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

Transcription

1 Recommenation ITU-R P (07/015) A pat-specific propagation preiction meto for point-to-area terrestrial services in te VHF an UHF bans P Series Raiowave propagation

2 ii Rec. ITU-R P Forewor Te role of te Raiocommunication Sector is to ensure te rational, equitable, efficient an economical use of te raiofrequency spectrum by all raiocommunication services, incluing satellite services, an carry out stuies witout limit of frequency range on te basis of wic Recommenations are aopte. Te regulatory an policy functions of te Raiocommunication Sector are performe by Worl an Regional Raiocommunication Conferences an Raiocommunication Assemblies supporte by Stuy Groups. Policy on Intellectual Property Rigt (IPR) ITU-R policy on IPR is escribe in te Common Patent Policy for ITU-T/ITU-R/ISO/IEC reference in Annex 1 of Resolution ITU-R 1. Forms to be use for te submission of patent statements an licensing eclarations by patent olers are available from ttp:// were te Guielines for Implementation of te Common Patent Policy for ITU-T/ITU-R/ISO/IEC an te ITU-R patent information atabase can also be foun. Series of ITU-R Recommenations (Also available online at ttp:// Series BO BR BS BT F M P RA RS S SA SF SM SNG TF V Title Satellite elivery Recoring for prouction, arcival an play-out; film for television Broacasting service (soun) Broacasting service (television) Fixe service Mobile, raioetermination, amateur an relate satellite services Raiowave propagation Raio astronomy Remote sensing systems Fixe-satellite service Space applications an meteorology Frequency saring an coorination between fixe-satellite an fixe service systems Spectrum management Satellite news gatering Time signals an frequency stanars emissions Vocabulary an relate subjects Note: Tis ITU-R Recommenation was approve in Englis uner te proceure etaile in Resolution ITU-R 1. Electronic Publication Geneva, 015 ITU 015 All rigts reserve. No part of tis publication may be reprouce, by any means watsoever, witout written permission of ITU.

3 Rec. ITU-R P Scope RECOMMENDATION ITU-R P * A pat-specific propagation preiction meto for point-to-area terrestrial services in te VHF an UHF bans (Question ITU-R 03/3) ( ) Tis Recommenation escribes a propagation preiction meto suitable for terrestrial point-to-area services in te frequency range 30 MHz to 3 GHz. It preicts signal levels at te meian of te multipat istribution exceee for a given percentage of time, p%, in te range 1% p 50% an a given percentage of locations, p, in te range 1% p 99%. Te meto provies etaile analysis base on te terrain profile. Te meto is suitable for preictions for raiocommunication systems utilizing terrestrial circuits aving pat lengts from 0.5 km up to about km istance, wit bot terminals witin approximately 3 km eigt above groun. It is not suitable for propagation preictions on eiter air-groun or space-eart raio circuits. Tis Recommenation complements Recommenation ITU-R P Te ITU Raiocommunication Assembly, consiering a) tat tere is a nee to give guiance to engineers in te planning of terrestrial raiocommunication services in te VHF an UHF bans; b) tat, for stations working in te same or ajacent frequency cannels, te etermination of te minimum geograpical istance of separation require to avoi unacceptable interference ue to long-istance terrestrial propagation is a matter of great importance, noting a) tat Recommenation ITU-R P.58 provies guiance on te preiction of point-to-area pat loss for te aeronautical mobile service for te frequency range 15 MHz to 30 GHz an te istance range up to km; b) tat Recommenation ITU-R P.45 provies guiance on te etaile evaluation of microwave interference between stations on te surface of te Eart at frequencies above about 0.1 GHz; c) tat Recommenation ITU-R P.617 provies guiance on te preiction of point-to-point (P-P) pat loss for trans-orizon raio-relay systems for te frequency range above 30 MHz an for te istance range 100 to km; ) tat Recommenation ITU-R P.1411 provies guiance on preiction for sort-range (up to 1 km) outoor services; e) tat Recommenation ITU-R P.530 provies guiance on te preiction of P-P pat loss for terrestrial os systems; * Raiocommunication Stuy Group 3 mae eitorial amenments to tis Recommenation in te year 016 in accorance wit Resolution ITU-R 1.

4 Rec. ITU-R P f) tat Recommenation ITU-R P.1546 provies guiance on te preiction of point-to-area fiel strengts in te VHF an UHF bans base principally on statistical analyses of experimental ata; g) tat Recommenation ITU-R P.001 provies a wie-range terrestrial propagation moel for te frequency range 30 MHz to 50 GHz incluing bot faing an enancement statistics wic is well suite for use in Monte-Carlo simulations; ) tat Recommenation ITU-R P.040 provies guiance on te effects of builing material properties an structures on raiowave propagation, recommens tat te proceure given in Annex 1 soul be use for te etaile evaluation of point-to-area signal levels in connection wit tese services. NOTE ong range propagation pats may also occur at VHF via te ionospere. Tese moes are summarize in Recommenation ITU-R P.844. Annex 1 1 Introuction Te propagation preiction meto escribe in tis Annex is recommene for te etaile evaluation of signal levels suitable for use in connection wit terrestrial point-to-area services in te VHF an UHF bans. It preicts te signal level (i.e. electric fiel strengt) exceee for a given percentage, p%, of an average year in te range 1% p 50% an p% locations in te range 1% p 99%. Terefore, tis meto may be use to preict bot te service area an availability for a esire signal level (coverage), an te reuctions in tis service area an availability ue to unesire, co- an/or ajacent-cannel signals (interference). Te propagation moel of tis meto is symmetric in te sense tat it treats bot raio terminals in te same manner. From te moel s perspective, it oes not matter wic terminal is te transmitter an wic is te receiver. However, for convenience in te moel s escription, te terms transmitter an receiver are use to enote te terminals at te start an en of te raio pat, respectively. Te meto is first escribe in terms of calculating basic transmission loss (B) not exceee for p% time for te meian value of locations. Te location variability element is ten caracterize statistically wit respect to receiver locations, in aition to te builing entry loss element from Recommenation ITU-R P.040. A proceure is ten given for converting to electric fiel strengt (B(μV/m)) for an effective raiate power of 1 kw. Tis meto is intene primarily for use wit systems using low-gain antennas. However, te cange in accuracy wen ig-gain antennas are use only affects te troposcatter element of te overall meto, an te cange in te preictions is small. For example, even wit 40 Bi antennas at bot ens of te link te over-estimation of troposcatter signals will amount to only about 1 B. Te meto is suitable for preictions for raiocommunication systems utilizing terrestrial circuits aving pat lengts from 0.5 km up to about km istance, wit bot terminals witin approximately 3 km eigt above groun. It is not suitable for propagation preictions on eiter air-groun or space-eart raio circuits.

