = βft f a ft re (3b) Calculate te stance term gven by: + 0log( X ) 7.6X for X.6 F X =.45 0log( X ) X for X <.6 (33) Defne a functon of normalze egt gven by: ( B.) 5log( B.) 8 for B > G ( Y ) = (34) 3 0log( B + 0.B ) oterwse Lmt G(Y) suc tat G( Y ) + 0log K /3 B = Y (35) βft Te frst-term spercal-eart ffracton loss s now gven by: L ft X ( ) G( Y ) = F G Y B (36) t r

16 4 Rec. ITU-R P Complete elta-bullngton ffracton loss moel Use te meto n 4.3. for te actual terran profle an antenna egts. Set te resultng Bullngton ffracton loss for te actual pat, L bulla = L bull as gven by equaton (). Use te meto n 4.3. for a secon tme, wt all profle egts, g, set to zero, an mofe antenna egts gven by ' ts ' rs = = ts rs st sr masl masl (37a) (37b) were te smoot-eart egts at transmtter an recever, st an sr, are gven n of Appenx. Set te resultng Bullngton ffracton loss for ts smoot pat, L bulls = L bull as gven by equaton (). Use te meto n 4.3. to calculate te spercal-eart ffracton loss L sp for te actual pat lengt km an wt: ' te = ts m (38a) ' re = rs m (38b) Dffracton loss for te general pat s now gven by: L = L + max{ L L, 0} B (39) bulla sp bulls Te ffracton loss not exceee for p% of te tme Use te meto n to calculate ffracton loss L for mean effectve Eart raus a e as gven by equaton (7a). Set mean ffracton loss L 50 = L. If p = 50% te ffracton loss not exceee for p% tme, L p, s gven by L 50, an ts completes te ffracton calculaton. If p < 50%, contnue as follows. Use te meto n to calculate ffracton loss L for effectve Eart raus not exceee for β 0 % tme a β as gven by equaton(7b). Set ffracton loss not exceee for β 0 % tme L β = L. Te applcaton of te two possble values of effectve Eart raus factor s controlle by an nterpolaton factor, F, base on a log-normal strbuton of ffracton loss over te range β 0 % < p 50%, gven by: = p I 00 β I 0 00 F = 0 f p = 50% (40a) f 50% > p > β0% (40b) = f β 0 % p (40c) were I(x) s te nverse complementary cumulatve normal strbuton as a functon of te probablty x. An approxmaton for I(x) wc may be use wt confence for x 0.5 s gven n Appenx 3 to ts Annex.

17 Rec. ITU-R P.8-5 Te ffracton loss, L p, not exceee for p% tme, s now gven by: L = L ) F B (4) p 50 + ( Lβ L 50 F s efne by equatons (40a-c), epenng on te values of p an β 0. Te mean basc transmsson loss assocate wt ffracton, L b50, s gven by: L = L + L B (4) b50 bfs 50 were L bfs s gven by equaton (8). Te basc transmsson loss assocate wt ffracton not exceee for p% tme s gven by: L = L 0 + L B (43) b b p p were L b0p s gven by equaton (0). 4.4 Propagaton by troposperc scatter NOTE At tme percentages muc below 50%, t s ffcult to separate te true troposperc scatter moe from oter seconary propagaton penomena wc gve rse to smlar propagaton effects. Te troposperc scatter moel aopte n ts Recommenaton s terefore an emprcal generalzaton of te concept of troposperc scatter wc also embraces tese seconary propagaton effects. Ts allows a contnuous consstent precton of basc transmsson loss over te range of tme percentages p from 0.00% to 50%, tus lnkng te uctng an layer reflecton moel at te small tme percentages wt te true scatter moe approprate to te weak resual fel exceee for te largest tme percentage. NOTE Ts troposcatter precton moel as been erve for nterference precton purposes an s not approprate for te calculaton of propagaton contons above 50% of tme affectng te performance aspects of trans-orzon rao-relay systems. Te basc transmsson loss ue to troposcatter, L bs (B), not exceee for any tme percentage, p, below 50%, s gven by: 50 Lbs = Lf + 0 log θ 0.5 N0 0.5 log B (44) p L f : frequency epenent loss: f L f = 5log( f ).5 log B (45) N 0 : pat centre sea-level surface refractvty, wc may be erve from Fg Propagaton by uctng/layer reflecton Te basc transmsson loss assocate wt uctng/layer-reflecton not exceee for p% tme, L ba (B), s gven by: L = A A ( p) B (46) ba f + 0.7

