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Mac-Anchored Crosslayer Design in Multihop Wireless Ad Hoc Networks

Permanent Link: http://ufdc.ufl.edu/UFE0024754/00001

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Title: Mac-Anchored Crosslayer Design in Multihop Wireless Ad Hoc Networks
Physical Description: 1 online resource (129 p.)
Language: english
Creator: Chen, Feng
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: crosslayer, medium, protocol, wireless
Electrical and Computer Engineering -- Dissertations, Academic -- UF
Genre: Electrical and Computer Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: This dissertation focuses on cross layer design for network protocols in wireless ad hoc networks. It studies the relationship between link scheduling at medium access control layer and physical or network layer. Link scheduling is a way of achieving the optimal MAC layer throughput while avoiding collisions. In this dissertation, it is modeled using graph theory concepts based on different interference model. MAC layer is served as an anchoring layer in our cross layer design which can collect physical layer information and provide information to network layer. The dissertation will discuss how the carrier sensing threshold, a physical layer parameter, impact the link scheduling strategy in achieving the optimal aggregate throughput at MAC layer. The dissertation will also investigate the joint routing and link scheduling problem using a graph theory based model. Further more, since solving the above joint design problems is usually NP-hard, we propose polynomial solutions for estimating the bounds for network capacity. In an effort to design MAC layer solution for real systems, we propose an opportunistic MAC for multichannel multiradio wireless networks which utilizes multiradio diversity at physical layer as well.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Feng Chen.
Thesis: Thesis (Ph.D.)--University of Florida, 2009.
Local: Adviser: Fang, Yuguang.

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Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0024754:00001

Permanent Link: http://ufdc.ufl.edu/UFE0024754/00001

Material Information

Title: Mac-Anchored Crosslayer Design in Multihop Wireless Ad Hoc Networks
Physical Description: 1 online resource (129 p.)
Language: english
Creator: Chen, Feng
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: crosslayer, medium, protocol, wireless
Electrical and Computer Engineering -- Dissertations, Academic -- UF
Genre: Electrical and Computer Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: This dissertation focuses on cross layer design for network protocols in wireless ad hoc networks. It studies the relationship between link scheduling at medium access control layer and physical or network layer. Link scheduling is a way of achieving the optimal MAC layer throughput while avoiding collisions. In this dissertation, it is modeled using graph theory concepts based on different interference model. MAC layer is served as an anchoring layer in our cross layer design which can collect physical layer information and provide information to network layer. The dissertation will discuss how the carrier sensing threshold, a physical layer parameter, impact the link scheduling strategy in achieving the optimal aggregate throughput at MAC layer. The dissertation will also investigate the joint routing and link scheduling problem using a graph theory based model. Further more, since solving the above joint design problems is usually NP-hard, we propose polynomial solutions for estimating the bounds for network capacity. In an effort to design MAC layer solution for real systems, we propose an opportunistic MAC for multichannel multiradio wireless networks which utilizes multiradio diversity at physical layer as well.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Feng Chen.
Thesis: Thesis (Ph.D.)--University of Florida, 2009.
Local: Adviser: Fang, Yuguang.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0024754:00001


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First,IwouldliketoexpressmysinceregratitudetoProf.YuguangFangwhohaveservedasmyPh.Dsupervisor.IamreallyfortunatetomeetDr.Fangandlearnfromhiminvariousaspects.IthankhimforcountlesshoursIhavespentwithhimdiscussingresearch,proofreadingpapersandtalkingaboutlifeingeneral.IalsothankhimforpushingmeintherightdirectionwhenIfeellackofmotivation,whichmakememorematurebothscholasticallyandpersonally.Second,IthankProfessorTanWong,JaniseMcNair,ShigangChenandYeXiaforservingonmysupervisorycommittee.TheirvaluablesuggestionandconstructivecriticismhavegreatlyhelpedtopolishedmythoughtsforthisPh.Dthesis.Third,IwouldalsoliketothankmycolleaguesandfriendsChiZhang,RongshengHuang,MiaoPan,YangSong,JinyuanSun,PanLi.Ithankthemfornumerousinspirationaldiscussionsandpresentations.Ialsothankthemfortheirfriendshipandcompanionduringthepastfouryears.IwouldliketoextendmythankfulnesstopreviousmembersofWINET:HongqiangZhai,JianfengWang,XiaoxiaHuang,ShushanWen,YunZhou,andWeiLiu.TheirgreateortsinresearchhavebeenatremendoustreasureforallthemembersinthelabandIlearnalotfromthemthroughtheirworks.Mostimportantlyofall,Iwouldliketothankmyparentsforsupportingmeforthelast26years.ItisthroughtheirforeverencouragementandselesscarethatIhavemadeitthroughallthestepstoreachthispointinmylife.Mydeepestthanksgotomyhusbandfortakingmeintohislife.ItisthroughhiseyesandmindthatIgrowmatureenoughtocontinueandcompletethejourneytoPh.D. 4

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page ACKNOWLEDGMENTS ................................. 4 LISTOFTABLES ..................................... 8 LISTOFFIGURES .................................... 9 ABSTRACT ........................................ 11 CHAPTER 1INTRODUCTION .................................. 12 1.1Motivation .................................... 12 1.2Organization .................................. 13 2OPTIMALCARRIERSENSINGTHRESHOLDINWIRELESSADHOCNETWORKS 16 2.1RelatedWork .................................. 19 2.1.1AnalyticalModelForCarrierSensingThresholdWithSpatialReuse 19 2.1.2IdentifyingTheOptimalCarrierSensingThreshold ......... 20 2.1.3End-To-EndPathCapacityAndAggregateEnd-To-EndFlowCapacityWithCarrierSensingThreshold .................... 21 2.1.4DistinctCarrierSensingThresholds .................. 22 2.1.5Others .................................. 22 2.2CapacityWithUniqueOptimalCarrierSensingThreshold ......... 23 2.2.1NetworkModel ............................. 23 2.2.2ConcurrentTransmissionSet ...................... 24 2.2.3CollisionsWithinConcurrentTransmissionSets ........... 24 2.2.4FindingPathCapacityAndTheOptimalCarrierSensingThreshold 26 2.2.5AggregateEnd-To-EndThroughputofMultipleFlowsWithTheOptimalCarrierSensingThreshold .................. 28 2.2.6AggregateLinkThroughputWithTheOptimalCarrierSensingThreshold 29 2.2.7AnAlgorithmToFindMaximalConcurrentTransmissionSets ... 30 2.3ThroughputWithDistinctCarrierSensingThresholds ........... 34 2.4PerformanceAnalysis .............................. 37 2.4.1AggregateLinkThroughputWithOptimalCarrierSensingThreshold 38 2.4.1.1Numberofows ....................... 38 2.4.1.2Sizeofthephysicaltopology ................. 40 2.4.1.3Hopdistance ......................... 41 2.4.1.4Randomnetworktopology .................. 41 2.4.1.5Comparisonwithsimulationresults ............. 42 2.4.2End-To-EndCapacityWithOptimalCarrierSensingThreshold .. 42 2.4.2.1Pathcapacitywithoptimalcarriersensingthreshold ... 42 5