5 Rec. ITU-R P Te propagation preiction meto in tis Annex is pat-specific. Point-to-area preictions using tis meto consist of series of many P-P (i.e. transmitter-point-to-receiver-multipoint) preictions, uniformly istribute over notional service areas. Te number of points soul be large enoug to ensure tat te preicte values of basic transmission losses or fiel strengts tus obtaine are reasonable estimates of te meian values, wit respect to locations, of te corresponing quantities for te elemental areas tat tey represent. In consequence, it is assume tat users of tis Recommenation are able to specify etaile terrain profiles (i.e. elevations above mean sea level) as functions of istance along te great circle pats (i.e. geoesic curves) between te terminals, for many ifferent terminal locations (receiver-points). For most practical applications of tis meto to point-to-area coverage an interference preictions, tis assumption implies te availability of a igital terrain elevation atabase, reference to latitue an longitue wit respect to a consistent geoetic atum, from wic te terrain profiles may be extracte by automate means. If tese etaile terrain profiles are not available, ten Recommenation ITU-R P.1546 soul instea be use for preictions. In view of te foregoing, te location variability element of tis Recommenation an te builing entry loss moel element of Recommenation ITU-R P.040 are caracterize via te statistics of lognormal istributions wit respect to receiver locations. Altoug tis statistical caracterization of te point-to-area propagation problem woul appear to make te overall moel unsymmetrical (i.e. non-reciprocal), users of tis Recommenation soul note tat te location variability coul, in principle, be applie at eiter en of te pat (i.e. eiter terminal), or even bot (i.e. te transmitter an te receiver). However, te location variability correction is only meaningful in situations wen exact location of a given terminal is unknown an a statistical representation over tat terminal s potential locations is require. Tere are unlikely to be many situations were tis coul meaningfully be applie to te transmitter location. If te locations of bot terminals are known exactly an tis proceure is being use in P-P moe, ten tis Recommenation is only applicable wit p = 50%. A similar point is true regaring builing entry losses. Te argument is sligtly more complicate tan for location variability owing to te fact tat te meian entry loss correction is non-zero. At te transmitter en, users soul also a te builing entry loss to te basic transmission loss if te transmitter is insie a builing, but users must also be aware tat te use of meian loss values may be misleaing if te transmitter is not in a meian location. Moel elements of te propagation preiction meto Tis propagation preiction meto takes account of te following moel elements: line-of-sigt (os) iffraction (embracing smoot-eart, irregular terrain an sub-pat cases) troposperic scatter anomalous propagation (ucting an layer reflection/refraction) eigt-gain variation in clutter location variability builing entry losses (from Recommenation ITU-R P.040).

6 4 Rec. ITU-R P Input parameters 3.1 Basic input ata Table 1 escribes te basic input ata, wic efines te raio terminals, te frequency, an te percentage time an locations for wic a preiction is require. Te latitue an longitue of te two stations are state as basic inputs on te basis tat tey are neee to obtain te pat profile. Raiometeorological parameters must be obtaine for a single location associate wit te raio pat, an for a long pat te pat-centre soul be selecte. It is appropriate to obtain te raiometeorological parameters for te transmitter location wen preicting its coverage area. TABE 1 Basic input ata Parameter Units Minimum Maximum Description f GHz Frequency (GHz) p % Percentage of average year for wic te calculate signal level is exceee p % 1 99 Percentage of locations for wic te calculate signal level is exceee φ t, φ r egrees atitue of transmitter, receiver ψ t, ψ r egrees ongitue of transmitter, receiver (positive = East of Greenwic) tg, rg m Antenna centre eigt above groun level Polarization Signal polarisation, e.g. vertical or orizontal w s m Wit of street. Te value of 7 soul be use unless specific local values are available. Polarisation in Table 1 is not a parameter wit a numerical value. Te information is use in in connection wit equations (9a), (9b) an (30). 3. Terrain profile A terrain profile for te raio pat is require for te application of te propagation preiction meto. In principle, tis consists of tree arrays eac aving te same number of values, n, as follows: i: istance from transmitter of i-t profile point (km) i: eigt of i-t profile point above sea level (m) gi i representative clutter eigt of i-t profilepoint (m) i: 1,, 3... n = inex of te profile point n: number of profile points. Tere must be at least one intermeiate profile point between te transmitter an te receiver. Tus n must satisfy n 3. Suc a small number of points is appropriate only for sort pats, less tan of te orer of 1 km. (1a) (1b) (1c)