18 6 Rec. ITU-R P.8- A f : total of fxe couplng losses (except for local clutter losses) between te antennas an te anomalous propagaton structure wtn te atmospere: A f = log f + 0 log( lt + lr ) + A lf + A st + A sr + A ct + A cr B (47) A lf : emprcal correcton to account for te ncreasng attenuaton wt wavelengt n ucte propagaton A lf (f) = f f B f f < 0.5 GHz (47a) A lf (f) = 0.0 B oterwse A st, A sr : ste-selng ffracton losses for te transmttng an recevng statons respectvely: ( θ ( f ) / ) / 3 0log t, r lt,lr θ t, r f B for θ t, r > 0 mra A st, sr = (48) 0 B for θ 0 mra t, r A ct, A cr : θ = θ 0. mra (48a) t, r t,r lt,lr over-sea surface uct couplng correctons for te transmttng an recevng statons respectvely: 0.5 ( tan(0.07(50 ))) ct,cr A = 3 e + B for ω 0.75 ct,cr ts,rs ct cr lt, lr, (49) ct, cr 5 km A 0 B for all oter contons (49a) ct, cr = It s useful to note te lmte set of contons uner wc equaton (49) s neee. A ( p) : γ : θ : tme percentage an angular-stance epenent losses wtn te anomalous propagaton mecansm: A ( p) = γ θ A ( p) B (50) specfc attenuaton: + 5 a e / 3 γ = 5 0 f B/mra (5) angular stance (correcte were approprate (va equaton (48a)) to allow for te applcaton of te ste selng moel n equaton (46)): θ = + θ + θ mra (5) 0 3 t r a e θ t, r = θt,r 0. lt,lr for for θ θ t,r t,r 0. > 0. lt,lr lt,lr mra mra (5a)

19 Rec. ITU-R P.8-7 A( p) : tme percentage varablty (cumulatve strbuton): 3 p p A ( p) = + ( ) log + B (53) β β (.0058 log β) 6. 3 ( log β (log β) ) e.0 Γ = (53a) μ : correcton for pat geometry: μ 0 μ μ3 Γ β = β % (54) 500 = ae Te value of μ sall not excee. ε : 3.5 τ : μ 3 : ( + ) te α = 0.6 ε 0 9 re 3. α (55) τ (55a) s efne n equaton (3), an te value of α sall not be allowe to ecrease below 3.4 correcton for terran rougness: an: μ 3 = e ( m 0) ( ) I for for m m 0 m > 0 m (56) = mn (, 40) km (56a) I Te remanng terms ave been efne n Tables an an Appenx to ts Annex. lt 4.6 Basc transmsson loss not exceee for p% tme an 50% locatons gnorng te effects of termnal clutter Te followng proceure soul be apple to te results of te foregong calculatons for all pats, n orer to compute te basc transmsson loss not exceee for p% tme an 50% locatons. In orer to avo pyscally unreasonable scontnutes n te precte notonal basc transmsson losses, te foregong propagaton moels must be blene togeter to get mofe values of basc transmsson losses n orer to aceve an overall precton for p% tme an 50% locatons. Calculate an nterpolaton factor, F j, to take account of te pat angular stance: lr ( θ Θ F j = tan3.0 ξ (57) Θ )

20 8 Rec. ITU-R P.8- Θ : ξ : fxe parameter etermnng te angular range of te assocate blenng; set to 0.3 fxe parameter etermnng te blenng slope at te en of te range; set to 0.8 θ : pat angular stance (mra) efne n Table 7. Calculate an nterpolaton factor, F k, to take account of te pat great-crcle stance: F k ( = + κ sw) tan 3.0 (58) sw : sw : great crcle pat lengt efne n Table 3 (km) fxe parameter etermnng te stance range of te assocate blenng; set to 0 κ : fxe parameter etermnng te blenng slope at te ens of te range; set to 0.5. Calculate a notonal mnmum basc transmsson loss, L mnb0p (B), assocate wt LoS propagaton an over-sea sub-pat ffracton: L mn Lb0 p + ( ω) Lp for p < β0 B b 0 p = (59) Lb50 + ( Lb0β + ( ω) Lp Lb50) F for p β0 B L b0p : notonal LoS basc transmsson loss not exceee for p% tme, gven by equaton (0) L b0β : notonal LoS basc transmsson loss not exceee for β 0 % tme, gven by equaton () L p : ffracton loss not exceee for p% tme, gven by equaton (4) L b50 : mean basc transmsson loss assocate wt ffracton, gven by equaton (4) F : Dffracton nterpolaton factor, gven by equaton (40). Calculate a notonal mnmum basc transmsson loss, L mnbap (B), assocate wt LoS an transorzon sgnal enancements: L mnbap L L ba b0 p = η η + η ln e e B (60) L ba : uctng/layer reflecton basc transmsson loss not exceee for p% tme, gven by equaton (46) L b0p : notonal LoS basc transmsson loss not exceee for p% tme, gven by equaton (0)

