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Simulcasting Using Slotted ALOHA in Ad-Hoc Networks


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Table page 2RoutingtableforradioAinFigure 2 ..................... 17 2ExamplepacketbufferforradioAfornetworkshowninFigure 2 ...... 19 3Positionofradiosinten-nodenetworkinFig. 2 ................ 41 iv

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Figure page 2Simplescenarioillustratingsimulationatthelinklevel. ............. 10 2Nonuniform4-PSKthatachievesdifferentlevelsoferrorprotectionforeachbit. 11 2Linkcapabilitiesforaten-nodewirelessnetwork.Solidlinesindicateless-capablelinks.Dashedlinesaremore-capablelinks.(a)NW1:Fordegrada-tionof0.5dBanddisparityof9.1dB(b)NW2:Fordegradationof0.3dBdisparityof11.4dB. ............................... 14 2Examplelinkmapforafour-nodewirelessnetwork. ............... 17 3Examplerouteforestimatingend-to-endthroughput. .............. 25 3End-to-endthroughputforsimulcastingingeometricdistributionforthenum-berofhopsat1 30 3End-to-endthroughputforsimulcastingingeometricdistributionforthenum-berofhopsat1 31 3End-to-endthroughputforsimulcastingingeometricdistributionforthenum-berofhopsat1 31 3End-to-endthroughputforsimulcastingingeometricdistributionforthenum-berofhopsat1 31 3End-to-endthroughputforsimulcastingingeometricdistributionforthenum-berofhopsat1 32 3End-to-endthroughputforsimulcastingingeometricdistributionforthenum-berofhopsat1 32 3Themaximumend-to-endthroughputsforsimulcastingwithvariousnetworkdensitysingeometricdistributionforthenumberofhops,attheexpectedvalueofthenumberofhops1 ...... 33 3Themaximumend-to-endthroughputsforsimulcastingwithvariousnetworkdensitysingeometricdistributionforthenumberofhops,attheexpectedvalueofthenumberofhops1 ...... 34 3End-to-endthroughputforsimulcastinginPoissondistributionforthenum-berofhopsatn=2 36 v

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36 3Themaximumend-to-endthroughputsforsimulcastingwithvariousnetworkdensitysinPoissondistributionforthenumberofhops,attheexpectedvalueofthenumberofhops=4andpropagationconstantn=2. .......... 38 3Themaximumend-to-endthroughputsforsimulcastingwithvariousnetworkdensitysinPoissondistributionforthenumberofhops,attheexpectedvalueofthenumberofhops=4andpropagationconstantn=4. .......... 38 3ThroughputinAWGNforthenetworkofnodesthatisillustratedinFig.3.ForNW1,thedegradationis0.5dB,andthedisparityis9.1dB.ForNW2,thedegradationis0.3dBandthedisparityis11.4dB. ................ 46 3NetworkdegreeasafunctionofforsimulcastingwithnonuniformQPSKinawirelessadhocnetworkwithrandomnodeplacement. ............ 46 3NetworkconnectivityasafunctionofforsimulcastingwithnonuniformQPSKinawirelessadhocnetworkwithrandomnodeplacement. ....... 47 3Proportionofnodeswithamore-capablelinkasafunctionofforsimulcast-ingwithnonuniformQPSKinawirelessadhocnetworkwithrandomnodeplacement. .................................... 47 3LinkthroughputforunicastingandsimulcastingwithnonuniformQPSKwith=25degreesinawirelessadhocnetworkwithrandomnodeplacement. ... 48 3MaximumlinkthroughputforsimulcastingwithnonuniformQPSKasafunc-tionoftheoffsetangle. ............................. 48 3AveragenumberofhopsinarouteforsimulcastingwithnonuniformQPSKasafunctionoftheoffsetangle. ........................ 49 3Maximum(overallattemptrates)end-to-endthroughputforsimulcastingwithnonuniformQPSKasafunctionofoffsetangle. ................ 49 3LinkthroughputinAWGNforamobilenetworkof15radioswithdegrada-tionof0.5dBanddisparityof9.1dBbythetimestationaryrandomwaypointsimulation. ..................................... 50 3End-to-endthroughputinAWGNforamobilenetworkof15radioswithdegra-dationof0.5dBanddisparityof9.1dBbythetimestationaryrandomway-pointsimulation. ................................. 50 4MaximumlinkthroughputbyPRBwithvariousAvaluesinrandomnet-worktopologyasthefunctionofoffsetangle. ................. 56 vi

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................ 57 4Min-maxfairnessbyPRBwithvariousAvaluesinrandomnetworktopol-ogyasthefunctionofoffsetangle. ....................... 57 4UtilitybasedfairnessbyPRBwithvariousFandAvaluesinrandomnet-worktopologyasthefunctionofoffsetangle. ................. 58 5Packettransmissionfromsourceradiotorandomlyselectedroutebasedonsimulcastingcapability. .............................. 60 5Topology1forunequalrandomrouteselectionbasedonsimulcastingcapability. 61 5Topology2forunequalrandomrouteselectionbasedonsimulcastingcapability. 62 5Topology3forunequalrandomrouteselectionbasedonsimulcastingcapability. 62 5Markovstatusdiagramforthenumberofpacketsinaqueue. .......... 63 5Linkmodel1foranalyzingqueuestatusinrandomrouteselectionbasedonsimulcastingcapability.Therelayradiodoesn'thaveamorecapablelink. ... 64 5Linkmodel2foranalyzingqueuestatusinrandomrouteselectionbasedonsimulcastingcapability.Therelayradiohasmorecapablelinks,butnotontheroute. ....................................... 65 5Linkmodel3foranalyzingqueuestatusinrandomrouteselectionbasedonsimulcastingcapability.Therelayradiohasmorecapablelinks,andoneofthemisincludedonthesourcesideoftheroute. ................. 65 5Linkmodel4foranalyzingqueuestatusinrandomrouteselectionbasedonsimulcastingcapability.Therelayradiohasmorecapablelinks,andoneofthemisincludedonthedestinationsideoftheroute. ............... 66 5Linkmodel5foranalyzingqueuestatusinrandomrouteselectionbasedonsimulcastingcapability.Therelayradiohasmorecapablelinks,andtwoofthemareincludedatthebothofsourceanddestinationsidesoftheroute. ... 67 5Maximumend-to-endthroughputversusrouteselectionrationforroute1athighdensitynetwork. ............................... 70 5Maximumend-to-endthroughputversusrouteselectionrationforroute1atlowdensitynetwork. ............................... 70 6Symbolmovementbyminimizedtransmissionpower. .............. 72 6Unequaltransmissionpowerallocation. ..................... 73 6Diagramoftransmissionpowerrangeforunicasting. .............. 74 vii

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............. 75 6Throughputandthroughputefciencybyunequaltransmissionpoweralloca-tion. ........................................ 78 6Fairnessbyunequaltransmissionpowerallocation. ............... 79 viii

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Previousstudiesusedunequalerror-protectiontechniquestoimprovethethroughputofawirelesscommunicationsysteminwhichatransmissionisreceivedbyseveralradioswithdifferentcapabilities.Thesecapabilitiesmaycorrespondtodifferencesinpathloss,fading,orinterference.Bytakingadvantageofthebroadcastnatureofthechannel,additionalmessagesforthemore-capablereceiverscanbeincludedontransmissionstotheless-capablereceiversatlittlecost(intermsofrequiredenergyatthetransmitterorerrorprobabilitiesatthereceivers).Thistechniquehasbeentermedsimulcastingormulticastsignaling. Weconsiderthistechniqueinanadhocnetwork.Thistechniqueimpactslinkthroughput,end-to-endthroughput,andnetworkconnectivity.First,weinvestigatedthebasicpropertiesofsimulcasting,includinghowthechoiceofparametersforthesimulcastingtechniqueaffectsseveralkeynetworkperformancemetrics.Theresultsshowthataproperlychosensimulcastingtechniquecanimprovethelinkandend-to-endthroughputinadhocwirelessnetworkswithonlyaslightdegradationinothermetricssuchasconnectivity.Next,weproposecross-layertechniquesforunequalresourceallocationtoimprovenetworkperformancewhenusingsimulcasting.Wethenproposeto ix

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x

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Inmostadhocwirelessnetworks,aradio'sneighborsoftenvaryconsiderablyintheirabilitytocommunicatewiththatradiobecauseofdifferencesinchannelconditions,suchaspropagationlossandinterferencelevels.Inunicasttransmissions,inwhichasingletransmittercommunicateswithasinglereceiver,thetransmittercancompensateforthesevariationsincapabilitybyusingadaptivesignalingifthechannelconditionsareaccuratelyknown.However,thesharedchannelisnotnecessarilyusedeffectivelybecauseasignalthatisintendedforoneradiomayalsobereceivedbyotherradiosinthesystemthathavemuchbetterlinkconditionsthantheoriginaldestinationreceiver.Werefertosuchradiosasmore-capableradios.Inthisscenario,additionalmessagescouldbeincludedforthemore-capableradiosatlittleexpensetotheoriginaldestinationoftheunicasttransmission.Similarly,broadcasttransmissions,whichareintendedforallofaradio'sneighbors,areoftenrequiredfornetworkmaintenanceinadhocnetworks.Broadcasttransmissionsaregenerallyineffectiveintheiruseofthesharedcommunicationmediumbecausethetransmissionsmustbedesignedtoallowreceptionbytheleast-capableofaradio'sneighbors.Thus,foranybroadcasttransmissionthereareoftenmanymore-capablereceiversthatcouldsuccessfullyreceiveadditionalmessagesthataresimultaneouslytransmittedwiththebroadcastmessage. TheconceptsbehindsimultaneoustransmissionsschemeswereoriginallyexploredinthecontextofbroadcastchannelsbyCoverandBergmans[ 1 ],[ 2 ].PursleyandSheapreviouslyshowedthatmodulationandcodingschemescanbemodiedtoallowtheinclusionofadditionalmessagesformore-capablereceiversatverylittlecosttotheperformanceattheless-capablereceiver[ 3 ][ 6 ].Inthesepapers,thetermmulticastsignalingisusedtorefertosuchtechniques.However,inadhocnetworks,multicasting 1

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referstoaprocessthatisprimarilyassociatedwiththenetworklayerinwhichasinglemessageisdeliveredtomultipledestinations,notallofwhicharenecessarilyneighborsofthesourceradio.Inthisdissertation,werefertoourtechniquesassimulcastingtodistinguishthemfrommulticastingandtoconveytheirabilitytosimultaneouslytransmitmultiplemessagestodifferentneighboringradiosofatransmitter.Previousworkshowsthatnonuniformphase-shift-key(PSK)constellationsprovideasimpleandeffectivewaytoconveymultiplemessagesfromasingletransmittertotworeceiversofdifferentcapabilities[ 3 ][ 6 ]. Unlikethepreviouswork,whichinvestigatedthephysical-layerdesignandper-formanceofsimulcastingschemes,weproposetoinvestigatetheopportunisticuseofsimulcastinginwirelessadhocnetworks.Weconsiderthenecessarymodicationstothehigher-layerprotocolstofullyutilizetheadditionalcapabilitiesprovidedbysimulcasting.Forcompletecross-layerdesignofsuchawirelesscommunicationsystemwithsimul-casting,thelink-andnetwork-layerprotocolsincludingthepacketselectionalgorithm,routingprotocol,andcollisionresolutionalgorithmshouldbeappropriatelydesigned.Thedesignofthesimulcastingschemewillimpactmanyaspectsofnetworkperformanceincludinglinkandend-to-endthroughput,networkconnectivity,androutelength.Weinvestigatetheoptimalsignalspacingfornonuniformquadraturephase-shift-keying(QPSK)forrandomlydistributedradios. WeconsiderasystemthatusesslottedALOHA[ 7 ][ 11 ]forchannelaccess.Theroutingalgorithmusedisaminimum-hoproutingalgorithmthatismodiedtoincorporatethesimulcastingcapability.Thepacketselectionmechanismisalsomodiedtoprovideefcientuseofthesimulcastingcapability.WeusenonuniformPSKtoshowhowthedesignofthesimulcastingtechniqueaffectslinkthroughput,end-to-endthroughput,andnetworkconnectivity.Werstpresentanalyticalandsimulationresultsforrandomtopologieswithoursimplegood/badchannelmodelandwithmobility.Forthesimplegood/badchannelmodel,inwhichwedonotconsiderany

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interference,whethertworadiosareneighborsdependsonlyonifoneoftheradiosisinthetransmissionrangeoftheother.Inthegood/badchannelmodel,thecollisionoccurswhenlinkedradio(s)toareceivertransmit(s)apacketsimultaneouslywhenthereceiverreceivesanotherpacket.Theresultsindicatethatsimulcasttransmissioncanimprovethelinkandend-to-endthroughputsinwirelessadhocatasmallcosttonetworkconnectivity. Weinvestigatethreecross-layerapproachestoimprovenetworkperformancewhensimulcastingisused.First,weproposetoadapttheparametersoftheMACprotocolbasedonsimulcastingcapabilities.Aradiothatcansimulcasttoitsneighborscantransmittwopacketsperslot,whereasaradiothatcannotsimulcastcanonlytransmitonepacketperslot.Intheterminologyof[ 12 ],thesimulcastingradiorequireslessefforttotransmitapacketthantheunicastingradio.Thus,toimprovelinkthroughput,morechannelresourcesshouldbeallocatedtosimulcastingradios.WeuseDianatietal.'snotionoffairsharetodeterminetheback-offparametersatdifferentnodestoprovideabalancebetweenchannelallocationthatignoreseffortandservicebasedallocation[ 13 ].Theseunequalback-offparameterscanimprovelinkthroughputattheexpenseoffairnessintheviewpointofeveness.Forinstance,theparameterscanbesuchthatafewradioswillnearlyalwaysbeabletotransmitwhiletheotherradiosareblocked.Thelinkthroughputincreasesbecausetherearefewcollisions,butthenetworkbecomesuselessastheend-to-endthroughputdecreasesandmostradiosareunabletotransmitanypackets.Therefore,incomparingdifferentback-offparameters,wealsoconsiderboththefairnessprovidedandend-to-endthroughput.Wepresentfairnessresultsusingthetypicalmin-maxfairnessindex[ 14 ]andtheutility-basedfairnessindexintroducedin[ 13 ]. Second,weconsiderhowtotakeadvantageofthesimulcastingcapabilityonaroutetoreducequeueingdelayandimproveend-to-endthroughput.Becauseradiosthatcansimulcastpacketssendmorepacketspertransmissionopportunity,itmaybeappropriatetoroutemorepacketsalongrouteswithmoremore-capablelinksandwithagreater

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numberofradioswithmore-capablelinks.WeproposeasimpleschemeinwhichpacketsaredistributedunequallyacrosstworoutesaccordingtoaBernoullirandomprocess.WeevaluatetheeffectofdifferentchoicesfortheBernoulliparameterontheend-to-endthroughputanddelayforseveralnetworktopologies.Theresultsshowthatunequaldistributionofthepacketsoverthetworoutesoffersthebestperformanceintermsofend-to-endthroughputanddelay. Third,weinvestigateadaptingthetransmissionpowerandoffsetangleofthesimul-castingmodulationbasedonthenumberofneighborsofthetransmitter.Forsystemsinwhichthetransmittedpowerisxed,thetransmissionpowerunderacertainradiodensitydecidesthenetworkdegree,whichisdenedastheaveragenumberofneighborsofaradioinanetwork,wheretworadiosareneighborsiftheycancommunicatedirectly.Whentheradiosinanetworkusealargetransmissionrange,therequirednumberofhopsforatransmittedpackettoreachadestinationfromasourceradiowillbesmall.However,alargetransmissionrangealsoresultsinalargenetworkdegree.Fromtheperspectiveofareceiver,asinterferencefromneighboringradiosbecomeslarge,theprobabilityofpacketcollisionwillincrease.Thelinkthroughputcanbeimprovedbydecreasingthetransmissionpowerandhencethenetworkdegree.However,forlownetworkdegree,theprobabilitythatthenetworkisconnectedwillbesmallandthenumberofhopsinaroutewillbelarge.So,thetradeoffamongtheeffectoftransmissionrangeonprobabilityofpacketcollision,numberofhopsinaroute,andnetworkconnectivityisacriticalproblemtosolveinanad-hocnetwork. Weinvestigateschemestoadaptthetransmissionpowerandsignalconstellationshapebasedonthedistancesbetweenthetransmitterandthereceiver(s).Weconsiderunequalpowerallocationsothatradiosthatcansimulcasthaveahigherprobabilityofpacketsuccessthanradiosthatcannotsimulcast.Wepresentanalyticalandsimulationresults.Theresultsindicatethatthereducedtransmissionenergyandtheunequal

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interferenceassignmentschemesimprovelinkandend-to-endthroughputaswellasthroughputefciency,whichisdenedasthroughputperunitenergyconsumption. Aspriorworksofsimulcasting,Cover[ 1 ]considersthesimultaneouscommuni-cationofinformationfromonesourcetoseveralreceiversandgivesupperandlowerboundsonthecapacityregionofsimultaneouslyachievablerates.Bergmans[ 2 ]considersseveraltransmittersusingasuperpositionschemethatpoolsthetime,bandwidth,andpowerallocationofthetransmitters.Hedeterminestheoptimalsetofratessimultane-ouslyachievable. PurselyandSheahavepreviouslyshownthatmodulationandcodingschemescanbemodiedtoallowtheinclusionofadditionalmessagesformore-capablereceiversatverylittlecosttotheperformanceattheless-capablereceiver[ 3 ][ 6 ].Thisgeneraltechniqueiscalledmulticastsignalingandusesunequalerror-protectionsignalingtotransmitmultiplemessagesthatrequiredifferentreceivercapabilitiesforaccuratereception.Aspreviouslymentioned,weusethetermsimulcastingforthesetechniquestodistinguishthemfromnetwork-orapplication-layermulticasting.In[ 3 ]-[ 6 ],theauthorsfocusontechniquesthatutilizenonuniformphase-shiftkeying(PSK)becauseofitssimplicity,adjustability,andconstantenvelope.Thispreviousworksisfocusedonphysical-layerconsiderations,primarilysignaldesignandlink-levelperformance,althoughsimulcasttransmissionalsorequiresinteractionswiththehigherlayersintheprotocolstack.Theyalsointroduceandanalyzeperformancemeasuresthatareusefulincharacterizingtheperformancetradeoffsinsimulcastpackettransmission. Simulcasttransmissioncanbeachievedthroughavarietyofotherunequalerror-protectiontechniques.Theseincludeothertypesofnonuniformmodulation[ 15 ]-[ 18 ],unequalerror-protectioncoding[ 19 ]-[ 24 ],combinedmodulationandcodingschemes[ 25 ]-[ 28 ],[ 5 ],andspace-timecoding[ 29 ].Anyofthesetechniquescanbeusedforsimulcastinginadhocnetworks.ThenonuniformPSKconstellationsdescribedinthisdissertationhaveseveraladvantagesovernonuniformQAM,proposedin[ 20 ],

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[ 25 ]forunequalerrorprotection,formobilewirelesscommunicationchannels.Forexample,PSKconstellationshaveconstantenvelopes,andknowledgeofthereceivedsignalamplitudeisnotrequiredfortheirdemodulation.SuchknowledgeisrequiredforoptimumdemodulationofQAMsignals,butthereceivedsignalamplitudemaybeunknownanddifculttoestimate.Thus,formobilewirelesscommunication,nonuniformPSKmayoftenbemoreappropriatethanQAM.ConvolutionalcodingandnonuniformQAMconstellationshavealsobeeninvestigatedin[ 20 ],[ 25 ],wherethegoalistoprovideunequalerrorprotectionformultiresolutionsource-encodedanaloginformation.LiandEphremidesstudiedpulseamplitudemodulation(PAM)andQAMforpassiverateadaptationinthepresenceofchanneluctuationduetofading[ 30 ].Thegoaloftheworkisthetradeoffbetweenmorereliabledetectionoffewerbitsandlessreliabledetectionofmorebits. Wirelessnetworkhasbecomeincreasinglypopularsincetheiremergenceinthe1970s.Theadhocnetworkisoneofthetwovariationsofmobilewirelessnetworks.Theadhocnetworkisinfrastructurelessandtheotheroneisinfrastructured.Foranadhocnetwork,allradioshavemobilityandcanbeconnecteddynamicallyinanarbitrarymannerwithouttheuseofxedrouters.Interconnectionsbetweenradioscanbechangedcontinuously.Characteristicsofanadhocnetworksuchasarbitraryspatialdistributionanddynamicconnectivityresultincommunicationlinkdisparitiesthatareexploitedinthedissertationviasimulcastsignaling. Inthesimulcastingschemesconsideredinthisdissertation,someradiosaremorecapablethanotherradiosinthattheycantransmittwopacketsperslotinsteadofone,soitmakessensetohaveanunequalallocationofresourcesinthenetworktoutilizethiscapability.Thefairnessofsuchanunequalallocationshouldbeassessed.Therearemanyapproachespreviouslyproposedformeasuringfairness[ 12 ][ 14 ],[ 32 ].TheMin-maxindex[ 14 ]isawellknownindexforfairnesswhichindicatesevennessofasystem,butitmaynotbegoodinindicatinghowthesystemusesavailableresourceseffectivelywhen

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differentradioshaveresourceutilizingcapabilities.Recently,Dianatietal.proposedaUtilityFairnessIndex(UFI)in[ 13 ].TheUFIisparameterizedtoallowatrade-offbetweenservicefairnessandeffortfairness. Variousprotocolsformultipathroutinghasbeenresearched[ 33 ]-[ 36 ].Multipathroutingexploitsnetworkresourceseffectivelytomaximizeutilization.Itreducesblockingprobabilityandaggregatesbandwidthonvariouspathssoastoallowhighertransmissionratetoanetworkcomparedtosinglepath[ 33 ].Inthisdissertation,multipathroutingisappliedtoexploitthesimulcastingcapabilityofradiosonaroute.Byassigninghighertransmissionratestorouteswithmoresimulcastingcapability,theend-to-endthroughputanddelaycanbeimproved. Manyresearchershaveinvestigatedtheoptimaltransmissionrangeinadhocnetworks[ 37 ]-[ 43 ].Kleinrocketal.[ 37 ],[ 38 ]interprettransmissionpowerinanadhocnetworkintermsofthenumberofneighborsofaradioandsuggestamagicnumberofneighborsbasedonmaximizingapacket'sexpectedforwardprogresstowarditsdestination.Theiranalysisindicatesthataradioshouldtransmitwithapowersothattheaveragenumberofneighborswithintransmissionrangeissix[ 37 ]oreight[ 38 ]tomaximizeoverallnetworkthroughput.Oneofthecriticalassumptionsintheiranalysisisthatthenetworkwillnotbecomedisconnectedbecauseofpowercontrol.However,asthepackettransmissionpowerdecreases,thenumberofneighborsofaradiodecreases,andthusthenetworkmayhaveahighprobabilityofbecomingdisconnected.GuptaandKumarconsidertheeffectoftransmissionpoweronconnectivityanddeterminethecriticalpowertoguaranteeconnectivityoftheoverallnetwork[ 42 ].In[ 43 ],theyshowthatifristherangeoftransmission,thentherelayingburdenduetoincrementofthenumberofhopsgrowslikeO(r1),buttheinterferencegrowslikeO(r2).Thus,theneteffect(theproduct)isagrowthofO(r).Theiranalysisimpliesthatthesmallertransmissionpowerthebetterintermsofmaximizingnetworkthroughput.However,ifonechoosestoosmallarange,thenthenetworkmaylooseconnectivity.So,they

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concludethattheoptimaltransmissionpowerinanadhocnetworkshouldbedeterminedbasedonnetworkconnectivity. Alongwiththeoptimaltransmissionrange,energyefciencyisoneofthekeyconcernsinwirelesscommunicationsystems.Therehasbeenalotofresearchontransmissionpowercontrolschemesoverthepastfewyears[ 44 ]-[ 50 ].Thechiefmotivationoftheseschemesistomitigatetheeffectofinterferencethatoneusercancausetoothers.Theresultsrangefromobtainingdistributedpowercontrolalgorithmstodeterminingtheinformationtheoreticcapacityachievableunderinterferencelimitations[ 51 ],[ 52 ].Whereasmostpowercontrolschemesaimatmaximizingtheamountofinformationsentforagivenaveragepowerconstraint,arecentstudy[ 53 ]considersminimizingthepowersubjecttoaspeciedamountofinformationbeingsuccessfullytransmitted.Ratherthanminimizingpower,[ 54 ]considersthequestionofminimizingenergydirectly,andcomparestheenergyefciency,denedastheratiooftotalamountdatadeliveredandtotalenergyconsumed,ofseveralmediumaccessprotocols.

