Lecture 5

LargeScaleFadingandNetworkDeployment

+Large Scale Fading

n “Large”scalevariationofsignalstrengthwithdistancen Consideraverage signalstrengthvalues

n Theaverageiscomputedeitherovershortperiodsoftimeorshortlengthsofdistance

n Astraightlineisfittotheaveragevalues

n Theslopeandtheinterceptgiveyoutheexpressionforthepathloss

n Thevariationaroundthefitistheshadowfadingcomponent

Received

signalstrength

Logdistance

Slope&Intercept

Variation

2

+Path Loss Models

n PathLossModelsarecommonlyusedtoestimatelinkbudgets,cellsizesandshapes,capacity,handoffcriteriaetc.

n “Macroscopic”or“largescale”variationofRSS

n Pathloss=lossinsignalstrengthasafunctionofdistancen Terraindependent(urban,rural,mountainous),groundreflection,diffraction,

etc.n Sitedependent(antennaheightsforexample)n Frequencydependentn Lineofsightornot

n Simplecharacterization:PL =L0 +10a log10(d)n L0istermedthefrequencydependentcomponentn Theparametera iscalledthe“pathlossgradient”orexponentn Thevalueofa determineshowquicklytheRSSfallswithdistance

3

+The Free Space Loss

n Assumptionn Transmitterandreceiverareinfreespacen Noobstructingobjectsinbetweenn Theearthisataninfinitedistance!

n ThetransmittedpowerisPt, andthereceivedpowerisPrn Thepathloss isLp =Pt (dB)– Pr (dB)

n Isotropicantennasn Antennasradiateandreceiveequallyinalldirectionswithunitgain

d

4

+The Free Space Model

n TherelationshipbetweenPt andPr isgivenby

Pr =Pt l2/(4pd)2

n Thewavelengthofthecarrierisl =c/f

n IndBPr (dBm)=Pt (dBm)- 21.98+20log10(l)– 20log10(d)

Lp(d)=Pt – Pr =21.98– 20log10(l)+20log10(d)=L0 +20log10(d)

n L0 iscalledthepathlossatthefirstmeter(putd =1)

n Wesaythereisa20dBperdecade lossinsignalstrength

5

+A simple explanation of free space lossn Isotropictransmitantenna:Radiatessignal

equallyinalldirections

n Assumeapointsourcen Atadistanced fromthetransmitter,the

areaofthesphereenclosingtheTx is:A =4pd2

n The“powerdensity”onthissphereis:Pt/4pd2

n Isotropicreceiveantenna:Capturespowerequaltothedensitytimestheareaoftheantennan Idealareaofantennais

Aant =l2/4p

n Thereceivedpoweris:Pr =Pt/4pd2 ´ l2/4p =Pt l2/(4pd)2

6

+Isotropic and Real Antennas

n Isotropicantennasare“ideal”andcannotbeachievedinpracticen Usefulasatheoreticalbenchmark

n Realantennashavegainsindifferentdirectionsn SupposethegainofthetransmitantennainthedirectionofinterestisGt andthatofthereceiveantennaisGr

n Thefreespacerelationis:Pr =Pt Gt Gr l2/(4pd)2

n ThequantityPt Gt iscalledtheeffectiveisotropicradiatedpower(EIRP)n Thisisthetransmitpowerthatatransmittershouldusewereithavinganisotropicantenna

7

+Summary: Free space loss

n TransmitpowerPt andreceivedpowerPr

n WavelengthoftheRFcarrierl =c/f

n Overadistanced therelationshipbetweenPt andPr isgivenby:

n where disinmeters

22

2

)4( dPP t

r pl

=

IndB,wehave:

Pr (dBm)=Pt (dBm)- 21.98+20log10 (l)– 20log10 (d)

PathLoss=Lp =Pt – Pr =21.98- 20log10(l)+20log10 (d)

8

+Free Space Propagation

nNoticethatfactorof10increaseindistancen =>20dBincreaseinpathloss(20dB/decade)

nNotethathigherthefrequencythegreaterthepathlossforafixeddistanceDistance PathLossat880MHz