21 Rec. ITU-R P.8-9 η =.5. Calculate a notonal basc transmsson loss, L ba (B), assocate wt ffracton an LoS or uctng/layer-reflecton enancements: Lb for Lmnbap > Lb Lba = B (6) Lmnbap + ( Lb Lmnbap) Fk for Lmnbap Lb L b : basc transmsson loss for ffracton not exceee for p% tme from equaton (43) L mnbap : notonal mnmum basc transmsson loss assocate wt LoS propagaton an trans-orzon sgnal enancements from equaton (60) F k : nterpolaton factor gven by equaton (58), accorng to te value of te pat great-crcle stance,. Calculate a mofe basc transmsson loss, L bam (B), wc takes ffracton an LoS or uctng/layer-reflecton enancements nto account: L bam = L + ( L 0 L ) F B (6) ba mnb p ba L ba : notonal basc transmsson loss assocate wt ffracton an LoS or uctng/layer-reflecton enancements, gven by equaton (6) L mnb0p : j notonal mnmum basc transmsson loss assocate wt LoS propagaton an over-sea sub-pat ffracton, gven by equaton (59) F j : nterpolaton factor gven by equaton (57), accorng to te value of te pat angular stance, θ. Calculate te basc transmsson loss not exceee for p% tme an 50% locatons gnorng te effects of termnal clutter, L bu (B), as gven by: L bu 0.L ( bs 0.L + 0 bam ) = 5log 0 B (63) L bs : basc transmsson loss ue to troposcatter not exceee for p% tme, gven by equaton (44) L bam : mofe basc transmsson loss takng ffracton an LoS uctng/layerreflecton enancements nto account, gven by equaton (6). 4.7 Atonal losses ue to termnal surrounngs Wen te transmtter or recever antenna s locate below te egt R t or R r representatve of groun cover surrounng te transmtter or recever, estmates of te atonal losses, A t, A r, are calculate as follows. Approprate values for R are scusse n 3.. Te meto gven below gves te mean of losses ue to fferent termnal surrounngs. Te possble mecansms nclue obstructon loss an reflectons ue to clutter objects at te representatve egt, an scatterng an reflecton from te groun an smaller clutter objects. Wen usng a computer mplementaton, wt terran profle extracte from a gtal terran moel, an wt te termnal surrounngs efne by a clutter category, t s not practcable to entfy nvual mecansms. Te meto use ere stnguses between two general cases: for

22 0 Rec. ITU-R P.8- woolan an urban categores t s assume tat te omnant mecansm s ffracton over clutter; for oter categores t s assume tat reflecton or scatterng omnates. Te meto for transmtter an recever s entcal, an n te followng, A = A t or A r, = tg or rg an R = R t or R r as approprate. If R ten A = 0 If < R, ten A can take one of two forms, epenng on clutter type (see Table ): or: J(ν) s calculate usng equaton (). Te terms ν an K are gven by: A = J (ν) 6.03 B (64a) A = K log( / R) B (64b) ν = K θ (64c) nu f clut f = R m (64) f θ = tan ( / 7) egrees (64e) clut K = log ( ) (64f) f K nu = f (64g) f: frequency (GHz). Te form of equaton (64a) represents Fresnel ffracton loss over an obstacle an woul be apple to clutter categores suc as bulngs. In partcular urban clutter woul be of ts type. Equaton (64b) represents te egt gan functon ue to te proxmty of te groun n more open locatons. Were specular groun reflecton occurs ts s typcal of sgnal varatons below te frst two-ray nterference maxmum. Were specular reflecton oes not occur te varatons below R are typcal of tose ue to saowng by mnor objects an rregulartes. A clearly-efne frst two-ray maxmum occurs only uner specal contons permttng groun reflecton, an cannot be entfe from te usual topograpc ata avalable for computer systems. Unless specal nformaton s avalable on te surrounng of a termnal, te value of R assocate wt te clutter category soul be use n equaton (64b). If specal nformaton s avalable wc entfes a flat, smoot reflectng surface wt aequate Fresnel clearance to support groun reflecton, ten R can be calculate usng te meto gven n Appenx 4. However, ts approac attempts to entfy a specfc pont on te multpat strbuton, wc s not consstent wt te prncples unerlyng pont-to-area precton, an s ncompatble wt te locaton-varablty calculaton gven n 4.8. Te etale estmaton of groun reflecton soul tus be restrcte to te use of te Recommenaton oter tan for pontto-area precton.

