Topic 7: Propagation

Transcription

1 Topic 7: Popagation Pofs. Javie Ramos & Euao Mogao Acaemic yea Concepts in this Chapte Popagation mechanisms Analytical Moels Fee-Space popagation Goun-Effect. Reflection. Diffaction. Fesnel's zones Attenuation: gases, ain, vegetation Empiical Moels ITU-R Okumua-Hata Cost 3 Theoy classes:.5 sessions (5 hous) Poblems esolution: 0.5 session ( hous)

2 Bibliogaphy Tansmisión po Raio. J. Henano Rábanos. Eitoial Univesitaia Ramón Aeces 3 Mobile Channels Chaacteization When Tx signal popagates though wieless channels (may be mobile) The eceive signal suffes a lage vaiety of petubation that equie a somehow complex mathematical moel to escibe them Quality of the eceive signal y quite wose than its countepat in guie tansmission (cable, fibe optic, etc.) Thee ae multitue of avese effects: eflection, multipath, noise, intefeence, inte-symbol intefeence, Such complexity of the aio channel affects: Design of the eceives to cope with vaiability of the quality of the eceive signal Maximum istance (coveage) fo a tansmitte to a eceive The channel is shae among many uses in the same fequency an location The esign an signaling of the netwok that has to cope with uneliable signal The behavio of the channel can be moele into two scales Lage scale: to etemine maximum ange Small scale: to esign both Tx an Rx an to ecie on magin to be left 4

3 Mobile Channels Chaacteization Aitionaly, if the Tx, Rx o both ae moving, channel vaies with tiem Blocking, multiple-ays (multipath), etc. May pouce api vaiations (e line) While you also have slow vaiations moe in accoance with the velocity of the teminals (blue line) Signal Amplitue t 5 Channel Moel an Netwok Planning Channel Moel has an impact to Unestan the capacity limits of the aio tansmission ove it To esign both Tx an Rx to ovecome channel egaation Channel Moel Channel Capacity Receive Design Design an Implementation of the Raio Netwok Two types of moels Naow ban Vali up to 00KHz of banwith It only consies space vaiations Boaban Consies also fequency istotion (time istotion) of the signal It equies some kin of equalization at the eceive 6

4 Channel Moel an Netwok Planning Naow Ban Moel It moels only the attenuation at a given location (not time vaiations) Lage Scale Aeas aoun wavelengths Povies aveage value fo attenuation between Tx an Rx Use fo aio-planning of netwoks Small Scale Faste (with location) vaiations of signal aoun Lage Scale aveage value Use fo Magin calculus in aio-planning an eceive esign Signal Amplitue t 7 Analytical Popagation Moels Geneal Popagation concepts Teain influence (Reflection Coefficient) Flat Eath moel Cuve Eath moel Refaction Attenuation 8

5 Analytical Popagation Moels. Geneal Concepts Analytical popagation moels They ae Lage Scale Moels Base on Ray Tacing appoach Useful fo point-to-point planning The compute the attenuation incluing Refaction an eflection Diffaction Dispesion Guie-wave effect Chaacteize by Exactness of the esults Nee fo etaile knowlege of the scenaio High computational cost Not ecommene fo Mobile communications Boacasting 9 Reflection an Reflaction Reflection: When a wave hits an inteface between two means, a potion of the impinging powe gets eflecte an the est goes though Both incient an eflecte waves in the same plane Reflection coefficient Snell: θ i = θ It allows passive epeates Refaction: When a wave hits an inteface between two means, potion of the powe that goes into the secon mean tavels though it with iffeent popataion spee Both incient an efacte waves in the same plane Reflection coefficient Snell: n senθi = n senθ t O.R. θ θ i O.I. n n θ i O.I. O.T. θ t 0