7 Rec. ITU-R P Note tat te first profile point is at te transmitter. Tus 1 is zero an 1 is te terrain eigt at te transmitter in metres above sea level. Similarly, te n-t profile point is at te receiver. Tus n is te pat lengt in km, an n te terrain eigt at te receiver in metres above sea level. No specific istance between profile points is given. Assuming tat profiles are extracte from a igital terrain elevation moel, a suitable spacing will typically be similar to te point spacing of te source ata. Te profile points are not require to be equally-space, but it is esirable tat tey are at a similar spacing for te wole profile. It is esirable to ave information on groun cover (clutter) along te pat. It is convenient to store clutter categories in an aitional array of n points to matc te profile eigt ata. Te representative clutter eigt R referre to in equation (1c) concerns statistical eigt information associate wit groun cover classification, suc as vegetation an builings, i.e., a single eigt value assigne to eac groun cover /clutter class. Aing representative clutter eigts to a profile is base on te assumption tat te eigts i represent te bare surface of te Eart. If te raio pat passes over woolan or urbanization were iffraction or sub-pat obstruction occurs, in general te effective profile eigt will be iger because te raio signal will travel over te clutter. Tus a more suitable representation of te profile can be obtaine by aing representative eigts to account for te clutter. Te appropriate aition is not necessarily pysical, suc as rooftop eigts in te case of builings. Were gaps exist between clutter objects, as seen by te raio wave, some energy may travel between rater tan over tem. In tis situation te presence of clutter is expecte to increase iffraction loss, but not by as muc as raising te profile to te pysical clutter eigt. Tis applies particularly to ig-rise urban areas. Categories suc as ense urban or ig-rise urban ten to be associate wit builing eigts of 30 metres or more. But some ig-rise areas ave large spaces between te tall builings, an it is possible for low-loss pats to exist passing aroun tem, rater tan over te roofs. At te oter extreme, even in areas classifie as open or rural it is unusual for te groun to be completely bare, tat is, free of any objects wic migt a to propagation losses. Tus small values of R, rater tan zero, migt be appropriate in many cases. Tus representative clutter eigt R epens not only on te typical pysical eigt of clutter objects but also on te orizontal spacing of objects an te gaps between tem. Tere is no accepte stanar as to wat a clutter category, suc as urban, represents in pysical terms in ifferent countries. Were available, representative clutter eigt information base on local clutter eigt statistics or oter sources soul be use, Table suggests efault values for R wic may be use in te absence of region/country specific information. Tere is a separate use of clutter information to estimate terminal clutter losses, as escribe in 4.7. Te concept of representative clutter eigt, R, is retaine, but may be interprete ifferently. Tis is to acknowlege te wier availability of ig resolution tree imensional clutter eigt information, suc as accurate builing eigts an vegetation. Were available, representative clutter eigts base on accurate clutter eigt information soul be use in 4.7.

8 6 Rec. ITU-R P Clutter type TABE Default information for clutter-loss moelling Representative clutter eigt (m) A to profile equation (1c) for i = to n - 1 Terminal clutter losses 4.7 an a to profile equation (1c) for i = 1 an n Terminal clutter loss moel Water/sea 0 10 Equation (64b) Open/rural 0 10 Equation (64b) Suburban Equation (64a) Urban/trees/forest Equation (64a) Dense urban 0 0 Equation (64a) Te meto escribe above, in wic representative clutter eigts are ae to a bare-eart or terrain profile, requires separate ata on terrain eigts an te presence of clutter. It is not suitable for te irect use of remotely-sense surface-eigt ata, were eigts inclue clutter wit no explicit istinction between terrain an clutter. It is important to note tat iffraction loss may be seriously over-estimate if terrain profiles are extracte irectly from surface, as oppose to bare-eart, eigt ata. 3.3 Raio-climatic zones Information is also neee on wat lengts of te pat are in te raio-climatic zones escribe in Table 3. For maximum consistency of results between aministrations te calculations of tis proceure soul be base on te ITU Digitize Worl Map (IDWM) wic is available from te BR. If all points on te pat are at least 50 km from te sea or oter large boies of water, ten only te inlan category applies. If te zone information is store in successive points along te raio pat, it soul be assume tat canges occur miway between points aving ifferent zone coes. TABE 3 Raio-climatic zones Zone type Coe Definition Coastal lan A1 Coastal lan an sore areas, i.e. lan ajacent to te sea up to an altitue of 100 m relative to mean sea or water level, but limite to a istance of 50 km from te nearest sea area. Were precise 100 m ata are not available an approximate value may be use Inlan A All lan, oter tan coastal an sore areas efine as coastal lan above Sea B Seas, oceans an oter large boies of water (i.e. covering a circle of at least 100 km in iameter).

9 Rec. ITU-R P Terminal istances from te coast If te pat is over zone B two furter parameters are require, ct, cr, giving te istance of te transmitter an te receiver from te coast (km), respectively, in te irection of te oter terminal. For a terminal on a sip or sea platform te istance is zero. 3.5 Basic raio-meteorological parameters Te preiction proceure requires two raio-meteorological parameters to escribe te variability of atmosperic refractivity. ΔN (N-units/km), te average raio-refractive inex lapse-rate troug te lowest 1 km of te atmospere, provies te ata upon wic te appropriate effective Eart raius can be calculate for pat profile an iffraction obstacle analysis. Note tat ΔN is a positive quantity in tis proceure. N0 (N-units), te sea-level surface refractivity, is use only by te troposcatter moel as a measure of variability of te troposcatter mecanism. If local measurements are not available, tese quantities can be obtaine from te maps in te integral igital proucts supplie wit tis Recommenation. Te maps are containe in te files DN50.txt an N050.txt, respectively. Te ata are from 0 o to 360 o in longitue an from +90 o to 90 o in latitue, wit a resolution of 1.5 o in bot latitue an longitue. Te ata are use in conjunction wit te companion ata files AT.txt an ON.txt containing respectively te latitues an longitues of te corresponing entries (gri points) in te files DN50.txt an N050.txt. For a location ifferent from te gri points, te parameter at te esire location can be erive by performing a bi-linear interpolation on te values at te four closest gri points, as escribe in Recommenation ITU-R P TABE 4 Integral igital proucts atitue ongitue Filename Origin From (eg) To (eg) Spacing (eg) From (eg) To (eg) Spacing (eg) DN50.txt P N050.txt P AT.txt P ON.txt P Tese igital maps were erive from analysis of a ten-year ( ) global ataset of raiosone ascents. Te igital maps are containe in te zip file Rec-P Supplement.zip. 3.6 Incience of ucting Te egree to wic signal levels will be enance ue to anomalous propagation, particularly ucting, is quantifie by a parameter β0 (%), te time percentage for wic refractive inex lapse-rates exceeing 100 N-units/km can be expecte in te first 100 m of te lower atmospere. Te value of 0 is calculate as follows. Calculate te parameter μ1, wic epens on te egree to wic te pat is over lan (inlan an/or coastal) an water:

10 8 Rec. ITU-R P were te value of μ1 sall be limite to μ1 1, an tm: lm: μ tm exp lm 0. (3) longest continuous lan (inlan + coastal) section of te great-circle pat (km) longest continuous inlan section of te great-circle pat (km). Te raio-climatic zones to be use for te erivation of tm an lm are efine in Table 3. If all points on te pat are at least 50 km from te sea or oter large boies of water, ten only te inlan category applies an tm an lm are equal to te pat lengt,. Calculate te parameter μ4, wic epens on μ1 an te latitue of te pat centre in egrees: Calculate β0: 4 4 ( ) φ: pat centre latitue (egrees). β μ μ1 1 μ 4 μ 4 % % for 70 for 70 for for () (4) (5) 3.7 Effective Eart raius Te meian effective Eart raius factor k50 for te pat is given by: 157 k50 (6) 157 N Te value of te average raio-refractivity lapse-rate, ΔN, may be obtaine from te integral igital map DN50.txt, using te latitue an longitue of te pat centre as representative for te entire pat. Te meian value of effective Eart raius ae is given by: a e 6371k 50 km (7a) Te effective Eart raius exceee for 0 time, a, is given by: aβ 6371 k β km (7b) were k = 3.0 is an estimate of te effective Eart-raius factor exceee for 0 time. A general effective Eart raius is efine, were ap = ae for 50% of time, an ap = aβ for β0% of time.

11 Rec. ITU-R P Parameters erive from te pat profile analysis Values for a number of pat-relate parameters necessary for te calculations, as inicate in Table 5, must be erive via an initial analysis of te pat profile base on te value of ae given by equation (7a). Information on te erivation, construction an analysis of te pat profile is given in Attacment 1 to tis Annex. 4 Te preiction proceure 4.1 General Te overall preiction proceure is escribe in tis section. First, te basic transmission loss, b (B), not exceee for te require annual percentage time, p%, an 50% locations is evaluate as escribe in (i.e. te basic transmission losses ue to os propagation, propagation by iffraction, propagation by troposperic scatter, propagation by ucting/layer reflection an te combination of tese propagation mecanisms to preict te basic transmission loss, respectively). In , metos to account for te inclusion of terminal clutter effects, te effects of location variability an builing entry loss are escribe. Finally, 4.11 gives expressions tat relate te basic transmission loss to te fiel strengt (B μv/m) for 1 kw effective raiate power. TABE 5 Parameter values to be erive from te pat profile analysis Parameter lt, lr θ t, θ r θ ts, rs tc, rc te, re b ω Great-circle pat istance (km) Description Distance from te transmit an receive antennas to teir respective orizons (km) Transmit an receive orizon elevation angles respectively (mra) Pat angular istance (mra) Antenna centre eigt above mean sea level (m) max( ts, g 1) an max( rs, g n) respectively Effective eigts of antennas above te terrain (m) Aggregate lengt of te pat sections over water (km) Fraction of te total pat over water: b / were is te great-circle istance (km) calculate using equation (73). For totally overlan pats: ω = ine-of-sigt propagation (incluing sort-term effects) Te following soul all be evaluate for bot os an trans-orizon pats. Te basic transmission loss ue to free-space propagation is given by: bfs log f 0 log B (8) Corrections for multipat an focusing effects at p an 0 percentage times, respectively, are given by:

12 10 Rec. ITU-R P lt lr p Esp.6 1 exp log B (9a) lt lr β0 E sβ.6 1 exp log B (9b) Calculate te basic transmission loss not exceee for time pe0rcentage, p%, ue to os propagation (regarless of weter or not te pat is actually os), as given by: E b0 p bfs sp B (10) Calculate te basic transmission loss not exceee for time percentage, 0%, ue to os propagation (regarless of weter or not te pat is actually os), as given by: b 0 bfs Es B (11) 4.3 Propagation by iffraction Diffraction loss is calculate by te combination of a meto base on te Bullington construction an sperical-eart iffraction. Te Bullington part of te meto is an expansion of te basic Bullington construction to control te transition between free-space an obstructe conitions. Tis part of te meto is use twice: for te actual pat profile, an for a zero-eigt smoot profile wit moifie antenna eigts referre to as effective antenna eigts. Te same effective antenna eigts are also use to calculate sperical-eart iffraction loss. Te final result is obtaine as a combination of tree losses calculate as above. For a perfectly smoot pat te final iffraction loss will be te output of te sperical-eart moel. Tis meto provies an estimate of iffraction loss for all types of pat, incluing over-sea or overinlan or coastal lan, an irrespective of weter te pat is smoot or roug, an weter os or transorizon. Tis iffraction meto is always use for meian effective Eart raius. If an overall preiction is require for p = 50%, no furter iffraction calculation is necessary. In te general case were p < 50%, te iffraction calculation must be performe a secon time for an effective Eart-raius factor equal to 3. Tis secon calculation gives an estimate of iffraction loss not exceee for β0% time, were β0 is given by equation (5). Te iffraction loss not exceee for p% time, for 1% p 50%, is ten calculate using a limiting or interpolation proceure escribe in Te meto uses an approximation to te single knife-ege iffraction loss as a function of te imensionless parameter, ν, given by: J ( ) 6.9 0log (1) Note tat J( 0.78) 0, an tis efines te lower limit at wic tis approximation soul be use. J(ν) is set to zero for ν Te overall iffraction calculation is escribe in sub-sections as follows:

13 Rec. ITU-R P Section escribes te Bullington part of te iffraction meto. For eac iffraction calculation for a given effective Eart raius tis is use twice. On te secon occasion te antenna eigts are moifie an all profile eigts are zero. Section 4.3. escribes te sperical-eart part of te iffraction moel. Tis is use wit te same antenna eigts as for te secon use of te Bullington part in Section escribes ow te metos in an 4.3. are use in combination to perform te complete iffraction calculation for a given effective Eart raius. Due to te manner in wic te Bullington an sperical-eart parts are use, te complete calculation as come to be known as te elta-bullington moel. Section escribes te complete calculation for iffraction loss not exceee for a given percentage time p% Te Bullington part of te iffraction calculation In te following equations slopes are calculate in m/km relative to te baseline joining sea level at te transmitter to sea level at te receiver. Te istance an eigt of te i-t profile point are i kilometres an gi metres above sea level respectively, i takes values from 1 to n were n is te number of profile points, an te complete pat lengt is kilometres. For convenience te terminals at te start an en of te profile are referre to as transmitter an receiver, wit eigts in metres above sea level ts an rs, respectively. Effective Eart curvature Ce km 1 is given by 1/ap were ap is effective eart raius in kilometres. Wavelengt in metres is represente by. Values to be use for ap are given in Fin te intermeiate profile point wit te igest slope of te line from te transmitter to te point. S tim were te profile inex i takes values from to n 1. gi 500Cei i tc max m/km (13) i Calculate te slope of te line from transmitter to receiver assuming a os pat: Two cases must now be consiere. Case 1. Diffraction pat is os If Stim < Str te iffraction pat is os. S tr rc tc m/km (14) Fin te intermeiate profile point wit te igest iffraction parameter : tc i rci gi Cei i 0.00 max max 500 (15) λi i were te profile inex i takes values from to n 1. In tis case, te knife-ege loss for te Bullington point is given by: uc J max B (16) were te function J is given by equation (1) for b greater tan 0.78, an is zero oterwise. Case. Diffraction pat is transorizon If Stim Str te iffraction pat is transorizon.

14 1 Rec. ITU-R P Fin te intermeiate profile point wit te igest slope of te line from te receiver to te point. S rim were te profile inex i takes values from to n 1. gi 500Cei i rc max m/km (17) i Calculate te istance of te Bullington point from te transmitter: S Calculate te iffraction parameter, b, for te Bullington point: b tc S tim rc tc rim bp km (18) Stim Srim bp tc bp In tis case, te knife-ege loss for te Bullington point is given by: rc bp 0.00 λ bp bp (19) uc J b B (0) For uc calculate using eiter equation (16) or (0), Bullington iffraction loss for te pat is now given by: 4.3. Sperical-Eart iffraction loss uc uc 1 exp B (1) bull 0 Te sperical-eart iffraction loss not exceee for p% time for antenna eigts tesp an resp (m), sp, is calculate as follows. Calculate te marginal os istance for a smoot pat: ap tesp 0. resp km () los 001 If los calculate iffraction loss using te meto in below for aft = ap to give ft, an set sp equal to ft. No furter sperical-eart iffraction calculation is necessary. Oterwise continue as follows: Calculate te smallest clearance eigt between te curve-eart pat an te ray between te antennas, se, given by: se se 1 se se tesp 500 resp 500 se1 a p a p m (3) (1 ) km (4a) se 1 b se se1 km (4b)

15 Rec. ITU-R P m c 1 π 1 3c 3mc b cos arccos 3 (4c) 3mc 3 3 ( mc 1) were te arccos function returns an angle in raians m c c tesp resp (4) tesp resp 50 (4e) a ( ) Calculate te require clearance for zero iffraction loss, req, given by: req p tesp resp se 1seλ m (5) If se > req te sperical-eart iffraction loss sp is zero. No furter sperical-eart iffraction calculation is necessary. Oterwise continue as follows: Calculate te moifie effective Eart raius, aem, wic gives marginal os at istance given by: Use te meto in for aft = aem to give ft. 500 a em km (6) tesp resp If ft is negative, te sperical-eart iffraction loss sp is zero, an no furter sperical-eart iffraction calculation is necessary. Oterwise continue as follows: Calculate te sperical-eart iffraction loss by interpolation: sp 1 se req First-term part of sperical-eart iffraction loss Tis sub-section gives te meto for calculating sperical-eart iffraction using only te first term of te resiue series. It forms part of te overall iffraction meto escribe in 4.3. above to give te first-term iffraction loss ft for a given value of effective Eart raius aft. Te value of aft to use is given in Set terrain electrical properties typical for lan, wit relative permittivity εr =.0 an conuctivity σ = S/m an calculate ft using equations (9) to (36) an call te result ftlan. Set terrain electrical properties typical for sea, wit relative permittivity εr = 80.0 an conuctivity σ = 5.0 S/m an calculate ft using equations (9) to (36) an call te result ftsea. First-term sperical iffraction loss is now given by: ft ftsea ft ( 1 ) were is te fraction of te pat over sea. ftlan Start of calculation to be performe twice, as escribe above: B B (7) (8)