1km 91.29dB

10km 111.29dB

Distance 880MHz 1960MHz

1km 91.29dB 98.25dB

7dBgreaterpathlossforPCSbandcomparedtocellularbandintheUS

9

+Example

n ConsiderDesignofaPoint-to-PointlinkconnectingLANsinseparatebuildingsacrossafreewayn Distance.25milen LineofSight(LOS)communication

n Unlicensedspectrum– 802.11bat2.4GHz

n Maximumtransmitpowerof802.11APisPt =24dBm

n Theminimumreceivedsignalstrength(RSS)for11Mbpsoperationis-80dBm

n Willthesignalstrengthbeadequateforcommunication?

n GivenLOSn CanapproximatepropagationwithFreeSpaceModel

10

+Example (Continued)

n Examplen Distance.25mile~400m;ReceiverSensitivityThreshold=- 80dBm

n TheReceivedPowerPr isgivenby: Pr =Pt - PathLoss

Pr =Pt - 21.98+20log10 (l)– 20log10 (d)

=24– 21.98+20log10 (3x108/2.4x109)– 20log10 (400)

=24-21.98-18.06-52.04

=24– 92.08=-68.08dBm

Pr iswellabovetherequired-80dBm forcommunicationatthemaximumdatarate– solinkshouldworkfine

L0 =40dBat2.4GHz

11

+Cell/Radio Footprint

n TheCellistheareacovered byasingletransmitter

n Pathlossmodelroughlydeterminesthesizeofcell

n Whatdoes“covered”mean?

12

+Link Budget

n TypicalFactorsinLinkBudgetn TransmitPower(indBm),n AntennaGain,DiversityGainn ReceiverSensitivityn Margins

n ShadowMargin,InterferenceMargin,FadingMarginn Losses

n VehiclePenetrationLoss(3-6dB)n BodyLoss(2-3dB)n BuildingPenetrationLoss(5-20dBdependingonbuildingmaterial

n ElectronicLosses:CombinerLoss,FilterLoss,etc.n Gainsareadded,Lossesaresubtracted(e.g.,f =1900MHz)

13

+Example of Link Budget

Link Uplink Downlink

Transmit power 30 dBm 30 dBmAntenna gain 3 dBi 5 dBiDiversity gain 5 dB 0 dBShadow margin 10 dB 10 dBBody penetration 2 dB 2 dBVehicle penetration 5 dB 5 dBReceiver sensitivity -105 dBm -90 dBmPath Loss Budget 126 dB 108 dB

TypicalCellularSystemisDownlinkLimited!

14

+Calculation of link Budget: Uplink

TransmitPower30dBm

DiversityGain5dBi33dBm

38dBm

ShadowMargin10dB

28dBmBodyLoss2dBVehicleLoss5dB 21dBm

ReceiverSensitivity-105dBm

PathLossBudget=126dB

AntennaGain3dBi

126dB

15

+Determining Coverage

n LinkBudgetn Usedtoplanusefulcoverageofcellsn Roundtripperformanceofsatellites,

etc.

n Simplyabalancesheetofallgainsandlossesonatransmissionpath.n Gainsareadded(transmitpower,

antennagains)n Lossesaresubtracted(pathloss)

n Usedtofindmaxallowablepathlossineachlink(i.e.,uplinkanddownlink)n EnsureadequateRSSatendofeach

link

n SimpleExamplen Thepathlossbudgetis108dBn Thepathlossmodelisgivenby

Lp =98+32log10d

(d isinkm)

n Thecellradiusshouldbe

98+32log10d =108=>log10d =10

d =10(10/32) =2.05km

16

+General Formulation of Path Loss

n Dependingontheenvironment,itisseenthatthepathloss(ortheRSS)variesassomepowerofthedistancefromthetransmitterd

n Herea iscalledthepath-lossexponentorthepath-lossgradientorthedistance-powergradient

n ThequantityL0 isaconstantthatiscomputedatareferencedistanced0n Thisreferencedistanceis1minindoorareasand100mor1kminoutdoorareas