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....................... 44 2.4.3AggressiveVsNonaggressiveScheduling ................ 46 2.4.4AggregateLinkThroughputWithDistinctCarrierSensingThresholds 47 2.5Conclusion .................................... 49 3AVAILABLEBANDWIDTHINMULTIRATEANDMULTIHOPWIRELESSNETWORKS ..................................... 50 3.1Introduction ................................... 50 3.2AvailableBandwidthinMultirateandMultihopWirelessSensorNetworks 52 3.2.1AvailableBandwidthProblem ..................... 52 3.2.2MultipleDiscreteRatesinWirelessSensorNetworks ......... 53 3.2.3FeasibleLinkDemands ......................... 53 3.2.4IndependentSetsinMultirateNetworks ................ 55 3.2.5LinearProgrammingFormulationOfTheAvailablePathBandwidthProblem ................................. 56 3.3UpperandLowerBounds ........................... 57 3.3.1CliquesinMultirateNetworks ..................... 57 3.3.2UpperBoundsDerivedFromCliques ................. 58 3.3.3LowerBoundsDerivedFromIndependentSets ............ 61 3.4JointOptimizationofQoSRoutingandLinkScheduling .......... 61 3.5PerformanceEvaluation ............................ 63 3.5.1SimpleScenariosIIwhereCliqueConstraintsBecomeInvalid,andLinkAdaptationCanImproveThroughput .............. 63 3.5.2CompareDistributedQoSRoutingMetrics .............. 65 3.5.3EstimationofPathAvailableBandwidth ............... 66 3.6Conclusions ................................... 67 4CAPACITYBOUNDSINMULTIRATEANDMULTIHOPWIRELESSADHOCNETWORKS ................................. 69 4.1Introduction ................................... 69 4.2RelatedWork .................................. 71 4.3NetworkModel ................................. 72 4.3.1DenitionofNetworkCapacity ..................... 72 4.3.2NPCompleteFormulationofOptimumNetworkCapacity ...... 73 4.4LowerBoundsofNetworkCapacity ...................... 74 4.4.1LowerBoundsofPerLinkCapacityinSingle-RateNetworks .... 75 4.4.2LowerBoundsofPerLinkCapacityinMultirateNetworks ..... 77 4.4.3Discussion:thelengthof,MandMi(1iN) .......... 81 4.4.4LowerBoundsofMinimumLinkCapacity .............. 82 4.4.5LowerBoundsofMinimumFlowCapacity .............. 83 4.4.6ConsiderationofPacketErrorRate .................. 84 4.5UpperBoundsofNetworkCapacity ...................... 84 4.6ComplexityandSomeRemarks ........................ 87 6

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........................... 87 4.6.2PolynomialAlgorithmtoFindFeasibleLinkScheduling ....... 88 4.6.3SomeRemarksonCapacityBounds .................. 89 4.7PerformanceEvaluation ............................ 90 4.7.1ImpactofOrderofLinksandRandomTopologies .......... 91 4.7.2ImpactofRoutingMetrics ....................... 91 4.7.3ImpactofNumberofFlowsandPerFlowCapacity ......... 92 4.7.4AsymptoticBounds ........................... 93 4.8Conclusions ................................... 94 5OPPORTUNISTICMULTIRADIOMACINWIRELESSADHOCNETWORKS 97 5.1Introduction ................................... 97 5.2DesignInspirations ............................... 99 5.2.1MultipleMACDiversityIssues ..................... 99 5.2.2Channel-BasedPacketScheduling ................... 100 5.2.3OpportunisticMACUsingMultipleRadios .............. 102 5.3ProtocolDescription .............................. 102 5.3.1RTSonCommonChannel(RTSC)andMulti-castRTSonDataChannel(RTSD) ................................. 103 5.3.2VirtualMulti-CTS ........................... 105 5.3.3OpportunisticPacketSchedulingforMultipleRadios ........ 105 5.3.4ChannelReservationFrameandDataTransmission ......... 107 5.3.5AnIllustrativeExample ........................ 108 5.4NumericalAnalysis ............................... 109 5.4.1Case1 .................................. 109 5.4.2Case2 .................................. 112 5.4.3NumericalResults ............................ 114 5.5SimulationResults ............................... 116 5.5.1Single-hopRectangularTopology ................... 118 5.5.2Single-hopRandomTopology ..................... 120 5.5.3Multi-hopRandomTopology ...................... 120 5.6Conclusion .................................... 121 6Conclusion ....................................... 123 REFERENCES ....................................... 124 BIOGRAPHICALSKETCH ................................ 129 7

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Table page 2-1AlgorithmforndingalltheMCTs ......................... 33 2-2Algorithmofndingallthemaximalorderedconcurrenttransmissionsets. ... 36 4-1Algorithmtondlinkinterferenceset(LIS)andmaximumITT(TLIS)andthemaximumsizeofLIS(M) .............................. 96 5-1ExperimentParameters ............................... 115 8

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Figure page 2-1Hiddenterminalproblemsinconcurrenttransmissionsets ............ 25 2-2Usingdierentcarriersensingrangestoachievethemaximalaggregatelinkthroughput 35 2-3Impactofnumberofowstotheoptimalcarriersensingthresholdsforaggregatelinkthroughput .................................... 39 2-4Impactofnumberofthesizeofphysicaltopologytotheoptimalcarriersensingthresholdsforaggregatelinkthroughput ...................... 39 2-5Impactofnumberofthehopdistancetotheoptimalcarriersensingthresholdsforaggregatelinkthroughput ............................ 40 2-6Impactofnetworktopologytotheoptimalcarriersensingthresholdsforaggregatelinkthroughput .................................... 43 2-7Comparisonbetweennumericalandsimulationresultsforaggregatelinkthroughput 43 2-8Impactofthenumberofhopsofpathsontheoptimalcarriersensingthresholdsforend-to-endpathcapacity ............................. 43 2-9Impactofhopdistanceontheoptimalcarriersensingthresholdsforend-to-endpaththroughput ................................... 45 2-10Impactofthenumberofowsontheoptimalcarriersensingthresholdsformultiowaggregatethroughput ................................. 45 2-11Impactofthesizeoftopologiesontheoptimalcarriersensingthresholdsformultiowaggregatethroughput ........................... 45 2-12Impactofnumberofowsontheoptimalcarriersensingthresholdswithnonaggressivetracformultiowaggregatethroughput ..................... 47 2-13Impactofsizeofthetopologyontheoptimalcarriersensingthresholdswithnonaggressivetracformultiowaggregatethroughput ............. 48 2-14Impactofdierentsetsofcarriersensingrangesonaggregatelinkthroughput 48 3-1Twosimpletopologies ................................ 51 3-2Randomtopology ................................... 65 3-3Availablebandwidth ................................. 65 3-4Estimatedavailablebandwidth ........................... 67 4-1Interferencesettransmissiontimeandinterferencecliquetransmissiontime ... 89 9