23 Rec. ITU-R P.8- Te basc transmsson loss not exceee for p% tme an 50% locatons, nclung te effects of termnal clutter losses, L bc (B), s gven by: L bu : A t, r : L = L + A + A B (65) bc bu t r te basc transmsson loss not exceee for p% tme an 50% locatons at (or above, as approprate) te egt of representatve clutter, gven by equaton (63) te atonal losses to account for termnal surrounngs, equatons (64a an 64b) as approprate. 4.8 Locaton varablty of losses In ts Recommenaton, an generally, locaton varablty refers to te spatal statstcs of local groun cover varatons. Ts s a useful result over scales substantally larger tan te groun cover varatons, an over wc pat varatons are nsgnfcant. As locaton varablty s efne to exclue multpat varatons, t s nepenent of system banwt. In te plannng of rao systems, t wll also be necessary to take multpat effects nto account. Te mpact of tese effects wll vary wt systems, beng epenent on banwts, moulatons an cong scemes. Guance on te moellng of tese effects s gven n Recommenaton ITU-R P.406. Extensve ata analyss suggests tat te strbuton of mean fel strengt ue to groun cover varatons over suc an area n urban an suburban envronments s approxmately lognormal wt zero mean. Values of te stanar evaton are epenent on frequency an envronment, an emprcal stues ave sown a conserable sprea. Representatve values for areas of m are gven by te followng expresson: σ = K.3log( f ) B (66) L + K = 5., for recevers wt antennas below clutter egt n urban or suburban envronments for moble systems wt omnrectonal antennas at car-roof egt K = 4.9 for recevers wt rooftop antennas near te clutter egt K = f : 4.4 for recevers n rural areas requre frequency (GHz). If te area over wc te varablty s to apply s greater tan m, or f te varablty s to relate to all areas at a gven range, rater tan te varaton across nvual areas, te value of σ L wll be greater. Emprcal stues ave suggeste tat locaton varablty s ncrease (wt respect to te small area values) by up to 4 B for a km raus an up to 8 B for a 50 km raus. Te percentage locatons, p L, can vary between % an 99%. Ts moel s not val for percentage locatons less tan % or greater tan 99%. It soul be note tat, for some plannng purposes (e.g. multlateral allotment plans) t wll generally be necessary to use a efnton of locaton varablty tat nclues a egree of multpat fang. Ts wll allow for te case of a moble recever, statonary n a multpat null, or