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Beforedevelopingtheapplicationofsimulcastinginadhocnetworks,werstprovideanoverviewofthenetworkmodelusedinthisresearch.Thenetworkmodelwaschosentobeasfundamentallysimpleaspossible,whilestillprovidinginsightintotheeffectsofusingsimulcasting.Thesystemisaslottedtransmissionsystem,whereweassumethatallradiosareperfectlysynchronized.ThepacketarrivalprocessismodeledbyaBernoullirandomprocess.Weassumethattheradioshavelargepacketbuffers.Multipleaccessisprovidedbyslotted-ALOHA[ 9 ]. Ourphysical-layermodelsarealsoselectedtoavoidobscuringtheeffectsofsimulcastingamongotherphysical-layerphenomena.Webeginbyspecifyingsomemaximumtransmissionrangeatwhichabasicmessagecanbereceivedwithatargeterrorprobability.Radiosareconsideredtobeneighborsiftheyarewithinthatmaximumtransmissionrange.Apacketcollisionoccurswheneveraradiotransmitsapacketduringatimeslotandthereisalsoatransmissionbyanyoftheneighborsofthepacket'sdesignatedrecipient.Weassumethatsignalsfromradiosthatarenotneighborscanneitherbereceivednorcauseapacketcollisionbyinterferingwithtransmissionsfromaradio'sneighbors.Furthermore,weassumethatallcollisionsresultinpacketerrorsandthatthereisimmediateandperfectfeedbackonpacketsthatcollidedorwereotherwisereceivedinerror.Retransmissionsoccurafteraback-offperiodthatischosenaccordingtoageometricrandomvariable,asdiscussedinSection 2.2 9

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Figure2. Simplescenarioillustratingsimulationatthelinklevel. 2 showsthisinthecaseoftworeceivers. Supposethatthepowerspectraldensityofthenoiseisthesameatthetworeceiversandtheonlydifferenceinreceivedpowerisduetothedifferenceinpropagationdis-tances.Thenreceiver2willbemore-capablethanreceiver1inthesensethatthehighersignal-to-noiseratioatreceiver2willallowittosuccessfullyrecoveramessagetransmit-tedwithahighercoderateorhigher-ordermodulationthancanbesuccessfullyrecoveredatreceiver1.Thus,intheterminologyof[ 3 ][ 6 ],receiver1isaless-capablereceiver,andreceiver2isamore-capablereceiver.Byusingunequalerror-protectionmodulationorcoding,eachtimethatthetransmittersendsamessagetoreceiver1,itcanincludeextramessagesthatcanberecoveredbyreceiver2becauseofitshighersignal-to-noiseratio.Inthiscase,themessageintendedforreceiver1iscalledabasicmessage,andthemessagesintendedforreceiver2arecalledadditionalmessages.Werefertotheseastheclassofthemessages. Simulcasttransmissioncanbeachieveinmanywaysbutdependsontheabilitytoachieveadifferentleveloferrorprotectionforthebasicmessagethanfortheadditionalmessages.Onesimplewaythatthisunequalerrorprotectioncanbeachievedisthrough

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Figure2. Nonuniform4-PSKthatachievesdifferentlevelsoferrorprotectionforeachbit. nonuniformmodulation[ 3 ],[ 4 ].Forinstance,oneofthesimplestexamplesisthenonuniformquadriphase-shiftkey(QPSK)constellationillustratedinFigure 2 Forthisconstellation,thenonuniformspacingmakesitmucheasierforareceivertocorrectlyrecovertherstbitthanthesecondbit.Thus,therstbitcanbeusedtosendabasicmessagethatisintendedforaless-capablereceiverorforallofaradio'sneighbors,whilethesecondbitisusedtoconveyanadditionalmessagethatcanonlyberecoveredbymore-capablereceivers.Thus,thistechniquecanbeusedtosimultaneouslysendtwopacketsinasingleslot,effectivelydoublingthelinkthroughput.However,theuseofthisoranyothersimulcastingtechniquewillresultinsomedegradationinperformanceattheless-capablereceiverifthetransmitpowerisunchanged. In[ 3 ],[ 4 ],twoimportantparametersareintroducedthatprovideasimplephysical-layercharacterizationofsimulcasttransmissionschemesthatcarryonlytwoclassesofmessages.Theparametersarethedegradationandthecapabilitydisparity.Bothoftheseparametersaretypicallyspeciedindecibels.Ingeneral,theseparametersmustbespeciedintermsofthetargeterrorprobabilitiesforthebasicandadditionalmessages.Inthisdissertation,thetargeterrorprobabilitiesforthesemessagesareassumedtobeequal.Byusingasimulcastsignalingschemeinsteadofatraditionalsignalingschemethatonlyconveysonebasicmessage,theperformanceofthebasicmessage

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mustbedegraded.Thedegradationmeasurestheadditionalamountofenergythatmustbereceivedtoachievethesameperformanceforthebasicmessagewithasimulcastsignalingschemeasisachievedwithatraditionalsignalingscheme.Thecapabilitydisparity,orsimplydisparity,isameasureofhowmuchmorecapableareceivermustbeinordertorecoveranadditionalmessageincomparisontoareceiverthatonlyrecoversthebasicmessage.Itcanbecalculatedastheamountofadditionalenergythatisrequiredatamore-capablereceivertorecovertheadditionalmessageatthetargeterrorprobabilityincomparisontotheamountofenergyrequiredataless-capablereceivertorecoverthebasicmessageatthetargeterrorprobability.InAWGNchannel,forthesameerrorprobabilitiesforbothofbasicandadditionalmessage,thedegradationandthedisparityaregivenbyfortheoffsetangle[ 4 ].Typicalvaluesforthedegradationanddisparityfrom[ 4 ]are0:5dBand9:1dB,respectively. Webeginbyconsideringsystemsinwhichthetransmitpowerisxed,andtheeffectsofthisdegradationonnetworkperformanceareinvestigated.Furthermore,weinitiallyassumethatthesimulcastingschemeisalsonotadaptedtothenetworktopology;inotherwords,theoffsetangleshowninFigure 2 isthesameatallradiosinthenetwork.InChater 6 ,weconsideradaptationofthesignalconstellationshapealongwiththepowerinresponsetothechannelconditionstotheintendedreceivers.Formostsimulcastingtechniques,whentheoffsetangleisxed,theperformancedegradationtotheless-capablereceiverscanbemadeverysmallwhilestillachievingasignicantgainfromtransmissionstomore-capablereceivers.Forexample,ifweconsideronlypathlossforthetransmissionofapacket,bythedenitionofdegradationanddisparity,thetransmissionrangeforbasicmessage,dl,andadditionalmessage,dm,aregivensimply

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fromthetransmissionrangeofunicasting,dU,as So,ifthetransmissionrangebyunicasting,dU,is1;000mundertheassumptionthatthepropagationconstantnis4,wecangain592:24mforthetransmissionrangeofadditionalmessageattheexpenseofjust28:37mreductionforthetransmissionrangeofbasicmessagewith0:5dBand9:1dBforvaluesofthedegradationanddisparity,respectively.FurtherdiscussionandexamplesaregiveninSection 3.1 Inordertobeabletodemonstratetheadvantagesanddisadvantagesofsimulcastinginthecontextofadhocnetworks,weemploythesimpleexampleofnonuniformQPSKdescribedabovefortheremainderofthisdissertation.Withthisscheme,eachtransmissioncanincludeatmosttwoclassesofmessage:abasicmessagepacketandanadditionalmessagepacket.Allpacketsareassumedtobeofthesamelength. Inthecontextofanadhocnetwork,theconceptsofmore-capableandless-capablereceiversmustbeextended,aseachradiomayactasatransmitterorreceiveratdifferenttimes.Whenaradioisactingasareceiver,itscapabilitylevelwilldependonitslink(channel)fromthetransmittingradio.Therefore,wedenetheradiolinksasbeingmore-capableorless-capablelinks.Fortheresultspresentedinthispaper,weassumethattheonlydifferencesinlinkqualitiesarecausedbydifferencesinpropagationdistance.Thisalsoimpliesthatlinksaresymmetric,soifthelinkfromradio1toradio2isamore-capablelink,thensoisthelinkfromradio2toradio1.Radiosareabletodiscoverthecapabilitiesofneighboringradiosduringnetworkmaintenanceorduringregularpackettransmission. AnexamplelinkmapfromoursimulationisillustratedinFigure 2 .Figure 23 showsthelinkcapabilitiesfortwodifferentvaluesofdegradationanddisparity,asexplainedbelow.Themapsarebasedontypicaldegradationanddisparityvaluesfrom

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Figure2. Linkcapabilitiesforaten-nodewirelessnetwork.Solidlinesindicateless-capablelinks.Dashedlinesaremore-capablelinks.(a)NW1:Fordegrada-tionof0.5dBanddisparityof9.1dB(b)NW2:Fordegradationof0.3dBdisparityof11.4dB. [ 4 ]andexponentialpathlossproportionaltothefourthpowerofdistance.Thegureillustratesthelinkcapabilitiesfortwoscenarios:(a)NW1isthecasethat=19:25degrees,whichyieldsadegradationof0:5dBanddisparityof9:1dB,and(b)NW2isthecasethat=15degrees,whichyieldsadegradationof0:3dBanddisparityof11:4dB.Thethinlinesrepresenttheless-capablelinks,andthethicklinesrepresentthemore-capablelinks.Inscenario2,NW2hasamorestringentrequirementonthedegradation,whichresultsinahigherdisparity.ThusNW1hasalargernumberofmore-capablelinksthanNW2. Theuseofsimulcastingalsocausessomeperformancedegradationtotheless-capablelinks.Foraxedtransmissionpower,thedegradationresultsinthetransmissionrangeforthebasicmessagebeingsmallerforsimulcastingthanforunicasting.Thus,somelinksmaybreak,whichwillcausetwomaineffectstothenetwork.First,alinkmaybecriticaltonetworkconnectivity,andwhenthatlinkbreaks,thenetworkwillbecomedisconnected.Secondly,someroutesmaybecomelongerbecauseanodethatisreachableinasinglehopwithunicastingmaynolongerbedirectlyreachable.Theincreaseinthe

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lengthofrouteswillreducetheend-to-endthroughput.Theexpectednumberoflinksthatbreakincreasesasthedegradationincreases,whiletheexpectednumberofmore-capablelinksincreasesasthedegradationincreases(andtherequireddisparitydecreases).Thus,thesimulcastsignalingschemeshouldbedesignedtoensurethattheincreaseinlinkthroughputfromhavingagreaternumberofmore-capablelinkstranslatesintoanincreaseinend-to-endthroughputandthattheimpactonnetworkconnectivityisminimal.ResultsonthistradeoffaregiveninSections 3.3 and 3.5 Aspreviouslymentioned,weassumethatthebasicandadditionalmessagesrequirethesameerrorprobability.Infact,weconsiderapacketcommunicationschemeinwhichanypacketmaybetransmittedaseitherabasicoradditionalmessage,dependingontheavailabilityofmore-capablelinks.Thefactthatapackethasbeentransmittedasoneclassofmessageoveralinkdoesnotaffecttheclasstowhichitwillbeassignedonlaterlinks.Thus,apacketmaystartoutasanadditionalmessage,betransmittedasabasicmessageoversomeintermediatelinks,andbesentoverthenallinktoitsdestinationasanadditionalmessage.Theonlyrequirementthatweplaceonthetransmissionsisthatadditionalmessagesshouldbetransmittedwheneverpossibleinordertoimprovethenetworkefciency.Thisapproachdiffersfromtheapproachesin[ 3 ][ 6 ],inwhichnonuniformsignalingtechniquesareusedtotransmitdifferentclassesofmultimediamessagesthatmayhavedifferentrequirementsonthepacketerrorprobability. Eachsimulcasttransmissioncontainstwofullpackets,eachofwhichhasfullheaders.Thus,whenaradiodetectsapacket,itwillattempttodemodulateanddecodetheheadersforboththebasicandadditionalmessage.Areceiverdoesnotneedtoknowaprioriwhetherapacketcontainsanadditionalmessage;ifnoadditionalmessageispresent,thereceiverwillnotrecoveravalidheaderforthatmessage(typicallytheCRCwillfail).Ifneitherofthepacketsisintendedforaradio,thenasusual,theradiocanturnoffitstransceiveruntilthenextslottoconserveenergy.Ifeitherorbothofthepacketsisintendedforaradio,thentheywillberecoveredintheusualway.Wenotethatwe

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assumethatallnodeswilllistentotheheadersatthebeginningofeachslot.Ifasleepscheduleisemployedtoconserveenergyattheradios,theperformanceofsimulcastingmaybesignicantlydegradedbyareductionofreceiverswithmore-capablelinksthatareawakeduringanyparticularslot. 3 ,eachradiousesthesameretransmissionprobabilityinanytimeslot.Weshowthesimulcastingperformancewhenweassignback-offtimeforretransmissionunequallyinChapter 4 .Byadjustingthistransmissionprobability,differentaveragenetworkattemptrates,G,canbeobtained. 31 ]inwhichtheroutingtablesaremodiedtoeffectivelyutilizethecapabilityofsimulcasting.Ourapproachtoincludingsimulcastinginthenetworkisdesignedtoallowthetransmis-sionofanadditionalmessagewheneverpossible.Aspreviouslymentioned,weallowanypackettobesentasanadditionalmessageifanappropriatelinkisavailable.Whetherapacketcanbesentasanadditionalmessageatanynodewilldependonthepacket'sdestinationandthelinkcapabilityofthenextlinkonanyminimum-hoproutetothatdestination.

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Figure2. Examplelinkmapforafour-nodewirelessnetwork. Table2. RoutingtableforradioAinFigure 2 Destination NextHop No.ofHops Normal B B 1 Entires C C 1 D B 2 Simulcast C C 1 Enties D C 2 Thenewroutingtablesareasupersetofthestandardmin-hoproutingtables.Thestandardmin-hoproutingtableisalwaysusedforselectionofthenext-hopradioforthebasicmessage.Tothisroutingtableisaddedasetofsimulcastentries.Foraroutingtableentrytobeavalidsimulcastentry,itmusthavearsthopthatisamore-capablelinkanditmustbeaminimum-hoproute.Itisnotrequiredthatthelinksaftertherstlinkbemore-capablelinks.Thus,aspreviouslymentioned,apacketthatistransmittedasanadditionalmessageoveronelinkmaybetransmittedasabasicmessageoverotherlinks,andviceversa. Toillustratethemodiedroutingtable,considerthesimplefour-nodenetworkshowninFigure 2 .Inthisgure,themore-capablelinksareshownasdashedlines,andtheless-capablelinksareshownassolidlines.Table 2 showsexampleroutingtableforradioA.Theroutingtableisformedasfollows.Thesimulcastentriesarespeciedrst.NotethattherewillbenosimulcastentryfordestinationradioBbecausethereisnominimum-hoprouteforwhichthenexthopfromAisamore-capablelink.However,therearesimulcastentriesfordestinationradiosCandD.BothdestinationsCandDcan

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bereachedintheminimumnumberofhopsbyrstsendingthepacketoverthemore-capablelinkAtoC.TheroutingtableentriesforthebasicmessagesarelabeledNormalEntriesinTable 2 andareselectedfromthepossiblemin-hoproutesintheusualway.FortheresultspresentedinthissectionandChapter 3 ,thenormalandsimulcastrouting-tableentriesforaparticulardestinationareallowedtobeidentical,evenifothermin-hoproutesexist. InChapter 5 ,weconsiderhowsimulcastingimpactsperformanceundermultipathrouting.Becauseradiosthatcansimulcastapacketsendmorepacketspertransmissionopportunity,itmaybeappropriatetoroutemorepacketsalongrouteswithmoremore-capablelinks. 2 ,radioAcansimultaneouslysendabasicmessagetoradioBandanadditionalmessagetoradioC. Thepacket-selectionalgorithmdetermineswhichpacket(s)inaradio'sbufferwillbetransmittedinanygivenpackettransmissioninterval.Thepacket-selectionalgorithmusedinthisdissertationisamodiedrst-in,rst-out(FIFO)algorithmthatensuresthatmore-capablelinksareutilizedwheneverpossible.Itfunctionsinthefollowingway.Aradiothathasatleastonemore-capablelinkwillrsttrytoselectfromitsqueuetherstpacketthatcanbesentasanadditionalmessage.Thiswillnotnecessarilybetherstpacketinitsqueue.Aftertheadditionalmessage(ifavailable)isselected,thentherstpacketfromtheremainingsetofpacketswillbesentasthebasicmessage.Intheabsence

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ofmobility,packetsintendedforaparticulardestinationwillbetransmittedinorder,therebyminimizingtheimpactofsimulcastingontheout-of-orderarrivalproblem. Table2. ExamplepacketbufferforradioAfornetworkshowninFigure 2 PacketID Destination 1 B 2 B 3 D 4 C Abriefexampleservestoillustratethispacketselectionalgorithm.SupposethatradioA'spacketbuffercontainsfourpackets,asshowninTable 2 .TherstandthesecondcolumnofthetableshowthepacketIDsandthedestinationsofeachpackets,respectively.ThenduringtherstintervalinwhichradioAtransmits,itrstsearchesitsbufferfortherstpacketthatcanbesentasanadditionalmessage.Todoso,itcomparesthedestinationforeachpackettothesetofdestinationsinthesimulcastentriesintheroutingtable.Inthiscase,therstpacketthatcanbesentasanadditionalmessageispacket3,which,basedonthesimulcastentryfordestinationDinTable 2 ,willbesenttonext-hopradioC.Packet1isthenselectedfortransmissionasthebasicmessage.So,whenradioAtransmits,itwillsimultaneouslysendmessagestoradiosBandCusingsimulcasttransmission.OnradioA'snexttransmission,packet4willbeselectedastheadditionalmessage,andpacket2willbesentasthebasicmessage.Notethatthissimulcasttransmissionschemeissignicantlydifferentthanmulticastingthatoccursatthenetworkorapplicationlayers,inwhichonemessageisdistributedtoagroupofdifferentreceivers.Insimulcasting,multiplemessagesaresimultaneouslytransmittedtoaoneormoreneighborsofthetransmittingradio.

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Inthischapter,weanalyzethelinkandend-to-endthroughputsforsimulcastinginanadhocnetwork.Weconsideraxednetworktopologywithanoise-freechannel.Thus,forunicastsignaling,thelinkthroughputdependsontheprobabilityofcollisionandthetimebetweentransmissionattempts,andend-to-endthroughputdependsonthelinkthroughputandthenumberofhopsthemessagesmusttravel.Forsimulcasting,thesethroughputswillalsodependonthesimulcastingparametersthroughthenumberofmessagesthatcanbesentasadditionalmessagesandthechangesinthenumberofhops,whicharecausedbychangesinthemaximumtransmissiondistanceforthebasicmessages. Theanalysisthatfollowsisforthreescenarios.Intherst,thenetworktopologyisxed,whichallowsthetopologicalparameterstobeeasilycalculated.Inthesecond,NradiosareuniformlydistributedoveranareaA.Edgeeffectsareneglectedinthecalcu-lations.Inthethirdscenario,thenodesaredistributedaccordingtoatwo-dimensionalPoissonpointprocessoveraninniteplane. 20

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randomnetworks.ForthenetworktopologyillustratedinFigure 2 ,Rm=7=10forD=0:5dB(=19:25degrees),andRm=4=10forD=0:3dB(=15degrees). Foroursimplegoodorbadchannelmodel,sincetheonlyfactorthataffectsthesignal-to-noiseratioisexponentialpath-loss(norandomfadingorshadowingisconsidered),whethertworadiossharealinkdependsonlyonthedistancebetweentheradios.LetdUdenotethemaximumlinkdistanceforunicastsignaling,andletdl()anddm()denotethemaximumlinkdistancesforless-andmore-capablelinks,respectively.ThesedistancescanbecalculatedasinSection 2.1 ,dl()=dU10D()=10n;dm()=dU10()=10n;

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transmissioncanbemadereasonablylargewithoutsignicantlyreducingthecoverageareaforthebasicmessage. ConsideranarbitrarynodeinanetworkwithnodesuniformlydistributedoverareaA.Letplandpmdenotetheprobabilitiesthatsomeothernodeisconnectedtothatnodebyaless-capablelinkandmorecapablelink,respectively.Thenpl()[dl()]2=A,andpm()[dm()]2=A,wheretheapproximationscomefromignoringtheedgeeffectsoftheniteareaoverwhichthenodesareplaced.Thenthenetworkdegreeisgivenby ForthesimulationresultsinSection 3.5 ,thetransmissiondistanceisclosetothedimensionofthesimulationarea,sotheedgeeffectmakes( 3 )yieldinaccurateestimatesifpl()anddl()aredeterminedasspeciedabove.However,wendthat( 3 )givesagoodapproximationifthecorrectvalueofNdeg()isfoundviasimpletopologicalsimulation;therefore,weusethisapproachfortheresultsinSection 3.5 .Theproportionofradioswithmore-capableneighborscanalsobesimplycalculatedby

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linkis 9 ].LetE[Di]betheexpectedvalueofthedelay(intermsofnumberofslots)requiredforapackettransmittedbyradioitobesuccessfullyreceivedbythedesignatednext-hopradio.Thenthelinkthroughputatradioi,Si,isdenedbySi=1=E[Di].TheaveragelinkthroughputforanetworkofNnodesisgivenby Weevaluate( 3 )fortwodifferentscenarios.Inunicasttransmission,simulcastingisnotallowed,andeachradiosendsatmostonepackettoonenext-hopradioduringatimeslot.Forsimulcasttransmission,twopacketscanbesentsimultaneouslybyaradioduringatimeslotifthatradiohasanymore-capablelinks,asdescribedinSection 2.1 .ThelinkthroughputsforunicastandsimulcasttransmissionaredenotedbySUandSS,respectively. Thelinkthroughputwilldependonseveralparameters.DeneGitobetheattemptrateoftheithradio.LetSU;iandSS;i()bethelinkthroughputatradioiforunicastandsimulcasttransmissionwithphaseoffset,respectively.ThethroughputatradioidependsonthenumberofneighborradiosBi(),theprobabilityofcollisionCi(),andtheretransmissionrateforunsuccessfulpacketsRi().

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radiocanbedeterminedasfollows.TheattemptratemustsatisfyGi=SU;i+Ri,whereRi=GiCi.Thenthethroughputisgivenby where,ifradioihasBineighborsandGistheaverageattemptrateoverallradios,then HereCi;jistheprobabilityofcollisionatthejthneighborofradioi,whichisgivenby whereBi;jisthenumberofneighborsofthejthneighborofradioi.Theresultin( 3 )isapproximatebecauseitassumesequalprobabilityoftransmissiontoeachneighbor,and( 3 )isapproximatebecausetheofferedloadfromthepotentialinterferersisreplacedbytheaverageofferedload.TheaveragelinkthroughputSUcanbeapproximatedbyusing( 3 )-( 3 )in( 3 ).

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andfortherandomnetwork, Soforlongpacketbuffersandhighpacketgenerationrates,simulcasttransmissionhasthecapabilitytoimprovethelinkthroughputbyafactorofuptoRm().However,itisnotclearthatthisincreaseinlinkthroughputwilltranslateintoacorrespondingincreaseinend-to-endthroughput.Thisisthetopicofthenextsubsection. 3 Figure3. Examplerouteforestimatingend-to-endthroughput. Weanalyzethethroughputbyconsideringthedelayrequiredtotransmittwopackets(correspondingtothetwotypesofmessages)oversucharoute.Underthebest-case

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scenario,oneofthepacketscanbesentasanadditionalmessageovereachofthemore-capablelinks(shownasdashedlines).Thenforeachless-capablelink(shownassolidlines),theexpecteddelayis2E[Di]forthetwopackets.Foreachmore-capablelink,theexpecteddelayisonlyE[Di]forthetwopackets.ThusfortheexampleinFigure 3 ,theexpecteddelayforbothpacketstoreachthedestination(notcountingqueuingdelays)is6E[D],whereE[D]istheexpecteddelayatanarbitrarynode.Thentheaverageend-to-endthroughputforeachpacketis 6E[D]SU 2.1 .Theningeneral,theend-to-endthroughputcanbeapproximatedby Thisexpressionisapproximatebecausethedistributionofthenumberofhopsforthepacketsthattakeamore-capablelinkmaybedifferentthanforthepacketsthatdonottakeanymore-capablelink.Forinstance,more-capablelinksmaybeusedmoreoftenthanless-capablelinkstotransmitapackettoitsdestination. NotealsothatSete()isanon-linearfunctionofRm().Unlikethelinkthroughput,theend-to-endthroughputdoesnotincreaseindirectproportiontoRm().NotethatthesummationtermwilldecreaseasandRm()increase,asthenumberofhopsincreases.Thenifthedistributionofthenumberofhopsisconstant,a50%increaseinend-to-endthroughputrequiresatleastRm()=2=3.Forlargeenoughtosatisfythisrequirement,theexpectednumberofhopsmaybesignicantlylargerthanforunicasting,therebyreducingthegainfromtheincreaseinlinkthroughput. WeinvestigatethevalueofthatmaximizesSetebyestimatingthedistributionofH()viaempiricalandanalyticaldistributions.Theresultsusingtheempirical

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distributionaregiveninSection 3.5 .HereweinvestigatetheperformanceundertwosimpleanalyticaldistributionsforH(). ConsideranetworkofradiosdistributedaccordingtoaPoissonpointprocessoveraplane.ConsiderrstthedistributionforH(0),thenumberofhopsinaroutewhenunicastingisemployed.Wewishtousedistributionssuchthat: 1)9k38i>k;j>k;P(H(0)=i)>P(H(0)>j)foralli0,i=1,2,... Therstcriterionprovideslocality.Beyondsomelocalneighborhood,itismorelikelyforapackettohaveacloserdestinationthanonefurtheraway.Thesecondcriterionallowsanyradiointhenetwork(otherthanthesource)tobeadestinationforthepacket. Werstanalyzetheperformanceforageometricdistributionforthenumberofhops.SupposerstthatH(0)hasgeometricdistributionwithparameter,andletH=E[H(0)], 1) Thelinkisstillwithincommunicationrange,sotherouteisnotaffected. 2) Thelinkisnotwithincommunicationrange,butanotherlinkcanbeusedtoachievethesamenumberofhopsintheroute. 3) Thelinkisnotwithincommunicationrangeandsothenumberofhopsintherouteincreasesbyone.

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4) Thelinkisnotwithincommunicationrangeandthatlinkfailurerequiressignicantrerouting,resultinginthenumberofhopsinthenumberofhopsintherouteincreasingbymorethanone. Basedontheprobabilityofbeingabletoreachthesame1-hopdestinationabove,wemodelH()asageometricrandomvariablewithparameters()=(cos)4=n.Thismostaccuratelymodelscases1and3above.Wenotealsothatcases2and4willhaveoppositeeffectsonH(),sothismodelseemsreasonable,ifperhapsabitoptimisticbecauseofthelargeimpactofcase4.ForthisdistributionE[H()]=H(cos)4=n. Fortheinnitenetwork,Rm()istheprobabilitythataradiohasatleastonemore-capablelinkandisgivenby 3.1 Theaverageend-to-endthroughputcanthenbeapproximatedby From[ 55 ],ln(1+z)=z1 2z2+1 3z31 4z4+::::: ln1

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Lettingq=(cos)4=nandusing( 3 )and( 3 )yields Although( 3 )istoocomplicatedtoallowthemaximumvaluetobefoundviadirectanalysis,themaximumvaluecaneasilybefoundvianumericalmethods. TheresultsofthisnumericaloptimizationareshowninFigures 3 3 forn=2andinFigures 3 3 forn=4.TheresultsinFigures 3 3 areforH=1 3 3 .Thegraphslabeled(a)illustrateGete,themaximalgainintheend-to-endthroughputfromusingsimulcastinginsteadofunicasting,Gete()=Sete()=Sete(0).Thegraphslabeled(b)illustratethevaluesofthatmaximizesGete,whichisdenedasoptimaloffsetangleo.Theresultsindicatethattheexpectedgainintheend-to-endthroughputforsimulcastingvariesfrom20:9%to62:2%forn=2andfrom60:1%to90:0%forn=4,wherevariesfrom4to12.Themaximumgainsfromsimulcastingareachievedwhenthedistributionsfavorsshorterroutes(1

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Figure3. (a)Maximalgaininend-to-endthroughput,Gete,and(b)optimaloffsetangle(degree),o,tomaximizeGete,at1 Theovariesfrom27.5degreesto34.5degreesforn=2andfrom18.9degreesto32.2degreesforn=4.Itdecreasesasincreases.Thatis,theoismaximumfordistributionsfavoringshorterroutesandfewerneighborsandisminimumfordistributionsfavoringlongerroutesandmanyneighbors.Itmeansthat,aswediscussed,undertheassumptionoffullconnectivityofnetwork,theeffectofincreasingroutelengthbyemployingsimulcastingislargerwithlongerroutes.Havingmoreneighborsincreasestheprobabilityofbeingabletoperformsimulcastingforevensmall.So,inordertomaximizetheend-to-endthroughput,smallerisrequiredtoavoidincreasingroutelengthbyemployingsimulcastingasthenumberofneighborsincreases. Figures 3 and 3 showthemaximumend-to-endthroughputsversussforvarioussatn=2andn=4,respectively,overtheattemptrateGof0to1withH=4.TheunicastingthroughputSUisassumedasunityinthisresults.Asincreasesfrom4to12,themwhichmaximizesthemaximumend-to-endthroughputdecreasesfromof35to25andfrom30to15degreesforn=2andn=4,respectively.Forn=4,thevalueofoissmalleranddecreasesinalargerrangeasincreasescomparedtoforn=2.Inotherwords,forn=4,oismoresensitivetocomparedtoforn=2.Thisisbecause,

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Figure3. (a)Maximalgaininend-to-endthroughput,Gete,and(b)optimaloffsetangle(degree),o,tomaximizeGete,at1 Figure3. (a)Maximalgaininend-to-endthroughput,Gete,and(b)optimaloffsetangle(degree),o,tomaximizeGete,at1 Figure3. (a)Maximalgaininend-to-endthroughput,Gete,and(b)optimaloffsetangle(degree),o,tomaximizeGete,at1

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Figure3. (a)Maximalgaininend-to-endthroughput,Gete,and(b)optimaloffsetangle(degree),o,tomaximizeGete,at1 Figure3. (a)Maximalgaininend-to-endthroughput,Gete,and(b)optimaloffsetangle(degree),o,tomaximizeGete,at1