6 Electomagnetic Wave Popagation Diffeent appoaches to estimate the behavio of the electomagnetic popagation Maxwell Equation: nice math moel but quite complex to solve fo specific contou conitions. Some scenaios have not close fom solution Appoach base on optical moel Empiical cuve fit to measuement campaigns Electomagnetic Wave Popagation Electomagnetic popagation chaacteistics epen on Conitions of the tajectoy between Tx an Rx obstacles (hills, builings, vegetation, ) Electical chaacteization of the teain (type of soil, smoothness, ) Physical popeties of the mean (humiity, gasses an vapos, ) Fequency of Tx Polaization Geneally speaking, the quantity to be estimate is the attenuation Basic methos to peict attenuation

7 Fequency Bans Ban Numbe Table of ITU Raio Bans Symbols Fequency Range Wavelength Range 4 VLF 3 to 30 khz 0 to 00 km 5 LF 6 MF 30 to 300 khz 300 to 3000 khz to 0 km 00 to 000 m 7 HF 3 to 30 MHz 0 to 00 m 8 VHF 9 UHF 30 to 300 MHz 300 to 3000 MHz to 0 m 0 to 00 cm 0 SHF 3 to 30 GHz to 0 cm EHF THF 30 to 300 GHz 300 to 3000 GHz to 0 mm 0. to mm 3 Fequency Bans Ban Name Min. Feq. Max. Feq. Max. λ Min. λ 4

8 Fequency Bans - Micowaves Ban Name Min. Feq. Max. Feq. Max. λ Min. λ 5 Pefee Sevices fo each Fequency Ban Fom 0 KHz to 50 KHz. Naval (an aeonautical) Geo-location systems Fom 50 KHz to 605 KHz. Auio Boacasting Amplitue Moulation Fom 605 to 5850 KHz Raiotelephony Fom 5950 KHz to 6, MHz. Amateu Raio.. Fom 6, to 4 MHz. Ionospheic Raio popagation. Militay communications Fom 4 MHz to 68 MHz. VHF Television Fom 88 MHz to 08 MHz. Auio Boacasting. Fequency Moulation Fom 6 MHz to 6 MHz. VHF Television Fom 6 to 470 MHz. RaioBeacons, Raiotelephony, Fom 470 MHz to 890 MHz. UHF Television Fom 890 MHz to 940 MHz. Mobile Communications Fom 960 to 350 MHz. Raiotelephony, Raa, telecomman an telemety Fom 350 to 700 MHz. Raiopobes, meteoology Fom 3GHz to 35 GHz satellite communications 6

9 VLF Popagation Guie Wave effect Eath-Ionosphee Ionosphee is a highly ionize laye of the atmosphee that eflects a high atio of the VLF powe. Its height is km above Eath suface At VLF (3kHz 30kHz) both eath goun an ionosphee behave as goo conuctos Distance between the two conuctos (60-00Km) is compaable with the wavelength (00Km-0Km), thus the popagation moel coespons to the one in a spheical guie-wave without losses. Even using physically lage antennas, they ae electically small (compaing it against the wavelength) Global coveage Naval an submaine communication an navigation ais ae main applications fo this ban. Fomely telegaphy was also an application. Ionosphee Toposphee Eath 7 LF, MF an HF Popagation Eath / Suface Wave LF, MF an HF (0 50MHz) popagation follows a moel whee the eath-ai iscontinuity guies the wave popagation Antennas usually use fo these bans ae monopoles of 50 to 00 metes height. Raio ange epens on the tansmitte powe an it vaies LF: fom 000 to 5000Km MF: fom 00 to 000Km HF: less than 00Km Usuall applications: naval communications an auio boacasting Toposphee Eath 8

10 MF an HF Popagation Ionospheic popagation Ionosphee laye of the atmosphee causes efaction of the MF an HF bans (0.3 30MHz) so the signal is peceive as bouncing on it On HF ban linea (hoizontal an vetical) polaizations ae use Range with only one-hop can each up to MF: 0 to 000Km HF: 50 to 4000Km Applications of naow-ban tansmissions ove long ange such as naval communications, aeonautical communications both point-topoint an boacast Ionosphee Eath Toposphee 9 VHF Popagation Topospheic popagation At this fequencies, above 30MHz, ionosphee becomes tanspaent, so popagation look moe like fee-space, with bounces on goun (eflections) an efaction, ispesion an attenuation at the toposphee Usage of iective antennas to obtain high gains an avoi eflection on goun Range vaies Fom tens of Km s to Km on satellite links Even millions of Km in eep space communications Application on auio an TV boacast, cellula communications, aa, satellite communications, fixe sevice links, Ionosphee Toposphee Eath 0