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................................... 92 4-3Pernodecapacity ................................... 93 4-4Perowcapacitywithdierent#ofows ..................... 93 4-5Networkcapacitywithdierent#ofows ..................... 94 4-6Pernodecapacity ................................... 94 5-1Illustrationforlinkdiversity,channeldiversity,andmulti-radiodiversity.NodeSisthesourcenode,nodeA,nodeB,nodeCarereceivers.ThereisanongoingtransmissionbetweennodeDandnodeEonchannel3.Thegureshowsdierencesingeographicallocationandinterferencelevelwhichgiverisetomultiplediversities. 100 5-2Illustrationforlocalizedoptimization.Foreachnext-hopaddress(corrspondingtoapacket),thelinkqualityondierentchannelmaybedierent.Foreachchannel,thelinkqualitywithdierentreceiversmaybedierent.FromFigure 5-1 ,duetotheongoingtransmission,themaximumsupportabledatarateonl3scisonly6.Thehorizontalellipserepresentspacket-basedscheduling,whileverticalellipserepresentschannel-basedscheduling. ............... 101 5-3TimelineforOMMAC.Assumethecurrenttransmissionuses4radiosatonetime.DuringtheprocessofRTSC-RTSD-CTS,thesenderisabletocollectchannelinformationon9linksifthenegotiationprocessissuccessful. .......... 102 5-4Throughputgainnormalizedoverthethroughputofonedataradio ....... 116 5-5ThroughputofOMMACincase1 .......................... 117 5-6ThroughputofOMMACincase2 ......................... 117 5-7Single-hopTopology:thesizeoftherectangleis200m200m.Sisthesourcenode. .......................................... 118 5-8ThroughputofOMMACasafunctionofnumberofradiosinthesingle-hoprectangulartopology ....................................... 119 5-9ThroughputofOMMACasafunctionofnumberofowswithdierentRiceanparameterscomparedwiththatofMOARinthesingle-hoprectangulartopology ............................................. 119 5-10ThroughputofOMMACasafunctionoftheRiceanparameterKinthesingle-hoprectangulartopology ................................. 120 5-11ThroughputofOMMACasafunctionofnumberofowsinthesinglehoprandomtopologyincomparisonwiththatofMOAR .................... 120 5-12ThroughputofOMMACasafunctionofnumberofowsinthemulti-hoprandomtopologyincomparisonwiththatofMOAR .................... 121 10

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Thisdissertationfocusesoncrosslayerdesignfornetworkprotocolsinwirelessadhocnetworks.Itstudiestherelationshipbetweenlinkschedulingatmediumaccesscontrollayerandphysicalornetworklayer.LinkschedulingisawayofachievingtheoptimalMAClayerthroughputwhileavoidingcollisions.Inthisdissertation,itismodeledusinggraphtheoryconceptsbasedondierentinterferencemodel.MAClayerisservedasananchoringlayerinourcrosslayerdesignwhichcancollectphysicallayerinformationandprovideinformationtonetworklayer.CrosslayerdesignbetweenMAClayerandphysicallayerorroutinglayercanprovidebetteroverallsystemperformance. Thedissertationwilldiscusshowthecarriersensingthreshold,aphysicallayerparameter,impactthelinkschedulingstrategyinordertoachievetheoptimalaggregatethroughputatMAClayer.Thedissertationwillalsoinvestigatethejointroutingandlinkschedulingproblemusingagraphtheorybasedmodel.Furthermore,sincesolvingtheabovejointdesignproblemsisusuallyNP-hard,weproposepolynomialsolutionsforestimatingtheboundsfornetworkcapacity.InaneorttodesignMAClayersolutionforrealsystems,weproposeanopportunisticMACformultichannelmultiradiowirelessnetworkswhichutilizesmultiradiodiversityatphysicallayeraswell. 11

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Oneofthesignicantcharacteristicsofwirelessnetworksisthebroadcastnatureofwirelesstransmission.Asetofnodesmaycontendforthetransmissionmediumatthesametimeresultinginpossiblecollisions.Atransmissionmayaecttheotherongoingtransmissionscausinginterferencetoothers.Thusmediumaccesscontrol(MAC)protocolmustbeusedtocoordinatethetransmissionsotherwiseahighcollisionrateandsevererinterferencelevelmayresultinauselessnetwork.InordertostudytheperformanceofMACprotocolandfurtherdecideproperMACparametersorproposebetterMACprotocols,itisveryimportanttostudytheinterferencerelationshipsamongdierentlinks. MAClayerlinkschedulinghasbeenincloserelationshipwithphysicallayerinformation.Unlikewirednetworks,wirelessnetworksconstantlyexperiencetime-varyingchannelsduetopathloss,fadingandinterference.Withthefeedbackfromphysicallayer,linkschedulingcanbeconductedwithamoreinformedway.Intuitively,reducingthetransmissionprobabilitywhenexperiencinglowchannelqualitymaysavetheenergyforretransmissionandreduceinterferenceforothers.Thus,schedulinglinktransmissionwiththeknowledgefromphysicallayermayhelptoachievehighernetworkcapacityandinthe 12

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MAClayerlinkschedulingalsohasgreatimpactontheroutingprotocolaswell.DierentMAClayerlinkschedulingstrategydirectlyimpactontherouteperformancewhichismeasuredbyroutingmetricssuchasaverage-transmission-timeandend-to-enddelay.Themostintuitiveexampleforshowingtheconstraintsbetweenthesetwolayersisthattheadjacentlinkonapathcannottransmitatthesameandhastobescheduledinnon-overlappingtimeslots.Thus,jointroutingandlinkschedulingdesignisnecessarytondtheroutesandprovidecertainlinkschedulingtoachievetheexpectedperformance. Intherealsystem,thelinkschedulingshouldbeachievedwithdistributedsolutions.AnoptimallinkschedulinginwirelessnetworksisusuallymodeledasaNP-hardproblem.Thuslocalheuristicsolutionswhichareeasytoimplementaresometimesusedinrealsystem.Thechallengeofhowtoobtaintheinformationonseverallevelofprotocollayersisoneofthekeyissuesindesigningapracticalprotocolsolution.Howtotakeadvantageoftheinformationfromseverallayertodesignbetternetworkprotocol,i.e.,crosslayerdesignisnecessary. 13