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Figure3. Themaximumend-to-endthroughputsforsimulcastingwithvariousnetworkdensitysingeometricdistributionforthenumberofhops,attheexpectedvalueofthenumberofhops1 atasamevalueof,thecoverageareasforbothofbasicandadditionalmessageswhensimulcastingisemployedaregreaterforn=4thanforn=2,andwhenislarge,theprobabilityofhavingamore-capableneighborincreases. TheMaximumend-to-endthroughputincreasesfrom0.55to0.73andfrom0.72to0.87forn=2andn=4,respectively,asincreasesfrom4to12.NotethatinFigures 3 and 3 ,forn=4,themaximalend-to-endthroughputachievedisgreatercomparedtoforn=2aspreviouslydiscussed. TheseconddistributionthatweconsiderforthenumberofhopsisamodiedPoissondistribution.ThePoissondistributionhasprobabilitymassatzero,whichisundesirableforourapplication,soweletH(0)1bePoissonwithexpectedvalue.Then,

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Figure3. Themaximumend-to-endthroughputsforsimulcastingwithvariousnetworkdensitysingeometricdistributionforthenumberofhops,attheexpectedvalueofthenumberofhops1 andH=+1.Followingsimilarargumentasforthegeometricdistribution,weletH()1bePoissonwithexpectedvalueof()givenby=(cos)4=n.Asforthegeometricdistribution,E[H()]=H(cos)4=n.Theaverageend-to-endthroughputcanthenbeapproximatedbySete=SUe()

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andGete=Sete() Figures 3 and 3 showtheanalyticalresultsfortheend-to-endthroughputofsimulcastingunderthePoissondistributionforthenumberofhopsforn=2andforn=4,respectively.Thegraphslabeled(a)illustrateGete,andthegraphslabeled(b)illustratethevaluesofoaccordingtovariousnetworkdensities. Theresultsindicatethattheexpectedgainintheend-to-endthroughputforsimul-castingvariesfrom10:0%to46:4%forn=2,andfrom53:1%to86:1%forn=4forintherangeof4to12.Themaximumgainsfromsimulcastingareachievedwhenthedistributionsfavorslargernumberofneighbors(=12)asthecaseofgeometricdistribution,butthegainsare5%to10%smallerthanforthegeometricdistribution.ThisisreasonablebecausethePoissondistributionhaslowerprobabilityofchoosingshorterroutesthanthegeometricdistribution,whichsignicantlyimpactsontheend-to-endthroughput.Thesimulcastinggainisalsogreaterforn=4thann=2forthesamereasondescribedforthegeometricdistribution. Theovariesfrom25.3to27.8degreesforn=2andfrom26.7to17.3degreesforn=4.Thesevaluesareabout5degreessmallerthanforthegeometricdistributionforbothofn=2andn=4.TheintuitiveexplanationisthattheeffectofincreasingroutelengthbyemployingsimulcastingwithrelativelylargeismoresignicantforthePoissondistribution. Mostly,theodecreasesasincreases.However,noticethatoisno-monotonicforn=2.ThisisbecausetheprobabilityofchoosingashortrouteislowforthePoissondistribution.Forthegeometricdistribution,oismaximalwiththeshortestroutesandthe

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Figure3. (a)Maximalgaininend-to-endthroughput,Gete,and(b)optimaloffsetangle(degree),o,tomaximizeGete,atn=2. Figure3. (a)Maximalgaininend-to-endthroughput,Gete,and(b)optimaloffsetangle(degree),o,tomaximizeGete,atn=4. fewestneighborsbecausetheeffectofincreasingroutelengthbyemployingsimulcastingislesswithshorterroutesandwithfewerneighbors,undertheassumptionoffullnetworkconnectivity.However,forthePoissondistribution,theeffectincreasesroutelengthwhensimulcastingisusedwithasmallnumberofneighborsbecauseofthesmallerprobabilityofchoosingashortroute.Forn=2,itismoreapparentbecausetheprobabilitythatthedestinationradioisstillwithincommunicationrangewhensimulcastingisemployed(cos)4=nissmallerforn=2thanforn=4. Figures 3 and 3 showthemaximumend-to-endthroughputsforsimulcastinginPoissondistributionforthenumberofhopsaccordingtovarioussalongwithvarious

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Asincreasesfrom4to12,themwhichmaximizesthemaximumend-to-endthroughputdecreasesfrom25to30andfrom15to25degreesforn=2andn=4,respectively.Asthegeometricdistribution,forn=4,theend-to-endthroughputismoresensitivetocomparedtoforn=2.Themaximalend-to-endthroughputrangesfrom0.33to0.46andfrom0.33to0.58forn=2andn=4,respectively.Theoverallpatternissimilarandcanbeexplainedwiththesamereasonasforthegeometricdistributioncase. Incomparisonwiththegeometricdistribution,forthePoissondistribution,theachievedmaximalend-to-endthroughputsandthevaluesofotoachievethemarelessandtherangeofooverthedomainofisrelativelysmaller.Aspreviouslydiscussed,itisbecausethePoissondistributionhaslowerprobabilityofchoosingshortroutesandthevariationofPoissondistributionislessthanforthegeometricdistribution.Basedontheanalysisandthenumericalresultsoftheend-to-endthroughput,ifthenumberofhopsfollowsthegeometricaldistribution,ahigherend-to-endthroughputisexpected,andifthenumberofhopsfollowsthePoissondistribution,arelativelystableend-to-endthroughputisachieved. 56 ]-[ 59 ]reportthatinsimulationsofmobileadhocnetworks,theprobabilitydistributiongoverningthemovementofthenodestypicallyvariesovertimeandconvergestoasteady-state,orstationarydistribution. Thusasimulationofanetworkofmobileradiosoftenexperiencesatransitoryperiodbeforeconveyingtothesteadystate.Oneapproachtodealwiththeuctuatingconditionsistothrowawaythesimulationdataforsomeinitialtimeperiod.Amoreefcientalternativeistochoosetheinitiallocationsandspeedsoftheradiosfromthe

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Figure3. Themaximumend-to-endthroughputsforsimulcastingwithvariousnet-workdensitysinPoissondistributionforthenumberofhops,attheexpectedvalueofthenumberofhops=4andpropagationconstantn=2. Figure3. Themaximumend-to-endthroughputsforsimulcastingwithvariousnet-workdensitysinPoissondistributionforthenumberofhops,attheexpectedvalueofthenumberofhops=4andpropagationconstantn=4.

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stationarydistributionsforthemobilitymodelsothatconvergenceisimmediateandnodataneedstobediscarded.However,becausetheinitiallocationandspeedswithstationarydistributionsbringacentralizedshapeofdistribution(themostconvergentspeedsandthelocationsaregatheredatacertainrangeofspeedandlocation),itishardtoseetheeffectsofmobilesmovingaroundinalargearea.Theuniformlydistributedsteady-stateneedstobestudied. Weusetherandomwaypointmobilitymodel,whichisoneofthemostpopularmobilitymodelsforcommunicationnetworks,foroursimulation.Inthismodel,aninitialpointp0andadestinationpointp1areassigneduniformlyintheareaA,andspeedisassignedtoamobileattheinitalpointuniformlyinanarbitraryrangeofspeed.Theinitialanddestinationpointsarechosenindependently.Oncethemobilereachesthedestination,anewdestinationischosenuniformly,independentlyofallpreviousdestinationsandspeeds.Mobilesmaypausewhenitreacheseachdestination,ortheymayimmediatelymovetothenextdestinationwithoutpausing.Iftheypause,thepausetimesarechosenindependentlyofspeedandlocation. Therandomwaypointmodelisacommonlyusedmobilitymodelinthesimulationofadhocnetworks.However,ithasproblemssuchasthedecayofaveragespeedsasthesimulationprogresses,adifferencebetweentheinitialandthenalnodesdistribution.Itisknownthatthespatialdistributionofnetworknodesmovingaccordingtothismodelis,ingeneral,nonuniform.Forexample,withthismodel,amobilespendsmoretimeatlowerspeed,thereforeitismorelikelytobesampledatlowspeed.TheinitialmobilepositionisuniformintheareaA,however,withtime,thedistributionofmobilepositionstendstobemoredensetowardsthemiddleofthearea. Toovercometheproblemsofrandomwaypointmodel,J.LeBoudec[ 59 ]recentlypresentedhowtoobtainthestationarydistributionoflocationandspeedsforthesimu-lationofmobilitymodelbasedonpalmcaculus.Bypalmcalculus,thehistogramoftheterminatingornon-terminatingergodicsimulationcanbepredicted.Itisappliedtothe

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randomwaypointmodeltoachieveaninitialdistributionequaltothestationarydistri-butionofrandomwaypoint.Simply,howtogeneratethestationarydistributionofthepreviousandnextwaypointandthecurrentmobilepositioncanbeobtainedasfollows.LetbeanupperboundonthediameterofareaA. 1.dodrawMo,M1iidUnif(A)drawVUnif[0;]untilV
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Table3. Positionofradiosinten-nodenetworkinFig. 2 NodeID Xposition(km) Yposition(km) 1 1.15 2.00 2 1.53 3.59 3 1.95 2.55 4 3.50 2.25 5 2.40 3.21 6 2.55 2.12 7 3.71 2.57 8 3.10 4.01 9 2.58 4.18 10 2.06 2.00 inFigure 2 .ThepositionsoftheseradiosaregiveninTable 3 .Thenetworkdegreeis2.2.ThelinkdistancesareguredoutwithincorporationoftransmissioninadditivewhiteGaussiannoise(AWGN),wherethebiterrorprobabilityatthemaximumtransmissionrangeof1kmis104.Itisassumedthatthepacketlengthis1000bitsandanerror-controlcodeisusedthatcancorrectupto10biterrors.Forthiscaseofnomobility,weexpectthattherewillbealmostnoperformancedegradationfromthenoise,asthetransmissionrangefornodestobeconsideredneighborsissuchthatthepacketerrorprobabilityisverysmall.Thesimulationresultsmatchcloselywiththeanalyticalresults. TheresultsinFigure 3 showthelinkthroughputperformanceofthenetworkasafunctionoftheaverageattemptrate.Solidlinesrepresenttheperformancepredictedbytheanalysisfrom( 3 )to( 3 ),and( 3 ).Themarkersillustratetheperformanceresultsfromoursimulation.Theperformanceisillustratedforthreedifferentnetworkcongurations.FortheresultsmarkedUnicast,thenodesareconstrainedtonotemploythesimulcastsignalingtechnique,andthuseachnodetransmitsatmostonepacketinatimeslot.FortheresultsmarkedSimulcast(NW1),simulcasttransmissionisused,wherethemore-capablelinksaredeterminedbasedonadegradationof0:5dBandadisparityof9:1dB.

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TheresultsmarkedSimulcast(NW2)illustratetheperformanceforanetworkwithfewermore-capablelinksbecausetherequiredcapabilitydisparityisincreasedto11:4dB,whichcorrespondstoadegradationof0:3dB.Thelinkthroughputforthesexedtopologieswithequalback-offtimesisillustratedinFigure 3 .Theresultsindicatethatsimulcastingcansignicantlyimprovethethroughputintheadhocnetwork. Next,letusconsideranetworkwithN=15radiosplaceduniformlyovera1kmby1kmarea.Weconsiderthesimplegood/badchannelmodelwithamaximumlinkdistanceforunicasting(or,equivalently,simulcastingwith=0o)of381m.WeconsiderrstsomebasicnetworkparametersasafunctionoftheoffsetangleofthenonuniformQPSKusedforsimulcasting.TheresultsinFigure 3 illustratethenetworkdegree(expectednumberofneighbors)asafunctionoftheoffsetangle.Theanalyticalresultsaredeterminedfrom( 3 ).Thesimulationresultsareshownfortwocases.Theresultsforallnetworksistheaverageover100randomtopologies.Theresultsforconnectednetworksonlyshowstheaveragenetworkdegreefor10oftherandomtopologiesthatformedaconnectednetworkforalldegrees.Theresultsshowthesensitivityofthenetworkdegreetotheparameter.Forallnetworks,unicasting(=0)yieldsanetworkdegreeofapproximately4.5,whileforQPSK(=45degrees),thenetworkdegreedropsto3.4.Wenotethatifweconsideronlyconnectednetworks,thenthenetworkdegreeisbiasedabovethevalueforallnetworks. Oneoftheprimaryeffectsofchangesinthenetworkdegreeisanimpactontheconnectivity,whichwedeneastheprobabilitythateverynodehasaroutetoeveryothernodeinarandomlygeneratednetwork.TheconnectivityisshownasafunctionoftheoffsetangleinFigure 3 .Theunicastlinkdistanceof381mwaschosenbecauseitprovidesconnectivityofapproximately0.9.Thenetworkconnectivitydecreasesasincreases.However,for<25degrees,theconnectivityremainsabove0.85.Thus,ifiskeptsmall,simulcastingcanbeusedwithrelativelylittleimpactonnetworkconnectivity.Asapproachesitsmaximumvalueof45degrees,theconnectivityrapidlydecreasesto

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approximately0.66.Thus,itisnotpossibletoswitchtoauniformQPSKconstellationwithoutasignicantlossinnetworkconnectivity. TheresultsinFigure 3 showtheexpectedproportionofradiosthathaveamore-capablelinkasafunctionof.AsshowninSection 3.1 ,thisparameterhasanimportanteffectonboththelinkandend-to-endthroughputs.Theresultsshowthatasincreasesfrom0,theproportionofradioswithamore-capablelinkincreasesrapidly.Theanalyticalexpression( 3 )isshowntocloselymatchthesimulationresults.Thereisnosignicanteffectonthisparameterofonlyconsideringconnectednetworksinsteadofallrandomlygeneratednetworks.Atthepreviouslymentionedvalueof=25degrees,theproportionofradioswithamore-capablelinkexceeds0.8.Thus,thereislittletogainfromincreasingfurther,andanyfurtherincreasecomesatasignicantexpenseintermsofnetworkconnectivity,asshowninFigure 3 Wenextrestrictedthesimulationsto10xedtopologiesthatareconnectedforall045degrees,whichwererandomlyselectedfromthe100randomlygeneratedtopologies.Inthisway,wecanbesurethatwecancalculateend-to-endthroughputforeachnetwork.However,thedistributionofthenodeswillnolongerbeuniform,whichwillaffecttheresults.Eachtopologystillconsistsof15nodesdistributedovera1km1kmarea,withmaximumlinkdistanceof381mforunicasting.Eachsimulationconsistedof1500timeslotsaftera100timeslotwarm-upperiod. TheresultsinFigure 3 showtheaveragelinkthroughputforunicastingandsimulcastingwithoffsetangle=25degreesforthenetworksdescribedabove.Thelinesrepresentanalyticalresultsandthemarkersrepresentsimulationresults.Thesimulationandanalyticalresultsdifferslightlybecausetheanalyticalresultsareforrandomlygeneratednetworks,butthesimulationresultsareforasetofconnectednetworks.Theresultsshowthatfor=25degrees,themaximumlinkthroughputisalmosttwiceashighwithsimulcastingascanbeachievedwithunicasting.FromFigure 316 ,thenetworkconnectivityfor=25degreesisapproximately0.85versus0.9for

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unicasting,sothelinkthroughputcanbesignicantlyincreasedwithlittlecosttonetworkconnectivity. TheresultsinFigure 3 showthemaximumlinkthroughputachievedasafunctionoftheoffsetangle.Here,themaximumistakenoverallpossibleattemptrates.Thelineistheanalyticalresult,andthecirclesarefromsimulations.Notethatasincreases,sodoesthelinkthroughputthatcanbeachieved.Thisisreasonablebecauseaslongasthenetworkremainsconnected,eachnodewillhaveatleastonenodetowhichitcantransmit.Furthermore,asincreases,theprobabilityofcollisiongoesdownalongwiththeexpectednumberofneighbors,andthenumberofnodeswithmore-capablelinksgoesup.Thecombinedeffectisthatthemaximumthroughputwith=45degreesisapproximately2.7timeshigherthanthemaximumthroughputwithunicasting.However,fromFigure 3 ,weseethatthenetworkconnectivitysuffersgreatlyasbecomeslarge. Inadditiontotheimpactonnetworkconnectivity,increasingalsoaffectsthelengthofroutesinthenetwork,whichmayimpacttheend-to-endthroughput.TheresultsinFigure 3 illustratetheaveragenumberofhopsinarouteasafunctionoftheoffsetangle.Asincreasesfrom0to45degrees,theaveragenumberofhopsincreasesfromapproximately2.25to4.2.Thenumberofhopsincreasesrapidlyasincreasesbeyond20degrees.TheresultsinFigure 3 illustratethemaximumaverageend-to-endthroughputasafunctionof.Here,themaximumisoverallattemptrates.Thesolidlineillustratestheanalyticalresults(usingtheempiricalvaluesfortheexpectednumberofhopes),andthesimulationresultsarethecircles.Theresultsshowthattheend-to-endthroughputisanon-monotonicfunctionof.Theanalyticalresultsareoptimisticfor>10degrees.However,theydoshowthesametrendsastheanalyticalresults.Webelievethattheprimarydifferencesinthetwocurvescomefromthefactthatthesimulationresultsarenotforrandomlygeneratednetworksbecausewehaveenforcedthatthenetworksmustbeconnected.Thesimulationresultsshow

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thattheend-to-endthroughputismaximizedby=30degrees.Theend-to-endthroughputat=30degreesisapproximately0.042versus0.027forunicasting.Thus,simulcastingresultsinanincreaseinend-to-endthroughputofover55%.Ifweuseamoreconservativevalueofintherange2025,thentheend-to-endthroughputisstillmorethan40%higherthanunicasting,whilehavingasmallerimpactonnetworkconnectivity.NotethatthesevaluesofmatchcloselywiththosefoundviaanalysisinSection 3 forainnitenetworkwithageometricdistributionforthenumberofhopsinaroute. Wenextinvestigatetheeffectofhavingout-of-dateinformationaboutthenetworklinksbecauseofmobility.Aradio'slinkinformationmayindicatethatanodeisaneighboreventhoughthataradiohasmovedoutofrange.Similarly,aradiomaybelievethatalinkisamore-capablelinkeventhoughtheradio'smovementshavereducedthecapabilityofalinktoanextentthatthepacketerrorprobabilityoverthatlinkdegradesperformance.Wemodeltheseeffectsbyonlyallowingforaperiodicupdateofroutingtables.Weassumeaslottimeof20msandaroutingtableupdateevery300slots(6s).Fifteenmobilesmovearoundwithconstantvelocitiesof30,50,or100km=hrina5Kmx5Kmarea.Weemployedthetimestationaryrandomwaypointmobilitymodeldescribedabove. Figures 3 and 3 showthesimulationresultsforthelinkandtheend-to-endthroughputs,respectively.Theyshowthatthethroughputsforbothunicastingandsimulcastingdegradeasvelocitiesincrease.However,simulcastingstillprovidesasignicantthroughputgain.Asexpected,highermobilitylevelsgenerallyresultinlowerthroughputasroutingtableinformationismorelikelyincorrect.Thisisobservedtobeespeciallytrueathighaverageattemptrates.

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Figure3. ThroughputinAWGNforthenetworkofnodesthatisillustratedinFig.3.ForNW1,thedegradationis0.5dB,andthedisparityis9.1dB.ForNW2,thedegradationis0.3dBandthedisparityis11.4dB. Figure3. NetworkdegreeasafunctionofforsimulcastingwithnonuniformQPSKinawirelessadhocnetworkwithrandomnodeplacement.

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Figure3. NetworkconnectivityasafunctionofforsimulcastingwithnonuniformQPSKinawirelessadhocnetworkwithrandomnodeplacement. Figure3. Proportionofnodeswithamore-capablelinkasafunctionofforsimul-castingwithnonuniformQPSKinawirelessadhocnetworkwithrandomnodeplacement.

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Figure3. LinkthroughputforunicastingandsimulcastingwithnonuniformQPSKwith=25degreesinawirelessadhocnetworkwithrandomnodeplace-ment. Figure3. MaximumlinkthroughputforsimulcastingwithnonuniformQPSKasafunctionoftheoffsetangle.

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Figure3. AveragenumberofhopsinarouteforsimulcastingwithnonuniformQPSKasafunctionoftheoffsetangle. Figure3. Maximum(overallattemptrates)end-to-endthroughputforsimulcastingwithnonuniformQPSKasafunctionofoffsetangle.

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Figure3. LinkthroughputinAWGNforamobilenetworkof15radioswithdegra-dationof0.5dBanddisparityof9.1dBbythetimestationaryrandomwaypointsimulation. Figure3. End-to-endthroughputinAWGNforamobilenetworkof15radioswithdegradationof0.5dBanddisparityof9.1dBbythetimestationaryrandomwaypointsimulation.

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Whenaradiosuffersacollision,theradiowillwaitarandomback-offtimethatisselectedaccordingtoageometricdistribution.Iftheaveragevalueoftheback-offtimeisspeciedasTB,thentheradiowillbeginitsretransmissionineachofthefollowingslotswithprobabilityTB1.Sofar,ourstudywasbasedonassigningequalprobabilityofretransmissiontoeveryradiowhenasourceradiorecognizesthatthetransmittedpackethascollidedwithanothertransmission.Inthisdissertation,weinvestigatetwoapproachestochoosetheparameterTB.Intherstapproach,theback-offtimeisequalforeveryradio,namedasEqualBack-off(EQB).TheperformanceofsimulcastingwiththisschemewasalreadyinvestigatedinChapter 3 .Theradiossimulcastingcantransmittwopacketswhiletheradiosunicastingcandojustonepacketpertimeslot,whichmeansresourceutilityavailablefortheradiossimulcastingcanbeuptotwicethatfortheradiounicasting.Thesecondapproach,thefocusofthischapter,isnamedasPriorityBack-off(PRB).InPRB,theback-offtimeischosenunequallytogivehigherretransmissionprobabilitiestoradiossimulcastingthantoradiosunicasting. Weinvestigatethefairnessofeachschemeintermsoftheachievedthroughputsacrosstheradiosinthenetwork.Themostsimpleinterpretationofthefairnessishowclosethedistributionistoevensharingofresourcesamongalltheradiosinanetwork.However,theconceptoffairnessismulti-faceteddependingonitsapplication.Forexam-ple,asdenedin[ 13 ],intermsoftheequalityofeachradio'slinkthroughput,fairnessshouldbetakenasevenness,denedasservicefairness,butintermsofmaximizationofnetworkthroughput,itshouldbetakenaseachradio'seffectiveutilizationamount,denedaseffortfairness.Inthisdissertation,Dianatietal.'sfairshareallocationand 51

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utilitybasedfairness[ 13 ]aremodiedtoallocateback-offtimeunequallyaccordingtosimulcastingcapability,andtomeasureservicefairnessandeffortfairnesswhenPRBisapplied. 13 ]toassignsahigherchanceofretransmissionineachslottotheradiosthathavemore-capablelinks.Thenormalizedfairshareresourceallocationofradioiisdenedas whereNtisthetotalnumberofradios,Aisaconstantfrom0to1,and Here,Aisusedtotradeoffbetweenservicefairnessandeffortfairness.WhenA=0,S(a)iisnotsensitivetotheeffortfairness,andwhenA=1,S(a)ihasmaximumsensitivitytotheeffortfairness.WeconsiderA=0,1=2,or1forourwork,whereA=0givesequalshareamount,A=1=2givesequalsensitivitytosharingthecommonresource(servicefairness)tousingitefciently(effortfairness),andA=1givesmaximizedsensitivitytoeffortfairnessforresourceallocation.Then,

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where,TEBisback-offtimebyEQBatacorrespondingaverageattemptrateG,andKisaconstanttoadjusttheresultantback-offtimetoyieldtheaverageattemptrateGbyTEB. 14 ]whichcomparestheratiooftheminimumtothemaximumamountofallocatedresourcesamongalltheusersinanetworkasbelow,wherexiistheamountofallocatedresourcetouseri.Inthisdissertationxiisreplacedwiththeachievedlinkthroughputofradioi. Aswediscussedfairnesshasdifferentfacetsspecieddifferentlyinthedifferentdomainofresourceallocation.Inotherwords,fairnesscannotalwaysbeconsideredasevenresourcedistributionbecauseasystemwhichisfairintermsofevenness(servicefairness)maynotbefairifitisviewedintermsoftheresourceallocationamounttoeachuserstomaximizenetworkperformances(effortfairness)whentheyhavedifferentresourceutilizingcapabilities.Dianatietal.proposedin[ 13 ]theUtilityFairnessIndex(UFI)tocapturethefairnesssensitivetoeffortfairness.Forexample,inoursimulcastingsystem,itmakessensetoprovideadditionalresourcestothoseradiosthat

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cansendatahigherrate(simulcasting),andtheyshouldnotbepenalizedforthatinthefairnessintheviewpointofoptimizedresourceutilization. BytheapplicationofDianatietal.[ 13 ],thenormalizedachievedthroughputisdenedas Thevalueofxiisreplacedwithlinkthroughputofradioi,overacertainattemptrateG.Then,theutilityfunctionUi(s(f)i)withthefairshareallocationatacertainvalueofisdenedas isthefairshareofradioi,andFindicatesthetradeoffbetweenservicefairnessandeffortfairness.Then,theUtilityFairnessIndex(UFI),isdenedasin[ 13 ]as 3.5 .SimulationsarecarriedoutwithvariousvaluesofA.Themarkers,,andrepresenttheresultsforAisequalto0:0,0:5,and1:0,respectively.The100differentuniformlydistributedrandomnetworkshavebeengenerated,and4fullyconnectednetworksarechosenfor

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simulationamongthem.Therunningtimeis5,000timeslotsforeachrandomnetwork.Thesimulationresultsareaveragedoverthe4fullyconnectednetworks. TheresultsinFigure 4 showsthesimulationresultsofmaximumlinkthroughputasafunctionoftheoffsetangle.ThemaximumistakenoverallpossibleattemptratesasinSection 3.5 .Notethatasincreases,sodoesthelinkthroughputthatcanbeachieved.Theresultsshowthat,intherelativelylargerangeofoffsetangle,from15to40degree,themaximumlinkthroughputincreasesuptoabout10%and20%byPRBwithAequalto0:5and1:0,respectively. TheresultsinFigure 4 showsthesimulationresultsofmaximumend-to-endthroughputasafunctionof.Themaximumistakenoverallpossibleattemptratesaswediscussed.Theresultsshowthattheend-to-endthroughputisanon-monotonicfunctionof.Thesimulationresultsshowthattheend-to-endthroughputismaximizedby=20degrees.Theresultsshowthat,intherelativelylargerangeofoffsetangle,from15to40degree,themaximumend-to-endthroughputalsoincreaseuptoaboutfrom3%to10%byPRBwithAequalto0:5and1:0,respectively. Figure 4 showsthesimulationresultsofMMIasafunctionof.Theresultsshowthattheevennessdegradesasweallocateback-offtobemoresensitivetoeffortfairness.TheevennessforallthreecaseswithdifferentAvaluesdeclinewhenisover25degrees. Figure 4 showsthesimulationresultsofUFIasafunctionof.TheUFIisobservedatthesamevaluesofFwithAoffairshareresourceallocationexceptforthemarker4whichindicatesthecasewithA=1:0,fullysensitivetoeffortfairnessforthefairshareresourceallocation,andF=0:0,fullysensitivetoservicefairnessforthefairnessindex.TheresultsshowthatwhiletheservicefairnessisdegradedbyPRB,there'snobigchangeinUFIasthevalueofAincreasescomparedtoMMI.However,theUFIalsobecomeworseasAincreases,whichmeans,assamereasonwithMMI

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Figure4. MaximumlinkthroughputbyPRBwithvariousAvaluesinrandomnet-worktopologyasthefunctionofoffsetangle. case,PRBisdependentofRm,andbecomesmoresensitiveatthevalueofover25degrees.

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Figure4. Maximumend-to-endthroughputbyPRBwithvariousAvaluesinrandomnetworktopologyasthefunctionofoffsetangle. Figure4. Min-maxfairnessbyPRBwithvariousAvaluesinrandomnetworktopol-ogyasthefunctionofoffsetangle.