ORPr(d) /✓Pt

d�

◆Pr(d) =

✓Pt

L0(d/d0)�

◆

17

+More Comments

n Pathlossisafunctionofavarietyofparametersn Terrainn Frequencyofoperationn Antennaheights

n Extremelysitespecificn Variesdependingonenvironment

n Example:indoorVsoutdoorn Example:microcellVsmacrocelln Example:ruralVsdenseurban

n Largenumberofmeasurementresultsareavailablefordifferentscenarios,frequenciesandsites

n Empiricalmodelsarepopular

18

+Environment Based Path Loss

n Basiccharacterization:Lp =L0 +10a log10(d)n L0 isfrequencydependentcomponent(oftenpathlossat1m)n Theparametera iscalledthe“pathlossgradient”orexponentn Thevalueofa determineshowquicklytheRSSfallswithd

n a determinedbymeasurementsintypicalenvironmentn Forexample

n a =2.5mightbeusedforruralarean a =4.8mightbeusedfordenseurbanarea(downtownPittsburgh)

n Variationsonthisapproachn Tryandaddmoretermstothemodeln Directlycurvefitdata

n TwopopularmeasurementbasedmodelsareOkumura-Hata,andCOST231n Dosomemeasurementsandfeeditintosimulations(raytracing)

19

+Okumura-Hata Model

n Okumuracollectedmeasurementdataandplottedasetofcurvesforpathlossinurbanareasaround900MHzn Hata cameupwithanempiricalmodelforOkumura’scurves

Lp =69.55+26.16logfc – 13.82loghte – a(hre)+(44.9–6.55loghte)log d

a(hre)=3.2(log[11.75hre])2 – 4.97dB

n Note:fc isinMHz,d isinkm,andantennaheightsareinmetersn Thisisvalidonlyfor400£ fc £ 1500MHzforalargecityn 30£ hte £ 200m;1£ hre£ 10m;

n Otherformsdependingonthescenario

20

+Example of Hata’s Model

n Considertheparametersn hre =2m– receiverantenna’sheightn hte =100m– transmitterantenna’sheightn fc =900MHz– carrierfrequency

n Lp =118.14+31.8logdn Thepathlossexponentforthisparticularcaseisa =3.18

n Whatisthepathlossatd =5km?n d =5kmè Lp =118.14+31.8log5=140.36dB

n Ifthemaximumallowedpathlossis120dB,whatdistancecanthesignaltravel?n Lp =120=118.14+31.8logd =>d =10(1.86/31.8) =1.14km

21

+COST 231 Modeln ModelsdevelopedbyCOST

n EuropeanCooperativeforScienceandTechnologyn Collectedmeasurementdatan Plottedasetofcurvesforpathlossinvariousareasaroundthe1900MHzband

n DevelopedaHata-likemodel

Lp =46.3+33.9logfc – 13.82loghte - a(hre)+(44.9–6.55loghte)log d +C

n Cisacorrectionfactorn C=0dBindenseurban;-5dBinurban;-10dBinsuburban;-17dBinrural

n Note:fc isinMHz(between1500and2000MHz),d isinkm,hte iseffectivebasestationantennaheightinmeters(between30and200m),hre ismobileantennaheight(between1and10m)

22

+Indoor Path Loss Models

n Indoorapplicationsn WirelessPBXsn WirelessLocalAreaNetworks

nApproachissimilartooutdoormodelsn Distancesaresmallern Sitespecificityismoreimportant

n Varietyofobstructionsn Walls,floors,vendingmachines,bookcases,humanbeingsetc.

23

+Motley-Keenan and Rappaport Models

n Assumethatthepathlossexponenta =2

n Drawastraightlinebetweenthetransmitterandreceiver

n AssignalossofsomedBtoeachobstructionthatisintersectedbythisstraightlinen Example:Concretewall7dB,Cubiclepartition4dB

n Thepathlossisgivenby:

n mi isthenumberofpartitionsoftypei andWi isthelossassociatedwiththatpartition

n nj isthenumberoffloorsoftypej andFj isthelossassociatedwiththatfloor

n L0 isdeterminedasbefore(thepathlossatonemeter)

∑∑ +++=j

jji

iip FnWmdLL log200

24

+Sample numbers

Signal attenuation of 2.4 GHz through dB

Window in brick wall 2

Metal frame, glass wall into building 6

Office wall 6

Metal door in office wall 6

Cinder wall 4

Metal door in brick wall 12.4

Brick wall next to metal door 3

Source:HarrisSemiconductors

25

Example of Partition Dependent Model

n Example:n Thestraightlineintersectstwobrickwallsandonecubiclepartition

n Lp =L0 +20logd +2Wbrick +Wcubicle

n Insomemodels,thepathlossexponenta isdifferentfrom2

TX

RX

d

Brick

Cubicle

Brick

26

+Some Notes

n Empiricalmodelshavetheirdisadvantagesn Example:Okumura-Hata modelappliestocitiesthatarelikeTokyo(whatdoesthatmean?WhenisacitylikeTokyo?)