11 Goun Effect on Raio Popagation Existence of both Diect Ray an Reflecte Ray Geneal moel fo popagation T RD ψ ψrr R Goun Effect on Raio Popagation Aitional attenuation: π l Angle: = λ L ex e0 = 0log e l : Diffeence λ :Wavelength = 0log + between [ R + ( R) A] exp( ja) RR an DR length Complex Reflection Coefficient: R = R e jβ Both R an β ae function of: Fequency Polaization Electical chaacteistics of the goun Angle ψ

12 Goun Effect on Raio Popagation Paticula case: Lage istance + low antenna height ψ 0 β π y R = DR RR l = = 0 RD an RR cancel each othe Goun popagation useful fo: Low height antennas (compae to λ) Fequency: f < 0MHz 3 Goun Effect on Raio Popagation Complex Pemittivity of the goun: Fom this paamete, it is efine the z as a function of polaization an incience angle ψ. Goun impeance (z): Vetical polaization: Hoizontal polaization: z = z = [ ε ψ ] 0 cos ε 0 ε = ε 60σλ 0 j [ ε ] 0 cos ψ 4

13 Goun Effect on Raio Popagation. Reflection Coefficient The Reflection Coefficient, R, of a plane suface is: Vetical Polaization: senψ z R = senψ + z Hoizontal Polaization: R V R H ε 0senψ = ε senψ + 0 senψ = sen ψ + ε cos ψ 0 ε cos ψ 0 ε cos ψ 0 ε cos ψ 0 5 Goun Effect on Raio Popagation. Reflection Coefficient Minima get softe an move leftwas If pefect conucto) Goun moeately Dy 6

14 Flat Eath Moel Applicable only fo shot Tx-Rx istance an flat teain P Angle of incience: ht + h ψ = actan l = TPR TR = Path Diffeence: Phase Diffeence: [ + ( h + h ) ] + ( h h ) t [ ] 4π t h = λ t h ht h 7 Flat Eath Moel 8

15 Flat Eath Moel Geneal equation fo popagation is: { + R ( A) exp[ j( + ) + A exp( ) ]} e = e j 0 β Calculus fo A (Bullington): A= + j λ ( π )( senψ + z) A < 0. 9 Flat Eath Moel If we neglect the Suface Wave: [ ] { + R exp[ j( + β )]} = e + R + ( + β ) e = e R 0 0 cos Thus the basic loss of popagation becomes: l b = + R 4π λ + R cos ( + β ) L b ( + R + R ( + β )) 4π = Lbf + Lex = 0log 0log cos λ 30

16 Flat Eath Moel In the paticula case of e = e >> h, h ψ 0, R y ( cos ) t, = e0 sen 0 = 0 πht h e sen λ e e 0 β π π ht h 4 λ 4π l λ b = 4π ht h λ = 4 ( h h ) t 4!! Flat Eath 3 Flat Eath Moel Fo fequencies bellow 50MHz the suface wave has to be consiee This wave can be inclue in the flat eath moel by substituting antenna heights, h t an h, by the new ones h t y h efine as h ' = t h ' = [ ] ( ) λ h + h h = ( ε ) + ( 60σλ ) t 0 π ( ) λ h + h h = ( ε + ) + ( 60σλ ) π 4 hoizontal 4 [ ] vetical pola. The paamete h 0 is non-negligible only fo vetical polaization an fequencies bellow 50MHz Othewise it can be set to zeo pola. 3

17 Flat Eath Moel h 0 values fo iffeent types of gouns an fequencies. Vetical Polaizationvetical Type of Goun A: Sea Watte B: Wet Soil D: Dy Soil E: Vey Dy Soil Fequency (MHz) Flat Eath Moel Accoingly, popagation losses ae 4 l = b ( h h ') t ' Expesse on Bs L b ( km) 0log( h ' h ') 0 40 log + = t Fequency inepenent Popotional to the istance to the 4th powe 34