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Figure4. UtilitybasedfairnessbyPRBwithvariousFandAvaluesinrandomnetworktopologyasthefunctionofoffsetangle.

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Inthischapter,weinvestigatehowthesimulcastingcapabilitycanbeexploitedatthenetworklayerbyadjustingthedistributionofpacketsacrossmultipleroutesinasystememployingmultipathrouting.Themodiedmin-hoproutingforsimulcastingthatweuseinprevioussectionsinthisdissertationispresentedinSection 2.3 .Basedonthismin-hoproutingalgorithm,wemayhaveseveralroutesthathavesamenumberofhopsfromasourceradiotoanaldestination.However,eachrouteisstilllikelytodifferintermsofsimulcastingcapabilitybecauseofdifferentnumbersofrelayradioswithmore-capablelinks.Routesthathavemorerelayradioswithmore-capablelinkswilltransmitmorepacketspertransmissionopportunityandthereforebemoreefcientinrelayingapacketalongtheroute.Ifaradiohasmultipleroutestoadestination,thiseffectshouldbeconsideredwhendeterminingwhatproportionofpacketstotransmitonaroute.Inthischapter,weprovideapreliminaryinvestigationofhowsimulcastingcapabilitycanbeexploitedinthenetworklayerintheallocationofpacketsacrossmultipleroutes.Weinvestigatetheperformanceofvaryingthepacketdistributionacrossrouteswithdifferentsimulcastingcapabilitiesforseveralnetworktopologies. 52 5 .Inordertoreducethesimulationcomplexityandruntime,wedonotsimulateradiosinthenetworkotherthanthoseonthetworoutesfromStoDasiftheywerepartofalargernetwork.EveryradioismodeledashavingthesameaverageattemptrateGandsamenumberofneighborsNb,whichisdenedasthenetworkdegree.So,givena 59

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transmission,thecollisionprobabilityisPC=PNbi=1CNbiGi(1G)NbiasinSection 3.2.1 .ThenthelinkthroughputbyunicastingisgivenbySU=G(1PC)andbysimulcastingisSS2G(1PC),asinChapter 2 .Thesevaluesdeterminestatisticsofthequeue,suchasthearrivalandtheserviceratesforaqueueofarelayradioonaroute.Ifapacketfromthesourceradiocollideswithanothertransmissionatoneoftheradiosalongtheroute,thepacketwillstayinthequeueofthetransmittingradiotowaitforre-transmission. WeconsideramultipathroutingschemeinwhichpacketsfromSaredistributedacrossthetworoutesaccordingtoarandomdistribution,asillustratedinFigure 5 .ThesourceStransmitspacketsatattemptrateGtoonlythedestinationD.ThetworouteshavesamenumberofhopstoD,butmayhavedifferentsimulcastingcapabilities.Wedenethemore-capablerouteastheroutewhichhaslargersimulcastingcapability,andtheless-capablerouteastheroutewhichhaslesssimulcastingcapability.WeselectaroutefortransmissionrandomlywithprobabilityR1forthemore-capablerouteandR2fortheless-capablerouteateachtransmission,whereR1+R2=1.Wealsodenetheoptimalrouteselectionrateastherouteselectionrateforthemore-capableroutetoachievethemaximumend-to-endthroughput. Figure5. Packettransmissionfromsourceradiotorandomlyselectedroutebasedonsimulcastingcapability.

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Wemodelthreetopologiesoftransmissionroutesinwirelessadhocnetworkswithidenticalwirelessradiosdeployedwithinatwo-dimensionalgeographicalterritory.Therearetworoutesaswementionedabove.Thetworouteshavesamenumberofhopsfromsourceradiotodestinationradio,butdifferentsimulcastingcapabilitiesduetothenumberofrelayradioswithsimulcasting,ordifferentnumberofmorecapablelinksalongeachroute.Theupperrouteisthemore-capableroute,andthelowerrouteistheless-capableroute.Weassumethateachroutedoesnotinterferewitheachotherbecausetheyarenotwithintransmissionrange.Wemeasuretheend-to-endthroughputasthenumberofpacketssuccessfullytransmittedfromStoDpertimeslot.Figures 5 5 showthethreetopologiesforwhichwepresentresults.Thelledcirclesrepresentradiosthatcanutilizesimulcastingbecausetheyhavemore-capableneighbors,andtheemptycirclesrepresentradiosthatcanonlyunicast.Theboldlinesrepresentmore-capablelinks,andthethinlinesrepresentless-capablelinks.Topology2hasmorerelayradioswithsimulcastingonthemore-capableroutethanontherouteoftopology1,butthenumberofmore-capablelinksarethesame.Topology3hasthesamenumberofrelayradioswithsimulcastingonthemore-capablerouteastopology2,buthasmoremore-capablelinks.Theconditionsoftheless-capableroutesaresameforalltopologies. Figure5. Topology1forunequalrandomrouteselectionbasedonsimulcastingcapa-bility.

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Figure5. Topology2forunequalrandomrouteselectionbasedonsimulcastingcapa-bility. Figure5. Topology3forunequalrandomrouteselectionbasedonsimulcastingcapa-bility. 5 .Thestatesnandn+1inthecirclesrepresentthenumberofpacketsinthequeue,pandqarearrivalrateandservicerate,respectively.Forthepurposesofmodelingpacketarrivalsanddeparturesattheradiosalongthetworoutes,wetreatthearrivalsanddeparturesasindependent.Infact,thesearenotindependent,asaradiomaynotsuccessfullytransmitandsuccessfullyreceivesimultaneously.However,weexpectthisapproximationwillhavelittleimpactonourresults.Then,Qistheprobabilityofnochangeinthenumberofpacketsafteronetransmissiontimeslot,whichweapproximatebyQ=pq+(1q)(1p)+(1p)P(0),whereP(0)representstheprobabilitythatthereisnopacketinthequeueatthecurrenttransmissiontimeslot. Thestatisticsofthequeuestatusdependonthesimulcastingcapability,whichisdeterminedbyseveralnetworkparameterssuchasthenumberofneighbors,thenumber

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Figure5. Markovstatusdiagramforthenumberofpacketsinaqueue. ofmore-capablelinksofaradio,andthenumberofmore-capablelinkontheroute.Figures 5 5 illustratepossiblelinkstatusesandtheirproperties.TheservicerateqsimplyincludesanypacketoutgoingwhichincludethepacketfromStoD.However,thearrivalratepbincludesonlybasicmessageincomingbyunicasting,andthearrivalrateduetoadditionalmessagesincomingbysimulcastingisrepresentedbythesymbolpa.ThetrafcgeneratedaccordingtoprobabilitiespbandpaisnotusedtomodelthetrafcfromStoD,whichisfullysimulated.Thetotalincomingratepisequaltopb+pa.ThedottedarrowsinFigures 5 and 5 representadditionalmessageotherthanfromthesourcethatisreceivedbysimulcastingataradioalongthemore-capableroute. Figure 5 representsoneofthepossiblelinkconditions,linkmodel1,thattherelayradiodoesn'thaveanymore-capablelink.So,it'sarrivalandserviceratecorrespondtothelinkthroughputbyunicasting.However,becausethetotalarrivalratepdoesn'tincludethetrafcincomingfromS,basedontheassumptionthateveryradioinvolvedinthetransmissioninthenetworkisidentical,andsendpacketsuniformlyoneachbranch,thearrivalratepisrelatedwiththeamountofpacketsincomingexceptfromonebranchamongallNbbranches.Then,p=Nb1

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Figure5. Figure 5 illustratesanotherpossiblelinkcondition,linkmodel2,thattherelayradiocansimulcastbutdoesn'thaveanymore-capablelinkontheroute.So,it'sarrivalandserviceratecorrespondtothelinkthroughputbysimulcasitng.Theservicerateqissimply2SU.Thearrivalratepisguredoutinsimilarwaywithlinkmodel1,butcorrespondstothroughputbysimulcasting,andbecausethisrelayradiocansimulcast,itincludesarrivalrateforadditionalmessagepa.Therelayradiodoesn'thaveanymore-capablelinkontheroute,sobasedontheassumptionthatsendingadditionalmessageoneachmore-capablelinksisuniformandindependentontransmissionofbasicmessage,paisSu(Nm=N2b).Then,withsimilaranalysisoflinkmodel1,whereNmisaveragenumberofmore-capablelinksofaradio,p=SUNb1 Figure 5 illustratesanotherpossiblelinkcondition,linkmodel3wheretherelayradiocansimulcastandhasamore-capablelinkonthesourcesideontheroute.So,it'sarrivalandserviceratecorrespondtothelinkthroughputbysimulcasitng.Theservicerateqissimply2SU.Thearrivalratepisguredoutassimilarwaywithlink

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Figure5. Figure5. Figure 5 illustratesanotherpossiblelinkcondition,linkmodel4,wheretherelaycansimulcastandhasmore-capablelinkonthedestinationsideoftheroute.Theonly

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differencewithlinkmodel3isthatanadditionalmessageincomingtotheradioisfromthedestinationside.So,thearrivalrateforadditionalmessagepaincludestheadditionalmessagefromaradioonthedestinationsideoftheroute.Then,p=SU(Nb1 Figure5. Figure 5 representsthenalpossiblelinkcondition,linkmodel5,wheretherelayradiocansimulcastandhasmore-capablelinkstobothneighborsontheroute.Thearrivalrateforadditionalmessagepainthisconditionissamewithlinkmodel3.Then,p=SU(Nb1 Intheabovenetworkmodel,weconsidertheend-to-endthroughputwhichismeasuredasthenumberofpacketssuccessfullytransmittedfromthesourceradiotothedestinationradiopertimeslot.Thestatisticsofthequeuedelayateachrelayradioforthe

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Figure5. trafcfromthesourceradiowillaffecttotheend-to-endthroughput.Now,weinvestigateunequalrandomrouteselectionwhichrandomlyassignsanunequalamountoftrafcfromthesourceradiotoeachroute. 5.2 .IfapackettransmittedfromsourceradioiscollidedbythecollisionprobabilityPCinSection 5.1 atanyrelayradioonaroute,thepacketstaysinthequeueoftheoriginalradiotowaitforretransmissionataverageattemptrateG.SimulationisperformedonvariousattemptratesGintherangefrom0to1.Ifapacketissuccessfullytransmitted,itmovestotheendofthearrivalqueueofthenextradio.ThepacketselectionisbasedonFIFOasmentionedinSection 2.4 .Weran100,000time

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slotstocountthenumbersofpacketsthatweretransmittedfromthesourceradioandthatarrivedatdestinationradiosuccessfullyforvariousprobabilitiesofR1andR2. Wealsoperformedsimulationsforahigh-densitynetworkscenarioinwhichthenetworkdegreeis8andtheaveragenumberofmore-capablelinksofaradiowithsimulcastingis4,andforalow-densitynetworkscenarioinwhichthenetworkdegreeis6andtheaveragenumberofmore-capablelinksofaradiowithsimulcastingis3.TheresultsinFigures 5 and 5 showthesimulationresultsformaximumthroughputinthehigh-densitynetworkandthelow-densitynetwork,respectively,ineachofthethreetopologies.Themarks,,andrepresentthesimulationresultsfortopology1,topology2,andtopology3,respectively.Thelow-densitynetworkresultsshowthesamepatternofend-to-endthroughputasinthehigh-densitynetwork,butgive43.24%,32.14%,and26.79%highermaximumend-to-endthroughputsintopology1,2,and3,respectively.Webelievethatthisisbecausethelownumberofneighborsgivesalowercollisionprobabilityatreceivers.Theresultsforthehigh-densitynetworkinFigure 5 showthattopology2and3givearound52%highermaximumend-to-endthroughputthantopology1,butalmostnodifferencebetweentopology2and3.Theresultsforthelow-densitynetworkinFigure 5 showthattopology2and3give39.62%and33.96%highermaximumend-to-endthroughputthantopology1,respectively,andthedifferencebetweentopology2and3isassmallas4.23%.Thisindicatesthattheend-to-endthroughputusingrandomrouteselectionisstronglydependentonthenumberofrelayradioswithsimulcasting,butnotasmuchonthenumberofmore-capablelinksonaroute. Theresultsforthehigh-densitynetworkinFigure 5 showthatthemaximumend-to-endthroughputsareimprovedby270%,450%,and410%fortopology1,2,and3,respectively,byrandomrouteselectioncomparedtothecasethatwechoosetheless-capablerouteonly.Comparetothecasethatwechoosethemore-capablerouteonly,themaximumend-to-endthroughputisimproved37.04%,27.27%,and33.33%,fortopology

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1,2,and3,respectively,byrandomrouteselection.Theoptimalrouteselectionrateisintherangefrom0.6to0.9whichisovertheequaldistributionpoint(0.5)forthetopology2and3.Fortopology1,itisintherangeof0.3to0.9,althoughitisveryslightlyhigherbetween0.7and0.9. Theresultsforthelow-densitynetworkinFigure 5 showthatthemaximumend-to-endthroughputsareimprovedby270%,410%and390%fortopology1,2,and3,respectively,byrandomrouteselectioncomparedtothecasethatwechoosetheless-capablerouteonly.Comparetothecasethatwechoosethemore-capablerouteonly,maximumend-to-endthroughputisimprovedby33.3%,24.1%,and21.1%,fortopology1,2,and3,respectively,byusingrandomrouteselection.Theoptimalrouteselectionrateisaround0.5,and0.7fortopology1,andtopologies2and3,respectively. Thesimulationresultsforboththehigh-densityandlow-densitynetworkshowthattheoptimalrouteselectionrateishigherfortopology2and3thanintopology1.Thisindicatesthattheoptimalrouteselectionrateisstronglydependentonthenumberofrelayradiossimulcastingonaroute.Thesimulationresultsindicatethatknowledgeofthesimulcastingcapabilitiesofradiosalongaroutecanbeutilizedinthenetworklayertoimproveend-to-endthroughputinasystememployingmulti-pathrouting.

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Figure5. Maximumend-to-endthroughputversusrouteselectionrationforroute1athighdensitynetwork. Figure5. Maximumend-to-endthroughputversusrouteselectionrationforroute1atlowdensitynetwork.

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Inthischapter,weshowthatsimulcastingisaneffectivetechniquetoimprovethroughputefciency,whichismeasuredasthethroughputperunitenergy,andproposesomedistributedpowercontrolapproachestofurtherimprovethethroughputefciencyofsimulcasting.Theadaptationofthetransmissionpowerandspacingofpointsintheconstellationareconsideredinordertoimprovethroughputefciency.Inthepowercontrolschemethatweconsider,thetransmissionpowerisadaptedbasedonthelinkdistanceoftheintendedreceiver.Wealsoconsidertheallocationofhighertransmissionpowersforradiossimulcasting.Simulationresultsshowthattheproposedapproachesimproveboththroughputandthroughputefciency. 6.1.1LinkAdaptiveTransmissionPower 71

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Figure6. Symbolmovementbyminimizedtransmissionpower. efciency,whichisdenedasthethroughputperunitenergy[ 60 ].Figure 6 illustratesthesignalconstellationchangebylinkadaptivetransmissionpowerforsimulcasting.Ebas;o,Eadd;o,andOffset orepresenttheoriginal,beforepowercontrol,energyforthebasicmessage,energyfortheadditionalmessage,andoffsetangle,respectively.Ebas;p,Eadd;p,andOffset prepresentthepower-controlledenergyforthebasicmessage,energyfortheadditionalmessage,andoffsetangle,respectively. 4 ,fairnessshouldbeinterpretedinmulti-facetedway.So,inthisChapter,weinvestigatethefairnessdescribedinChapter 4 whenunequaltransmissionpowerisapplied.

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Figure6. Unequaltransmissionpowerallocation. Figure 6 illustratestheunequaltransmissionpowerallocationscheme.Inthegure,dlanddmindicatethelinkdistancesfromthetransmittertotheless-capableandmore-capablereceivers,respectively.Ptindicatestransmissionpowerforunicasting,andPt;bandPt;aindicatethetransmissionpowerforbasicmessageandadditionalmessage,respectively,whenaradioissimulcasting.Hereand,,arepowercontrolfactorforsimulcastingandunicasting,respectively. 6 and 6 illustratethetransmissionpowerallocationforunicastingandsimulcasting,respectively.WeconsideronlythepathlossincomputingminimumtransmissionpowerPt,Pt;b,orPt;atoachieveatargeterrorprobabilityatareceiverinanAWGNchannelwithoutconsiderationofinterference.Thenthecomputedminimumtransmissionpowerisunequallyadjustedbypowerweightsandforunicastingandsimulcasting,respectively.TheweightedtransmissionpowerPUandPSforunicastingandsimulcasting,respectively,areconstrainedsuchthatthetransmissionrangebypowercontrolwillnotbeovertheoriginaltransmissionpowerrangeR,whichfordiscussionpurposewenormalizeto1.0.WealsonormalizetheoriginaltransmissionpowerPo,whichisrequiredforatargeterrorprobabilityattheboundaryR,as1.0.InFigure 6 ,RMisthetransmissionrangeforanadditionalmessage,sotheradiounicastingexistsintherangebetweenRMandR.RUisthelimitthatthetransmissionrangeweightedby

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Figure6. Diagramoftransmissionpowerrangeforunicasting. isnotoverRwhenaradioisinsideoftherange.So,whenaradioisoutsideofRU,thevalueofshouldbeadjustedsoasnaltransmissionrangeisnotoverR.InFigure 6 ,RSisthetransmissionrangeforbasicmessageandisthelimitthatthetransmissionrangeweightedbyisnotoverRwhenaradioisinsideoftherange.So,whenaradioisoutsideofRS,thevalueofshouldbeadjustedsoasnaltransmissionrangeisnotoverR. LetAbetheeventthatareceiverradioisintherangebetweenRMandRU,and A:RU
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Figure6. Diagramoftransmissionpowerrangeforsimulcasting. thepowerweightfactorforsimulcasting,,isPS=8><>:S=p B:s>RS; A:RU<>:;B:sRS^sn; B:s>RS;

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where^s=8><>:dl;forbasicmessagedm;foradditionalmessage: LetZbesignaltointerferenceandnoiseratio(SINR)atthereceiver.Then,Z=8><>:Sr;S PSef=Sete

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Figure 6 showsthesimulationresultsforlinkthroughputin(a),linkthroughputefciencyin(b),end-to-endthroughputin(c),andend-to-endthroughputefciencyin(d).Theresultsindicatethatlinkthroughputaswellasthroughputefciencycanbeincreasedbyproperlyallocatingtransmissionpower.Forthelinkandtheend-to-endthroughputs,theperformancesincreaseasbothandincrease,andatthevaluesover3,theyarealmostsaturated.Forthelinkandtheend-to-endthroughputefciencies,theperformancesarenotsosensitivetoasto,buthaveagreaterdependenceon.Byallocatingthetransmissionpowerunequallywithpowerallocationweightsof=1:0and=2:5,thelinkandtheend-to-endthroughputefcienciesincreaseabout34:4%and34:3%,respectively,withdegradationof17:8%and15%forthelinkandtheend-to-endthroughput,respectively.Dependingontheapplications,theweightscanbechosentoprovideatradeoffbetweenthroughputandthroughputefciency.Forexample,byallocating=1:6and=2:5,thelinkandtheend-to-endthroughputefcienciesincreaseabout15:6%and16:0%,respectively,withdegradationofonly6:7%and4:0%forthelinkandtheend-to-endthroughput,respectively,comparedtothemaximumvalueswefound.

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Figure6. Throughputandthroughputefciencybyunequaltransmissionpoweralloca-tion. Figure 6 showsthesimulationresultsofMMIin(a),UFIwithF=0:0in(b),UFIwithF=0:5in(c),andUFIwithF=1:0in(d)asdiscussedinChapter 4 .FairnessintermsofMMIdecreasesfrom0:22to0:05asdecreasefrom2:4to1:0overtherangeofgreaterthan2.IntermsofUFI,itdecreasesfrom0:75to0:60atthesamevariationofand.AllthefairnessindexwhichincludetheMMIandtheUFIswiththreedifferentFhassimilarpatterns.Thatmeanstheunequaltransmissionpowerallocationdoesn'tsignicantlyaffectthetradeoffbetweenservicefairnessandeffortfairness.

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Figure6. Fairnessbyunequaltransmissionpowerallocation.

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Weintroducedtheuseofsimulcasttransmissiontechniquesforadhocnetworks.Weappliedacross-layerapproachinwhichthelink-andnetwork-layerprotocolsweremodiedtoeffectivelyutilizethenewcapabilitypresentedbysimulcasting.Weproposedsomemodicationstotherouting,packet-selection,andback-offalgorithms.Theper-formanceofsimulcastsignalingwasanalyzedandsimulatedforanetworkthatemploysslottedALOHA.WepresenteddetailedresultsontheeffectsofvaryingtheoffsetanglewhennonuniformQPSKisusedforsimulcasting.Weshowedthatwecannotsimplyincreasethesignalconstellationsizetoalargerconstellationwithuniformspacingwithoutseverelyaffectingthenetworkconnectivityandend-to-endthroughput.Theanalyticalandsimulationresultsconrmthatbychoosingthesimulcastingparametersappropriately,simulcastingcansignicantlyimprovebothlinkandend-to-endthroughputforstaticnetworksattheexpenseofaslightdecreaseinnetworkconnectivity. Unequalresourceallocationswerestudiedtoeffectivelyutilizesimulcastingcapability.First,modicationstotheback-offparametersweresimulated.Apriority-basedMACprotocolwasinvestigatedinwhichtheretransmissionprobabilitieswereincreasedforthoseradiosthathaveamore-capablereceiveranddecreasedforthoseradiosthathaveonlyless-capablelinks.Increasingtheprioritywasfoundtoallowahigheraveragelinkthroughputtobeachievedathighaverageattemptrates.Second,weinvestigatedrandommultiplerouteselectionbasedonthesimulcastingcapabilitiesoftheradiosalongtworoutesinasystemthatemploysmulti-pathrouting.Thesimulationresultsshowthattheend-to-endthroughputwassubstantiallyincreasedbyusingmultipleroutesandassigninggreatertransmissionratesalongthemore-capableroute.Third,unequaltransmissionpowerforsimulcastingwasinvestigated.Thesimulationresults 80

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showthatthroughputandthroughputefciencydenedasthroughputperunitpowerconsumptionareincreasedbyassigningrelativelyhighertransmissionpowertotheradiosimulcasting.Overall,unequalresourceallocationforsimulcastingincreasesthroughputandthroughputefciencyatacertainexpenseoffairness.

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[28] M.Isaka,M.P.C.Fossorier,R.H.Morelos-Zaragoza,S.Lin,andH.Imai,Multi-levelcodedmodulationforunequalerrorprotectionandmultistagedecoding-partII:Asymmetricconstellations,IEEETrans.Commun.,vol.48,pp.774-786,May2000. [29] E.G.Larsson,Unitarynonuniformspace-timeconstellationsforthebroadcastchannel,IEEE.Commun.Letters,vol.7,pp.21-23,Jan.2003. [30] YunLiandAnthonyEphremides,SimpleRateControlforFluctuatingChannelsinAdHocWirelessNetworks,IEEETrans.Commun.,vol.53,No.7,pp.1200-1209,Jul.2005. [31] C.-K.Toh,WirelessATMandAd-HocNetworks:ProtocolsandArchitectures.Kluwer,1997. [32] A.KumarandJ.Kleinberg,Fairnessmeasureforresourceallocation,inProc.IEEESymposiumonFoundationofComputerScience,2000,pp.568-578. [33] H.SuzukiandF.A.Tobagi,Fairbandwidthreservationschemewithmulti-linkandmulti-pathroutinginATMnetworks,inProc.ofIEEEINFOCOM,1992. [34] P.NarvaezandK.Y.Siu,EfcientAlgorithmforMulti-PathLinkStateRouting,ISCOM'99,Kaohsiung,Tiwan,1999. [35] S.VutukuryandJ.J.Garcia-Luna-Aceves,ASimpleApproximationtoMinimum-DelayRouting,SIGCOMM'99,Sept.1999. [36] D.ThalerandC.Hopps,MultipathIssuesinUnicastansMulticastNext-hopSelection,IETFRFC2001,2000. [37] L.KleinrockandJ.A.Silvester,Optimumtransmissionradiiforpacketradionetworksorwhysixisamagicnumber,inProc.IEEENat.Telecommun.Conf.,Dec.1978,pp.4.3.1-4.3.5 [38] HideakiTakakiandL.Kleinrock,Optimaltransmissionrangesforrandomlydistributedpacketradioterminals,IEEETrans.Commun.,vol.COM-32,pp-246-257,Mar.1984. [39] T.C.HouandV.O.K.Li,Transmissionrangecontrolinmultihoppacketradionetworks,ioninmobilewirelessnetworks,IEEETrans.Commun.,vol.COM-34,pp-38-44.Jan.1986. [40] E.S.SousaandJ.A.Sivester,Optimumtransmissionrangesinadirectsequencespreadspectrummultihoppacketradionetwork,IEEEJ.Select.AreasCommun.,vol.8,No.5,pp.762-771,June1990. [41] E.M.Royer,P.M.Melliar-Smith,andL.E.Moser,AnanalysisoftheoptimumnodedensityforAdhocmobilenetworks,inProc.IEEEICC2001,vol.3,pp.857-861

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KiungJungreceivedtheB.S.andM.S.degreesinElectronicMaterialEngineeringfromKwangwoonUniversity,Seoul,Koreain1988and1990,respectively,andtheM.S.degreeinElectricalandComputerEngineeringfromUniversityofFlorida,Gainesville,FL,in2001.From1990to2002,hewaswithElectronicsandTelecommunicationsResearchInstitute(ETRI),Taejon,Korea,wherehewasmainlyinvolvedintheprojectofdevelopingTDX-10digitalswitchingsystem,andCDMAMobileCommunicationSystem.Hiscurrentresearchisonwirelesscommunicationwithemphasizingphysicallayersignaling,applicationoferrorcontrolcoding,adhocnetwork,collaborativecommunications,cross-layer(physicalMAC)designinad-hocnetwork. 87


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SIMULCASTING USING SLOTTED ALOHA IN AD-HOC NETWORKS


By

KIUNG JUNG

















A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA


2006



































Copyright 2006

by

Kiung Jung


















To my parents ..
