16 14 Rec. ITU-R P Normalize factor for surface amittance for orizontal an vertical polarization: an K H a ft f 1/3 18σ (εr 1) f 1/4 1/ (orizontal) (9a) 18 σ KV K H εr (vertical) (9b) f If te polarization vector contains bot orizontal an vertical components, e.g. circular or slant, ecompose it into orizontal an vertical components, calculate eac separately an combine te results by a vector sum of te fiel amplitue. In practice tis ecomposition will generally be unnecessary because above 300 MHz a value of 1 can be use for ft in equation (30). Calculate te Eart groun/polarisation parameter: were K is KH or KV accoring to polarisation. Normalize istance: Normalize transmitter an receiver eigts: K 0.67K ft (30) K 1.53K X 1/3 f 1.88 β ft (31) a ft Y t 1/3 f β ft tesp (3a) a ft Calculate te istance term given by: Y r 1/3 f β ft resp (3b) a ft 1110log( X ) 17.6X for X 1.6 F X 1.45 (33) 0log( X ) X for X 1.6 Define a function of normalize eigt given by: ( B 1.1) 5log( B 1.1) 8 for B > G ( Y ) (34) 3 0log( B 0.1B ) oterwise imit G(Y) suc tat G( Y) 0log K Te first-term sperical-eart iffraction loss is now given by: B ft Y (35)

17 ft Rec. ITU-R P X GY Complete elta-bullington iffraction loss moel F G Y B (36) t Use te meto in for te actual terrain profile an antenna eigts. Set te resulting Bullington iffraction loss for te actual pat, bulla = bull as given by equation (1). Use te meto in for a secon time, wit all profile eigts, gi, set to zero, an moifie antenna eigts given by: tc tc st r ' m (37a) ' m (37b) rc rc were te smoot-eart eigts at transmitter an receiver, st an sr, are given in 5.6. of Attacment 1. Set te resulting Bullington iffraction loss for tis smoot pat, bulls = bull as given by equation (1). Use te meto in 4.3. to calculate te sperical-eart iffraction loss sp for te actual pat lengt km an wit: Diffraction loss for te general pat is now given by: sr ' tesp tc m (38a) ' resp rc m (38b) max{ bulls, 0} B (39) bulla sp Te iffraction loss not exceee for p% of te time Use te meto in to calculate iffraction loss for meian effective Eart raius ap = ae as given by equation (7a). Set meian iffraction loss 50 =. If p = 50% te iffraction loss not exceee for p% time, p, is given by 50. If p < 50%, te iffraction loss not exceee for p% time, p, soul be calculate as follows. Use te meto in to calculate iffraction loss for effective Eart raius not exceee for 0% time ap = a as given by equation (7b). Set iffraction loss not exceee for 0% time =. Te application of te two possible values of effective Eart raius factor is controlle by an interpolation factor, Fi, base on a log-normal istribution of iffraction loss over te range 50% > p β0%, given by: p I 100 F i if 50% p 0% (40a) β0 I 100 = 1 if 0 % p (40b) were I(x) is te inverse complementary cumulative normal istribution as a function of te probability x. An approximation for I(x) wic may be use wit confience for x 0.5 is given in Attacment to tis Annex. Te iffraction loss, p, not exceee for p% time, is now given by:

18 16 Rec. ITU-R P ) F B (41) p 50 ( 50 Fi is efine by equations (40a-b), epening on te values of p an 0. Te meian basic transmission loss associate wit iffraction, b50, is given by: were bfs is given by equation (8). b50 bfs 50 i B (4) Te basic transmission loss associate wit iffraction not exceee for p% time is given by: were b0p is given by equation (10). 4.4 Propagation by troposperic scatter b 0 B (43) b p p NOTE 1 At time percentages muc below 50%, it is ifficult to separate te true troposperic scatter moe from oter seconary propagation penomena wic give rise to similar propagation effects. Te troposperic scatter moel aopte in tis Recommenation is terefore an empirical generalization of te concept of troposperic scatter wic also embraces tese seconary propagation effects. Tis allows a continuous consistent preiction of basic transmission loss over te range of time percentages p from 0.001% to 50%, tus linking te ucting an layer reflection moel at te small time percentages wit te true scatter moe appropriate to te weak resiual fiel exceee for te largest time percentage. NOTE Tis troposcatter preiction moel as been erive for interference preiction purposes an is not appropriate for te calculation of propagation conitions above 50% of time affecting te performance aspects of trans-orizon raio-relay systems. Te basic transmission loss ue to troposcatter, bs (B), not exceee for any time percentage, p, below 50%, is given by: p bs.1 f 0 log θ 0.15 N log B (44) f : frequency epenent loss: 0.7 f f 5log( f ).5 log B (45) N0: pat centre sea-level surface refractivity 4.5 Propagation by ucting/layer reflection Te basic transmission loss associate wit ucting/layer-reflection not exceee for p% time, ba (B), is given by: Af : ba A A ( p) B (46) f total of fixe coupling losses (except for local clutter losses) between te antennas an te anomalous propagation structure witin te atmospere: A f f 0log lt lr Alf Ast Asr Act Acr log B (47)

19 Rec. ITU-R P Alf : empirical correction to account for te increasing attenuation wit wavelengt in ucte propagation Ast, Asr: A st, sr A lf f f 9.5 f 0 B B for for f 0.5GHz f 0.5GHz (47a) site-sieling iffraction losses for te transmitting an receiving stations respectively: 0 log t, r 0 Act, Acr: f lt,lr 1/ 0.64t, r f 1/ 3 B B for t, r for t, r 0 mra 0 mra (48) θ 0.1 mra (48a) t, r t,r lt,lr over-sea surface uct coupling corrections for te transmitting an receiving stations respectively: A 3exp tan0.07 A ct,cr 3exp ct, cr 50 ts, rs B for tan ct, cr B B for for ω 0.75 ct, cr ct, cr ts, rs ct, cr lt, lr 5km all oter conitions It is useful to note te limite set of conitions uner wic equation (49) is neee. A (p): γ: (49) time percentage an angular-istance epenent losses witin te anomalous propagation mecanism: specific attenuation: A ( p) A( p) B (50) γ 5 1/3 510 a e f B/mra (51) : angular istance (correcte were appropriate (via equation (48a)) to allow for te application of te site sieling moel in equation (46)): mra (5) 10 3 t r a e