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Inchapter3,westudythepathavailablebandwidthproblemwithbackgroundtracinmultirateandmultihopwirelessnetworks.Weformulatethepathavailablebandwidthproblemusinglinearprogrammingandproposetheconceptsofindependentsetsandcliquestotakeintoconsiderationoftheadvantagesoflinkadaptation.Anindependentsetandacliquearenotonlyspeciedbyasetoflinksbutalsospeciedbythelinkrates.Byallowinglinkstousedierentratesatdierenttime,thenetworkcanobtainshigherpathavailablebandwidthcomparedtocaseswithanyxedrateassignments.Weanalyzetheupperboundsderivedfromcliques,whichshowsthatthecliqueconstraintbecomesinvalidforthefeasiblelinkthroughputvector,andweaccordinglyconstructanewupperbound.WealsoextendthepathavailablebandwidthproblemintoajointdesignofQoSroutingandlinkschedulingtondpathswithhighavailablebandwidth. Inchapter4,wefurtherstudythroughputcapacityofmultihopandmultiratewirelessadhocnetworks.withgiventopologiesandtracpatterns.Weproposepolynomial-timealgorithmstocomputelowerandupperboundsofnetworkcapacitywithinputsofsource-destinationpairs,pathsbetweenthem,andagivencapacityallocationvectoramongsources.Theseboundsarecomputedusingconceptsofinterferencelinksetandinterferencelinkclique.Toprovethatthelowerboundisachievable,weuseatimedivisionMACprotocolandagloballinkschedulingalgorithm,whichisalsoapolynomial-timealgorithm.Thelowerboundisequaltotheupperboundinspecialcases,andisclosetoeachotheringeneral.Forexample,thedierenceis21%onaveragefornetworkswith400randomlyanduniformlydistributednodes,anditincreaseswhenthenumberofnodesincreases,andisupto45%for1000-noderandomnetworks.Inthetheoreticalmodelofthecapacitybounds,wedonotassumeanyspecicinterference 14

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35 ),orthediskmodel,aslongaswecandeterminewhethertwoormorewirelesslinkscansuccessfullytransmitdatasimultaneouslyornot.Wealsodonotlimitthelocationandthenumberofsourcesanddestinations,orthevalueofcapacityallocationvectoramongows.Whenallnodesaresourcesandrandomlychooseadestination,andallofthemhavethesamethroughput,i.e.,thecapacityallocationvectorisanall-onevector,thecapacitybecomesthepernodethroughputcapacitystudiedin( 35 ). Inchapter5,weproposeadistributedlinkschedulingsolutioninmultiradiowirelessnetworks.Theexistenceofmultiplechannelsandmultipleradioshasgreatlyexpandedmanageableresourcespace,i.e.,channel,radio,user,andtime,toimprovethenetworkperformance.Thequestionofhowtoecientlyusetheavailableresourcesinmultiradiowirelessnetworksisofgreatimportance.TheproposedopportunisticmultiradioMAC(OMMAC)isdesignedtoexploitmulti-radiodiversityinordertoenhancethethroughputperformance.Inordertoexploitmulti-radiodiversity,OMMACusesmulti-castRTSandvirtualmulti-CTStocollectreceiver-measuredchannelqualityinformationoverseveralcandidatetransmissionlinks.Theabovementionedtechniquesmakeitpossibletomeasureseveralchannelssimultaneouslyandsendbackasetofqualityinformationatthesametime.Asandistributedsolution,thoughOMMACdoesnotprovidesystem-wideoptimalsolution,weusesimulationresultstovalidateitsimprovementinperformancecomparedwithpriorrelevantsolutions. 15

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InCSMA/CAbasedMediumAccessControl(MAC)protocols,thecarriersensingmechanismisanimportantcomponentinpreventingcollisionswithoutthehelpofpre-existinginfrastructure.Accordingtothephysicalcarriersensingmechanism,eachnodeneedstosensethemediumbeforeaccessingthemedium.Ifthereceivedpowerinairisgreaterthanapredenedvalue,i.e.,thecarriersensingthreshold,thechannelisregardedbusyandthesensingnodedefersitstransmission.Otherwise,thechannelisregardedidle.Insteadofallowingblindaccesstothemedium,thecarriersensingmechanismattemptstoseparateconcurrenttransmissionsfarenoughandhencereducescollisions. Inadditiontothephysicalcarriersensingmechanism,thevirtualcarriersensingmechanismisanothermethodtoreducecollisionsbytheexchangeofRTSandCTSframesbeforeaDATAtransmissionbetweenatransmitterandareceiver.However,aspointedoutin( 16 ),thevirtualcarriersensingmechanismrequiresreceiverstocorrectlydecodetheMACheaderoftheRTSandCTSframes.Duetothedecodingerrorsandtherelativelyshorttransmissionrange(comparedwithcarriersensingrange),thevirtualcarriersensingcannoteectivelypreventcollisionswithinthetransmissionrangeandisincapableofavoidingcollisionsoutofthetransmissionrange( 3 ),thoughitdoesrelievethehiddenterminalproblemsifusedtogetherwithphysicalcarriersensingmechanism.Inthispaper,wefocusoninvestigatingthephysicalcarriersensingmechanismanditsimpactontheend-to-endpathcapacity,aggregateend-to-endowcapacityandaggregatelinkcapacitywhicharedenedasfollows: 16

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Previousworksuchas( 7 )( 8 )( 12 )haveshownthatdierentcarriersensingthresholdshavesignicantimpactsontheaggregatelinkthroughput.Generally,alargercarriersensingthresholdallowsmoreconcurrenttransmissionswithinagivenareaandhenceimprovesthespatialreusewhichleadstohigheraggregatelinkthroughput,especiallyinthedensewirelessnetworks.However,thelargerthecarriersensingthresholdis,themorethehiddenterminals( 16 )thereareoutsideofthecarriersensingrange.Incontrast,decreasingthecarriersensingthreshold,thoughresultinginalargercarriersensingrange,mayleadtoatooconservativestrategyinaccessingthemediumandhenceincreasingthenumberofexposedterminals( 16 ).Boththehiddenandtheexposedterminalproblemcoulddecreasethenetworkthroughput.Inaddition,thecarriersensingrangealsohasimpactonthecollisionareaduetothesimultaneoustransmissions( 12 ).Thus,howtosetcarriersensingthresholdisaquestionofgreatimportanceinordertoimproveaggregatelinkthroughput. Consideringthemulti-ratecapabilityofwirelesslinks,theinterplaybetweenthecarriersensingthresholdandtheinterference-limiteddataratesalsohasverycloserelationshipwiththeaggregatelinkthroughput.Thecarriersensingmechanismseparatesconcurrenttransmissionsbythecarriersensingrange.Theclosertheconcurrenttransmissionsare,themoreinterferencethereceiverssense.Sinceadatarateisdeterminedbysignaltointerferenceplusnoiseratio(SINR)andreceiversensitivityrequirements,alargercarriersensingthresholdmakesatransmitteradapttoalowerdataratewhichmightdecreasetheaggregatelinkthroughputeventuallyandviceversa.Thus,coupledwithdierentdataadaptationstrategies,theproblemofhowtosettheoptimalcarriersensingthresholdbecomesmorecomplicatedandchallenging. Inthispaper,theimpactofthedierentcarriersensingthresholdsonaggregatelinkthroughputandtheirinteractionwithmultipledataratesareinvestigatedthroughour 17