LIST OF TABLES


Table page

2-1 Routing table for radio A in Figure 2-4 . . . . . 17

2-2 Example packet buffer for radio A for network shown in Figure 2-4. ....... 19

3-1 Position of radios in ten-node network in Fig. 2-3 . . . . 41
















LIST OF FIGURES
Figure page

2-1 Simple scenario illustrating simulation at the link level. . . . 10

2-2 Nonuniform 4-PSK that achieves different levels of error protection for each bit. 11

2-3 Link capabilities for a ten-node wireless network. Solid lines indicate less-
capable links. Dashed lines are more-capable links. (a) NW1: For degrada-
tion of 0.5 dB and disparity of 9.1 dB (b) NW2: For degradation of 0.3 dB
disparity of 11.4 dB . . . . . . . 14

2-4 Example link map for a four-node wireless network . ..... ... 17

3-1 Example route for estimating end-to-end throughput. . . . 25

3-2 End-to-end throughput for simulcasting in geometric distribution for the num-
ber of hops at 1 2, andn 2 . . . . . . 30

3-3 End-to-end throughput for simulcasting in geometric distribution for the num-
ber of hops at 1 4, and n 2 . . . . . . 31

3-4 End-to-end throughput for simulcasting in geometric distribution for the num-
ber of hops at 1 8, and n 2 . . . . . . 31

3-5 End-to-end throughput for simulcasting in geometric distribution for the num-
ber of hops at 1 2, and n 4 . . . . . . 31

3-6 End-to-end throughput for simulcasting in geometric distribution for the num-
ber of hops at 1 4, andn 4 . . . . . . 32

3-7 End-to-end throughput for simulcasting in geometric distribution for the num-
ber of hops at 1 8, andn 4 . . . . . . 32

3-8 The maximum end-to-end throughputs for simulcasting with various network
density As in geometric distribution for the number of hops, at the expected
value of the number of hops = 4, and propagation constant n 2. . 33

3-9 The maximum end-to-end throughputs for simulcasting with various network
density As in geometric distribution for the number of hops, at the expected
value of the number of hops = 4, and propagation constant n 4. . 34

3-10 End-to-end throughput for simulcasting in Poisson distribution for the num-
ber of hops at n 2 . . . . . . . . 36










3-11 End-to-end throughput for simulcasting in Poisson distribution for the num-
ber of hops at n 4 . . . . . . . . 36

3-12 The maximum end-to-end throughputs for simulcasting with various network
density As in Poisson distribution for the number of hops, at the expected value
of the number of hops 7 = 4 and propagation constant n = 2. . . 38

3-13 The maximum end-to-end throughputs for simulcasting with various network
density As in Poisson distribution for the number of hops, at the expected value
of the number of hops 7 = 4 and propagation constant n = 4. . . 38

3-14 Throughput in AWGN for the network of nodes that is illustrated in Fig.3.
For NW1, the degradation is 0.5dB, and the disparity is 9.1 dB. For NW2, the
degradation is 0.3dB and the disparity is 11.4dB. . . . . 46

3-15 Network degree as a function of 0 for simulcasting with nonuniform QPSK in
a wireless ad hoc network with random node placement. . . . 46

3-16 Network connectivity as a function of 0 for simulcasting with nonuniform
QPSK in a wireless ad hoc network with random node placement. .. . 47

3-17 Proportion of nodes with a more-capable link as a function of 0 for simulcast-
ing with nonuniform QPSK in a wireless ad hoc network with random node
place ent . . . . . . . . . 47

3-18 Link throughput for unicasting and simulcasting with nonuniform QPSK with
0 = 25 degrees in a wireless ad hoc network with random node placement. 48

3-19 Maximum link throughput for simulcasting with nonuniform QPSK as a func-
tion of the offset angle 0. . . . . . . . 48

3-20 Average number of hops in a route for simulcasting with nonuniform QPSK
as a function of the offset angle 0 . . . . . . 49

3-21 Maximum (over all attempt rates) end-to-end throughput for simulcasting with
nonuniform QPSK as a function of offset angle 0. . . . . 49

3-22 Link throughput in AWGN for a mobile network of 15 radios with degrada-
tion of 0.5dB and disparity of 9.1 dB by the time stationary random waypoint
sim ulation . . . . . . . . . 50

3-23 End-to-end throughput in AWGN for a mobile network of 15 radios with degra-
dation of 0.5dB and disparity of 9.1 dB by the time stationary random way-
point sim ulation . . . . . . . . 50

4-1 Maximum link throughput by PRB with various aA values in random net-
work topology as the function of offset angle 0. . . . . 56










4-2 Maximum end-to-end throughput by PRB with various aA values in random
network topology as the function of offset angle 0. . . . . 57

4-3 Min-max fairness by PRB with various aA values in random network topol-
ogy as the function of offset angle 0 . . . . . 57

4-4 Utility based fairness by PRB with various aF and aA values in random net-
work topology as the function of offset angle 0. . . . . 58

5-1 Packet transmission from source radio to randomly selected route based on
simulcasting capability . . . . . . . 60

5-2 Topology 1 for unequal random route selection based on simulcasting capability. 61

5-3 Topology 2 for unequal random route selection based on simulcasting capability. 62

5-4 Topology 3 for unequal random route selection based on simulcasting capability. 62

5-5 Markov status diagram for the number of packets in a queue. . ... 63

5-6 Link model 1 for analyzing queue status in random route selection based on
simulcasting capability. The relay radio doesn't have a more capable link. 64

5-7 Link model 2 for analyzing queue status in random route selection based on
simulcasting capability. The relay radio has more capable links, but not on the
rou te . . . . . . . . . 6 5

5-8 Link model 3 for analyzing queue status in random route selection based on
simulcasting capability. The relay radio has more capable links, and one of
them is included on the source side of the route. . . . . 65

5-9 Link model 4 for analyzing queue status in random route selection based on
simulcasting capability. The relay radio has more capable links, and one of
them is included on the destination side of the route. . . . 66

5-10 Link model 5 for analyzing queue status in random route selection based on
simulcasting capability. The relay radio has more capable links, and two of
them are included at the both of source and destination sides of the route. 67

5-11 Maximum end-to-end throughput versus route selection ration for route 1 at
high density network . . . . . . . 70

5-12 Maximum end-to-end throughput versus route selection ration for route 1 at
low density netw ork . . . . . . . 70

6-1 Symbol movement by minimized transmission power. . . . 72

6-2 Unequal transmission power allocation. .................. .. 73

6-3 Diagram of transmission power range for unicasting. . . . 74











6-4 Diagram of transmission power range for simulcasting. ...... . 75

6-5 Throughput and throughput efficiency by unequal transmission power alloca-
tio n . . . . . . . . . . 7 8

6-6 Fairness by unequal transmission power allocation...... . . 79
















Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

SIMULCASTING USING SLOTTED ALOHA IN AD-HOC NETWORKS

By

Kiung Jung

August 2006

Chair: John M. Shea
Major Department: Electrical and Computer Engineering

Previous studies used unequal error-protection techniques to improve the throughput

of a wireless communication system in which a transmission is received by several radios

with different capabilities. These capabilities may correspond to differences in path

loss, fading, or interference. By taking advantage of the broadcast nature of the channel,

additional messages for the more-capable receivers can be included on transmissions

to the less-capable receivers at little cost (in terms of required energy at the transmitter

or error probabilities at the receivers). This technique has been termed simulcasting or

multicast signaling.

We consider this technique in an ad hoc network. This technique impacts link

throughput, end-to-end throughput, and network connectivity. First, we investigated

the basic properties of simulcasting, including how the choice of parameters for the

simulcasting technique affects several key network performance metrics. The results

show that a properly chosen simulcasting technique can improve the link and end-to-end

throughput in ad hoc wireless networks with only a slight degradation in other metrics

such as connectivity. Next, we propose cross-layer techniques for unequal resource

allocation to improve network performance when using simulcasting. We then propose to










allocate the channel more often to radios that can simulcast. This unequal channel access

is achieved by a simple modification to the back-off parameter in the MAC algorithm. We

then consider the distribution of traffic over multiple routes according to the simulcasting

capabilities of the radios along the routes. Finally, we propose schemes to adapt the

transmit power and signal constellation shape based on the channel conditions to the

intended receivers. Results show that these cross-layer approaches effectively enhance the

performance of simulcasting in wireless ad hoc networks.
















CHAPTER 1
INTRODUCTION

In most ad hoc wireless networks, a radio's neighbors often vary considerably in

their ability to communicate with that radio because of differences in channel conditions,

such as propagation loss and interference levels. In unicast transmissions, in which a

single transmitter communicates with a single receiver, the transmitter can compensate

for these variations in capability by using adaptive signaling if the channel conditions

are accurately known. However, the shared channel is not necessarily used effectively

because a signal that is intended for one radio may also be received by other radios in

the system that have much better link conditions than the original destination receiver.

We refer to such radios as more-capable radios. In this scenario, additional messages

could be included for the more-capable radios at little expense to the original destination

of the unicast transmission. Similarly, broadcast transmissions, which are intended

for all of a radio's neighbors, are often required for network maintenance in ad hoc

networks. Broadcast transmissions are generally ineffective in their use of the shared

communication medium because the transmissions must be designed to allow reception

by the least-capable of a radio's neighbors. Thus, for any broadcast transmission there are

often many more-capable receivers that could successfully receive additional messages

that are simultaneously transmitted with the broadcast message.

The concepts behind simultaneous transmissions schemes were originally explored

in the context of broadcast channels by Cover and Bergmans [1], [2]. Pursley and Shea

previously showed that modulation and coding schemes can be modified to allow the

inclusion of additional messages for more-capable receivers at very little cost to the

performance at the less-capable receiver [3]-[6]. In these papers, the term multicast

signaling is used to refer to such techniques. However, in ad hoc networks, multicasting










refers to a process that is primarily associated with the network layer in which a single

message is delivered to multiple destinations, not all of which are necessarily neighbors

of the source radio. In this dissertation, we refer to our techniques as simulcasting to

distinguish them from multicasting and to convey their ability to simultaneously transmit

multiple messages to different neighboring radios of a transmitter. Previous work shows

that nonuniform phase-shift-key (PSK) constellations provide a simple and effective

way to convey multiple messages from a single transmitter to two receivers of different

capabilities [3]-[6].

Unlike the previous work, which investigated the physical-layer design and per-

formance of simulcasting schemes, we propose to investigate the opportunistic use of

simulcasting in wireless ad hoc networks. We consider the necessary modifications to the

higher-layer protocols to fully utilize the additional capabilities provided by simulcasting.

For complete cross-layer design of such a wireless communication system with simul-

casting, the link- and network- layer protocols including the packet selection algorithm,

routing protocol, and collision resolution algorithm should be appropriately designed.

The design of the simulcasting scheme will impact many aspects of network performance

including link and end-to-end throughput, network connectivity, and route length. We

investigate the optimal signal spacing for nonuniform quadrature phase-shift-keying

(QPSK) for randomly distributed radios.

We consider a system that uses slotted ALOHA [7]-[11] for channel access.

The routing algorithm used is a minimum-hop routing algorithm that is modified to

incorporate the simulcasting capability. The packet selection mechanism is also modified

to provide efficient use of the simulcasting capability. We use nonuniform PSK to

show how the design of the simulcasting technique affects link throughput, end-to-

end throughput, and network connectivity. We first present analytical and simulation

results for random topologies with our simple "good/bad" channel model and with

mobility. For the simple "good/bad" channel model, in which we do not consider any










interference, whether two radios are neighbors depends only on if one of the radios is

in the transmission range of the other. In the "good/bad" channel model, the collision

occurs when linked radio(s) to a receiver transmit(s) a packet simultaneously when the

receiver receives another packet. The results indicate that simulcast transmission can

improve the link and end-to-end throughputs in wireless ad hoc at a small cost to network

connectivity.

We investigate three cross-layer approaches to improve network performance when

simulcasting is used. First, we propose to adapt the parameters of the MAC protocol

based on simulcasting capabilities. A radio that can simulcast to its neighbors can

transmit two packets per slot, whereas a radio that cannot simulcast can only transmit

one packet per slot. In the terminology of [12], the simulcasting radio requires less effort

to transmit a packet than the unicasting radio. Thus, to improve link throughput, more

channel resources should be allocated to simulcasting radios. We use Dianati et al.'s

notion of fair share to determine the back-off parameters at different nodes to provide

a balance between channel allocation that ignores effort and service based allocation

[13]. These unequal back-off parameters can improve link throughput at the expense

of fairness in the view point of eveness. For instance, the parameters can be such that

a few radios will nearly always be able to transmit while the other radios are blocked.

The link throughput increases because there are few collisions, but the network becomes

useless as the end-to-end throughput decreases and most radios are unable to transmit any

packets. Therefore, in comparing different back-off parameters, we also consider both the

fairness provided and end-to-end throughput. We present fairness results using the typical

min-max fairness index [14] and the utility-based fairness index introduced in [13].

Second, we consider how to take advantage of the simulcasting capability on a route

to reduce queueing delay and improve end-to-end throughput. Because radios that can

simulcast packets send more packets per transmission opportunity, it maybe appropriate

to route more packets along routes with more more-capable links and with a greater










number of radios with more-capable links. We propose a simple scheme in which packets

are distributed unequally across two routes according to a Bernoulli random process.

We evaluate the effect of different choices for the Bernoulli parameter on the end-to-end

throughput and delay for several network topologies. The results show that unequal

distribution of the packets over the two routes offers the best performance in terms of

end-to-end throughput and delay.

Third, we investigate adapting the transmission power and offset angle of the simul-

casting modulation based on the number of neighbors of the transmitter. For systems in

which the transmitted power is fixed, the transmission power under a certain radio density

decides the network degree, which is defined as the average number of neighbors of a

radio in a network, where two radios are neighbors if they can communicate directly.

When the radios in a network use a large transmission range, the required number of hops

for a transmitted packet to reach a destination from a source radio will be small. However,

a large transmission range also results in a large network degree. From the perspective

of a receiver, as interference from neighboring radios becomes large, the probability of

packet collision will increase. The link throughput can be improved by decreasing the

transmission power and hence the network degree. However, for low network degree, the

probability that the network is connected will be small and the number of hops in a route

will be large. So, the tradeoff among the effect of transmission range on probability of

packet collision, number of hops in a route, and network connectivity is a critical problem

to solve in an ad-hoc network.

We investigate schemes to adapt the transmission power and signal constellation

shape based on the distances between the transmitter and the receiverss. We consider

unequal power allocation so that radios that can simulcast have a higher probability of

packet success than radios that cannot simulcast. We present analytical and simulation

results. The results indicate that the reduced transmission energy and the unequal










interference assignment schemes improve link and end-to-end throughput as well as

throughput efficiency, which is defined as throughput per unit energy consumption.

As prior works of simulcasting, Cover [1] considers the simultaneous communi-

cation of information from one source to several receivers and gives upper and lower

bounds on the capacity region of simultaneously achievable rates. Bergmans [2] considers

several transmitters using a superposition scheme that pools the time, bandwidth, and

power allocation of the transmitters. He determines the optimal set of rates simultane-

ously achievable.

Pursely and Shea have previously shown that modulation and coding schemes can be

modified to allow the inclusion of additional messages for more-capable receivers at very

little cost to the performance at the less-capable receiver [3]-[6]. This general technique

is called multicast signaling and uses unequal error-protection signaling to transmit

multiple messages that require different receiver capabilities for accurate reception. As

previously mentioned, we use the term simulcasting for these techniques to distinguish

them from network- or application- layer multicasting. In [3]-[6], the authors focus on

techniques that utilize nonuniform phase-shift keying (PSK) because of its simplicity,

adjustability, and constant envelope. This previous works is focused on physical-layer

considerations, primarily signal design and link-level performance, although simulcast

transmission also requires interactions with the higher layers in the protocol stack. They

also introduce and analyze performance measures that are useful in characterizing the

performance tradeoffs in simulcast packet transmission.

Simulcast transmission can be achieved through a variety of other unequal error-

protection techniques. These include other types of nonuniform modulation [15]-[18],

unequal error-protection coding [19]-[24], combined modulation and coding schemes

[25]-[28], [5], and space-time coding [29]. Any of these techniques can be used for

simulcasting in ad hoc networks. The nonuniform PSK constellations described in

this dissertation have several advantages over nonuniform QAM, proposed in [20],










[25] for unequal error protection, for mobile wireless communication channels. For

example, PSK constellations have constant envelopes, and knowledge of the received

signal amplitude is not required for their demodulation. Such knowledge is required

for optimum demodulation of QAM signals, but the received signal amplitude may be

unknown and difficult to estimate. Thus, for mobile wireless communication, nonuniform

PSK may often be more appropriate than QAM. Convolutional coding and nonuniform

QAM constellations have also been investigated in [20], [25], where the goal is to provide

unequal error protection for multiresolution source-encoded analog information. Li

and Ephremides studied pulse amplitude modulation (PAM) and QAM for passive rate

adaptation in the presence of channel fluctuation due to fading [30]. The goal of the work

is the tradeoff between more reliable detection of fewer bits and less reliable detection of

more bits.

Wireless network has become increasingly popular since their emergence in the

1970s. The ad hoc net work is one of the two variations of mobile wireless networks.

The ad hoc network is infrastructureless and the other one is infrastructure. For an ad

hoc network, all radios have mobility and can be connected dynamically in an arbitrary

manner without the use of fixed routers. Interconnections between radios can be changed

continuously. Characteristics of an ad hoc network such as arbitrary spatial distribution

and dynamic connectivity result in communication link disparities that are exploited in

the dissertation via simulcast signaling.

In the simulcasting schemes considered in this dissertation, some radios are more

capable than other radios in that they can transmit two packets per slot instead of one, so

it makes sense to have an unequal allocation of resources in the network to utilize this

capability. The fairness of such an unequal allocation should be assessed. There are many

approaches previously proposed for measuring fairness [12]-[14], [32]. The "Min-max

index" [14] is a well known index for fairness which indicates evenness of a system, but it

may not be good in indicating how the system uses available resources effectively when










different radios have resource utilizing capabilities. Recently, Dianati et al. proposed a

"Utility Fairness Index(UFI)" in [13]. The UFI is parameterized to allow a trade-off

between service fairness and effort fairness.

Various protocols for multipath routing has been researched [33]-[36]. Multipath

routing exploits network resources effectively to maximize utilization. It reduces blocking

probability and aggregates bandwidth on various paths so as to allow higher transmission

rate to a network compared to single path [33]. In this dissertation, multipath routing is

applied to exploit the simulcasting capability of radios on a route. By assigning higher

transmission rates to routes with more simulcasting capability, the end-to-end throughput

and delay can be improved.

Many researchers have investigated the optimal transmission range in ad hoc

networks [37]-[43]. Kleinrock et al. [37], [38] interpret transmission power in an ad hoc

network in terms of the number of neighbors of a radio and suggest a "magic number"

of neighbors based on maximizing a packet's expected forward progress toward its

destination. Their analysis indicates that a radio should transmit with a power so that

the average number of neighbors within transmission range is six [37] or eight [38] to

maximize overall network throughput. One of the critical assumptions in their analysis

is that the network will not become disconnected because of power control. However, as

the packet transmission power decreases, the number of neighbors of a radio decreases,

and thus the network may have a high probability of becoming disconnected. Gupta

and Kumar consider the effect of transmission power on connectivity and determine

the critical power to guarantee connectivity of the overall network [42]. In [43], they

show that if r is the range of transmission, then the relaying burden due to increment

of the number of hops grows like O(r-1), but the interference grows like O(r2). Thus,

the net effect (the product) is a growth of O(r). Their analysis implies that the smaller

transmission power the better in terms of maximizing network throughput. However,

if one chooses too small a range, then the network may loose connectivity. So, they










conclude that the optimal transmission power in an ad hoc network should be determined

based on network connectivity.

Along with the optimal transmission range, energy efficiency is one of the key

concerns in wireless communication systems. There has been a lot of research on

transmission power control schemes over the past few years [44]-[50]. The chief

motivation of these schemes is to mitigate the effect of interference that one user can

cause to others. The results range from obtaining distributed power control algorithms to

determining the information theoretic capacity achievable under interference limitations

[51], [52]. Whereas most power control schemes aim at maximizing the amount of

information sent for a given average power constraint, a recent study [53] considers

minimizing the power subject to a specified amount of information being successfully

transmitted. Rather than minimizing power, [54] considers the question of minimizing

energy directly, and compares the energy efficiency, defined as the ratio of total amount

data delivered and total energy consumed, of several medium access protocols.
















CHAPTER 2
NETWORK MODEL AND PROTOCOLS FOR SIMULCASTING IN AD HOC
NETWORKS

Before developing the application of simulcasting in ad hoc networks, we first

provide an overview of the network model used in this research. The network model was

chosen to be as fundamentally simple as possible, while still providing insight into the

effects of using simulcasting. The system is a slotted transmission system, where we

assume that all radios are perfectly synchronized. The packet arrival process is modeled

by a Bernoulli random process. We assume that the radios have large packet buffers.

Multiple access is provided by slotted-ALOHA [9].

Our physical-layer models are also selected to avoid obscuring the effects of

simulcasting among other physical-layer phenomena. We begin by specifying some

maximum transmission range at which a basic message can be received with a target

error probability. Radios are considered to be neighbors if they are within that maximum

transmission range. A packet collision occurs whenever a radio transmits a packet

during a time slot and there is also a transmission by any of the neighbors of the packet's

designated recipient. We assume that signals from radios that are not neighbors can

neither be received nor cause a packet collision by interfering with transmissions from a

radio's neighbors. Furthermore, we assume that all collisions result in packet errors and

that there is immediate and perfect feedback on packets that collided or were otherwise

received in error. Retransmissions occur after a back-off period that is chosen according

to a geometric random variable, as discussed in Section 2.2.













8TX




Figure 2-1. Simple scenario illustrating simulation at the link level.


2.1 Simulcast Transmission

Simulcasting has the potential to increase the average link throughput by allowing

some radios to simultaneously transmit multiple packets to several different receivers

while using approximately the same network resources as are required to transmit a

single packet with unicasting. The easiest way to visualize this is in terms of propagation

distance, which generally results in lower average received energy at the more-distant

receivers. Figure 2-1 shows this in the case of two receivers.

Suppose that the power spectral density of the noise is the same at the two receivers

and the only difference in received power is due to the difference in propagation dis-

tances. Then receiver 2 will be more-capable than receiver 1 in the sense that the higher

signal-to-noise ratio at receiver 2 will allow it to successfully recover a message transmit-

ted with a higher code rate or higher-order modulation than can be successfully recovered

at receiver 1. Thus, in the terminology of [3]-[6], receiver 1 is a less-capable receiver,

and receiver 2 is a more-capable receiver. By using unequal error-protection modulation

or coding, each time that the transmitter sends a message to receiver, it can include

extra messages that can be recovered by receiver 2 because of its higher signal-to-noise

ratio. In this case, the message intended for receiver 1 is called a basic message, and the

messages intended for receiver 2 are called additional messages. We refer to these as the

class of the messages.

Simulcast transmission can be achieve in many ways but depends on the ability to

achieve a different level of error protection for the basic message than for the additional

messages. One simple way that this unequal error protection can be achieved is through













S2 (10) \ So (00)

I i
S!I
S3 (11) S, (01)



Figure 2-2. Nonuniform 4-PSK that achieves different levels of error protection for each
bit.

nonuniform modulation [3], [4]. For instance, one of the simplest examples is the

nonuniform quadriphase-shift key (QPSK) constellation illustrated in Figure 2-2.

For this constellation, the nonuniform spacing makes it much easier for a receiver to

correctly recover the first bit than the second bit. Thus, the first bit can be used to send a

basic message that is intended for a less-capable receiver or for all of a radio's neighbors,

while the second bit is used to convey an additional message that can only be recovered

by more-capable receivers. Thus, this technique can be used to simultaneously send two

packets in a single slot, effectively doubling the link throughput. However, the use of this

or any other simulcasting technique will result in some degradation in performance at the

less-capable receiver if the transmit power is unchanged.

In [3], [4], two important parameters are introduced that provide a simple physical-

layer characterization of simulcast transmission schemes that carry only two classes

of messages. The parameters are the degradation and the capability disparity. Both of

these parameters are typically specified in decibels. In general, these parameters must be

specified in terms of the target error probabilities for the basic and additional messages.

In this dissertation, the target error probabilities for these messages are assumed to

be equal. By using a simulcast signaling scheme instead of a traditional signaling

scheme that only conveys one basic message, the performance of the basic message










must be degraded. The degradation measures the additional amount of energy that must

be received to achieve the same performance for the basic message with a simulcast

signaling scheme as is achieved with a traditional signaling scheme. The capability

disparity, or simply disparity, is a measure of how much more capable a receiver must be

in order to recover an additional message in comparison to a receiver that only recovers

the basic message. It can be calculated as the amount of additional energy that is required

at a more-capable receiver to recover the additional message at the target error probability

in comparison to the amount of energy required at a less-capable receiver to recover

the basic message at the target error probability. In AWGN channel, for the same error

probabilities for both of basic and additional message, the degradation and the disparity

are given by for the offset angle 0 [4]. Typical values for the degradation and disparity

from [4] are 0.5 dB and 9.1 dB, respectively.


DdB(O) = 20loglo(sec0), (2-1)

6dB(O) = 20loglo(cot ). (2-2)

We begin by considering systems in which the transmit power is fixed, and the effects

of this degradation on network performance are investigated. Furthermore, we initially

assume that the simulcasting scheme is also not adapted to the network topology; in

other words, the offset angle 0 shown in Figure 2-2 is the same at all radios in the

network. In Chater 6, we consider adaptation of the signal constellation shape along

with the power in response to the channel conditions to the intended receivers. For most

simulcasting techniques, when the offset angle 0 is fixed, the performance degradation

to the less-capable receivers can be made very small while still achieving a significant

gain from transmissions to more-capable receivers. For example, if we consider only path

loss for the transmission of a packet, by the definition of degradation and disparity, the

transmission range for basic message, di, and additional message, dm, are given simply










from the transmission range of unicasting, du, as


d1(0) = d10-D(O)/10n, (2-3)

d, () = dl0O-'()/10". (2-4)

So, if the transmission range by unicasting, du, is 1, 000m under the assumption

that the propagation constant n is 4, we can gain 592.24m for the transmission range of

additional message at the expense of just 28.37m reduction for the transmission range

of basic message with 0.5 dB and 9.1 dB for values of the degradation and disparity,

respectively. Further discussion and examples are given in Section 3.1.

In order to be able to demonstrate the advantages and disadvantages of simulcasting

in the context of ad hoc networks, we employ the simple example of nonuniform

QPSK described above for the remainder of this dissertation. With this scheme, each

transmission can include at most two classes of message: a basic message packet and an

additional message packet. All packets are assumed to be of the same length.

In the context of an ad hoc network, the concepts of more-capable and less-capable

receivers must be extended, as each radio may act as a transmitter or receiver at different

times. When a radio is acting as a receiver, its capability level will depend on its link

(channel) from the transmitting radio. Therefore, we define the radio links as being

more-capable or less-capable links. For the results presented in this paper, we assume that

the only differences in link qualities are caused by differences in propagation distance.

This also implies that links are symmetric, so if the link from radio 1 to radio 2 is a more-

capable link, then so is the link from radio 2 to radio 1. Radios are able to discover the

capabilities of neighboring radios during network maintenance or during regular packet

transmission.

An example link map from our simulation is illustrated in Figure 2-3. Figure 2-

3 shows the link capabilities for two different values of degradation and disparity, as

explained below. The maps are based on typical degradation and disparity values from











(a) (b)

9 9
2 2




10 10

1 1

0 0
0 1 2 3 4 5 0 1 2 3 4 5
[Km] [Km]

Figure 2-3. Link capabilities for a ten-node wireless network. Solid lines indicate less-
capable links. Dashed lines are more-capable links. (a) NW1: For degrada-
tion of 0.5 dB and disparity of 9.1 dB (b) NW2: For degradation of 0.3 dB
disparity of 11.4 dB.


[4] and exponential path loss proportional to the fourth power of distance. The figure

illustrates the link capabilities for two scenarios: (a) NW1 is the case that 0 = 19.25

degrees, which yields a degradation of 0.5 dB and disparity of 9.1 dB, and (b) NW2 is the

case that 0 15 degrees, which yields a degradation of 0.3 dB and disparity of 11.4 dB.

The thin lines represent the less-capable links, and the thick lines represent the more-

capable links. In scenario 2, NW2 has a more stringent requirement on the degradation,

which results in a higher disparity. Thus NW1 has a larger number of more-capable links

than NW2.

The use of simulcasting also causes some performance degradation to the less-

capable links. For a fixed transmission power, the degradation results in the transmission

range for the basic message being smaller for simulcasting than for unicasting. Thus,

some links may break, which will cause two main effects to the network. First, a link may

be critical to network connectivity, and when that link breaks, the network will become

disconnected. Secondly, some routes may become longer because a node that is reachable

in a single hop with unicasting may no longer be directly reachable. The increase in the










length of routes will reduce the end-to-end throughput. The expected number of links that

break increases as the degradation increases, while the expected number of more-capable

links increases as the degradation increases (and the required disparity decreases). Thus,

the simulcast signaling scheme should be designed to ensure that the increase in link

throughput from having a greater number of more-capable links translates into an increase

in end-to-end throughput and that the impact on network connectivity is minimal. Results

on this tradeoff are given in Sections 3.3 and 3.5.