24 Rec. ITU-R P.8- for a rooftop antenna were a number of frequences are to be receve an te antenna cannot be optmally postone for all. Atonally, suc plannng may also nee to conser varablty over a greater area tan tat assume n ts Recommenaton. In ts context, te values gven n Table 5 ave been foun approprate for te plannng of a number of rao servces. TABLE 5 Values of locaton varablty stanar evatons use n certan plannng stuatons Stanar evaton 00 MHz 600 MHz 000 MHz Broacastng, analogue (B) Broacastng, gtal (B) Te locaton varablty correcton soul not be apple wen te recever/moble s ajacent to te sea. Wen te recever/moble s locate on lan an outoors but ts egt above groun s greater tan or equal to te egt of representatve clutter, t s reasonable to expect tat te locaton varablty wll ecrease monotoncally wt ncreasng egt untl, at some pont, t vanses. In ts Recommenaton, te locaton varablty egt varaton, u(), s gven by: u( ) = ( R) u( ) = 0 u( ) = 0 for for for 0 < R R < R + 0 R + 0 (67) were R (m) s te egt of representatve clutter at te recever/moble locaton. Terefore, for a recever/moble locate outoors, te stanar evaton of te locaton varablty, σ L, as gven by eter equaton (66) or Table 5, soul be multple by te egt varaton functon, u(), gven n equaton (67), wen computng values of te basc transmsson loss for values of p L % fferent from 50%. 4.9 Bulng entry loss Bulng entry loss s efne as te fference (B) between te mean fel strengt (wt respect to locatons) outse a bulng at a gven egt above groun level an te mean fel strengt nse te same bulng (wt respect to locatons) at te same egt above groun level. For noor recepton two mportant parameters must also be taken nto account. Te frst s te bulng entry loss an te secon s te varaton of te bulng entry loss ue to fferent bulng materals. Te stanar evatons, gven below, take nto account te large sprea of bulng entry losses but o not nclue te locaton varablty wtn fferent bulngs. It soul be note tat tere s lmte relable nformaton an measurement results about bulng entry loss. Provsonally, bulng entry loss values tat may be use are gven n Table 6.

25 Rec. ITU-R P.8-3 TABLE 6 Bulng entry loss (), L be, σ be () F Mean value, L be (B) Stanar evaton, σ be (B) 0. GHz GHz 6.5 GHz 6 Tese values may ave to be upate wen more expermental ata become avalable. For frequences below 0. GHz, L be = 9 B, σ be = 3 B; for frequences above.5 GHz, L be = B, σ be = 6 B. Between 0. GHz an 0.6 GHz (an between 0.6 GHz an.5 GHz), approprate values for L be an σ be can be obtane by lnear nterpolaton between te values for L be an σ be gven n te Table for 0. GHz an 0.6 GHz (0.6 GHz an.5 GHz). Te fel-strengt varaton for noor recepton s te combne result of te outoor varaton, σ L, an te varaton ue to bulng attenuaton, σ be. Tese varatons are lkely to be uncorrelate. Te stanar evaton for noor recepton, σ can terefore be calculate by takng te square root of te sum of te squares of te nvual stanar evatons. L be σ = σ + σ (68) were σ L s te stanar evaton of locaton varablty, as gven by equaton (66) or Table 5. For example, for gtal emssons wt banwt greater tan MHz, at VHF, were te sgnal stanar evatons are 5.5 B an 3 B respectvely, te combne value s 6.3 B. In Ban IV/V, were te sgnal stanar evatons are 5.5 B an 6 B, te combne value s 8. B. 4.0 Basc transmsson loss not exceee for p% tme an p L % locatons In orer to compute te esre percentage locatons, te mean loss, L loc, an te stanar evaton, σ loc, are gven by: an: loc L = 0 (outoors) (69a) loc L loc = L be (noors) (69b) σ = u( ) σ (outoors) (70a) L σ loc = σ (noors) (70b) were te mean bulng entry loss, L be, s gven n Table 6, te egt functon, u(), s gven by equaton (67) an te stanar evatons, σ L an σ, are gven by equaton (66) (or Table 5) an equaton (68), respectvely. Te basc transmsson loss not exceee for p% tme an p L % locatons, L b (B), s gven by: L p maxl + L b0 p, Lbc Lloc I σ B (7) 00 b = loc

26 4 Rec. ITU-R P.8- L b0p : basc transmsson loss not exceee for p% tme an 50% locatons assocate wt LoS wt sort term enancements, gven by equaton (0) L bc : basc transmsson loss not exceee for p% of tme an 50% locatons, nclung te effects of termnal clutter losses, gven by equaton (65) L loc : mean value of te locaton loss, as gven by equatons (69a) an (69b) I(x) : nverse complementary cumulatve normal strbuton as a functon of probablty, x. An approxmaton for I(x) wc may be use for x s gven n Appenx 3 to ts Annex σ loc : combne stanar evaton (.e. bulng entry loss an locaton varablty), gven by equatons (70a) an (70b). Te percentage locatons, p L, can vary between % an 99%. Ts moel s not val for percentage locatons less tan % or greater tan 99%. 4. Te fel strengt exceee for p% tme an p L % locatons Te fel strengt normalze to kw effectve raate power exceee for p% tme an 50% locatons, E p B(μV/m), may be calculate usng: E = log( f ) B(μV/m) (7) p L b L b : basc transmsson loss not exceee for p% tme an p L % locatons calculate by equaton (7) f: requre frequency (GHz).