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Theotherimportantissuesinthefocusofthispaperaretheend-to-endpathcapacityandaggregateend-to-endcapacity.Tothebestoftheauthors'knowledge,thosenetworkperformancemetricshavenotbeensystematicallystudiedwithrespecttothecarriersensingthresholdinthepreviouswork.Tosupportend-to-endcommunicationinwirelessmultihopmultiratenetworks,itisnecessarytondapathormultiplepathswiththemaximumcapacity,whichisoneoftheimportanttasksofQoSrouting.Theinformationabouttheoptimalend-to-endpaththroughputcapacityoraggregateend-to-endcapacityofmultipleowsisalsousefulforadmissioncontrolinprovidingQoSinwirelessmultihopmultiratenetworks.However,itisdiculttoquantifytheend-to-endpathcapacityortheaggregateend-to-endowcapacityinthemultihopmultiratewirelessnetworkduetothefactorssuchasthetime-varyingwirelesschannelcondition,interferencefromconcurrenttransmittinglinksandthemultiratecapability.AsillustratedindetailinSection 2.2 ,carriersensingthresholdshavegreatimpactonbothend-to-endpaththroughputandaggregateend-to-endthroughputofmultipleows.Previousworkinvestigatingthepathcapacityandmultiowcapacitysuchas( 15 )( 18 )identifythemaximumpaththroughputwithoutconsideringtheimpactofcollisionallowedbythecarriersensingmechanism.Incontrast,weendeavortoidentifytheoptimalcarriersensingthresholdwhichwillmaximizethosenetworkmetricsinthenetworkswherethephysicalcarriersensingmechanismisusedandthereexistscollisionduetothehiddenterminalproblem.The 18

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Therestofthepaperisorganizedasfollows.AfterreviewingtherelatedworkinSection 2.1 ,weproceedtoexplaininSection 2.2 theproposedapproachindetail.Thereweintroducethekeyconceptsaboutconcurrenttransmissionsetsandtheproblemformulationofndingtheoptimalcarriersensingthresholdwiththeobjectiveofmaximizingtheend-to-endpaththroughput.Thenweshowhowtheapproachisusedtostudytherelationshipbetweenthecarriersensingthresholdandaggregateend-to-endthroughputofmultipleowsoraggregatelinkthroughput.Moreover,weextendtheapproachbyintroducingorderedconcurrenttransmissionsettostudytheimpactofnon-uniquecarriersensingrangesonthenetworkperformanceinSection 2.3 .TheperformanceanalysisisgiveninSection 2.4 .Finally,wedrawtheconclusioninSection 2.5 2.1.1AnalyticalModelForCarrierSensingThresholdWithSpatialReuse 1 ),Guoetal.investigatedtheoptimalspatialreusefortworegularnetworktopologies,i.e.,1-Dchainnetworkand2-Dgridnetwork,wherethesametransmissionpoweranddatarateareused.In( 2 ),Wongetal.modeledtheinhibitingeectofnearbytransmissionsusingthe 19

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4 ),Fuemmeleretal.adoptedthecarriersensethresholdmodelandassumedthattheinterferenceiscomingfromthekworstinterferenceswiththeco-locationapproximation.In( 11 ),Maetal.proposedastochasticmodelincorporatingtheimpactofcarriersensingthresholdandthebackomechanismviaaMarkovchainmodelforsaturationcase.Itoptimizesthecarriersensingthresholdintermsoftheprobabilityofpacketcollisionsandtheaggregatelinkthroughput. Dierentfromtheaboveapproachesbasedonprobabilitytheory,weusegraphtheoryconceptsandlinearprogrammingtostudytherelationshipbetweenaggregatethroughputandcarriersensingthreshold,whichcanbeappliedtoanygivennetworktopologyandtrac.Inthispaperwedonotstudytherandombackomechanismsothatwecanfocusontheimpactofthecarriersensingmechanismonnetworkperformance. 5 )( 7 )proposedtondtheoptimalphysicalcarriersensingwithadynamictuningprocess.Dengetal( 22 )denedacostfunctionconsideringenergyconsumption,queuingdelay,computationalpoweroranintegralofmultipleofthosefactorsandrewardfunctionforsuccessfultransmissions.Thedynamicaltuningcarriersensingrangeisusedtomaximizethetotalreward.In( 19 ),Royetal.proposedtominimizethecostfunctionoftheunionofhiddenandexposedterminalareawithcarriersensingthresholdasavariable.In( 14 ),Zhuetal.developedaheuristicadaptivecarriersensingschemetoimprovetheaggregatethroughput. Despitepreviouseortsuchas( 5 )( 7 )( 8 )( 9 ),therelationshipbetweentheoptimalcarriersensingthresholdandtheaggregatethroughputtogetherwiththeavailabilityofmultipledataratesinwirelessnetworkshasnotbeenfullyprobed.Morerecently,Lin 20

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12 )studiedtheissueofbalancingtheinterplayofspatialreuseanddatarateselectionthatcanbesustainedforagivenSINRvalue.Theirultimateobjectiveistomaximizetheaggregatelinkthroughputbasedonthemodiedmodelfrom( 20 ).Theyproposedtheconceptofcollisionzoneandattemptedtotoleratethesimultaneoustransmissionswithinthecarriersensingareabutoutsideofthecollisionzones.Findingoptimalcarriersensingthresholdinwirelessmultiratemultihopnetworksisstillanongoingresearch. Noticethatmostofthepreviousworkmentionedabovestudiedtheaggregatelinkthroughputbycalculatingtheproductofnumberofconcurrenttransmissionsandthethroughputpernode.Theyarenoteasilyusedtoaccuratelyobtaintheend-to-endthroughputonapathormultipleowsoverthewholenetwork.Moreover,themodelseitherassumesomeregulartopologiesorrelyonaspecialprobabilitydistributionofnodelocationsuchasthetwo-dimensionPoissonpointprocess. Inthispaper,wedemonstratetheimpactofcarriersensingthresholdonseveralnetworkperformancemetricsincludingtheaggregatelinkcapacity,theend-to-endpathcapacityandtheaggregateend-to-endowcapacity.Ourapproachdoesnotrelyontheprobabilitydistributionofnodelocationandusesthelinearprogrammingformulationtocalculatethoseend-to-endnetworkmetricsaswellastheaggregatelinkthroughputandtoidentifytheoptimalcarriersensingthresholdforgiventopologiesandtrac. 15 )( 18 )attemptedtoobtainthemaximumpaththroughputforgiventopologies.Theirprimalgoalistondtheend-to-endpaththroughputormultiowthroughputinacomputationallyecientway.ThesenetworkperformancemetricsalsoservedasthebasistondmoreproperroutingmetricstomeettheQoSrequirementortoanalyzetheroutingcapacity.Ourworkdiersfromtherelatedworkintwoaspects: 21