As previously mentioned, we assume that the basic and additional messages require

the same error probability. In fact, we consider a packet communication scheme in which

any packet may be transmitted as either a basic or additional message, depending on the

availability of more-capable links. The fact that a packet has been transmitted as one

class of message over a link does not affect the class to which it will be assigned on later

links. Thus, a packet may start out as an additional message, be transmitted as a basic

message over some intermediate links, and be sent over the final link to its destination

as an additional message. The only requirement that we place on the transmissions is

that additional messages should be transmitted whenever possible in order to improve

the network efficiency. This approach differs from the approaches in [3]-[6], in which

nonuniform signaling techniques are used to transmit different classes of multimedia

messages that may have different requirements on the packet error probability.

Each simulcast transmission contains two full packets, each of which has full

headers. Thus, when a radio detects a packet, it will attempt to demodulate and decode

the headers for both the basic and additional message. A receiver does not need to know

apriori whether a packet contains an additional message; if no additional message is

present, the receiver will not recover a valid header for that message (typically the CRC

will fail). If neither of the packets is intended for a radio, then as usual, the radio can turn

off its transceiver until the next slot to conserve energy. If either or both of the packets

is intended for a radio, then they will be recovered in the usual way. We note that we










assume that all nodes will listen to the headers at the beginning of each slot. If a sleep

schedule is employed to conserve energy at the radios, the performance of simulcasting

may be significantly degraded by a reduction of receivers with more-capable links that are

awake during any particular slot.

2.2 Medium Access Control

In the system that we consider, radios contend for the channel via slotted-ALOHA.

We assume that the radios have long packet buffers such that every radio will always have

a packet to transmit. When a radio suffers a collision, the radio will wait a random back-

off time that is selected according to a geometric distribution. When a radio is successful

in transmitting, it may immediately transmit in the following slot. For the system

parameters that we consider, the performance is dominated by the effects of contention.

Thus, the way that the probability of retransmitting in each slot (or equivalently, the

average number of slots that the system will back off after a collision) is determined can

have a significant effect on the performance of the system. For the results presented in

the Chapter 3, each radio uses the same retransmission probability in any time slot. We

show the simulcasting performance when we assign back-off time for retransmission

unequally in Chapter 4. By adjusting this transmission probability, different average

network attempt rates, G, can be obtained.

2.3 Routing Algorithm

In this dissertation, we consider a form of minimum-hop (min-hop) routing [31] in

which the routing tables are modified to effectively utilize the capability of simulcasting.

Our approach to including simulcasting in the network is designed to allow the transmis-

sion of an additional message whenever possible. As previously mentioned, we allow any

packet to be sent as an additional message if an appropriate link is available. Whether

a packet can be sent as an additional message at any node will depend on the packet's

destination and the link capability of the next link on any minimum-hop route to that

destination.




















Figure 2-4. Example link map for a four-node wireless network.

Table 2-1. Routing table for radio A in Figure 2-4.

Destination Next Hop No. of Hops
Normal B B 1
Entires C C 1
D B 2
Simulcast C C 1
Enties D C 2


The new routing tables are a superset of the standard min-hop routing tables. The

standard min-hop routing table is always used for selection of the next-hop radio for the

basic message. To this routing table is added a set of simulcast entries. For a routing table

entry to be a valid simulcast entry, it must have a first hop that is a more-capable link

and it must be a minimum-hop route. It is not required that the links after the first link

be more-capable links. Thus, as previously mentioned, a packet that is transmitted as an

additional message over one link may be transmitted as a basic message over other links,

and vice versa.

To illustrate the modified routing table, consider the simple four-node network

shown in Figure 2-4. In this figure, the more-capable links are shown as dashed lines, and

the less-capable links are shown as solid lines. Table 2-1 shows example routing table

for radio A. The routing table is formed as follows. The simulcast entries are specified

first. Note that there will be no simulcast entry for destination radio B because there is

no minimum-hop route for which the next hop from A is a more-capable link. However,

there are simulcast entries for destination radios C and D. Both destinations C and D can










be reached in the minimum number of hops by first sending the packet over the more-

capable link A to C. The routing table entries for the basic messages are labeled "Normal

Entries" in Table 2-1 and are selected from the possible min-hop routes in the usual

way. For the results presented in this section and Chapter 3, the normal and simulcast

routing-table entries for a particular destination are allowed to be identical, even if other

min-hop routes exist.

In Chapter 5, we consider how simulcasting impacts performance under multipath

routing. Because radios that can simulcast a packet send more packets per transmission

opportunity, it may be appropriate to route more packets along routes with more more-

capable links.

2.4 Packet Selection Algorithm

The packet-selection algorithm should also be modified to ensure efficient use of

the simulcasting capability. At each time that a radio transmits, it will attempt to utilize a

more-capable link if one is available. By doing so, the link throughput can be increased

because two packets are sent simultaneously by a radio in a single packet transmission

interval whenever possible. An important feature of the simulcasting technique is that the

basic and additional messages in a transmission do not have to have the same next-hop

radio. Thus, for the network illustrated in Figure 2-4, radio A can simultaneously send a

basic message to radio B and an additional message to radio C.

The packet-selection algorithm determines which packet(s) in a radio's buffer will

be transmitted in any given packet transmission interval. The packet-selection algorithm

used in this dissertation is a modified first-in, first-out (FIFO) algorithm that ensures that

more-capable links are utilized whenever possible. It functions in the following way. A

radio that has at least one more-capable link will first try to select from its queue the first

packet that can be sent as an additional message. This will not necessarily be the first

packet in its queue. After the additional message (if available) is selected, then the first

packet from the remaining set of packets will be sent as the basic message. In the absence










of mobility, packets intended for a particular destination will be transmitted in order,

thereby minimizing the impact of simulcasting on the out-of-order arrival problem.

Table 2-2. Example packet buffer for radio A for network shown in Figure 2-4.

Packet ID Destination
1 B
2 B
3 D
4 C


A brief example serves to illustrate this packet selection algorithm. Suppose that

radio A's packet buffer contains four packets, as shown in Table 2-2. The first and the

second column of the table show the packet IDs and the destinations of each packets,

respectively. Then during the first interval in which radio A transmits, it first searches its

buffer for the first packet that can be sent as an additional message. To do so, it compares

the destination for each packet to the set of destinations in the simulcast entries in the

routing table. In this case, the first packet that can be sent as an additional message is

packet 3, which, based on the simulcast entry for destination D in Table 2-1, will be sent

to next-hop radio C. Packet 1 is then selected for transmission as the basic message. So,

when radio A transmits, it will simultaneously send messages to radios B and C using

simulcast transmission. On radio A's next transmission, packet 4 will be selected as

the additional message, and packet 2 will be sent as the basic message. Note that this

simulcast transmission scheme is significantly different than multicasting that occurs

at the network or application layers, in which one message is distributed to a group of

different receivers. In simulcasting, multiple messages are simultaneously transmitted to a

one or more neighbors of the transmitting radio.
















CHAPTER 3
PERFORMANCE OF SIMULCASTING IN AD HOC NETWORKS WITH FIXED
BACK-OFF ALGORITHM

In this chapter, we analyze the link and end-to-end throughputs for simulcasting

in an ad hoc network. We consider a fixed network topology with a noise-free channel.

Thus, for unicast signaling, the link throughput depends on the probability of collision

and the time between transmission attempts, and end-to-end throughput depends on the

link throughput and the number of hops the messages must travel. For simulcasting,

these throughputs will also depend on the simulcasting parameters through the number

of messages that can be sent as additional messages and the changes in the number of

hops, which are caused by changes in the maximum transmission distance for the basic

messages.

The analysis that follows is for three scenarios. In the first, the network topology is

fixed, which allows the topological parameters to be easily calculated. In the second, N

radios are uniformly distributed over an area A. Edge effects are neglected in the calcu-

lations. In the third scenario, the nodes are distributed according to a two-dimensional

Poisson point process over an infinite plane.

3.1 Network Parameters

We begin by considering the effects of simulcasting on the network topology. In

particular, we consider two network parameters that have a significant effect on the link

and end-to-end throughputs. The first is the network degree, Ndeg, which is the average

number of neighbors of a radio. Here, we define a neighbor as any radio that is directly

connected to the radio of interest by either a less-capable or more-capable link. The

second parameter is R,, which is the proportion of radios with more-capable links for

fixed networks and the probability that a radio has at least one more-capable link for










random networks. For the network topology illustrated in Figure 2-3, Rm = 7/10 for

D = 0.5 dB(08 19.25 degrees), and Rm = 4/10 for D = 0.3 dB (0 = 15 degrees).

For our simple "good or bad" channel model, since the only factor that affects

the signal-to-noise ratio is exponential path-loss (no random fading or shadowing is

considered), whether two radios share a link depends only on the distance between the

radios. Let du denote the maximum link distance for unicast signaling, and let d (0) and

dm(0) denote the maximum link distances for less- and more-capable links, respectively.

These distances can be calculated as in Section 2.1,


d1(0) = dulO-D(O)/ln,

dm(O) = dul0-5(0) /n,


where D(O) and d(O) are the degradation and disparity (both in decibels), respectively.

For nonuniform QPSK, these simplify to


d,(0) = du[cos(0)],

d(O) = du[sin(0),


where n is the path-loss exponent. It is interesting to consider the coverage area of a

transmitter, which is defined as the area of the region in which radios will have a link

to that transmitter. Then the coverage areas for the basic and additional messages are

given by 7rd12 and 7rd,2, respectively. Consider the coverage area as a proportion of the

coverage area for unicasting, 7rdu2. For 0 = 10 degrees, the proportions of coverage for

the basic and additional messages are given by 0.985 and 0.174, respectively. Thus, for

a reduction in coverage area of 1.5%, 17.4% of the coverage area supports more-capable

links. If 0 = 20 degrees, the coverage area for the basic message is 6.0% less than that

of unicasting, but the coverage area for the additional message is increased to 34.2% of

unicasting. Thus, by appropriately choosing 0, the coverage area for additional message










transmission can be made reasonably large without significantly reducing the coverage

area for the basic message.

Consider an arbitrary node in a network with nodes uniformly distributed over area

A. Let pl and pm denote the probabilities that some other node is connected to that node

by a less-capable link and more capable link, respectively. Then pl(0) [ [d1(O)]2/A, and

Pm(0) [dm(0)]2/A, where the approximations come from ignoring the edge effects of
the finite area over which the nodes are placed. Then the network degree is given by


Ndeg(0) = (N l)pl(0)
S(7) [d,()]2
(N 1)
A2
=Nd, (O) [cos(O)]4/n. (3-1)

For the simulation results in Section 3.5, the transmission distance is close to the

dimension of the simulation area, so the edge effect makes (3-1) yield inaccurate

estimates ifpl(0) and d1(0) are determined as specified above. However, we find that

(3-1) gives a good approximation if the correct value of Ndeg(0) is found via simple

topological simulation; therefore, we use this approach for the results in Section 3.5. The

proportion of radios with more-capable neighbors can also be simply calculated by

Rm(0) = [1 pm(O0)]

Now consider an infinite network with nodes distributed in a plane according to a two-

dimensional Poisson point process. Let A denote the expected number of neighbors for

unicasting. I.e., the expected number of radios in the area of size 7rdu2 is A. Then for

simulcasting with parameter 0, a radio is a neighbor of a particular radio if it is within

distance d (0) = du[cos 0]2/,. The neighbors of a radio lie within an area 7rdu2 [os 0]4/T,

and thus the number of neighbors is a Poisson random variable with expected value

Ndeg() = A[cos 0]4/ Then, the probability that a radio has at least one more-capable










link is


Rm(0) = P(> 1 neighbors in area d (sin 0)4/')

S 1 P( 0 neighbors in area 7rd2 (sin 0)4/~)

1 e-A(sin 8)4/n


3.2 Link Throughput

We apply the conventional techniques for link-throughput analysis of slotted

ALOHA [9]. Let E[Di] be the expected value of the delay (in terms of number of slots)

required for a packet transmitted by radio i to be successfully received by the designated

next-hop radio. Then the link throughput at radio i, Si, is defined by Si = 1/E[Di]. The

average link throughput for a network of N nodes is given by

N
S i. (3-2)
i= 1

We evaluate (3-2) for two different scenarios. In unicast transmission, simulcasting

is not allowed, and each radio sends at most one packet to one next-hop radio during a

time slot. For simulcast transmission, two packets can be sent simultaneously by a radio

during a time slot if that radio has any more-capable links, as described in Section 2.1.

The link throughputs for unicast and simulcast transmission are denoted by Su and Ss,

respectively.

The link throughput will depend on several parameters. Define Gi to be the attempt

rate of the ith radio. Let Su,i and Ss,i(0) be the link throughput at radio i for unicast

and simulcast transmission with phase offset 0, respectively. The throughput at radio i

depends on the number of neighbor radios Bi(0), the probability of collision Ci(0), and

the retransmission rate for unsuccessful packets Ri(0).

3.2.1 Unicast Transmission

For unicast transmission, a radio sends only a single message in a slot, and that

message is intended for only one of its neighbors. In this case, the throughput for the ith










radio can be determined as follows. The attempt rate must satisfy Gi = Su,i + Ri, where

Ri = GiCi. Then the throughput is given by


S'u, = G (1 C,), (3-3)

where, if radio i has B, neighbors and G is the average attempt rate over all radios, then


C, C (3-4)
j= 1

Here Cij is the probability of collision at the jth neighbor of radio i, which is given by


S (1- G)B', (3-5)


where Bij is the number of neighbors of the jth neighbor of radio i. The result in (3-4) is

approximate because it assumes equal probability of transmission to each neighbor, and

(3-5) is approximate because the offered load from the potential interferers is replaced by

the average offered load. The average link throughput Su can be approximated by using

(3-3)-(3-5) in (3-2).

3.2.2 Simulcast Transmission

We consider the link throughput of simulcasting using nonuniform QPSK with

parameter 0. First consider the throughput for the basic message. Although the number

of neighbors that can be reached by direct transmission is reduced, the interference range

stays constant. Thus the link throughput for the basic message will be approximately

equal to the link throughput for unicasting, Su,i. Now consider the additional message.

For the case of long packet buffers, if the packet generation rate is sufficiently high

then a radio that has a more-capable link will always have a packet that can be sent

as an additional message. Then the link throughput for the ith radio with simulcast

transmission, Ss,i(0) can be approximated as Ss,i(0) a 2Su,i if radio i has a more-

capable link and Ss,i(O) = Su,i, otherwise. For a network of N nodes, and let M(O, i)

be an indicator function such that M(O, i) = 1 if radio i has a more-capable link and










M(O, i) = 0 otherwise. Then the throughput for simulcast transmission for the fixed

network can be approximated by


S [2Su,iM(O, i) + S,( M(O, ))], (3-6)
j=1

and for the random network,

S a E[Su,M(0, i) + Su,(1 M(0, i))1

Su,[1 + Rm(0)]. (3-7)

So for long packet buffers and high packet generation rates, simulcast transmission

has the capability to improve the link throughput by a factor of up to Rm(0). However,

it is not clear that this increase in link throughput will translate into a corresponding

increase in end-to-end throughput. This is the topic of the next subsection.

3.3 End-to-end Throughput

We consider the end-to-end throughput for simulcasting as a function of 0. Then

the end-to-end throughput for unicasting can be found by setting 0 = 0. The end-to-end

throughput over T time slots is defined by

N (T)
Sete ~
T

where ND (T) is the number of packets that reach their final destination in T time

slots. We are interested in steady-state conditions and consider the expected value of

Sete, which is not a function of T. Consider a generic route, as shown in Figure 3-1.

S A -- B C -( D


Figure 3-1. Example route for estimating end-to-end throughput.


We analyze the throughput by considering the delay required to transmit two packets

(corresponding to the two types of messages) over such a route. Under the best-case










scenario, one of the packets can be sent as an additional message over each of the more-

capable links (shown as dashed lines). Then for each less-capable link (shown as solid

lines), the expected delay is 2E[Di] for the two packets. For each more-capable link, the

expected delay is only E[Di] for the two packets. Thus for the example in Figure 3-1,

the expected delay for both packets to reach the destination (not counting queuing delays)

is 6E[D], where E[D] is the expected delay at an arbitrary node. Then the average

end-to-end throughput for each packet is

2 su
St- 6E[D] 3

Let H(O) be a random variable representing the number of hops in an arbitrary route.

Note that as 0 changes, the distribution of H changes, as discussed in Section 2.1. Then in

general, the end-to-end throughput can be approximated by

N 2P(H(O) = i) (3-8
Sete S iR,(0)E[D] + 2i[1 R,(O)E[D]'

This expression is approximate because the distribution of the number of hops for

the packets that take a more-capable link may be different than for the packets that do not

take any more-capable link. For instance, more-capable links may be used more often

than less-capable links to transmit a packet to its destination.

Note also that St,(0) is a non-linear function of R, (0). Unlike the link throughput,

the end-to-end throughput does not increase in direct proportion to R,(0). Note that the

summation term will decrease as 0 and Rm(0) increase, as the number of hops increases.

Then if the distribution of the number of hops is constant, a 50% increase in end-to-end

throughput requires at least R,(0) = 2/3. For 0 large enough to satisfy this requirement,

the expected number of hops may be significantly larger than for unicasting, thereby

reducing the gain from the increase in link throughput.

We investigate the value of 0 that maximizes Set, by estimating the distribution

of H(0) via empirical and analytical distributions. The results using the empirical










distribution are given in Section 3.5. Here we investigate the performance under two

simple analytical distributions for H(O).

Consider a network of radios distributed according to a Poisson point process over

a plane. Consider first the distribution for H(O), the number of hops in a route when

unicasting is employed. We wish to use distributions such that:

1) 3 k Vi > k,j > k, P(H(O) =i) > P(H(O) > j) for all i < j, and

2) P(H(O) =i) > 0, i=1,2,...

The first criterion provides locality. Beyond some local neighborhood, it is more

likely for a packet to have a closer destination than one further away. The second criterion

allows any radio in the network (other than the source) to be a destination for the packet.

We first analyze the performance for a geometric distribution for the number of

hops. Suppose first that H(0) has geometric distribution with parameter a, and let

H = E[H(O)],

a(l-a- 1i=1,2,....
P(H(0) =i) i=1,2...
0, otherwise.

Then, the distribution of H(O), 0 < 0 < 45 degrees, should be geometric with parameter

3(0), 3(0) < a. To determine a reasonable estimate for 3(0), consider the probability

of having a 1-hop route for unicasting P(H(0) = 1) = a. The probability that the

destination radio is still within communication range when simulcasting is employed is

(rd')/{(rd') = (cos0)4/". There are four cases to consider for a particular link along a

route in going from 0 = 0 to 0 > 0:

1) The link is still within communication range, so the route is not affected.

2) The link is not within communication range, but another link can be used to achieve

the same number of hops in the route.

3) The link is not within communication range and so the number of hops in the route

increases by one.










4) The link is not within communication range and that link failure requires significant

rerouting, resulting in the number of hops in the number of hops in the route

increasing by more than one.

Based on the probability of being able to reach the same 1-hop destination above, we

model H(O) as a geometric random variable with parameters 3(0) = a(cosO)4/". This

most accurately models cases 1 and 3 above. We note also that cases 2 and 4 will have

opposite effects on H(0), so this model seems reasonable, if perhaps a bit optimistic

because of the large impact of case 4. For this distribution E[H(O)] = H(cos 0)-4/.

For the infinite network, Rm(O) is the probability that a radio has at least one

more-capable link and is given by


Rm(O) = 1 Pb(O radios in area 7rdi(sinO)4/)

Let A' = (sinO)4/n Then, as previously calculated the proportion of the radios with

more-capable link(s) Rm(0) in Section 3.1,


Rm(O) 1 e-

1 e-A(sin)4/". (3-9)


The average end-to-end throughput can then be approximated by

SU a(cosO)4/ [1- c(cosO)4/n]i-1
Sete t (3-10)
1 0.5[1 e-A(sino)4/]

From [55],

In(1 + z) = z -z2 + 4 .....
n1 ) r2 3 4

Then,


In(t) -(1 q)' (3-11)
i= 1










Letting q = c(cos 0)4/n and using (3-10) and (3-11) yields

5____ S^ ____ a(cosO)4/ [ 1
Sac SU a(cos)4/" In ]. (3-12)
1 0.5[1 e-A(sino)4/] 1 a(cos0)4/ n a(cos)4/ "

Although (3-12) is too complicated to allow the maximum value to be found via direct

analysis, the maximum value can easily be found via numerical methods.

The results of this numerical optimization are shown in Figures 3-2-3-4 for n = 2

and in Figures 3-5-3-7 for n = 4. The results in Figures 3-2-3-4 are for H = is equal

to 2, 4, and 8, respectively, as are the results in Figures 3-5-3-7. The graphs labeled (a)

illustrate Gete, the maximal gain in the end-to-end throughput from using simulcasting

instead of unicasting, Get(0) = Sete()/Sete(0). The graphs labeled (b) illustrate the

values of 0 that maximizes Gete, which is defined as optimal offset angle 0o. The results

indicate that the expected gain in the end-to-end throughput for simulcasting varies from

20.9' to 62..'', for n = 2 and from 60.1 to 90.0' for n = 4, where A varies from 4

to 12. The maximum gains from simulcasting are achieved when the distributions favors

shorter routes ( = 2) and larger number of neighbors (A = 12). This is reasonable

because the impact of simulcasting on increasing route length will be smallest when the

routes are shortest for unicasting under assumption of full connectivity of network. When

A is large, the probability of having a more-capable neighbor increases, and thus more

radios can transmit two messages in each interval. The simulcasting gain is greater for

n = 4 than n = 2 because of the way that the exponential path loss translates differences

in energy into differences in distance. The energy for the basic and additional messages

scale as cos20 and sin20, respectively. However, the coverage areas for the basic and

additional messages scales as (cos0)4/" and (sinO)4/", respectively. Consider 0 = 30

degrees. For n = 2, the coverage areas for the basic and additional messages are 7.'.

and 25'., respectively, of that for unicasting. For n = 4, the coverage areas for the basic

and additional messages are 86.1.'. and 50' ., respectively, of that of unicasting. Thus for











(a) (b)
1.7 35
34
a 1.6
W c 33
-1.5 32
32

I 1.4 31
M 0 30
1.3
29
1.2 28
4 6 8 10 12 4 6 8 10 12
X X

Figure 3-2. (a) Maximal gain in end-to-end throughput, Gete, and (b) optimal offset
angle(degree), 0o, to maximize Gete, at 1 2, and n 2.


n = 4, the coverage areas for both the basic and additional messages are significantly

greater than for n = 2 at the same value of 0.

The 0o varies from 27.5 degrees to 34.5 degrees for n = 2 and from 18.9 degrees

to 32.2 degrees for n = 4. It decreases as A increases. That is, the 0o is maximum for

distributions favoring shorter routes and fewer neighbors and is minimum for distributions

favoring longer routes and many neighbors. It means that, as we discussed, under the

assumption of full connectivity of network, the effect of increasing route length by

employing simulcasting is larger with longer routes. Having more neighbors increases

the probability of being able to perform simulcasting for even small 0. So, in order to

maximize the end-to-end throughput, smaller 0 is required to avoid increasing route

length by employing simulcasting as the number of neighbors increases.

Figures 3-8 and 3-9 show the maximum end-to-end throughputs versus Os for

various As at n = 2 and n = 4, respectively, over the attempt rate G of 0 to 1 with H = 4.

The unicasting throughput Su is assumed as unity in this results. As A increases from 4 to

12, the 0m which maximizes the maximum end-to-end throughput decreases from of 35

to 25 and from 30 to 15 degrees for n = 2 and n = 4, respectively. For n = 4, the value

of 0o is smaller and decreases in a larger range as A increases compared to for n = 2. In

other words, for n = 4, 0o is more sensitive to A compared to for n = 2. This is because,





















4 6 8 10 12
X


Figure 3-3.


(a) Maximal gain in end-to-end throughput, Gete, and (b)
angle(degree), 0o, to maximize Gete, at = 4, and n 2.


optimal offset


4 6 8 10 12
X


4 6 8 10 12
X


Figure 3-4.


(a) Maximal gain in end-to-end throughput, Gete, and
angle(degree), 0o, to maximize Gete, at = 8, and n


optimal offset


4 6 8 10 12


6 8 10 12


X X

Figure 3-5. (a) Maximal gain in end-to-end throughput, Get,, and (b) optimal offset
angle(degree), 0o, to maximize Gete, at 1 2, and n 4.


1.6

- 1.5

(_ 1.4
E
S1.3

1.2
r


1.6

S1.5
(.
(0 1.4
E
7 1.3

1.2


.



































4 6 8
x


10 12


4 6 8 10 12
x


Figure 3-6.



















1.9
0)
(0

S 1.8

E
m 1.7
7


(a) Maximal gain in end-to-end throughput, Gete, and (b) optimal offset
angle(degree), 0o, to maximize Gete, at = 4, and n 4.















(a) (b)


4 6 8
X


Figure 3-7.


10 12


4 6 8
X


10 12


(a) Maximal gain in end-to-end throughput, Gete, and (b) optimal offset
angle(degree), 0o, to maximize Gete, at = 8, and n 4.


1.9
0)
(.

1.8

E
m 1.7












0.9

0.85

0.8 X=12
X=1 0
0.75- k=8 k=
k=6
0.7-

0.65

S0.6-

0.55

0.5

0.45 -

0.4
0 5 10 15 20 25 30 35 40 45
Offset Angle, 0

Figure 3-8. The maximum end-to-end throughputs for simulcasting with various network
density As in geometric distribution for the number of hops, at the expected
value of the number of hops I 4, and propagation constant n 2.


at a same value of 0, the coverage areas for both of basic and additional messages when

simulcasting is employed are greater for n = 4 than for n = 2, and when A is large, the

probability of having a more-capable neighbor increases.

The Maximum end-to-end throughput increases from 0.55 to 0.73 and from 0.72

to 0.87 for n = 2 and n = 4, respectively, as A increases from 4 to 12. Note that in

Figures 3-8 and 3-9, for n=4, the maximal end-to-end throughput achieved is greater

compared to for n = 2 as previously discussed.

The second distribution that we consider for the number of hops is a modified

Poisson distribution. The Poisson distribution has probability mass at zero, which is

undesirable for our application, so we let H(0) 1 be Poisson with expected value 7.

Then,

S-7,7k k=1,2,...
P(H(O) k)= (k)
0, otherwise,


























20 25
Offset Angle, 0


Figure 3-9. The maximum end-to-end throughputs for simulcasting with various network
density As in geometric distribution for the number of hops, at the expected
value of the number of hops = 4, and propagation constant n 4.


and H = A + 1. Following similar argument as for the geometric distribution, we let

H(O) 1 be Poisson with expected value of 7(0) given by 7/(cos 8)4/". As for the

geometric distribution, E[H(O)] = H(cos 0)-4/n. The average end-to-end throughput can

then be approximated by


Sete


Sue-s(0) 0
1 0.5[1 e-A(sino)4/n] k1


7(0)k-1
k(k- 1)!


Note that


7(0)k-1
4f(k -lt)!


71 7k1


Thus,


Su
1 0.5[1 e-A(sino)4/](0)










and


Gete S(O)

(cos())4/
1- 0.5[1 e-Asin")4 "

Note that, for the Poisson distribution for the number of hops, the simulcasting gain is

independent on the average number of hops.