18 Cuve Eath Moel When link length is lage than the Raioelectic In-Sight Distance ( v ): v = sum of the istances to the hoizont T R ( ) ( ) t ht 0 ht t v kr0 + h = + kr kr0h ht ht h h ht h ( km) = 3.57 ( km) = 3.57 kh ( m) t kh ( m) kr 0 This in-sight istance incesaes with k = v v ( kht kh ) = 4. ( h h ) Ej: ( k = 4 / 3) + t 35 Cuve Eath Moel Objective = compute popagation losses assuming: Staight tajectoy Eath aios moify to become kr 0. Map the cuve eath moel to the flat one: L = L 0log+ R + R cos( β + ) b bf [ ] To o that:. Heights h t an h, an the phase iffeence ae compute. Check that eath oes not block the link 3. Upate the eflection coefficient R: Using ivegence Using teain oughness. 4. Compute popagation losses 36

19 Cuve Eath Moel Reflection moel: Diect Ray + Reflecte Ray Data: Link length (km), absolute antenna height (h t, h ) an k facto fo the eath aios 37 t h h T R t h h RD RR ψ ψ Cuve Eath Moel Fou equation with fou unknowns let us to fin the eflection point 38 ( ) = = = = = h kr h h kr h h kr h h kr h h t t t t t t ( ) ( ) = + + = + + = 3.74 cos cos p h h k h h k p p t t φ φ π

20 Cuve Eath Moel Once istances an (km) ae compute, antenna heights ae to be calculate 4 4 h t = ht ; h = h 5k 5k An the incience angle h t + h ψ ( ma) = Reflection theoy is vali if ψ >ψ /3 lim ( ma ) = (5400 / f ) Path iffeence is h th l( m) = 0 3 An theefoe the phase iffeence is π f l ( a) = Cuve Eath Moel The eflection ove a spheical suface pouces a ivegence that euces the effective eflection coefficient Efficient Reflection Coefficient R e / 5 = R D D = + ( D < ) 6k h t In aition to the coection of the Reflection Coefficient, it can be inclue an aition attenuation ue to the oughness of the teain 4πσ ( ψ ) whee γ = zsen λ R e = R D e γ an σ z is the stana eviation of the teain iegulaities 40

21 Cuve Eath Moel Using all the above factos Whee is compute fom h t, h an is accoingly upate Thus the basic popagation loss [ + R + ( + ) ] / e R e e = e0 cos β R e [ + Re + Re cos( + ) ] L = L 0log β bf 4 Topospheic Popagation: Refaction Atmospheic layes ae not unifom Refaction (efaction inex vaies with height) Non-staight tajectoy but cuve On satellite links: it affects to the pointing of the antenna to the satellite On eath links: it affects to the potential blocking of obstacles f > 0GHz gases an vapos (oxigen an wate vapo mainly) Electomagnetic enegy absotion Atmospheic attenuation an ain pouce aitionaly an incease of the noise tempeatue of the Rx antenna, an some e-polaization of the signal 4

22 Topospheic Popagation: Refaction To simplify the analysis, the Eath aius is change an staight popagation is assume It has to be compute How much the tajectoy is cuve computing the new equivalent Eath aius How to apply the flat eath moel Moele by 43 Topospheic Popagation Refaction Inex: Ray Tajectoy h n The ay suffes sucesive iffactions that cuve it away fom the staight line popagation n senϕ = n sen =... = const ϕ n > ϕ n senϕ > sen The ay gets cuve 44

23 Topospheic Popagation Refaction Inex fo Febuay 45 Diffaction What happens when the ay hits an obstacle? If an optical popagation appoach wee use, the tansmission woulb be totaly blocke It is obseve that thee is still enegy eceive even in the non-linof-sight scenaio 46

24 Diffaction Diffaction is the effect (ispesion an cuvatue) on the popagation of a plane-wave ue to an obstacle which imensions ae compaable to the wavelength When the imensions of the obstacle ae lage than the wavelength popagation keeps on staight line h λ 47 Diffaction Huygens pinciple genealization: Each spatial point of an electomagnetic fiel becomes a seconay souce of aiation. 48