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Second,theproposedapproachconsiderstheeectofcollisionswithintheconcurrenttransmissionset.Sincecarriersensingmechanismcannotpreventallthecollisionsresultingfromhiddenterminalproblems,simultaneoustransmissions,orSINRdissatisfaction,itisnecessarytoconsidertheeectofcollisionsontheavailabledatarateandconsequentlythethroughputperformance.However,previousworksuchas( 15 )( 18 )usestheconceptofindependentsetwhichdoesnotconsiderthecollisionwithintheset.Byconsideringthecarriersensingmechanisminconstructingtheconcurrenttransmissionset,weareabletoaccountfortheeectofcollisionswithintheconcurrenttransmissionset.Inthisway,wendtheoptimalcarriersensingthresholdinthewirelessmultirateandmultihopnetworkswherecarriersensingmechanismisused. 12 ),distinctcarriersensingthresholdsmayfacilitatethelocaltuningforcarriersensingthreshold.Andwedemonstratethatusingthedistinctcarriersensingthresholdscanhelpimprovethenetworkperformanceinthenetworkswithnonhomogeneousnodedensitydistribution. 21 )concludingthattuningthecarriersensingthresholdwillactuallyreduceaggregatethroughputunderextremeloadsandwastepotentialtransmissionopportunities.Whatismore,Kimetal.in( 13 )comparetheeectofpowercontrolwiththatoftuningcarriersensingthreshold,andconcludethattuningthetransmitpoweroersseveraladvantagesthatwillnotbeabletobeachievedbyonlyadjustingthecarriersensingthreshold 22

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Onlywhenthechannelissensedidle,atransmittercanstartthetransmissionprocessoverthesharedmedium.CorrespondingtothecarriersensingthresholdTcs,thecarriersensingrangedcscanbefoundviacommonlyusedchannelpropagationmodelasfollows: whereKisaconstantandisthepathlossexponent,typically25.Ptisthetransmissionpower. Inordertofocusonthecarriersensingmechanism,wedonotstudytherandombackomechanisminthispaper.Weinvestigatethecasewithnopowercontrolscheme.Thetransmissionpowerateachnodeisthesame. 23

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12 )). Aconcurrenttransmissionsetwithacommoncarriersensingrangeisdenedasalinkset,inwhichtransmittersareoutsideofeachother'scarriersensingrange.SupposethereareNnodesinthenetworks.Letlidenotethelinkwithnodeiasitstransmitterandnodei+1asitsreceiver.Letdijbethedistancefromtransmitteroflinkitothatoflinkj.Linkiandlinkjcanbeinaconcurrenttransmissionsetaslongas Theconcurrenttransmissionsetcanbefoundrecursivelyfromallthelinksinthenetworkusingtheaboverules. Nowwearereadytodenethemaximalconcurrenttransmissionset(MCTS).Amaximalconcurrenttransmissionsetwithacommoncarriersensingthresholdisdenedasaconcurrenttransmissionsetsatisfyingthepropertythataddinganyotherlinkintothesetresultsinasetwhichisnotaconcurrenttransmissionsetanymore.Foreachlinklj,theremaybemultipleMCTSs. Theconstructionoftheconcurrenttransmissionsetsimulatestheeectofcarriersensingmechanismwhichseparatesthetransmissionsfarenoughfromtheviewoftransmitters.MCTSsindicatethepossiblemaximumspatialreuse. 24

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Hiddenterminalproblemsinconcurrenttransmissionsets thereceiverside.However,thehiddenterminalproblemcouldstillexistinthescenarioswhereanodeisoutofthecarriersensingrangeofatransmitterandthetransmissionrangeofthereceiver,butwithintheinterferencerangeofthereceiver.AsshowninFigure 2-1 ,nodemisacaseinpoint.Herethetransmissionrange,denotedasDt,indicatesthedistanceatwhichthereceivedsignalstrengthattenuatestothereceiversensitivity.Theinterferencerange,denotedasDi,isdeterminedby( 35 ): Usually,theinterferencerangeslargerthanthetransmissionrange.InNS2,thedefaultsettingforcarriersensingrangeis2.2timesofthetransmissionrange,andtheinterferencerangeisabout1:78timesofthetransmissionrangewhenthereceiversensitivityissetto10dB. 25

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ToobtainthethroughputforeachMCTS,weneedtocalculatetheinterferencelevelatreceiversofalllinksineachMCTS.Givenamaximalconcurrenttransmissionset,theinterferencelevelatthereceiveroflinklm,denotedasIm,andtheSINRatthereceiveroflinklmaredeterminedby: and wherePNisthenoisepower,andPrmnisthereceivedsignalstrengthatthereceiverofthelinklmfromthetransmissionoverlinkln.ThedatarateisdeterminedbyboththeSINRandthereceiversensitivityrequirementatthereceiversideofeachlink. Oneoftheimportantfeatureswhichmakeourworkdierentfromotherssuchas( 16 )( 18 )isthattheconcurrenttransmissionsetcontainslinkswhichcancausecollisions.Thoughthoselinkswhichexperiencecollisiondonotcontributetothepaththroughput,buttheinterferencefromthoselinksaswellastheirconsequentinuenceontheavailabledatarateshouldbeconsidered.Incontrast,theindependentset( 16 )( 18 )onlyincludeslinkswhichcantransmitsuccessfullyatthesametime. 2.2.2 .ConsiderapathwithalinksetL.ThetimeshareassociatedwitheachMCTSCiisdenotedbyi 26