Figures 3-10 and 3-11 show the analytical results for the end-to-end throughput

of simulcasting under the Poisson distribution for the number of hops for n = 2 and for

n = 4, respectively. The graphs labeled (a) illustrate Gt,, and the graphs labeled (b)

illustrate the values of 0, according to various network densities.

The results indicate that the expected gain in the end-to-end throughput for simul-

casting varies from 10.(' to 46. !' for n = 2, and from 53.1 to 86.1 for n = 4

for A in the range of 4 to 12. The maximum gains from simulcasting are achieved when

the distributions favors larger number of neighbors (A = 12) as the case of geometric

distribution, but the gains are 5% to 10% smaller than for the geometric distribution. This

is reasonable because the Poisson distribution has lower probability of choosing shorter

routes than the geometric distribution, which significantly impacts on the end-to-end

throughput. The simulcasting gain is also greater for n = 4 than n = 2 for the same

reason described for the geometric distribution.

The 0, varies from 25.3 to 27.8 degrees for n = 2 and from 26.7 to 17.3 degrees

for n = 4. These values are about 5 degrees smaller than for the geometric distribution

for both of n = 2 and n = 4. The intuitive explanation is that the effect of increasing

route length by employing simulcasting with relatively large 0 is more significant for the

Poisson distribution.

Mostly, the 0, decreases as A increases. However, notice that 0, is no-monotonic for

n = 2. This is because the probability of choosing a short route is low for the Poisson

distribution. For the geometric distribution, 0, is maximal with the shortest routes and the












(a) (b)
1.5 28

co 27.5
S1.4 -
27




1.2
0 25.5

1.1 25
4 6 8 10 12 4 6 8 10 12
X X

Figure 3-10. (a) Maximal gain in end-to-end throughput, Gete, and (b) optimal offset
angle(degree), 0o, to maximize Gete, at n = 2.

(a) (b)
1.9 28

co 26
1.8 _
(,9 24

D 1.7 22
F0
E 20

0 18

1.5 16
4 6 8 10 12 4 6 8 10 12
X X

Figure 3-11. (a) Maximal gain in end-to-end throughput, Get,, and (b) optimal offset
angle(degree), 0o, to maximize Gete, at n = 4.


fewest neighbors because the effect of increasing route length by employing simulcasting

is less with shorter routes and with fewer neighbors, under the assumption of full network

connectivity. However, for the Poisson distribution, the effect increases route length when

simulcasting is used with a small number of neighbors because of the smaller probability

of choosing a short route. For n = 2, it is more apparent because the probability that

the destination radio is still within communication range when simulcasting is employed

(cos 8)4/n is smaller for n = 2 than for n = 4.

Figures 3-12 and 3-13 show the maximum end-to-end throughputs for simulcasting

in Poisson distribution for the number of hops according to various Os along with various










As for n = 2 and n = 4, respectively, over the G of 0 to 1 with 7 4. The unicasting

throughput Su is assumed as unity as of geometric distribution case.

As A increases from 4 to 12, the 0m which maximizes the maximum end-to-end

throughput decreases from 25 to 30 and from 15 to 25 degrees for n = 2 and n = 4,

respectively. As the geometric distribution, for n = 4, the end-to-end throughput is more

sensitive to A compared to for n = 2. The maximal end-to-end throughput ranges from

0.33 to 0.46 and from 0.33 to 0.58 for n = 2 and n = 4, respectively. The overall pattern

is similar and can be explained with the same reason as for the geometric distribution

case.

In comparison with the geometric distribution, for the Poisson distribution, the

achieved maximal end-to-end throughputs and the values of 0o to achieve them are less

and the range of 0o over the domain of A is relatively smaller. As previously discussed,

it is because the Poisson distribution has lower probability of choosing short routes and

the variation of Poisson distribution is less than for the geometric distribution. Based

on the analysis and the numerical results of the end-to-end throughput, if the number of

hops follows the geometrical distribution, a higher end-to-end throughput is expected,

and if the number of hops follows the Poisson distribution, a relatively stable end-to-end

throughput is achieved.

3.4 Mobility

The mobility model is an important issue in the study of mobile ad hoc networks.

Recent studies [56]-[59] report that in simulations of mobile ad hoc networks, the

probability distribution governing the movement of the nodes typically varies over time

and converges to a "steady-state", or stationary distribution.

Thus a simulation of a network of mobile radios often experiences a transitory

period before conveying to the steady state. One approach to deal with the fluctuating

conditions is to throw away the simulation data for some initial time period. A more

efficient alternative is to choose the initial locations and speeds of the radios from the


























X=10 \
X=8


0 35


0 5 10 15 20 25 30 35 40 45
Offset Angle, 0


Figure 3-12. The maximum end-to-end throughputs for simulcasting with various net-
work density As in Poisson distribution for the number of hops, at the
expected value of the number of hops 7 = 4 and propagation constant
n =2.




0.5
k= 12
/ =10

0.45- / =6
=4



0.4



T 0.35

LU


0.3



0.25
0 5 10 15 20 25 30 35 40 45
Offset Angle, 0


Figure 3-13. The maximum end-to-end throughputs for simulcasting with various net-
work density As in Poisson distribution for the number of hops, at the
expected value of the number of hops 7 = 4 and propagation constant
n = 4.










stationary distributions for the mobility model so that convergence is immediate and

no data needs to be discarded. However, because the initial location and speeds with

stationary distributions bring a centralized shape of distribution (the most convergent

speeds and the locations are gathered at a certain range of speed and location), it is hard

to see the effects of mobiles moving around in a large area. The uniformly distributed

"steady-state" needs to be studied.

We use the random waypoint mobility model, which is one of the most popular

mobility models for communication networks, for our simulation. In this model, an

initial point po and a destination point pl are assigned uniformly in the area A, and

speed is assigned to a mobile at the initial point uniformly in an arbitrary range of speed.

The initial and destination points are chosen independently. Once the mobile reaches

the destination, a new destination is chosen uniformly, independently of all previous

destinations and speeds. Mobiles may pause when it reaches each destination, or they

may immediately move to the next destination without pausing. If they pause, the pause

times are chosen independently of speed and location.

The random waypoint model is a commonly used mobility model in the simulation

of ad hoc networks. However, it has problems such as the decay of average speeds as the

simulation progresses, a difference between the initial and the final nodes distribution. It

is known that the spatial distribution of network nodes moving according to this model

is, in general, nonuniform. For example, with this model, a mobile spends more time at

lower speed, therefore it is more likely to be sampled at low speed. The initial mobile

position is uniform in the area A, however, with time, the distribution of mobile positions

tends to be more dense towards the middle of the area.

To overcome the problems of random waypoint model, J. Le Boudec [59] recently

presented how to obtain the stationary distribution of location and speeds for the simu-

lation of mobility model based on palm caculus. By palm calculus, the histogram of the

terminating or non-terminating ergodic simulation can be predicted. It is applied to the










random waypoint model to achieve an initial distribution equal to the stationary distri-

bution of random waypoint. Simply, how to generate the stationary distribution of the

previous and next waypoint and the current mobile position can be obtained as follows.

Let A be an upper bound on the diameter of area A.

1. do

draw M1 lid Unif (A)

draw V Unif[0, A]

until V < || 1 ML,,|

Prev(t) = .. and Next(t) = M1

2. Draw U Unif [0, 1]

3. M = (1 U) L,, + UM

3 and M1 are initial and next waypoint, respectively. Note that the initial waypoint of

time stationary waypoint simulation is obtained by the above procedure, not by drawing

a point uniformly in A. Once a node reaches the initial next waypoint, the later next

waypoint is chosen uniformly. In our simulation, the mobile velocity is always constant.

So, we don't consider time stationary distribution of the mobile speed. There are 15

mobiles in the area of 5Km x 5Km. Mobile speed is constant as 30Km/h. Warmed-up

and final status are at 1,000 and 15,000 time slots of running, respectively. Throughput is

counted after warmed-up status. The simulation result is shown in Section 3.5

3.5 Simulation and Results

The performance of simulcasting in ad hoc networks is evaluated using the analytical

expressions described previously in this chapter and Monte Carlo simulations. We

used a custom simulation programmed in MATLAB because this provided us a simple

approach to develop a simulation that incorporates the ability to transmit multiple packets

to multiple different receivers in a single transmission slot and to adapt the link- and

network-layer protocols to take advantage of the simulcasting capability. We begin by

considering the link throughput for the fixed network topology of ten nodes illustrated










Table 3-1. Position of radios in ten-node network in Fig. 2-3

Node ID X position (km) Y position (km)
1 1.15 2.00
2 1.53 3.59
3 1.95 2.55
4 3.50 2.25
5 2.40 3.21
6 2.55 2.12
7 3.71 2.57
8 3.10 4.01
9 2.58 4.18
10 2.06 2.00


in Figure 2-3. The positions of these radios are given in Table 3-1. The network

degree is 2.2. The link distances are figured out with incorporation of transmission in

additive white Gaussian noise (AWGN), where the bit error probability at the maximum

transmission range of 1 km is 10-4. It is assumed that the packet length is 1000 bits

and an error-control code is used that can correct up to 10 bit errors. For this case of no

mobility, we expect that there will be almost no performance degradation from the noise,

as the transmission range for nodes to be considered neighbors is such that the packet

error probability is very small. The simulation results match closely with the analytical

results.

The results in Figure 3-14 show the link throughput performance of the network as

a function of the average attempt rate. Solid lines represent the performance predicted

by the analysis from (3-2) to (3-5), and (3-7). The markers illustrate the performance

results from our simulation. The performance is illustrated for three different network

configurations. For the results marked "Unicast", the nodes are constrained to not employ

the simulcast signaling technique, and thus each node transmits at most one packet in

a time slot. For the results marked "Simulcast(NW1)", simulcast transmission is used,

where the more-capable links are determined based on a degradation of 0.5 dB and a

disparity of 9.1 dB.










The results marked "Simulcast(NW2)" illustrate the performance for a network

with fewer more-capable links because the required capability disparity is increased to

11.4dB, which corresponds to a degradation of 0.3 dB. The link throughput for these

fixed topologies with equal back-off times is illustrated in Figure 3-14. The results

indicate that simulcasting can significantly improve the throughput in the ad hoc network.

Next, let us consider a network with N = 15 radios placed uniformly over a 1km

by 1km area. We consider the simple good/bad channel model with a maximum link

distance for unicasting (or, equivalently, simulcasting with 0 = 0) of 381 m. We consider

first some basic network parameters as a function of the offset angle 0 of the nonuniform

QPSK used for simulcasting. The results in Figure 3-15 illustrate the network degree

(expected number of neighbors) as a function of the offset angle 0. The analytical results

are determined from (3-1). The simulation results are shown for two cases. The results

for "all networks" is the average over 100 random topologies. The results for "connected

networks only" shows the average network degree for 10 of the random topologies that

formed a connected network for all degrees. The results show the sensitivity of the

network degree to the parameter 0. For all networks, unicasting (0 0) yields a network

degree of approximately 4.5, while for QPSK (0 = 45 degrees), the network degree drops

to 3.4. We note that if we consider only connected networks, then the network degree is

biased above the value for all networks.

One of the primary effects of changes in the network degree is an impact on the

connectivity, which we define as the probability that every node has a route to every other

node in a randomly generated network. The connectivity is shown as a function of the

offset angle 0 in Figure 3-16. The unicast link distance of 381m was chosen because

it provides connectivity of approximately 0.9. The network connectivity decreases as 0

increases. However, for 0 < 25 degrees, the connectivity remains above 0.85. Thus, if 0 is

kept small, simulcasting can be used with relatively little impact on network connectivity.

As 0 approaches its maximum value of 45 degrees, the connectivity rapidly decreases to










approximately 0.66. Thus, it is not possible to switch to a uniform QPSK constellation

without a significant loss in network connectivity.

The results in Figure 3-17 show the expected proportion of radios that have a

more-capable link as a function of 0. As shown in Section 3.1, this parameter has an

important effect on both the link and end-to-end throughputs. The results show that as

0 increases from 0, the proportion of radios with a more-capable link increases rapidly.

The analytical expression (3-2) is shown to closely match the simulation results. There is

no significant effect on this parameter of only considering connected networks instead of

all randomly generated networks. At the previously mentioned value of 0 = 25 degrees,

the proportion of radios with a more-capable link exceeds 0.8. Thus, there is little to gain

from increasing 0 further, and any further increase comes at a significant expense in terms

of network connectivity, as shown in Figure 3-16.

We next restricted the simulations to 10 fixed topologies that are connected for all

0 < 0 < 45 degrees, which were randomly selected from the 100 randomly generated

topologies. In this way, we can be sure that we can calculate end-to-end throughput for

each network. However, the distribution of the nodes will no longer be uniform, which

will affect the results. Each topology still consists of 15 nodes distributed over a 1 km 1

km area, with maximum link distance of 381 m for unicasting. Each simulation consisted

of 1500 time slots after a 100 time slot warm-up period.

The results in Figure 3-18 show the average link throughput for unicasting and

simulcasting with offset angle 0 = 25 degrees for the networks described above. The lines

represent analytical results and the markers represent simulation results. The simulation

and analytical results differ slightly because the analytical results are for randomly

generated networks, but the simulation results are for a set of connected networks.

The results show that for 0 = 25 degrees, the maximum link throughput is almost

twice as high with simulcasting as can be achieved with unicasting. From Figure 3-

16, the network connectivity for 0 = 25 degrees is approximately 0.85 versus 0.9 for










unicasting, so the link throughput can be significantly increased with little cost to network

connectivity.

The results in Figure 3-19 show the maximum link throughput achieved as a

function of the offset angle Here, the maximum is taken over all possible attempt rates.

The line is the analytical result, and the circles are from simulations. Note that as 0

increases, so does the link throughput that can be achieved. This is reasonable because as

long as the network remains connected, each node will have at least one node to which it

can transmit. Furthermore, as 0 increases, the probability of collision goes down along

with the expected number of neighbors, and the number of nodes with more-capable links

goes up. The combined effect is that the maximum throughput with 0 = 45 degrees is

approximately 2.7 times higher than the maximum throughput with unicasting. However,

from Figure 3-16, we see that the network connectivity suffers greatly as 0 becomes

large.

In addition to the impact on network connectivity, increasing 0 also affects the

length of routes in the network, which may impact the end-to-end throughput. The

results in Figure 3-20 illustrate the average number of hops in a route as a function

of the offset angle. As 0 increases from 0 to 45 degrees, the average number of hops

increases from approximately 2.25 to 4.2. The number of hops increases rapidly as

0 increases beyond 20 degrees. The results in Figure 3-21 illustrate the maximum

average end-to-end throughput as a function of 0. Here, the maximum is over all attempt

rates. The solid line illustrates the analytical results (using the empirical values for

the expected number of hopes), and the simulation results are the circles. The results

show that the end-to-end throughput is a non-monotonic function of 0. The analytical

results are optimistic for 0 > 10 degrees. However, they do show the same trends as

the analytical results. We believe that the primary differences in the two curves come

from the fact that the simulation results are not for randomly generated networks because

we have enforced that the networks must be connected. The simulation results show










that the end-to-end throughput is maximized by 0 = 30 degrees. The end-to-end

throughput at 0 = 30 degrees is approximately 0.042 versus 0.027 for unicasting. Thus,

simulcasting results in an increase in end-to-end throughput of over 55%. If we use a

more conservative value of 0 in the range 20 < 0 < 25, then the end-to-end throughput

is still more than 40% higher than unicasting, while having a smaller impact on network

connectivity. Note that these values of 0 match closely with those found via analysis in

Section 3 for a infinite network with a geometric distribution for the number of hops in a

route.

We next investigate the effect of having out-of-date information about the network

links because of mobility. A radio's link information may indicate that a node is a

neighbor even though that a radio has moved out of range. Similarly, a radio may believe

that a link is a more-capable link even though the radio's movements have reduced the

capability of a link to an extent that the packet error probability over that link degrades

performance. We model these effects by only allowing for a periodic update of routing

tables. We assume a slot time of 20ms and a routing table update every 300 slots (6

s). Fifteen mobiles move around with constant velocities of 30, 50, or 100 km/hr in a

5Km x 5Km area. We employed the time stationary random waypoint mobility model

described above.

Figures 3-22 and 3-23 show the simulation results for the link and the end-to-

end throughputs, respectively. They show that the throughputs for both unicasting and

simulcasting degrade as velocities increase. However, simulcasting still provides a

significant throughput gain. As expected, higher mobility levels generally result in lower

throughput as routing table information is more likely incorrect. This is observed to be

especially true at high average attempt rates.



















Simulcast(NW1)


Simulcast(NW2)




Unicast


10-2
Average Attempt Rate


101 1V


Figure 3-14. Throughput in AWGN for the network of nodes that is illustrated in Fig.3.
For NW1, the degradation is 0.5dB, and the disparity is 9.1 dB. For NW2,
the degradation is 0.3dB and the disparity is 11.4dB.






4.8 Simulation results,
6 ,, connected networks only
4.6 "" /


4.42-

/4 '4
4
Simulation results, '* '"
3.8 all networks '*

3.6

Analysis
3.4

3.2

3
0 5 10 15 20 25 30 35 40 45
Offset Angle 0 (degrees)

Figure 3-15. Network degree as a function of 0 for simulcasting with nonuniform QPSK
in a wireless ad hoc network with random node placement.


0.2




5 0.15

I-
_ 0J
" 0.1


0
* \

















o0.95


o)


0.85
0

, 0.8

-c
o 0.75
0.


0.7
0)
C
( 0.65


0 5 10 15 20 25 30 35 40 45
Offset Angle 0 (degrees)


Figure 3-16. Network connectivity as a function of 0 for simulcasting with nonuniform
QPSK in a wireless ad hoc network with random node placement.






Analysis
70.8- "00

0.7
Simulation results,
a0.6 connected networks only

10.5 /

S0.4-
0. Simulation results,
a all networks
0.3

S0.2 -

0.1 -


0 5 10 15 20 25 30 35 40 45
Offset Angle 0 (degrees)

Figure 3-17. Proportion of nodes with a more-capable link as a function of 0 for simul-
casting with nonuniform QPSK in a wireless ad hoc network with random
node placement.


F


I


)















0.14


Simulcasting Analysis



Simulcasting Simulation


I-
C,
2 0.08



S0.06



0.04



0.02


Unicasting Analysis


10-1
Average Attempt Rate


Figure 3-18. Link throughput for unicasting and simulcasting with nonuniform QPSK

with 0 = 25 degrees in a wireless ad hoc network with random node place-
ment.






015-

014

Analysis s"
0 13- t

-oil
20112




0 019
< A\
E X\
I 009-

SSimulation
0 08 *' (random topology with full connectivity)

007 / A

006 -

005
0 5 10 15 20 25 30 35 40 45
Offset Angle 0 (degrees)


Figure 3-19. Maximum link throughput for simulcasting with nonuniform QPSK as a
function of the offset angle 0.










































5 20 25
Offset Angle 0 (degrees)


Figure 3-20. Average number of hops in a route for simulcasting with nonuniform QPSK
as a function of the offset angle 0.








005

Analysis

0 045



._ 004

LU
-4
S0 035 -



S003 (random topology with full connectivity)



0 025



0 5 10 15 20 25 30 35 40 45
Offset Angle 0 (degrees)

Figure 3-21. Maximum (over all attempt rates) end-to-end throughput for simulcasting
with nonuniform QPSK as a function of offset angle 0.

















02
-0- 30 [Km/h]- Unicasting
-n- 50 [km/h]- Unicasting
0 18 100 [Km/h]- Unicasting
-0- 30 [Km/h] Simulcasting
-i- 50 [km/h] Simulcasting
0 16 -- 100 [Km/h]- Simulcasting


0 12

0-
0 01

e 008
4


10
Average Attempt Rate


Figure 3-22. Link throughput in AWGN for a mobile network of 15 radios with degra-

dation of 0.5dB and disparity of 9.1 dB by the time stationary random

waypoint simulation.


-0- 30 [Km/h]- Unicasting
-a- 50 [km/h]- Unicasting
-*- 100 [Km/h]- Unicasting
0035 -e- 30 [Km/h] Simulcasting
-0- 50 [km/h] Simulcasting
-- 100 [Km/h]- Simulcasting


10
Average Attempt Rate


Figure 3-23. End-to-end throughput in AWGN for a mobile network of 15 radios with

degradation of 0.5dB and disparity of 9.1 dB by the time stationary random

waypoint simulation.
















CHAPTER 4
PERFORMANCE OF SIMULCASTING WITH ADAPTIVE BACK-OFF
ALGORITHMS FOR SIMULCASTING

When a radio suffers a collision, the radio will wait a random back-off time that is

selected according to a geometric distribution. If the average value of the back-off time

is specified as TB, then the radio will begin its retransmission in each of the following

slots with probability TB-1. So far, our study was based on assigning equal probability of

retransmission to every radio when a source radio recognizes that the transmitted packet

has collided with another transmission. In this dissertation, we investigate two approaches

to choose the parameter TB. In the first approach, the back-off time is equal for every

radio, named as "Equal Back-off (EQB)". The performance of simulcasting with this

scheme was already investigated in Chapter 3. The radios simulcasting can transmit two

packets while the radios unicasting can do just one packet per time slot, which means

resource utility available for the radios simulcasting can be up to twice that for the radio

unicasting. The second approach, the focus of this chapter, is named as "Priority Back-

off(PRB)". In PRB, the back-off time is chosen unequally to give higher retransmission

probabilities to radios simulcasting than to radios unicasting.

We investigate the fairness of each scheme in terms of the achieved throughputs

across the radios in the network. The most simple interpretation of the fairness is how

close the distribution is to even sharing of resources among all the radios in a network.

However, the concept of fairness is multi-faceted depending on its application. For exam-

ple, as defined in [13], in terms of the equality of each radio's link throughput, fairness

should be taken as evenness, defined as "service fairness", but in terms of maximization

of network throughput, it should be taken as each radio's effective utilization amount,

defined as "effort fairness". In this dissertation, Dianati et al.'s fair share allocation and










utility based fairness [13] are modified to allocate back-off time unequally according to
simulcasting capability, and to measure "service fairness" and "effort fairness" when PRB

is applied.

4.1 Priority Back-off

In this section, we modified Dianati et al.'s fair share allocation scheme [13] to
assigns a higher chance of retransmission in each slot to the radios that have more-

capable links. The normalized fair share resource allocation of radio i is defined as


S ( S, 1 )aA (4-1)

where Nt is the total number of radios, aA is a constant from 0 to 1, and

u) _[1 + m4(O)]
S[1 + mi()] (4-2)

Here, aA is used to trade off between service fairness and effort fairness. When aA = 0,

S~) is not sensitive to the effort fairness, and when aA 1, S') has maximum sensitivity
to the effort fairness. We consider aA = 0, 1/2, or 1 for our work, where aA = 0 gives
equal share amount, aA = 1/2 gives equal sensitivity to sharing the common resource

(service fairness) to using it efficiently (effort fairness), and aA = 1 gives maximized

sensitivity to effort fairness for resource allocation .Then,

S(- t-a A) _L + m =0,
Sa) -t Nt[l+R- (O)]
(a) S ( 1 A)- 1 2NA[ ,m i() 1
i,1 [ A + Nt[1+-R(A(0 ) -

We select the unequal back-off time Tf for PRB with simulcasting based according

to

TE
TP TB (4-3)
KS i)










where, TfJ is back-off time by EQB at a corresponding average attempt rate G, and

K is a constant to adjust the resultant back-off time to yield the average attempt rate G by

Tr.

4.2 Fairness Index

Using unequal back-off parameters can improve link throughput at the expense of

evenness. For instance, the parameters can be such that radios simulcasting will nearly

always be able to transmit while the other radios are blocked. The link throughput

increases because there are few collisions for the radios simulcasting by blocking the

radios unicasting, but the network might become useless as the unequal back-off scheme

would cause significant blocking of a certain radios unicasting. Therefore, in comparing

different back-off parameters, we also consider the fairness provided using two different

fairness metrics. The first is the well known "Min-max index(MMI)" [14] which compares

the ratio of the minimum to the maximum amount of allocated resources among all the

users in a network as below, where xi is the amount of allocated resource to user i. In this

dissertation xi is replaced with the achieved link throughput of radio i.



min(xi)
min-max max(x) (4-4)
max(xi)

As we discussed fairness has different facets specified differently in the different

domain of resource allocation. In other words, fairness cannot always be considered as

even resource distribution because a system which is fair in terms of evenness (service

fairness) may not be fair if it is viewed in terms of the resource allocation amount to

each users to maximize network performances (effort fairness) when they have different

resource utilizing capabilities. Dianati et al. proposed in [13] the "Utility Fairness

Index(UFI)" to capture the fairness sensitive to effort fairness. For example, in our

simulcasting system, it makes sense to provide additional resources to those radios that










can send at a higher rate (simulcasting), and they should not be penalized for that in the

fairness in the view point of optimized resource utilization.

By the application of Dianati et al. [13], the normalized achieved throughput is

defined as

i = (4-5)
Zx i

The value of xi is replaced with link throughput of radio i, over a certain attempt rate

G. Then, the utility function Ui(sf)) with the fair share allocation at a certain value of a

is defined as




SS ) otherwise,

where


sf) 1 F 1 +mi() 1 (46
Nt t + Tn)) a (4-6)N

is the fair share of radio i, and aC indicates the trade off between service fairness

and effort fairness. Then, the "Utility Fairness Index(UFI)", is defined as in [13] as


[- 2
F(x) = (4-7)



4.3 Simulation and Results

We perform simulation of back-off allocation by PRB based on utility based back-

off allocation in the random network previously described in Section 3.5. Simulations

are carried out with various values of aA. The markers *, o, and E represent the results

for aA is equal to 0.0, 0.5, and 1.0, respectively. The 100 different uniformly distributed

random networks have been generated, and 4 fully connected networks are chosen for










simulation among them. The running time is 5,000 time slots for each random network.

The simulation results are averaged over the 4 fully connected networks.

The results in Figure 4-1 shows the simulation results of maximum link throughput

as a function of the offset angle 0. The maximum is taken over all possible attempt

rates as in Section 3.5. Note that as 0 increases, so does the link throughput that can be

achieved. The results show that, in the relatively large range of offset angle, from 15 to 40

degree, the maximum link throughput increases up to about 10% and 20% by PRB with

aA equal to 0.5 and 1.0, respectively.

The results in Figure 4-2 shows the simulation results of maximum end-to-end

throughput as a function of 0. The maximum is taken over all possible attempt rates as we

discussed. The results show that the end-to-end throughput is a non-monotonic function

of 0. The simulation results show that the end-to-end throughput is maximized by 0 = 20

degrees. The results show that, in the relatively large range of offset angle, from 15 to 40

degree, the maximum end-to-end throughput also increase up to about from 3% to 10%

by PRB with aA equal to 0.5 and 1.0, respectively.

Figure 4-3 shows the simulation results of MI as a function of 0. The results

show that the evenness degrades as we allocate back-off to be more sensitive to effort

fairness. The evenness for all three cases with different aA values decline when 0 is over

25 degrees.

Figure 4-4 shows the simulation results of UFI as a function of 0. The UFI is

observed at the same values of aF with aA of fair share resource allocation except for the

marker A which indicates the case with aA = 1.0, fully sensitive to effort fairness for

the fair share resource allocation, and aF = 0.0, fully sensitive to service fairness for

the fairness index. The results show that while the service fairness is degraded by PRB,

there's no big change in UFI as the value of aA increases compared to MMI. However,

the UFI also become worse as aA increases, which means, as same reason with MLI






















C 0.2

1-

0.15
-1
E
E
S 0.1



0.05-
-0- A=0.0
aA=0.5
-- A=1.0
0
0 5 10 15 20 25 30 35 40 45
Offset Angle, 0


Figure 4-1. Maximum link throughput by PRB with various aA values in random net-
work topology as the function of offset angle 0.



case, PRB is dependent of Rm, and becomes more sensitive at the value of 0 over 25


degrees.



