27 Rec. ITU-R P.8-5 Appenx to Annex Rao-meteorologcal ata requre for te precton proceure Fgure gves average annual values of ΔN as postve values n N-unts/km. N FIGURE Average annual values of ΔN, N-unts/km Lattue (egrees) S W Longtue (egrees) E P.8-0 Fgure gves average annual values of sea-level surface refractvty, N 0, n N-unts. Parameter N 0 s use only n te troposperc-scatter part of te overall meto.

28 6 Rec. ITU-R P.8- FIGURE Sea-level surface refractvty, N-unts N Lattue (egrees) S W E Longtue (egrees) P.8-0 Appenx to Annex Pat profle analyss Introucton For pat profle analyss, a pat profle of terran egts above mean sea level s requre. Te parameters tat nee to be erve from te pat profle analyss for te purposes of te propagaton moels are gven n Table 7. Constructon of pat profle Base on te geograpcal coornates of te transmttng (φ t, ψ t ) an recevng (φ r, ψ r ) statons, terran egts (above mean sea level) along te great-crcle pat soul be erve from a topograpcal atabase or from approprate large-scale contour maps. Te stance resoluton of te profle soul be as far as s practcable to capture sgnfcant features of te terran. Typcally, a stance ncrement of 30 m to km s approprate. In general, t s approprate to use longer stance ncrements for longer pats. Te profle soul nclue te groun egts at te transmttng an

29 50 Rec. ITU-R P.8-7 recevng staton locatons as te start an en ponts. Te equatons of ts secton take Eart curvature nto account were necessary, base on te value of a e foun n equaton (7a). Altoug equally space profle ponts are consere preferable, t s possble to use te meto wt non-equally space profle ponts. Ts may be useful wen te profle s obtane from a gtal map of terran egt contours. However, t soul be note tat te Recommenaton as been evelope from testng usng equally space profle ponts; nformaton s not avalable on te effect of non-equally space ponts on accuracy. For te purposes of ts Recommenaton te pont of te pat profle at te transmttng staton s consere as pont, an te pont at te recevng staton s consere as pont n. Te pat profle terefore conssts of n ponts. Fgure 3 gves an example of a pat profle of terran egts above mean sea level, sowng te varous parameters relate to te actual terran. FIGURE 3 Example of a (trans-orzon) pat profle -t terran pont θ Interferng staton (T) θ t tg lt Mean sea level l lr θr ts gt a k a e = Interfere-wt staton (R) gr rg rs Note Te value of as rawn wll be negatve. θ t P.8-03 Table 7 efnes parameters use or erve urng te pat profle analyss.

30 8 Rec. ITU-R P.8- TABLE 7 Pat profle parameter efntons Parameter a e f λ ts rs θ t θ r θ st sr m te re Effectve Eart s raus (km) Great-crcle pat stance (km) Descrpton Incremental stance for regular (.e. equally space) pat profle ata (km) Frequency (GHz) Wavelengt (m) Transmtter antenna egt (m) above mean sea level (amsl) Recever antenna egt (m) (amsl) For a trans-orzon pat, orzon elevaton angle above local orzontal (mra), measure from te transmttng antenna. For a LoS pat ts soul be te elevaton angle of te recevng antenna For a trans-orzon pat, orzon elevaton angle above local orzontal (mra), measure from te recevng antenna. For a LoS pat ts soul be te elevaton angle of te transmttng antenna Pat angular stance (mra) Hegt of te smoot-eart surface (amsl) at te transmttng staton locaton (m) Hegt of te smoot-eart surface (amsl) at te recevng staton locaton (m) Hegt of te -t terran pont amsl (m) : groun egt of te transmtter n : groun egt of recever Terran rougness (m) Effectve egt of transmttng antenna (m) Effectve egt of recevng antenna (m) 3 Pat lengt Te pat lengt can be obtane usng great-crcle geometry from te geograpcal coornates of te transmttng (φ t, ψ t ) an recevng (φ r, ψ r ) statons. Alternatvely te pat lengt can be foun from te pat profle. Te pat lengt, (km), can be foun from te pat profle ata: = n km (73) For regularly space pat profle ata t s also true tat: ( ) = km (74) for =,, n, were s te ncremental pat stance (km).