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whereNcisthetotalnumberofdierentMCTSs.AssociatedwitheachCi,thereisarowvector~RiwithsizeofjLjrepresentingthedatarateonthelinksinthesetCi.LetriebetheSINRdeterminedhighestavailablediscretedatarateonlinke2Ci.Fore2L=Ci,letrie=0.Thus,~Ri=frieje2Lg.Letfedenotethedemandforlinke2L.Thedemandvector,~f=ffeje2Lg,isfeasibleifthereexistsaschedulingsatisfying Thentheproblemofndingthepathcapacityisformulatedas: maxmine2Lfe;s:t:P1iNci1;P1iNci~Ri~f;i0;81iNcfe0;e2L:(2{9) Letdenotemine2Lfe.Thentheabovecanbefurtherexpressedintoalinearprogrammingproblem: max;s:t:P1iNci1;P1iNci~Ri~I;i0;81iNc0;(2{10) where~IisanallonevectorindimensionofL.Toprobetherelationshipbetweenpathcapacityandcarriersensingthreshold,wediscretizethecarriersensingthresholdintoa 27

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argmaxn:Tn2Tn;s:t:P1iNncni1;P1iNncni~Rin~I;ni0;81iNncn0:(2{11) Ifaggressiveschedulingisused2,thenalltheMCTSareusedtocalculatetheoptimalend-to-endpathcapacity.Otherwise,alltheconcurrenttransmissionsetsareused. InSection 2.2.7 ,therelationshipbetweenMCTSsfordierentcarriersensingthresholdsisusedtoderiveacomputationallyecientalgorithmforndingalltheMCTSsforeachcarriersensingthreshold.Wewillrevisittheproblemofhowtodiscretizethecarriersensingthresholdsagaintoreducethesamplingsizeforcarriersensingthresholds. 28

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Let~fdenotetheowdemandvectorforallMpathsand~f=ffmj1mMg.fnmistheowdemandforthemthpathgivencarriersensingthresholdTn.~fnistheowdemandvectorforallMpathsgivencarriersensingthresholdTnand~fn=ffnmj1mMg. Theoptimalcarriersensingthresholdcanbefoundbysolvingthefollowinglinearprogrammingproblemwhichmaximizestheaggregateend-to-endthroughputofallthoseowsamongNsourceanddestinationpairs: argmaxn:Tn2TMPm=1fnm;s:t:P1iNncni1;P1iNncni~RniH~fn;ni0;81iNncfnm0;1mM(2{12) whereHisthepathindicatormatrixofsizejLjM,andtheithcolumnofHisequaltoI(Pi). 29

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argmaxn:Tn2TjLjPj=1fnjs:t:P1iNncni1;P1iNncniRni(j)fnj;8j2Lfnj0;8j2Lni0;81iNnc;(2{13) whereRni(j)isthejthelementinthevector~RniwhichistheratevectorfortheithMCTSgiventhecarriersensingthresholdTn. Thealgorithmisbasedonthefollowingtheorem: 30

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Proofcompletes. Apparently,fortwodierentMCTSsofS,MCTSi(S)andMCTSj(S),theirunionMCTSi(S)SMCTSj(S)cannotbeaCTSofS. SupposeRS>RL.Thereexistiandj(i6=j;1iRS;1jRS),andthereexistsk(1kRL)suchthatMCTSi(S)MCTSk(L)andMCTSj(S)MCTSk(L).Therefore,MCTSi(S)SMCTSj(S)MCTSk(L).Thatistosay,MCTSi(S)SMCTSj(S)isaCTSofL.SinceMCTSi(S)SandMCTSj(S)S,MCTSi(S)SMCTSj(S)isaCTSofStoo.Thisisnottrueasshownabove.Proofcompletesbycontradiction. UsingTheorem1,wecanreducethecomputationalcomplexityinndingallthemaximalconcurrenttransmissionsetseachtimewhenweincreasethecarriersensingrange.Furthermore,wecanalsoprovethatthefollowingalgorithmndsallMCTSsforalargercarriersensingrangegivenallmaximalindependentsetsforasmallercarriersensingrange.ThebasicideaofthefollowingalgorithmisonlytocomputesomesubsetsofallknownMCTSsforthesmallercarriersensingrangewhenthecarriersensingrangeisincreased. ConsiderlinksetL.TherearejLjlinksandtotalQ=jLj(jLj1) 2dierentpairsoflinks.Analgorithmtondallmaximalconcurrenttransmissionsetisasfollows: 31

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2)Letn=0andd0cs=1,thereisonlyoneMCTS,whichisthelinkssetLitself.M0=fMCTS01=Lgandr0=1.Herethe1isaninitialstepofthealgorithm.0issetasone. 3)Determinethenextcarriersensingrangedn+1csbyfollowingeitherthestep3a)orthestep3b). 3a)Letdn+1cs=dn+,whereisaconstantsatisfyingthatforany1i;jQ,di+
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AlgorithmforndingalltheMCTs fori=1:rn,j=1:rnandj6=i end elseifMCTSinSi=MCTSjnSj elseifi>j,x[j][k2]=1,andMbk1(i)Mbk2(j) end end end forallx[i][k]=1(1irn;1kqi) (MCTSinSi)SMbk(i)isaMCTSfordn+1cs transmittersMCTSi=fT1;T2;:::;Tpig,wherepi=jMCTSij.Letmj(1jpi)bethenumberoflinkswithnodeTjasthetransmitter,wecanobtainQpij=1mjMCTSsofLbyreplacingTjinMCTSiwithoneofthecorrespondingmjlinks. Analgorithmtondallconcurrenttransmissionsets:AftergettingalltheMCTSs,itiseasytogetallconcurrenttransmissionsetsbyenumeratingallsubsetsofallthemaximalconcurrenttransmissionsetsandremovingthesameones. AlgorithmComplexitytondallmaximalconcurrenttransmissionsets Letkn+1=nn.Apparently,qi<2jSij22kn+1.FromTheorem2,qirn+1sinceSiL.Therefore,qiminf22kn+1;rn+1g=q.ForeachpairofMCTSs(MCTSi;MCTSj)(i
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Toshowtheadvantagesofdistinctcarriersensingranges,oneexampleisillustratedinFigure 2-2 .Therearethreeactivelinksinthenetwork.Nodes1,2and3aretransmittersandnodes4,5and6aretheirreceivers,respectively.Usingpreviousnotation,letlidenotethelinkwithnodeiastransmitter.Thedistancesbetweenthetransmittersared.Letdcs(i)(1i3)denotethecarriersensingrangesofthetransmitteri.Suppose1Mbpsdatarateisused,andtheSINRrequirementforsuccessfultransmissionsis10dB.Wemakethefollowingcomparison: 34