25 Diffaction Fesnel s Zones: Maximum succession (constuctive intefeence) y minimum (estuctive intefeence) Tajectoies with opose phases efine the iffeent zones st Fesnel s Zone: Constuctive (phase iff. < π) n Fesnel s Zone: Destuctive (π < phase iff. < π) 49 Diffaction Fesnel s Zones What is the attenuation cause by an obstacle? Positive Effect: elimination of the estuctive contibution Negative Effect: feasible link Vey Negative Effect 50

26 Diffaction Computation of the Fesnel s Zones: Phase Diffeence λ Tx CRx TxRx = nπ = n nλ R n = 5 Diffaction If the fist Fesnel s zone is fee of obstacles thee is no nee to compute the influence of teain on the popagation losses λ R = When the iect ay goes nea an obstacle o it is block by it, thee is an aitional popagation loss We efine height magin, h, as the istance between the ay an the obstacle T R h > 0 R h < 0 T 5

27 Diffaction An accuate moel fo the popagation loss ue to obstacles is quite complex In pactice, appoximate methos ae employe with a enought accuacy espect actual losses These methos epen on the teain type between Tx an Rx Teain with low unulation: low iegulaities, cuve Eath moel Isolate obstacles: one o few aisolate obstacles Unulate teain: small hills whee thee is no one clealy highe than the est 53 Diffaction T Shap object h > 0 θ > 0 T R h < 0 R θ < 0 Diffaction Angle Nomalize magin L D Losses ( ν ) log ν = h + λ = θ λ( + ) ( ν 0.) + + ν 0. siν >

28 Diffaction Roune obstacle: one object is consiee oune if its aea is smalle than / ( ) 3 = 0.04 λ θ ht z ht h z h h T R A = LD ( ν ) + T ( m, n) 55 Diffaction If two obstacles in the path T R z x x Thee iffeent situations Empiical moel (EMP) Epstein-Peteson moel Recommenation UIT-R P.56 moel z z z

29 Diffaction Two obstacles isolate: empiical moel None obstacle blocks the iect ay, but the magin is not enough (- 0.7 ν 0) T h h R 0 x x L = L ( ν ) + L ( ν ) D D D 57 Diffaction Two obstacles isolate: Epstein-Peteson moel The two obstacles block the iect ay, but they have simila heights T h h R 0 s s s3 x x L = L ) + L D D ( ν ) + LD ( ν C L C = 0log ( s )( ) + s s + s3 s ( + + ) s s s3 58

30 Diffaction Two obstacles isolate: UIT-R P.56 moel One of the obstacles is clealy highe than the othe T 0 O h h s s s3 x x L C ν 0log α / π ν = R α = tg ( s + s s ) s + ss3 3 ν / L = L R) + L D D ( TOR) + LD ( TOO C 59 Attenuation ue to Vegetation If thee is a foestall zone in between the Tx an Rx, thee is an aitional loss ue to the enegy absoption of the vegetation when the ay goes though it Vetical Hoizontal Polaization 60

31 Attenuation ue to Vegetation If non the Tx no the Rx ae in foestal zones, but Pat of the tajectoy cosses foestal aeas (l veg ), An the fequency is bellow GHz. L veg = l veg γ When eithe the Tx o the Rx ae in foestal aea: An pat of the tajectoy cosses foestal aea, if L m is the loss without any foestation along the ay e γ = L m veg Lm When the attenuation is high (i.e. high fequencies) iffaction shoul be consiee f > GHz iffaction, ispesion, eflections, L 6 Attenuation Due to Gases an Atmospheic Vapos Due to absoption of enegy by 0 an H O molecules High impact fo f > 0 GHz. Fo low inclination paths, nea to goun, fo a istance : A a = γ a whee is the specific attenuation (B/m), that can be compute as γ γ + a = 0 γ w Oxigen Wate Vapo 6

