Average Rate of Downlink Heterogeneous Cellular Networks

3050IEEETRANSACTIONSONCOMMUNICATIONS,VOL.61,NO.7,JULY2013

AverageRateofDownlinkHeterogeneousCellularNetworksoverGeneralizedFadingChannels:

AStochasticGeometryApproach

MarcoDiRenzo,Member,IEEE,AlessandroGuidotti,StudentMember,IEEE,

andGiovanniE.Corazza,SeniorMember,IEEE

Abstract—Inthispaper,weintroduceananalyticalframeworktocomputetheaveragerateofdownlinkheterogeneouscellularnetworks.Theframeworkleveragesrecentapplicationofstochas-ticgeometrytoother–cellinterferencemodelingandanalysis.TheheterogeneouscellularnetworkismodeledasthesuperpositionofmanytiersofBaseStations(BSs)havingdifferenttransmitpower,density,path–lossexponent,fadingparametersanddistri-bution,andunequalbiasingfor exibletierassociation.Along–termaveragedmaximumbiased–received–powertierassociationisconsidered.ThepositionsoftheBSsineachtieraremodeledaspointsofanindependentPoissonPointProcess(PPP).Undertheseassumptions,weintroduceanewanalyticalmethodologytoevaluatetheaveragerate,whichavoidsthecomputationoftheCoverageProbability(Pcov)andneedsonlytheMomentGeneratingFunction(MGF)oftheaggregateinterferenceattheprobemobileterminal.Thedistinguishablecharacteristicofouranalyticalmethodologyconsistsinprovidingatractableandnumericallyef cientframeworkthatisapplicabletogeneralfadingdistributions,includingcompositefadingchannelswithsmall–andmid–scale uctuations.Inaddition,ourmethodcanef cientlyhandlecorrelatedLog–Normalshadowingwithlittleincreaseofthecomputationalcomplexity.TheproposedMGF–basedapproachneedsthecomputationofeitherasingleoratwo–foldnumericalintegral,thusreducingthecomplexityofPcov–basedframeworks,whichrequire,forgeneralfadingdistributions,thecomputationofafour–foldintegral.

IndexTerms—Heterogeneouscellularnetworks,aggregatein-terferencemodeling,stochasticgeometry,averagerate.

characterofthewirelesschannel[2].Forthisreason,accurateperformanceanalysisisusuallyconductedviacostly,time–consuming,andoftenproprietarysystem–levelsimulators[3].Thisapproach,however,seldomprovidesinsightfulinforma-tiononsystemdesignandonthedependencyofthesystemparameterstooptimize.Thissituationisevenexacerbatedinfuturecellulardeployments,whicharebecomingmoreheterogeneouswiththeintroductionofnewinfrastructureelements,e.g.,femto/picoBSs, xed/mobilerelays,cognitiveradios,anddistributedantennas[4]–[9]and[10]forasurvey.A.AbstractionModelsforAnalysisandDesignofCellularNetworks

Tocircumventthisproblem,communicationstheoristsusu-allyresortto“abstractions”fortractableother–cellinterfer-encemodelingandforperformanceanalysis.Theseabstrac-tionsusuallyencompasssimpli edspatialmodelsforthelocationsoftheBSs.Inparticular,threeabstractionmodelsarecommonlyadopted:i)theWynermodel[11];ii)thesingle–cellinterferingmodel[12];andiii)theregularhexagonalorsquaregridmodel[13].Theseabstractionmodels,however,areofteneitherover–simplisticorinaccurate[14].Further-more,insomecases,asfortheregularhexagonal/squaregridmodel,theystillrequireeitherintensivenumericalsim-ulationsormulti–foldnumericalintegrations.Finally,theseabstractionmodelsusuallyprovideinformationforspeci cBSsdeployments,andtypicallyfailtoprovideusefulinfor-mationformorerandom,unplanned,and/orclusteredBSsdeployments,whicharetypicalofemergingheterogeneouscellularnetworkswith,e.g.,overlaidfemtocellsandpicocells[9],[10].Motivatedbytheseconsiderations,anewabstractionmodeliscurrentlyemergingandgainingpopularity,accordingtowhichthepositionsoftheBSsaremodeledaspointsofaPoissonPointProcess(PPP)andpowerfultoolsfromappliedprobability,suchasstochasticgeometry,areleveragedtodeveloptractableintegralsandclosed–formmathematicalframeworksforimportantperformancemetrics(e.g.,coverageandaveragerate)[15]–[17].

B.StochasticGeometrybasedModelingofHeterogeneousCellularNetworks

Thestochasticgeometrybasedabstractionmodelfortheanalysisofcellularnetworksdatesbackto(atleast)1997

I.INTRODUCTION

T

HEanalyticalperformancemodelingofcellularnetworksisalong–standingopenissue[1].Themathematicalintractabilitymainlyarisesfromthedif cultyofaccuratelymodelingother–cellinterferencebytakingintoaccountthespatialpositionsoftheBaseStations(BSs)andthestochastic

ManuscriptreceivedNovember18,2012;revisedMarch18,2013.TheeditorcoordinatingthereviewofthispaperandapprovingitforpublicationwasM.Tao.

M.DiRenzoiswiththeLaboratoiredesSignauxetSyst`emes,Unit´eMixtedeRecherche8506,CentreNationaldelaRechercheScienti que–´´EcoleSup´erieured’Electricit´e–Universit´eParis–SudXI,91192Gif–sur–YvetteCedex,France(e–mail:marco.direnzo@lss.supelec.fr).

A.GuidottiandG.E.CorazzaarewiththeDepartmentofElectronics,Com-puterScience,andSystems,theUniversityofBologna,VialeRisorgimento2,40136Bologna,Italy(e-mail:{a.guidotti,giovanni.corazza}@unibo.it)http://doc.guandang.netmun.Conf.(ICC),Ottawa,Canada,June2012.

ThisworkwassupportedinpartbytheEuropeanCommissionundertheauspicesoftheFP7–PEOPLEMITN–CROSSFIREproject(grant317126)andtheFP7–ICTNoE–NEWCOM#project(grant318306).

DigitalObjectIdenti er10.1109/TCOMM.2013.050813.120883

c2013IEEE0090-6778/13$31.00

DIRENZOetal.:AVERAGERATEOFDOWNLINKHETEROGENEOUSCELLULARNETWORKSOVERGENERALIZEDFADINGCHANNELS...3051

[3],[18].Subsequently,asimilarshotgun–based,i.e.,PPP–based,abstractionmodelwasproposedin[19],anditwasshownthat,comparedwiththetraditionalhexagonalgridmodel,theshotgunapproachprovidesupperperformancebounds.Morerecently,thePPPmodelhasbeenusedfortheanalysisofspatialandopportunisticAlohaprotocols[20],andforthecharacterizationoftheSignal–to–Interference–Ratio(SIR)of(single–tier)cellularnetworks[21].InspiteoftheseinitialandpioneeringattemptsofapplyingthePPPmodelandstochasticgeometrytotheanalysisofcellularnetworks,onlyrecentlytherandom–basedabstractionmodelforthepositionsoftheBSshasreceivedtheattentionitdeserved.Inparticular,itsemergenceandwidespreadadoptionforcellularnetworksanalysisanddesignismostlydueto[22],whereacomprehensiveframeworktocomputecoverage …… 此处隐藏：63127字，全部文档内容请下载后查看。喜欢就下载吧 ……