n Dependsontheinterpretationofpeoplen SomepeoplemayconsiderPittsburghtobeasmallcityn Othersmaythinkofitasamediumcity

n Somemodelshavelimitedapplicabilityn Example:COST-231modelcannotbeusedifhte <hroof wherehroof istheaverageheightofbuildingsinthearea

n Therearemanyothermodelsn Modelsformicrocellularenvironmentsn Terraindependent(e.g.,Longley-Rice)

27

+Shadow Fading

n Shadowingoccurswhenlineofsightisblocked- ModeledbyarandomsignalcomponentXs

n MeasurementstudiesshowthatXs canbemodeledwithalognormaldistributionènormalindBwithmean=zeroandstandarddeviations dB

n Thusatthe“designedcelledge”only50%ofthelocationshaveadequateRSS

n SinceXs canbemodeledindBasnormallydistributedwithmean=zeroandstandarddeviations dB,s determinesthebehavior

Pr =Pt – Lp +Xs

28

+How shadow fading affects system designn Typicalvaluesforσ are

n Rural3dB,suburban6dB,urban8dB,denseurban10dB

n SinceXisnormalindBPrisnormaln Pr =Pt – Lp +Xσ

n Prob {Pr (d)>Threshold}canbefoundfromanormaldistributiontablewithmeanPr andstandarddeviationσ

n InordertomakeatleastY%ofthelocationshaveadequateRSSn Reducecellsizen Increasetransmitpowern Makethereceivermoresensitive

29

+Example of Shadowing Calculationsn ThepathlossofasystemisgivenbyLp =47+40log10 d – 20log10hbwherehb =10m,Pt =0.5W,receiversensitivity=-100dBm.Whatisthecellradius?

n Pt =10log10500=27dBm;Thepermissiblepathlossis27-(-100)=127dB

n 20log10hb =20log1010=20dB

n 127=47+40log10d – 20=>d =316m

n Buttherealpathlossatanylocationisn 127+X whereX isarandomvariablerepresentingshadowingn NegativeX =betterRSS;PositiveX =worseRSS

n Iftheshadowfadingcomponentisnormallydistributedwithmeanzeroandstandarddeviationof6dB. WhatshouldbetheshadowmargintohaveacceptableRSSin90%ofthelocationsatthecelledge?

30

+Example again

n LetX betheshadowfadingcomponent

n X =N(0,6)andweneedtofindF suchthatP{X >F}=0.1orweneedtosolveQ(F/s)=0.1

n Usetablesorsoftware

n InthisexampleF =7.69dB

n Increasetransmitpowerto27+7.69=34.69dBm =3W

n Makethereceiversensitivity-107.69dBm

n Reducethecellsizeto203.1m

n Inpracticeuse.9or.95quantile valuestodetermine the ShadowFadingMargin

FadingMarginistheamountofextrapathlossaddedtothepathlossbudgettoaccountforshadowing

.9à SFM=1.282s

.95à SFM=1.654s

31

+Cell Coverage modeling

n Simplepathlossmodelbasedonenvironmentusedasfirstcutforplanningcelllocations

n Refinewithmeasurementstoparameterizemodel

n Alternatelyuseraytracing:approximatetheradiopropagationbymeansofgeometricaloptics- considerlineofsightpath,reflectioneffects,diffractionetc.

n CADdeploymenttoolswidelyusedtoprovidepredictionofcoverageandplan/tunethenetwork

32

+Cellular CAD Tools

nUseGISterraindatabase,alongwithvehicletraffic/populationdensityoverlaysandpropagationmodels

nOutputmapwithcellcoverageatvarioussignallevelsandinterferencevaluesn Toplanoutcellcoveragearea,cellplacement,handoffareas,interferencelevelfrequencyassignment

33

+Use GIS maps

nThisshowspossiblelocationofcellsiteandpossiblelocationofuserswheresignalstrengthpredictionisdesired

34

+Outdoor Model

CADToolsprovideavarietyofpropagationmodels:freespace,Okumura-Hata,etc.