32 Attenuation Due to Gases an Atmospheic Vapos Specific Attenuation γ a Tempeatue: 5ºC Pessue: 03 hpa Wate Vapo: 7.5 g/m3 Spectal Winow 63 Rain Attenuation an Depolaization Rain attenuation is a facto to consie on Fixe Sevice (teestial) links an Satellite links High impact at f > 6 GHz. Rain attenuation exceee uing a time pecentage p% A( R, p) = γ ( R, P) L ef Efective Length: L ef = + / Specific Attenuation: (B/km) - Rain intensity Rp(mm/h) - Time pecentage p(%) γ = k R α p k α Depens on f an polaization R 0 = 35 e R0.0 = 00( mm / h) De-polaization loss facto L polaizacion = e tx e * x 64

33 Empiical Moels fo Popagation Losses Outoo UIT-R P.546 Recommenation Okumua-Hata Moel COST-3 Moel Popagation though an heteogeneous mean Longley-Rice Moel Othe moels 65 Empiical Moels. Intouction Pevious methos to compute the popagation losses Requie knowlege of the teain hills, houses, foest, They may be appopiate to fixe point-to-point links Distance Obstacles, iffaction Reflections Peiction of the Popagation Losses 66

34 Empiical Moels. Intouction But, what if we want to peict the attenuation fo a egion, not fo a specific point? Peiction fo each aial: minimum Long pocess with high computational cost In uban envionment: moeling of obstacles quite complex, an usually not enough infomation, an changing 67 Empiical Moels. Intouction Moel Fitting Moel Utilization Measuments Campaings Math Moel Fitting Extaction of Paametes of the Moel Measuements of the Envionment Paametes Losses Calculation 68

35 Outoo Empiical Moels Initially, seveal ecaes ago, they wee pesente by tables an gaphs Because the usage of softwae to semi-automatic aio planning, it is moe convenient to fit a close fom mathematical moel Basic Popeties Fitting of close fom equations to multiple (lage numbe of) measuements Easy an fast estimation, but with lage eo magin Most use moels UIT-R P.546 (Rual) Okumua-Hata COST 3 69 UIT-R P.546 Recommenation Pesentation as nomalize gaphs Peiction of the electical fiel intensity (V/m) Designe fo fixe sevice point-to-point links in ual aeas Intenational stana use by public aministations all ove the wol especific usage on coss-boes intefeence calculations Limits Fequency fom 30 to MHz Distance fom to.000 Km 70

36 UIT-R P.546 Recommenation Cuves Electical fiel as function of the istance (BuV/m) Nomalize fequencies (00, 600 an 000 MHz) Diffeent popagation scenaios: lan, wam ocean, col ocean Tx antenna height: fom 0 to 00 m Rx antenna height: 0 m. Value of intensity exceee 50% of locations fo %, 0% an 50% of the time Methoology inclues a specification to convet it into a numeical value (softwae) Intepolation Extapolation Coection tems 7 UIT-R P.546 Recommenation 7

37 UIT-R P.546 Recommenation Gaphs usage When one o moe paametes of the system une consieation o not match the gaphs Coection The obtaine value neve shoul be lage (lowe attenuation) than Lan: fee space attenuation Sea, with istance an T pecentage of time: E se =.38 [ exp( / 8.94) ] log( 50 / T ) Basic coections Tx powe Tx antenna height Tx fequency RX antenna height Shot tajectoy ove uban/sububan teain Height magin of the Rx Pecentage of locations Pecentage of time 73 UIT-R P.546 Recommenation Example of coections Tx antenna height h TX is efine as: height of the antenna, expesse in metes, fom the aiation cente of the antenna above the aveage level of the teain at istance between 3 an 5 Km fom the Tx to the Rx If the antenna height oes not match the one in the gaph logaithmic intepolation E = E inf + (E sup -E inf ) log(h TX /h inf ) log(h sup /h inf ) E sup h sup E inf h inf h inf <h TX <h sup Fequency If the fequency is iffeent fom 00, 600 o 000 MHz, but it is in between one the these values logaithmic intepolation 74