20 18 Rec. ITU-R P t, r θt,r 0.1 lt,lr for for θ θ t,r t,r A(p): time percentage variability (cumulative istribution): lt,lr lt,lr mra (5a) mra 3 p p A ( p) 1 ( ) log 1 B (53) β β exp log β (log β) 10 (53a) log β μ: correction for pat geometry: 0μμ3 β β % (54) an: μ 500 ae Te value of μ sall not excee 1. : 3.5 te 3.1 re α 9 (55) α 0.6 τ ε 10 (55a) : is efine in equation (3), an te value of sall not be allowe to ecrease below 3.4 μ3: correction for terrain rougness: μ 3 1 exp ( m 10) (43 6 ) I for for m m 10 m 10 m (56) min (, 40) km (56a) I lt lr Te remaining terms ave been efine in Tables 1 an an Attacment 1 to tis Annex. 4.6 Basic transmission loss not exceee for p% time an 50% locations ignoring te effects of terminal clutter Te following proceure soul be applie to te results of te foregoing calculations for all pats, in orer to compute te basic transmission loss not exceee for p% time an 50% locations. In orer to avoi pysically unreasonable iscontinuities in te preicte notional basic transmission losses, te foregoing propagation moels must be blene togeter to get moifie values of basic transmission losses in orer to acieve an overall preiction for p% time an 50% locations. Calculate an interpolation factor, Fj, to take account of te pat angular istance:

21 Rec. ITU-R P ( θ Θ F j tan 3.0 ξ (57) Θ Θ: fixe parameter etermining te angular range of te associate blening; set to 0.3 ξ: fixe parameter etermining te blening slope at te en of te range; set to 0.8 θ: pat angular istance (mra) efine in Table 7. Calculate an interpolation factor, Fk, to take account of te pat great-circle istance: F k ( sw) tan 3.0 (58) sw : great circle pat lengt efine in Table 3 (km) sw: fixe parameter etermining te istance range of te associate blening; set to 0 κ: fixe parameter etermining te blening slope at te ens of te range; set to 0.5. Calculate a notional minimum basic transmission loss, minb0p (B), associate wit os propagation an over-sea sub-pat iffraction: b0p: b0: min b0 p b0 p b50 (1 ω) ( b0 p (1 ω) p b50 ) F i ) for p β for p β 0 0 B B (59) notional os basic transmission loss not exceee for p% time, given by equation (10) notional os basic transmission loss not exceee for 0% time, given by equation (11) p: iffraction loss not exceee for p% time, given by equation (41) b50: meian basic transmission loss associate wit iffraction, given by equation (4) Fi: Diffraction interpolation factor, given by equation (40). Calculate a notional minimum basic transmission loss, minbap (B), associate wit os an transorizon signal enancements: ba: b0p: ba b0 p minbap ηlnexp exp B (60) η η ucting/layer reflection basic transmission loss not exceee for p% time, given by equation (46) notional os basic transmission loss not exceee for p% time, given by equation (10)

22 0 Rec. ITU-R P η =.5. Calculate a notional basic transmission loss, ba (B), associate wit iffraction an os or ucting/layer-reflection enancements: b: minbap: Fk: ba b minbap ( b minbap ) F k for for minbap minbap b b B (61) basic transmission loss for iffraction not exceee for p% time from equation (43) notional minimum basic transmission loss associate wit os propagation an trans-orizon signal enancements from equation (60) interpolation factor given by equation (58), accoring to te value of te pat great-circle istance,. Calculate a moifie basic transmission loss, bam (B), wic takes iffraction an os or ucting/layer-reflection enancements into account: ba: minb0p: Fj: ( 0 ) F B (6) bam ba minb p ba notional basic transmission loss associate wit iffraction an os or ucting/layer-reflection enancements, given by equation (61) notional minimum basic transmission loss associate wit os propagation an over-sea sub-pat iffraction, given by equation (59) interpolation factor given by equation (57), accoring to te value of te pat angular istance, θ. Calculate te basic transmission loss not exceee for p% time an 50% locations ignoring te effects of terminal clutter, bu (B), as given by: bs: bam: bu 0. bs 0. bam j 5log B (63) basic transmission loss ue to troposcatter not exceee for p% time, given by equation (44) moifie basic transmission loss taking iffraction an os ucting/ layer-reflection enancements into account, given by equation (6). 4.7 Aitional losses ue to terminal surrounings Wen te transmitter or receiver antenna is locate below te eigt Rt or Rr representative of groun cover surrouning te transmitter or receiver, estimates of te aitional losses, At, Ar, are calculate as follows. Appropriate values for R are iscusse in 3.. Te meto given below gives te meian of losses ue to ifferent terminal surrounings. Te possible mecanisms inclue obstruction loss an reflections ue to clutter objects at te representative eigt, an scattering an reflection from te groun an smaller clutter objects. Wen using a computer implementation, wit terrain profile extracte from a igital terrain moel, an wit te terminal surrounings efine by a clutter category, it is not practicable to ientify iniviual