35

+ Typical City pattern

MicrocelldiamondRadiationpattern

36

+Ray Tracing Mode

37

+Indoor Models

38

+Cellular CAD Tools

nCADtool– firstcutcellsiteplacement,augmentedbyextensivemeasurementstorefinemodelandtunelocationandantennaplacement/type

Temporarycell

39

+Signal strength prediction for Indoor WLANS

n MotorolaLANPlanner

n Lucent:WiSEtool

n Givenbuilding/spacetobecoveredandparametersofbuildingandAP– predictssignalcoverage

40

+Site Survey Tools

n Softwaretomeasuresignalstrengthandrecordinginordertoconstructacoveragemapofstructure– mustdrive/walkaroundstructuretogatherdata

n NOKIAsitesurveytool,Ekahau SiteSurvey,MotorolaLANsurvey,etc.

41

+How about Interference?

nCoverageimpliesthereisenoughsignalstrengthnButhowaboutcompetingsignalstrengthfromadifferentbasestation?

n Interferencehasasignificantimpactonthequalityofaradiochannel

nNextwelookatinterferenceandfrequencyreuse

42

+Basic Interference Scenario –Two links

Pr =KPt

d↵= KPtd

�↵

Sr =Pr�d

Pr�I=

KPt�dR�↵

KPt�ID�↵=

Pt�d

Pt�I

✓D

R

◆↵

43

K =const

+ Design and Deployment in Cellular Networks

n Adhocnetworksn Usuallynoarchitecturaldesignn Mostdesignisattheprotocollevel– routing,MACetc.

n Infrastructurenetworksn Deployacellulartopologybasedonsomerequirements

n Frequencyreusen Startwithlargecellsinitially

n Asdemandincreasesn Capacityenhancementtechniques

n Reusepartitioningn Sectoredcellsn Migrationtodigitalsystemsn Dynamicchannelallocation

44

+Design Challenge

nHowcanwereusefrequencybandssuchthatn Interferenceisnotsohighastomakecommunicationsimpossible

nTheavailablespectrumisreusedtomakethebestuseofcapacity

45

+Cellular Concept

n ProposedbyBellLabsin1971

n GeographicServicedividedintosmaller“cells”

n Neighboringcellsdonotusesamesetoffrequenciestopreventinterference

n Oftenapproximatecoverageareaofacellbyanidealizedhexagon

n Increasesystemcapacitybyfrequencyreuse

46

+The Cellular Concept

nDeployalargenumberoflow-powertransmitters(BaseStations)eachhavingalimitedcoveragearea

nReusethespectrumseveraltimesintheareatobecoveredtoincreasecapacity

n Issues:n Capacity(trafficload)inacellnOnemeasure=numberofcommunicationchannels thatareavailable

n Performancen Callblockingprobability,handoffdroppingprobability,throughputetc.

n Interference

47

+Cellular Concept

n Whynotalargeradiotowerandlargeservicearea?n Numberofsimultaneoususerswouldbeverylimited(tototalnumberoftrafficchannelsT)

n Mobilehandsetwouldhavegreaterpowerrequirement

n Cellularconcept- smallcellswithfrequencyreusen Advantages

n Lowerpowerhandsetsn Increasessystemcapacitywithfrequencyreuse

n Drawbacks:n Costofcellsn Handoffsbetweencellsmustbesupportedn Needtotrackusertorouteincomingcall/message

48

+Recap: Communication Channel

n Afrequencybandallocatedforvoiceordatacommunicationsn Simplestexample:Frequencydivisionmultipleaccess(FDMA)withFrequencyDivisionDuplexing(FDD)n 30kHzbandsareallocatedforoneconversationn Separatebandsareallocatedforuplink(MHtoBS)anddownlink(BStoMH)

n Asetoftimeslotsallocatedforvoiceordatacommunications

n Asetofspread-spectrumcodesallocatedforvoiceordatacommunications

49

+Types of Interference

nTDMA/FDMAbasedsystemsnCo-channelinterferencen Interferencefromsignalstransmittedbyanothercellusingthesameradiospectrum