38 UIT-R P.546 Recommenation Example of coections Location pecentage Example: esign objective is to guaanty 90% of locations A given statistical istibution of the eceive electical fiel is assume Statistical istibution epening on one, o seveal, paamete, povie on tables by ITU-R. Example: log-nomal istibution with paamete σ L. The paamete σ L is foun in coesponing ITU-R table epening on scenaio (uban, ual, etc). The value of the electical fiel exceee L% of the location is E( q) = E + σ G L E( q) = E σ G L ( L/00) ( L/00) fo L 50 fo 50 L 99 whee E is the mean value of the fiel G - is a specific function given in the ecommenation 75 UIT-R P.546 Recommenation Example : Estimation of the intensity of the electical fiel at a istance = 0 Km, antenna height h TX = 0 m, an a fequency 450 MHz. Fom the ITU-R gaphs, we can ea the fiel intensity at 00 an 600 MHz: E inf = 58 Bu. E sup = 55 Bu. Intepolation: E = 58 + (55-58) log(450/00)/log(600/00) = 55.5 Bu. E sup f sup E inf f inf f inf < f TX < f sup 76

39 UIT-R P.546 Recommenation Example : Given a cellula system - In an uban aea - woking at f = 450 MHz - Mean value of the fiel intensity is Em = 30 Bu. It is neee the value of the fiel intensity that is exceee at 90% of the locations Fo this sevice: σ L =, +,3 log 450 = 4,6 B. Aitionally: G - (-0.9) =,8. Theefoe, E = 30 4,6,8 = 4 Bu. 77 Okumua-Hata Moel Objective: efine simple close-fom mathematical moel fo the popagation attenuation applicable to the aio planning of cellula netwoks, specially fo uban aeas Stating point: a quite lage measuement campaing one in Japan Okumua: gaphs poviing mean values fo electomagnetic file in uban aeas, fo Seveal antenna heights Fequency bans of 50 MHz, 450 MHz an 900 MHz. EIRP = KW. Rx antenna height:,5 m. 78

40 Okumua-Hata Moel The pevious gaphs, wee complemente by coection factos fo: Unulation of the teain Heteogeneity of the teain Rx antenna height Tx EIRP Steets oientation Builings ensity Hata: evelopment of close-fom mathematical expessions fo the nomalize Okumua gaphs 79 Okumua-Hata Moel Okuma gaphs fo the fequency vaiation 80

41 Okumua-Hata Moel Okumua gaph fo the eceive fiel intensity (f=900mhz) 8 Okumua-Hata Moel Close-Fom moel: logaitmic fitting of the gaphs Losses fo uban envionment: L Oku = A + B log( ) + C 8

42 Okumua-Hata Moel Whee f = fequency MHz Limits: 50 < f < 500MHz h t = Effective Tx Antenna Height (m) Limits: 30 < h t < 00m h = Effective Rx Antenna Height (m) Limits: < h < 0m = Distance (Km) Note: moel vali only up to 500 MHz Aaptation Hata-COST3: Extension of the moel fo uppe ban in cellula netwoks (between 800 an 000 MHz) 83 Okumua-Hata Moel Results 84

43 Okumua-Hata Moel Results 85 Okumua-Hata Moel Results 86

44 COST-3 Moel Okumua-Hata moel oes not inclue any paamete about the teain. To achieve moe pecision, moels consieing next paametes have been consiee Steets stuctue Builings imension Al the paametes in the Okumua-Hata moel The most upate moel is the COST3, which was aopte as UIT-R ecommenation Vali fo non-line-of-sight scenaios 87 COST-3 Moel Paametes BS antenna height MS antenna height Aveage height of builings Boaness of the steet whee the MS is locate Distance between cente of builings BS-MS istance Angle of incience 88

45 COST-3 Moel Paametes: Angle with espect the steet axis BS height above the aveage builing height Aveage builings height above MS antenna height 89 COST-3 Moel Close fom math moel L 0 = log(f) + 0 log() L ts = log(w) + 0 log(f) + 0 log( h R ) + L oi whee L oi epens on the angle between the ay an the steet axis L ms = estimation of the iffaction pouce by multiple obstacles Applicability limits: 800 < f <.000 MHz 4 < h B < 50 m < h m < 3 m 0.0 < < 5 km 90