23 Rec. ITU-R P mecanisms. Te meto use ere istinguises between two general cases: for woolan an urban categories it is assume tat te ominant mecanism is iffraction over clutter; for oter categories it is assume tat reflection or scattering ominates. Te meto for transmitter an receiver is ientical, an in te following, A = At or Ar, = tg or rg an R = Rt or Rr as appropriate. If R ten A = 0 If < R, ten A can take one of two forms, epening on clutter type (see Table ): or: J(ν) is calculate using equation (1). Te terms ν an K are given by: ws: f: frequency (GHz) A J() 6.03 B (64a) A K log( / R) B (64b) Knu if θ clut (64c) if R m (64) if θ clut arctan egrees (64e) ws K f log ( ) (64f) K nu f (64g) relates to te wit of te street. Tis soul be set to 7 unless tere is specific local information available. Te form of equation (64a) represents Fresnel iffraction loss over an obstacle an woul be applie to clutter categories suc as builings. In particular urban clutter woul be of tis type. Equation (64b) represents te eigt gain function ue to te proximity of te groun in more open locations. Were specular groun reflection occurs tis is typical of signal variations below te first two-ray interference maximum. Were specular reflection oes not occur te variations below R are typical of tose ue to saowing by minor objects an irregularities. A clearly-efine first two-ray maximum occurs only uner special conitions permitting groun reflection, an cannot be ientifie from te usual topograpic ata available for computer systems. Unless special information is available on te surrouning of a terminal, te value of R associate wit te clutter category soul be use in equation (64b). If special information is available wic ientifies a flat, smoot reflecting surface wit aequate Fresnel clearance to support groun reflection, ten R can be calculate using te meto given in Attacment 3. However, tis approac attempts to ientify a specific point on te multipat istribution, wic is not consistent wit te principles unerlying point-to-area preiction, an is incompatible wit te location-variability calculation given in 4.8. Te etaile estimation of groun reflection soul tus be restricte to te use of te Recommenation oter tan for point-toarea preiction.

24 Rec. ITU-R P Te basic transmission loss not exceee for p% time an 50% locations, incluing te effects of terminal clutter losses, bc (B), is given by: bu: bc bu At Ar B (65) te basic transmission loss not exceee for p% time an 50% locations at (or above, as appropriate) te eigt of representative clutter, given by equation (63) At,r: te aitional losses to account for terminal surrounings, equations (64a an 64b) as appropriate. 4.8 ocation variability of losses In tis Recommenation, an generally, location variability refers to te spatial statistics of local groun cover variations. Tis is a useful result over scales substantially larger tan te groun cover variations, an over wic pat variations are insignificant. As location variability is efine to exclue multipat variations, it is inepenent of system banwit. In te planning of raio systems, it will also be necessary to take multipat effects into account. Te impact of tese effects will vary wit systems, being epenent on banwits, moulations an coing scemes. Guiance on te moelling of tese effects is given in Recommenation ITU-R P Extensive ata analysis suggests tat te istribution of meian fiel strengt ue to groun cover variations over suc an area in urban an suburban environments is approximately lognormal wit zero mean. Values of te stanar eviation are epenent on frequency an environment, an empirical stuies ave sown a consierable sprea. Representative values for areas of m are given by te following expression: K = K = K = σ 1.3 log ( f ) B (66) K 5.1, for receivers wit antennas below clutter eigt in urban or suburban environments for mobile systems wit omniirectional antennas at car-roof eigt 4.9 for receivers wit rooftop antennas near te clutter eigt 4.4 for receivers in rural areas f: require frequency (GHz). If te area over wic te variability is to apply is greater tan m, or if te variability is to relate to all areas at a given range, rater tan te variation across iniviual areas, te value of will be greater. Empirical stuies ave suggeste tat location variability is increase (wit respect to te small area values) by up to 4 B for a km raius an up to 8 B for a 50 km raius. Te percentage locations, p, can vary between 1% an 99%. Tis moel is not vali for percentage locations less tan 1% or greater tan 99%. It soul be note tat, for some planning purposes (e.g. multilateral allotment plans) it will generally be necessary to use a efinition of location variability tat inclues a egree of multipat faing. Tis will allow for te case of a mobile receiver, stationary in a multipat null, or for a rooftop antenna were a number of frequencies are to be receive an te antenna cannot be optimally positione for

25 Rec. ITU-R P all. Aitionally, suc planning may also nee to consier variability over a greater area tan tat assume in tis Recommenation. In tis context, te values given in Table 6 ave been foun appropriate for te planning of a number of raio services. TABE 6 Values of location variability stanar eviations use in certain planning situations Stanar eviation 100 MHz 600 MHz 000 MHz Broacasting, analogue (B) Broacasting, igital (B) Te location variability correction soul not be applie wen te receiver/mobile is ajacent to te sea. Wen te receiver/mobile is locate on lan an outoors but its eigt above groun is greater tan or equal to te eigt of representative clutter, it is reasonable to expect tat te location variability will ecrease monotonically wit increasing eigt until, at some point, it vanises. In tis Recommenation, te location variability eigt variation, u(), is given by: u( ) 1 ( R) u( ) 1 10 u( ) 0 for for for 0 R R R 10 R 10 were R (m) is te eigt of representative clutter at te receiver/mobile location. Terefore, for a receiver/mobile locate outoors, te stanar eviation of te location variability, σ, as given by eiter equation (66) or Table 6, soul be multiplie by te eigt variation function, u(), given in equation (67), wen computing values of te basic transmission loss for values of p% ifferent from 50%. 4.9 Builing entry loss Definitions, teoretical moels an references to empirical results relating to builing entry loss can be foun in Recommenation ITU-R P.040. Te fiel-strengt variation for inoor reception is te combine result of te outoor variation,, an te variation ue to builing attenuation, be (see Recommenation ITU-R P.040). Tese variations are likely to be uncorrelate. Te stanar eviation for inoor reception, i can terefore be calculate by taking te square root of te sum of te squares of te iniviual stanar eviations. i be (67) B (68) were σ is te stanar eviation of location variability, as given by equation (66) or Table 6. For example, for igital emissions wit banwit greater tan 1 MHz, at VHF, were te signal stanar eviations are 5.5 B an 3 B respectively, te combine value is 6.3 B. In Ban IV/V, were te signal stanar eviations are 5.5 B an 6 B, te combine value is 8.1 B.