nAdjacentchannelinterferencen Interferencefromsignalstransmittedinthesamecellwithoverlappingspectralsidelobes

nCDMAsystemsn Interferencefromwithinthecelln Interferencefromoutsidethecell

50

+Clustering in TDMA/FDMA

nAdjacentcellsCANNOTusethesamechannelsn Co-channelinterferencewillbetoosevere

nTheavailablespectrumisdividedintochunks(sub-bands)thataredistributedamongthecells

nCellsaregroupedintoclustersn Eachclusterofcellsemploytheentireavailableradiospectrum

n Thespatialallocationofsub-bandshastobedonetominimizeinterference

51

+Cellular Concept (cont)

nLetT =totalnumberofduplexchannelsNc cells=sizeofcellcluster(typically4,7,9,12,21)L =T/Nc =numberofchannelspercell

nForaspecificgeographicarea,ifclusters arereplicatedM times,thentotalnumberofchannelsn Systemcapacity=M×Tn ChoiceofNc determinesdistancebetweencellsusingthesamefrequencies– termedco-channelcells

n Nc dependsonhowmuchinterferencecanbetoleratedbymobilestationsandpathloss

52

+Cell Design - Reuse Pattern

n Example:cellclustersizeNc =7,frequencyreusefactor=1/7;

nAssumeT =490totalchannels,L =T/Nc =70channelspercell

B

A

E

C

D

G

F

B

A

E

C

D

G

F

B

A

E

C

D

G

FAssumeT=490totalchannels,Nc =7,N=70channels/cell

ClustersarereplicatedM=3times

Systemcapacity=3x490=1470totalchannels

53

+Cellular Geometry

n Propagationmodelsrepresentcellasacirculararea

n Approximatecellcoveragewithahexagon- allowseasieranalysis

n FrequencyassignmentofFMHzforthesystem

n ThemultipleaccesstechniquestranslatesF toT trafficchannels

n ClusterofcellsNc =groupofadjacentcellswhichuseallofthesystemsfrequencyassignment

54

+Cellular Geometry

nCellsdonothavea“nice”shapeinreality

nAmodelisrequiredfornPlanningthearchitecturenEvaluatingperformancenPredictfuturerequirements

nSimpleModel:nAllcellsareidenticalnTherearenoambiguousareasnTherearenoareasthatareNOTcoveredbyanycell

55

+Possibilities for cell geometry model

nEquilateraltriangle,squareorregularhexagon

56

+Why hexagon?

nAmongthethreechoices,thehexagonistheclosestapproximationtoacircle

nForagivenradius(largestpossibledistancefromcenterofapolygontoitsedge)ahexagonhasthelargestarea

nAcircleissometimesusedwhencontinuousdistributionsarebeingconsidered

57

+ Determining co-channel cells and the reuse factor

-1 -1

0,

1

2

3

1 2

3 4

u

v n Co-channelcellsmustbeplacedasfarapartaspossibleforagivenclustersize

n Hexagonalgeometryhassomepropertiesthatcanbeemployedtodeterminetheco-channelcell

n Co-ordinatesystem: u and vco-ordinates

Cellsareplacedsothattheircentershaveintegerco-ordinates

58

+Finding (placing) Co-channel cells (continued)n Moveadistancei alongtheudirectionandadistancej alongthev direction

n TheclustersizeNc =i2 +ij +j2

,

A

u

A

A

A

A

A

A

59

+

C

D

B

A

E

G

F

C

D

B

A

E

G

F

C

D

B

A

E

G

F

C

D

B

A

E

G

F

C

D

B

A

E

G

F

C

D

B

A

E

G

F

C

D

B

A

E

G

F

Example: i = 2, j = 1ClustersizeNc=7

UsedinAdvancedMobilePhoneService(AMPS)

60

+MoreExamples

132

43 1

4

21

23

41

3142

6 751

1

11

1

1

Nc =4(i =2,j=0)

Nc =7(i =2,j =1)

2

98

6

71

3

1011

124

5

65

8

6

7

98

124

5

3

1011

124

910

11

Nc =12(i=2,j=2)