0.045


20 25
Offset Angle, e


Figure 4-2. Maximum end-to-end throughput by PRB with various aA values in random
network topology as the function of offset angle 0.





0.5 4

0.4OA


0.05


5 10 15 20 25
Offset Angle, 6


A=0.0
-- A=0.5
-- A=1.0
30 35 40


Figure 4-3. Min-max fairness by PRB with various aA values in random network topol-
ogy as the function of offset angle 0.































































5 10 15 20 25
Offset Angle, e


-*- A=0.0, aF=0.0
aA=0.5, aF=0.5
-- A=1.0, aF=1.0
aA=1.0, aF=0.0

30 35 40


Figure 4-4. Utility based fairness by PRB with various aF and aA values in random
network topology as the function of offset angle 0.


0.9.

0.8

0.7
0.6
0.6-
















CHAPTER 5
UNEQUAL RANDOM ROUTE SELECTION FOR SIMULCASTING

In this chapter, we investigate how the simulcasting capability can be exploited

at the network layer by adjusting the distribution of packets across multiple routes in a

system employing multipath routing. The modified min-hop routing for simulcasting

that we use in previous sections in this dissertation is presented in Section 2.3. Based

on this min-hop routing algorithm, we may have several routes that have same number

of hops from a source radio to a final destination. However, each route is still likely to

differ in terms of simulcasting capability because of different numbers of relay radios

with more-capable links. Routes that have more relay radios with more-capable links will

transmit more packets per transmission opportunity and therefore be more efficient in

relaying a packet along the route. If a radio has multiple routes to a destination, this effect

should be considered when determining what proportion of packets to transmit on a route.

In this chapter, we provide a preliminary investigation of how simulcasting capability can

be exploited in the network layer in the allocation of packets across multiple routes. We

investigate the performance of varying the packet distribution across routes with different

simulcasting capabilities for several network topologies.

5.1 Network Model

The example networks that we consider have a source(S) and a destination(D)

radio connected by two routes with same number of hops but different simulcasting

capabilities. The three network topologies that we consider are shown in Figures 5-

2-5-4. In order to reduce the simulation complexity and run time, we do not simulate

radios in the network other than those on the two routes from S to D as if they were part

of a larger network. Every radio is modeled as having the same average attempt rate G

and same number of neighbors Nb, which is defined as the network degree. So, given a











transmission, the collision probability is Pc = z CNbG'(1 G)Nb- as in Section

3.2.1. Then the link throughput by unicasting is given by Su = G(1 Pc) and by

simulcasting is Ss w 2G(1 Pc), as in Chapter 2. These values determine statistics

of the queue, such as the arrival and the service rates for a queue of a relay radio on a

route. If a packet from the source radio collides with another transmission at one of the

radios along the route, the packet will stay in the queue of the transmitting radio to wait

for re-transmission.

We consider a multipath routing scheme in which packets from S are distributed

across the two routes according to a random distribution,as illustrated in Figure 5-1. The

source S transmits packets at attempt rate G to only the destination D. The two routes

have same number of hops to D, but may have different simulcasting capabilities. We

define the more-capable route as the route which has larger simulcasting capability, and

the less-capable route as the route which has less simulcasting capability. We select a

route for transmission randomly with probability R1 for the more-capable route and R2

for the less-capable route at each transmission, where R1 + R2 = 1. We also define

the optimal route selection rate as the route selection rate for the more-capable route to

achieve the maximum end-to-end throughput.




S X R1
G R1 + R2= 1
9g R2

\0--

Figure 5-1. Packet transmission from source radio to randomly selected route based on
simulcasting capability.










We model three topologies of transmission routes in wireless ad hoc networks with

identical wireless radios deployed within a two-dimensional geographical territory. There

are two routes as we mentioned above. The two routes have same number of hops from

source radio to destination radio, but different simulcasting capabilities due to the number

of relay radios with simulcasting, or different number of more capable links along each

route. The upper route is the more-capable route, and the lower route is the less-capable

route. We assume that each route does not interfere with each other because they are

not within transmission range. We measure the end-to-end throughput as the number of

packets successfully transmitted from S to D per time slot. Figures 5-2-5-4 show the

three topologies for which we present results. The filled circles represent radios that can

utilize simulcasting because they have more-capable neighbors, and the empty circles

represent radios that can only unicast. The bold lines represent more-capable links,

and the thin lines represent less-capable links. Topology 2 has more relay radios with

simulcasting on the more-capable route than on the route of topology 1, but the number

of more-capable links are the same. Topology 3 has the same number of relay radios with

simulcasting on the more-capable route as topology 2, but has more more-capable links.

The conditions of the less-capable routes are same for all topologies.


S D




Figure 5-2. Topology 1 for unequal random route selection based on simulcasting capa-
bility.












S/ \D




Figure 5-3. Topology 2 for unequal random route selection based on simulcasting capa-
bility.



S \D




Figure 5-4. Topology 3 for unequal random route selection based on simulcasting capa-
bility.


5.2 Link Properties

In this section, we describe how we generate packets at the intermediate radios

along the routes from S and D as if these radios were part of a larger network but without

simulcasting the other radios in the network. We model the inflow and out flow of traffic

to the queue of a radio along the route, as illustrated in Figures 5-5. The states n and

n + 1 in the circles represent the number of packets in the queue, p and q are arrival rate

and service rate, respectively. For the purposes of modeling packet arrivals and departures

at the radios along the two routes, we treat the arrivals and departures as independent. In

fact, these are not independent, as a radio may not successfully transmit and successfully

receive simultaneously. However, we expect this approximation will have little impact on

our results. Then, Q is the probability of no change in the number of packets after one

transmission time slot, which we approximate by Q = pq + (1 q)( p) + (1 p)P(O),

where P(O) represents the probability that there is no packet in the queue at the current

transmission time slot.

The statistics of the queue status depend on the simulcasting capability, which is

determined by several network parameters such as the number of neighbors, the number















q Q q Q q

Figure 5-5. Markov status diagram for the number of packets in a queue.


of more-capable links of a radio, and the number of more-capable link on the route.

Figures 5-6 5-10 illustrate possible link statuses and their properties. The service rate

q simply includes any packet outgoing which include the packet from S to D. However,

the arrival rate pb includes only basic message incoming by unicasting, and the arrival rate

due to additional messages incoming by simulcasting is represented by the symbol pa.

The traffic generated according to probabilities pb and pa is not used to model the traffic

from S to D, which is fully simulated. The total incoming rate p is equal to pb + Pa. The

dotted arrows in Figures 5-9 and 5-10 represent additional message other than from the

source that is received by simulcasting at a radio along the more-capable route.

Figure 5-6 represents one of the possible link conditions, link model 1, that the relay

radio doesn't have any more-capable link. So, it's arrival and service rate correspond

to the link throughput by unicasting. However, because the total arrival rate p doesn't

include the traffic incoming from S, based on the assumption that every radio involved in

the transmission in the network is identical, and send packets uniformly on each branch,

the arrival rate p is related with the amount of packets incoming except from one branch

among all Nb branches. Then,

Nb -
p = U + g,
Nb
q = Su.


Also, because the link on the route from S is a less-capable link, traffic from the

source will be one packet at a time.











p
Traffic from
source




q

Figure 5-6. Link model 1 for analyzing queue status in random route selection based on
simulcasting capability. The relay radio doesn't have a more capable link.


Figure 5-7 illustrates another possible link condition, link model 2, that the relay

radio can simulcast but doesn't have any more-capable link on the route. So, it's arrival

and service rate correspond to the link throughput by simulcasitng. The service rate q

is simply 2Su. The arrival rate p is figured out in similar way with link model 1, but

corresponds to throughput by simulcasting, and because this relay radio can simulcast, it

includes arrival rate for additional message p,. The relay radio doesn't have any more-

capable link on the route, so based on the assumption that sending additional message on

each more-capable links is uniform and independent on transmission of basic message, pa

is S,(Nm/Nl ). Then, with similar analysis of link model 1, where N, is average number

of more-capable links of a radio,

P suNb-1 b N
P + S+ 2 +g,

q = 2Su.


Because the link on the source side on the route is a less-capable link, the traffic

coming from that direction arrive one packet per transmission.

Figure 5-8 illustrates another possible link condition, link model 3 where the relay

radio can simulcast and has a more-capable link on the source side on the route. So,

it's arrival and service rate correspond to the link throughput by simulcasitng. The

service rate q is simply 2Su. The arrival rate p is figured out as similar way with link











Pb
Pa
Traffic from
source





q

Figure 5-7. Link model 2 for analyzing queue status in random route selection based on
simulcasting capability. The relay radio has more capable links, but not on
the route.


model 2. However, one additional message comes from the source side. So, the amount of

additional messages included in pa is lessened by the proportion of one branch among Nm

branches. Then, the arrival rate for the additional message is given by Su(Nm 1)/(Nb).

Then,


J (Nb 1+ N7. 1) ,

q = 2Su.


Because the link on the source side on the route is a more-capable link, traffic

coming from that direction arrive two packets per transmission.


Pb
Pa
Traffic from
source





q

Figure 5-8. Link model 3 for analyzing queue status in random route selection based on
simulcasting capability. The relay radio has more capable links, and one of
them is included on the source side of the route.


Figure 5-9 illustrates another possible link condition, link model 4, where the relay

can simulcast and has more-capable link on the destination side of the route. The only











difference with link model 3 is that an additional message incoming to the radio is from

the destination side. So, the arrival rate for additional message pa includes the additional

message from a radio on the destination side of the route. Then,

-Nb1 N-
P = g(,+)+

q = 2Su.


Because the link on the source side of the route is a less-capable link, traffic from the

source side will arrive with only one packet per transmission.

Pb
/ Pa
Traffic from
the source





q

Figure 5-9. Link model 4 for analyzing queue status in random route selection based on
simulcasting capability. The relay radio has more capable links, and one of
them is included on the destination side of the route.


Figure 5-10 represents the final possible link condition, link model 5, where the

relay radio can simulcast and has more-capable links to both neighbors on the route. The

arrival rate for additional message pa in this condition is same with link model 3. Then,


P = S( +- g

q = 2Su


Because the link on the source side of the route is a more-capable link, the traffic from

that direction will arrive with two packets per transmission.

In the above network model, we consider the end-to-end throughput which is

measured as the number of packets successfully transmitted from the source radio to the

destination radio per time slot. The statistics of the queue delay at each relay radio for the











Pb
/ Pa
Traffic from /
source





q

Figure 5-10. Link model 5 for analyzing queue status in random route selection based on
simulcasting capability. The relay radio has more capable links, and two of
them are included at the both of source and destination sides of the route.


traffic from the source radio will affect to the end-to-end throughput. Now, we investigate

unequal random route selection which randomly assigns an unequal amount of traffic

from the source radio to each route.

5.3 Simulation and Results

We performed separate simulations for each of the three network topologies with

variations in the network degree and average number of more-capable links of a radio

with simulcasting. The source radio transmits packets at the same attempt rate as the

rest of the radio in the network, and all the packets transmitted by the source radio are

destined to destination radio. We randomly select a route for a packet to be transmitted

with probability of R1 for the more-capable route and R2 for the less-capable route.

The probabilities R1 and R2 are varied subject to 0 < R1 < 1, 0 < R2 < 1, and

R1 + R2 = 1. The queue status of each relay radio is determined by the statistics

mentioned in Section 5.2. If a packet transmitted from source radio is collided by the

collision probability Pc in Section 5.1 at any relay radio on a route, the packet stays

in the queue of the original radio to wait for retransmission at average attempt rate G.

Simulation is performed on various attempt rates G in the range from 0 to 1. If a packet

is successfully transmitted, it moves to the end of the arrival queue of the next radio. The

packet selection is based on FIFO as mentioned in Section 2.4. We ran 100,000 time










slots to count the numbers of packets that were transmitted from the source radio and that

arrived at destination radio successfully for various probabilities of R1 and R2.

We also performed simulations for a high-density network scenario in which the

network degree is 8 and the average number of more-capable links of a radio with

simulcasting is 4, and for a low-density network scenario in which the network degree is

6 and the average number of more-capable links of a radio with simulcasting is 3. The

results in Figures 5-11 and 5-12 show the simulation results for maximum throughput

in the high-density network and the low-density network, respectively, in each of the

three topologies. The marks *, D, and o represent the simulation results for topology

1, topology 2, and topology 3, respectively. The low-density network results show the

same pattern of end-to-end throughput as in the high-density network, but give 43.24%,

32.14%, and 26.79% higher maximum end-to-end throughputs in topology 1, 2, and 3,

respectively. We believe that this is because the low number of neighbors gives a lower

collision probability at receivers. The results for the high-density network in Figure 5-11

show that topology 2 and 3 give around 52% higher maximum end-to-end throughput

than topology 1, but almost no difference between topology 2 and 3. The results for

the low-density network in Figure 5-12 show that topology 2 and 3 give 39.62% and

33.96% higher maximum end-to-end throughput than topology 1, respectively, and the

difference between topology 2 and 3 is as small as 4.23%. This indicates that the end-

to-end throughput using random route selection is strongly dependent on the number of

relay radios with simulcasting, but not as much on the number of more-capable links on a

route.

The results for the high-density network in Figure 5-11 show that the maximum

end-to-end throughputs are improved by 270%, 450%, and 410% for topology 1, 2, and

3, respectively, by random route selection compared to the case that we choose the less-

capable route only. Compare to the case that we choose the more-capable route only, the

maximum end-to-end throughput is improved 37.04%, 27.27%, and 33.33%, for topology










1, 2, and 3, respectively, by random route selection. The optimal route selection rate is in

the range from 0.6 to 0.9 which is over the equal distribution point (0.5) for the topology

2 and 3. For topology 1, it is in the range of 0.3 to 0.9, although it is very slightly higher

between 0.7 and 0.9.

The results for the low-density network in Figure 5-12 show that the maximum

end-to-end throughputs are improved by 270%, 410% and 390% for topology 1, 2, and

3, respectively, by random route selection compared to the case that we choose the less-

capable route only. Compare to the case that we choose the more-capable route only,

maximum end-to-end throughput is improved by 33.3%, 24.1%, and 21.1%, for topology

1, 2, and 3, respectively, by using random route selection. The optimal route selection rate

is around 0.5, and 0.7 for topology 1, and topologies 2 and 3, respectively.

The simulation results for both the high-density and low-density network show that

the optimal route selection rate is higher for topology 2 and 3 than in topology 1. This

indicates that the optimal route selection rate is strongly dependent on the number of

relay radios simulcasting on a route. The simulation results indicate that knowledge of

the simulcasting capabilities of radios along a route can be utilized in the network layer to

improve end-to-end throughput in a system employing multi-path routing.















006



005


01 02 03 04 05 06 07 08 09
Route selection ratio, R1


Figure 5-11. Maximum end-to-end throughput versus route selection ration for route 1 at
high density network.




008


007


04 05 06
Route selection ratio, R1


Figure 5-12. Maximum end-to-end throughput versus route selection ration for route 1 at
low density network.
















CHAPTER 6
UNEQUAL POWER ALLOCATION FOR SIMULCASTING

In this chapter, we show that simulcasting is an effective technique to improve

throughput efficiency, which is measured as the throughput per unit energy, and propose

some distributed power control approaches to further improve the throughput efficiency

of simulcasting. The adaptation of the transmission power and spacing of points in the

constellation are considered in order to improve throughput efficiency. In the power

control scheme that we consider, the transmission power is adapted based on the link

distance of the intended receiver. We also consider the allocation of higher transmission

powers for radios simulcasting. Simulation results show that the proposed approaches

improve both throughput and throughput efficiency.

6.1 Power Allocation Scheme

6.1.1 Link Adaptive Transmission Power

The proposed strategy in this section is based on the assumption that the transmitter

can estimate the signal attenuation at a receiver by a certain channel measurement before

the actual transmission. Before the transmitter transmits a packet, it estimates the received

transmission power to satisfy target error probabilities for the basic and additional

messages, which adaptively determine the signal constellation point for simulcasting. So,

the offset angle 0 is varied for each transmission based on the condition of the links to the

less-capable and more-capable receivers. The main purpose of this scheme is to reduce

the transmission power needed while satisfying a certain target error probability, so as

to reduce network interference to the rest of the radios in the network and minimize the

required transmit energy. The throughput may not be affected with this scheme because

the received signal power comes less at the same ratio that the network interference

does. However, it is expected to improve network performance in terms of throughput



















Ebas p Ebas o


Eadd o

Ead
add_p


V Offset_p
Offset o


Figure 6-1. Symbol movement by minimized transmission power.


efficiency, which is defined as the throughput per unit energy [60]. Figure 6-1 illustrates

the signal constellation change by link adaptive transmission power for simulcasting.

Ebas,o, Eadd,o, and Offset_o represent the original, before power control, energy for the

basic message, energy for the additional message, and offset angle, respectively. E, ,,,

Eadd,p, and Offsetp represent the power-controlled energy for the basic message, energy

for the additional message, and offset angle, respectively.

6.1.2 Unequal Transmission Power Allocation

In order to better utilize the simulcasting capability, we also investigate allocating

more transmission power for simulcasting. Because a simulcast transmission delivers two

messages at a time, letting simulcasting have a relatively higher probability of successful

packet transmission by allocating more transmission energy is expected to increase both

throughput and throughput efficiency. In this dissertation, the additional transmission

power that is allocated to the radios is a parameter that is varied. Because allocating

higher transmission power to the radios simulcasting will cause higher interference to

the radios unicasting, the improved network performance by unequal transmission power

is achieved at the expense of unbalanced evenness such that the radios simulcasting

blocks the radio unicasting. However, as we discussed in Chapter 4, fairness should be

interpreted in multi-faceted way. So, in this Chapter, we investigate the fairness described

in Chapter 4 when unequal transmission power is applied.











Rcy less Roy less




Rcv more aPt,b bPt







Figure 6-2. Unequal transmission power allocation.


Figure 6-2 illustrates the unequal transmission power allocation scheme. In the

figure, dl and dm indicate the link distances from the transmitter to the less-capable and

more-capable receivers, respectively. Pt indicates transmission power for unicasting, and

Pt,b and Pt,a indicate the transmission power for basic message and additional message,

respectively, when a radio is simulcasting. Here a and 3, a > 3, are power control factor

for simulcasting and unicasting, respectively.

6.2 Network Model

Figures 6-3 and 6-4 illustrate the transmission power allocation for unicasting

and simulcasting, respectively. We consider only the path loss in computing minimum

transmission power Pt, Pt,b, or Pt,a to achieve a target error probability at a receiver in

an AWGN channel without consideration of interference. Then the computed minimum

transmission power is unequally adjusted by power weights 3 and a for unicasting and

simulcasting, respectively. The weighted transmission power Pu and Ps for unicasting

and simulcasting, respectively, are constrained such that the transmission range by power

control will not be over the original transmission power range R, which for discussion

purpose we normalize to 1.0. We also normalize the original transmission power Po,

which is required for a target error probability at the boundary R, as 1.0. In Figure 6-3,

RM is the transmission range for an additional message, so the radio unicasting exists in

the range between RM and R. Ru is the limit that the transmission range weighted by 3



























Figure 6-3. Diagram of transmission power range for unicasting.


is not over R when a radio is inside of the range. So, when a radio is outside of Ru, the

value of / should be adjusted so as final transmission range is not over R. In Figure 6-4,

Rs is the transmission range for basic message and is the limit that the transmission

range weighted by a is not over R when a radio is inside of the range. So, when a radio is

outside of Rs, the value of a should be adjusted so as final transmission range is not over

R.

Let A be the event that a receiver radio is in the range between RM and Ru, and A is

the event that the radio is out of Ru. Then the adjusted transmission power for unicasting,

Pu, for a certain target error probability at a receiver distance di from the transmitter is



A = '.i,, A :RM

1, A: Ru < d < 1,

where Au = d7. RM = 2-1/" is the maximum transmission range for additional

messages. Similarly, for simulcasting, the adjusted transmission power, Ps, weighted by



























Figure 6-4. Diagram of transmission power range for simulcasting.


the power weight factor for simulcasting, a, is

Sas = adT, B : s < Rs

1, B : s > Rs,

where s = /d + d and dm is the link distance of more-capable receiver. B is the

event that a receiver radio is in the range Rs, and B is the event that the radio is out of

Rs. Then, the received signal strengths Sr,u and Sr,s by unicasting and simulcasting,

respectively, at the receiver sites distances dl and dm for the basic and additional message,

respectively, are


/3 A: RM < u R
d A:Ru < u <,




,s a, B: s< Rs
B r, > R
B:s>Rs,











where

SdI, for basic message

dm, for additional message.

Then, the interference at the receiver from an interferer i, Ii, when the interferer i

transmits a packet, is


li = P4d-"


where Pi is the adjusted transmission power of the interferer i, di is the distance between

the interferer i and the receiver. Then, the total interference, I, at the receiver is



iET

where T is the set of interferers which transmit simultaneously with the packet under

consideration.

Let Z be signal to interference and noise ratio (SINR) at the receiver. Then,

sss if M =1
z { No+I f
S"U ifM 0.
No+I '

where M is the indicator that indicates a radio simulcasting when M 1= or unicasting

when M = 0. Now, the transmitted packet is considered as collided at the receiver when

Z < 7, where 7 is the target SINR. We measure the throughput efficiency defined as

throughput per unit energy consumption,


Si S

Sete
P

where Sif and Sef are the link throughput efficiency and end-to-end throughput effi-

ciency, respectively. S, Set, and P are link throughput, end-to-end throughput, and

average power consumption.










6.3 Simulation Results

We let the target error probability be 10-4, the transmission range by unicasting

without power control, R, be 1Km, the original transmission power, P,, for the target

error probability at the boundary R be 1, and the thermal noise, No, be -8.4dB. The

simulation was carried out over G from 0 to 1. The optimal G to maximize the link and

the end-to-end throughput is variable, and the effect of power control on the link and

the end-to-end throughput is quite different over the range of G. So, we measure the

performances of the link and the end-to-end throughput as the summation of the link and

the end-to-end throughput over G from 0.1 to 1, which includes the maximal attempt rate,

Gm, which maximize the throughputs and call them the "total link throughput" and "total

end-to-end throughput", respectively.

Figure 6-5 shows the simulation results for link throughput in (a), link throughput

efficiency in (b), end-to-end throughput in (c), and end-to-end throughput efficiency

in (d). The results indicate that link throughput as well as throughput efficiency can be

increased by properly allocating transmission power. For the link and the end-to-end

throughputs, the performances increase as both a and 3 increase, and at the a values

over 3, they are almost saturated. For the link and the end-to-end throughput efficiencies,

the performances are not so sensitive to a as to 3, but have a greater dependence on

/3. By allocating the transmission power unequally with power allocation weights of

S= 1.0 and a = 2.5, the link and the end-to-end throughput efficiencies increase about
34.4% and 34.3%, respectively, with degradation of 17.8% and 15% for the link and the

end-to-end throughput, respectively. Depending on the applications, the weights can be

chosen to provide a trade off between throughput and throughput efficiency. For example,

by allocating / = 1.6 and a = 2.5, the link and the end-to-end throughput efficiencies

increase about 15.6% and 16.0%, respectively, with degradation of only 6.7% and 4.0%

for the link and the end-to-end throughput, respectively, compared to the maximum

values we found.












(a) (b)
0.5 4.5

0.45 .-
5 4o
0.4

0.35- ) 3.5
S13^ P=1.0 2 =1.0
0.3 -e- p=1.2 -e- p=1.2
S-- p=1.6 3 -- P=1.6
0.25 P=2.0 P=2.0
P=2.4 P 1=2.4
0.2 2.5
1 1.5 2 2.5 3 1 1.5 2 2.5 3
a a

(c) (d)
0.22 1.8
0.2
0.18 U1
2 0.16 C-
1.4
w 0.14 +! P=1.0 2 + 1p=1.0
S ,_// -e- p=1.2 -- p=1.2
0.12 -B- p=1.6 1.2 -8- P=1.6
0.1 P=2.0 1 P=2.0
1=2.4 P =2.4
0.08 1
1 1.5 2 2.5 3 1 1.5 2 2.5 3
a a

Figure 6-5. Throughput and throughput efficiency by unequal transmission power alloca-
tion.


Figure 6-6 shows the simulation results of MMI in (a), UFI with cF = 0.0 in (b),

UFI with cF = 0.5 in (c), and UFI with cF = 1.0 in (d) as discussed in Chapter 4.

Fairness in terms of MMI decreases from 0.22 to 0.05 as 3 decrease from 2.4 to 1.0

over the range of a greater than 2. In terms of UFI, it decreases from 0.75 to 0.60 at the

same variation of a and 3. All the fairness index which include the MMI and the UFIs

with three different caF has similar patterns. That means the unequal transmission power

allocation doesn't significantly affect the tradeoff between service fairness and effort

fairness.





































0.8
o




U)

0()


I 0.2
..


u


0
II
_ 0.6
LL

S0.4
U)
U)

S0.2
LL


1 1.5 2 2.5 3


- P- p=1.0
-e- p=1.2
-a- p=1.6
P=2.0
P=2.4


1 1.5 2 2.5 3
a

(d)


^^^^-9-^


1.5 2 2.5 3


Figure 6-6. Fairness by unequal transmission power allocation.
















CHAPTER 7
CONCLUSIONS

We introduced the use of simulcast transmission techniques for ad hoc networks.

We applied a cross-layer approach in which the link- and network-layer protocols were

modified to effectively utilize the new capability presented by simulcasting. We proposed

some modifications to the routing, packet-selection, and back-off algorithms. The per-

formance of simulcast signaling was analyzed and simulated for a network that employs

slotted ALOHA. We presented detailed results on the effects of varying the offset angle

0 when nonuniform QPSK is used for simulcasting. We showed that we cannot simply

increase the signal constellation size to a larger constellation with uniform spacing

without severely affecting the network connectivity and end-to-end throughput. The

analytical and simulation results confirm that by choosing the simulcasting parameters

appropriately, simulcasting can significantly improve both link and end-to-end throughput

for static networks at the expense of a slight decrease in network connectivity.

Unequal resource allocations were studied to effectively utilize simulcasting

capability. First, modifications to the back-off parameters were simulated. A priority-

based MAC protocol was investigated in which the retransmission probabilities were

increased for those radios that have a more-capable receiver and decreased for those

radios that have only less-capable links. Increasing the priority was found to allow a

higher average link throughput to be achieved at high average attempt rates. Second, we

investigated random multiple route selection based on the simulcasting capabilities of

the radios along two routes in a system that employs multi-path routing. The simulation

results show that the end-to-end throughput was substantially increased by using multiple

routes and assigning greater transmission rates along the more-capable route. Third,

unequal transmission power for simulcasting was investigated. The simulation results







81


show that throughput and throughput efficiency defined as throughput per unit power

consumption are increased by assigning relatively higher transmission power to the radio

simulcasting. Overall, unequal resource allocation for simulcasting increases throughput

and throughput efficiency at a certain expense of fairness.
















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BIOGRAPHICAL SKETCH

Kiung Jung received the B.S. and M.S. degrees in Electronic Material Engineering

from Kwangwoon University, Seoul, Korea in 1988 and 1990, respectively, and the M.S.

degree in Electrical and Computer Engineering from University of Florida, Gainesville,

FL, in 2001. From 1990 to 2002, he was with Electronics and Telecommunications

Research Institute (ETRI), Taejon, Korea, where he was mainly involved in the project

of developing TDX-10 digital switching system, and CDMA Mobile Communication

System. His current research is on wireless communication with emphasizing physical

layer signaling, application of error control coding, ad hoc network, collaborative

communications, cross-layer (physical MAC) design in ad-hoc network.