46 Moels Compaison An estimation of popagation losses is to be one fo a big city fo the aio planning of a cellula netwok at 900 MHz. Base Station height is 35m while the mobile stations have an antenna at,5m hight. The avege height of the builings is 5 floos The aveage boaness of the steets coespons to a lines each iection, plus 3 metes fo the siewalk each sie. Two paking lines ae also consiee Aveage istance between builing is 45m. Figue: compaison between Okumua-Hata an Cost3 moels 9 Popagation ove an Heteogeneous Mean Some scenaios ae bette consiee as concatenation of iffeent aeas with iffeent electomagnetic popeties Each section is bette moele by a iffeent mathematical moel Lb() = k n Lb = losses expesse on natual units. k = constant. D = istance. n = paamete epening of the mean To a the effect of iffeent moels the following moel can be use (example fo thee sections) n p ( ) = p () p ( ) = p () p ( ) = p () n + n n + n n n + n3 n3 9

47 Popagation ove an Heteogeneous Mean The exponent on the pevious moel, n, takes a value fom.4 an 5, as function of the envionment Envionment Exponent, n Fee Space Uban Uban with lage builings 3-5 Inoo with LOS.6-.8 Inoo without LOS -3 Sububan -3 Inustials aeas. 93 Longley-Rice Moel Also known as ITS Iegula Teain Moel Base on electomagnetic theoy an statistical analysis of the teain chaacteistics an measuement campaign Outcome: aveage value fo attenuation as function of the istance, an a moel fo the vaiation with time an space It contains a point-to-point moel an a aea peiction moel. System paametes: associate to the aio equipment an inepenent of the envionment Fequency between 0MHz an 40GHz Distance between Km an 000Km Antenna height between 0.5m an 3000m above the teain Polaization: hoizontal an vetical 94

48 Longley-Rice Moel Paametes escibing statistically the envionment Aveage unulation of the teain ( h): Atmosphee efactivity: etemines the bening o cuvatue of the aio popagation Othe moels inclue this paamete in the effective cuvatue of the Eath, typically 4/3 (.333). Longley-Rice moel inclues iectly the efactivity value Range fom 50 to 400 Units of n (coesponing to effective Eath cuvatue between.3 an.767). Effective cuvatue of the Eath of 4/3 (=.333) coesponing to a efactivity of 30 Units of n. (ecommene value fo aveage atmospheic conitions) Relation between paametes k an n : 95 Longley-Rice Moel Envionment paametes Dielectic constant of the teain Relative pemittivity o ielectic constant (ε). Conuctivity: Climate: 7 moels fo climate Equatoial (Ex. Congo) Subtopical Continental (Ex. Suan) Subtopical Maitime (Ex. Afica shoe) Deset (Ex. Sahaa) Wam Continental Wam Eath Maitime (Ex. UK an EU) Wam Maitime Sea 96

49 Longley-Rice Moel Statistical Paametes Time vaiation: (of the atmospheic changes an othe effects) Location vaiation Othe vaiations o hien vaiables 97 Othe Moels Walfish-Betoni Dukin Sakagami-Kuboi Ibahim-Pasons 98

50 Summay of Moels Moel Out / Inoo Fequency Range UIT-R P.546 Outoo 3000MHz Boacast Okumua-Hata Outoo 500(000)MHz Uban COST-3 Outoo 000MHz Any Heteogeneus Mean Outoo Any Any Applicability Longley-Rice Outoo 40GH< Any although it is quite complex 99 Summay of Concepts in this Chapte We have seen iffeent moels to peict the aio popagation loss Fist classification: Deteministic moels, whee you nee to know accuately the envionment Empiical moels: aveage estimation is fitte to a measuements campaign peviously one Seveal useful Outoo empiical moels epening on Fequency Teain Rual o Uban envionment Distance Moels Tae-off between complexity an accuacy Softwae tools inclue popagation moels to geatly simplify aio planning 00