61

+Some results

nNc =numberofcellsinacluster

nR =radiusofacell

nD =distancebetweenco-channelcells

nNc canonlytakevaluesthatareoftheformi2 +ij +j2 ;i,j areintegers

n Thereareexactlysixco-channelcellsforahexagonalgeometry

D

R=

p3Nc

62

+Revisiting Signal to interference ratio calculation

nGeneral:

nOnedesiredsignalandoneinterferingsignalatdistancesd1 andd2

Sr =PdesiredPInterference,i

i∑

a

a

a

÷÷ø

öççè

æ== -

-

1

2

2

1

dd

dKPdKPSt

tr

d1

d2

63

+Sr in a hexagonal architecture

nWithJs interferingbasestations

n Js =6forahexagonalarchitecturen a =4forurbanareas

nMaximumdistanceoftheMSfromadesiredBSisR

n ApproximatedistanceoftheMSfromeachoftheco-channelinterferersisD

n TheexpressionforSr is:

å=

=sJ

nn

r

d

dS

1

0

a

a

Sr ≈R−4

JsD−4 =

R−4

6D−4 =16DR

#

$%

&

'(4

=32Nc2

SolveforD/R

64

+Sr as a function of the cluster size

4 6 8 10 12 14 16 18Frequency Reuse Factor

12

14

16

18

20

22

24

26

28

SIR

in d

B65

+Issues Revisited

nClustersize Nc determinesn Theco-channelinterferencen Thenumberofchannelsallocatedtoacell

n Larger Nc is,smalleristheco-channelinterference

n Larger Nc is,smalleristhenumberofchannelsavailableforagivencelln Capacityreduces

nWhatNc shouldweusebasedonSIRorC/I?

66

+Example: AMPS

n Voicechannelsoccupy30kHzandusefrequencymodulation(FM)

n 25MHzisallocatedtotheuplinkand25MHzforthedownlink

n 12.5MHzisallocatedtonon-traditionaltelephoneserviceproviders(BlockA)

n 12.5MHz/30kHz=416channels

n 395arededicatedforvoiceand21forcontrol

824 MHz

849 MHz

869 MHz

894 MHz

45 MHz

Uplink Band Downlink Band

Block A Block B

21 Control & 395 Voice Channels

30 kHz

67

+Reuse in AMPS

nSubjectivevoicequalitytestsindicatethatSr =18dBisneededforgoodvoicequality

nThisimplies Nc =7nSeenextslidealso

nCellsdonotactuallyconformtoahexagonalshapeandusuallyareusefactorof Nc =12isneeded

68

+Frequency Reuse

Example:Considercellularsystemwith• Sr requirementof 18dB• Suburbanpropagationenvironmentwitha =4.Determinetheminimumclustersize.

18dBè 18=10log10 (x)è1.8=log10 (x)è x =101.8 èx =63.0957.

Nc =1/3 × (6 × 63.0957)0.5 =6.4857

Since Nc mustbeaninteger,yourounduptonearestfeasibleclustersize=>Nc =7

SolvingforD/R resultsin

Remember ,whichresultsin

DR= 6Sr( )1/α

Nc =136Sr( )2/α

D / R = 3Nc

69

+AMPS: Adjacent channel interference

nClustersizeisNc =7

nConsiderthe395voicechannelsn 1:869.00– 869.03MHzn 2:869.03– 869.06MHz…

nCellAisallocatedchannels1,8,15…

nCellBisallocatedchannels2,9,16…

nChannelswithinthecellhavesufficientseparationsothatadjacentchannelinterferenceisminimized

70

+Frequency Assignment

n TypicalC/Ivaluesusedinpracticeare13-18dB.

n OncethefrequencyreuseclustersizeNcisdetermined,frequenciesmustbeassignedtocells

n MustmaintainC/Ipatternbetweenclusters

n Withinacluster– seektominimizeadjacentchannelinterference

n Adjacentchannelinterferenceisinterferencefromfrequencyadjacentinthespectrum

n Example:Youareoperatinga cellularnetworkwith25KHzNMTtrafficchannels1through12.n Labelthetrafficchannelsas{f1,f2,

f3,f4,f5,f6,f7,f8,f9,f10,f11,f12}

n Placethetrafficchannelsinthecellsabovesuchthatafrequencyreuseclustersizeof4isusedandadjacentchannelinterferenceisminimized

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