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Usingdierentcarriersensingrangestoachievethemaximalaggregatelinkthroughput therearethreemaximalconcurrenttransmissionset:fl1g,fl2gandfl3g.Theoptimalaggregatelinkthroughputisstill1Mbps. Insomesense,thedistinctcarriersensingthresholdshelprelievetheexposedterminalproblemandthusimprovingthenetworkperformance. Inordertoanalyzetheimpactofdistinctcarriersensingthresholdsonthenetworkperformance,weneedtoextendthepreviousapproach.Oneoftheimportantdierencesariseinthewayofndingtheconcurrenttransmissionset.Ifdierentcarriersensingrangesareusedinthenetwork,adierentorderoftheoccurrenceoftransmissionscanresultindierentconcurrenttransmissionsets.Forexample,inFigure 2-2 ,wesetdcs(1)d.Ifwerstputlinkl1intheconcurrenttransmissionset,l2cannotbeputinthesamesetbecaused
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Algorithmofndingallthemaximalorderedconcurrenttransmissionsets. j=1; fori=1toL end FunctionfindMCTS(E,F,i) end end ifflag==0 foralllj2F end end ifflag==1andE6= Eisamaximalorderedconcurrenttransmissionset transmitterofljifbothliandljareinthesetandlicomesbeforeljintheorder.Intheaboveexample,whendcs(1)d,thesetfl2;l1gisanorderedconcurrenttransmissionsetwhilethesetfl1;l2gisnot.Amaximalorderedconcurrenttransmissionsetisdenedasanorderedconcurrenttransmissionsetsuchthataddinganylinkwhichisnotinthesetaccordingtothespeciedordermakesitnolongeraconcurrenttransmissionset.Forinstance,inFigure 2-2 ,whendcs(1)danddcs(3)
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2-2 ,onlylinksinasetwithnomorethan(Lk)linkswillbecheckedtojudgewhethereachofthemsensesthetransmissionofthelinkthatislastinsertedinaconcurrenttransmissionsetwithklinks,andtoconcludeaccordinglythatwhetheraddingeachofthemintotheconcurrenttransmissionsetstillresultsinaconcurrenttransmissionset.Therefore,thereareatmostL!timesdistancecomparisonsandothercorrespondingoperations,andthecomplexityofthisalgorithmisO(L!). Byusingallthemaximalorderedconcurrenttransmissionsetsintheoptimizationproblemstudiedintheprevioussections,wecanndtheoptimalsetofcarriersensingrangesforallnodestomaximizethenetworkperformancemetricssuchasaggregatelinkthroughput,end-to-endpaththroughputoraggregateend-to-endowthroughput.However,thisproblemhasarelativehighercomplexitythantheproblemwithauniquecarriersensingrange.ThetotalnumberofdierentordersoflinksisL!.Ifsometransmittersusethesamecarriersensingrange,theexchangeofthesetransmittersintheorderdoesnotmakeasignicantdierence.Howtoutilizethisfeaturetoreducethecomplexityislefttothefuturework. 37

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16 ).TheroutesarefoundbyusingETT(EstimatedTransmissionTime)( 15 )insteadofhopcountastheroutingmetrictomakeabetteruseofthemultiratecapability. First,wewouldliketoshedsomelightononecommonphenomenaweobservefromFiguresinthissection:Theaggregatelinkthroughputincreasesuntilreachingtheoptimalvalueasthecarriersensingrangeincreases.Whenthesmallercarriersensingrangeisused,theloweraggregatelinkthroughputmayresultfromtheover-aggressivemediumaccesspolicy.TheinterferencesensedintheairisalwayshigherthanthatallowedbytheSINRrequirementwhichleadstocollisions.Howeverasthecarriersensingrangeincreases,thethroughputmaydecreaseatsomepointbecauseoftheover-conservativemediumaccesspolicyandasmallerdegreeofspatialreuse.Fromthenumericalresults,theapproachclearlycapturesthetradeobetweenspatialreuseandcollision. Next,weillustratetheimpactofseveralfactorsontheoptimalcarriersensingthresholdseparatelyasfollows: 38

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Impactofnumberofowstotheoptimalcarriersensingthresholdsforaggregatelinkthroughput Figure2-4. Impactofnumberofthesizeofphysicaltopologytotheoptimalcarriersensingthresholdsforaggregatelinkthroughput networkwith4;8;12;16;20ows.Thepathlengthvaryfrom1to4hops.TheaggregatelinkthroughputforthoseowsisshowninFigure 2-3 .Fordierentnumberofowsinthesamenetwork,therangesoftheoptimalcarriersensingthresholdaredierent.Wecanobservefromthegurethatthesmallercarriersensingrangeisoftenpreferredwhenmoreowsexistinthenetwork.Clearly,themoreowsthereexistinthenetwork,themoreimportantthespatialreuseis,andasmallercarriersensingrangeisthereforepreferredsinceitprovidesabetterspatialreuse. 39

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Impactofnumberofthehopdistancetotheoptimalcarriersensingthresholdsforaggregatelinkthroughput 2-4 ,theoptimalaggregatelinkthroughputforthecaseof22nodesisobtainedwhenthecarriersensingrangeincreasesto190m,whiletheothertworeachtheiroptimalthroughputatthe210mand300m.Atcarriersensingrangeof250m,forexample,thethroughputofthenetworkwith22nodesisoptimalwhilethethroughputoftheonewith10nodesisalmostzero. Inthisexperiment,thesource-destinationdistanceincreasesalongwiththenetworksize.Althoughthenodedensitydoesnotchange,thedensityofactivelinksusedbyowsincreasessincetherearemorehopsbetweeneachsourceanditsdestinationwhenthenetworksizeincreases.Therefore,asshowninFigure 2-4 ,asmallercarriersensingthresholdispreferredforalargenetworkduetothesamereasonasdiscussedin 2.4.1.1 40

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2-5 .Duetothesmallsizeofthenetwork,wecanguaranteethataroutesatisfyingthehopdistancerequirementalwaysexists.AccordingtotheFigure 2-5 ,thepathswithlargerhopdistanceshavelargeroptimalcarriersensingranges,andviceversa.Theoptimalcarriersensingrangeisdierentforeachcase.Asmallerhopdistanceallowsahigherdatarate.Italsoinvolvesmorelinksintheselectedpaths.Thus,itisimportanttoimprovethespatialreuseandasmallercarriersensingrangeispreferred. Noticethatwhenthehopdistanceofalinkfallsintooneoftheintervals,itdoesnotmeanthatthelinkwilladoptthemaximumdataratesatisfyingthetransmissionrangelargerthenthehopdistance,e.g.11Mbpsfortheinterval(183;304],becausethedataratehastobechosentomeettheSINRrequirementaswell.Thatiswhythelineforhopdistance(183;304]hasthethroughputof6Mbpssincetheremightbeonlyonelinkwithsuccessfultransmissionsintheconcurrenttransmissionsetanditsmaximumsuccessfulrateis6Mbpsduetotheinterferencefromothertransmissionsintheconcurrentset. 2-6 ,wecanseetheoptimalcarriersensingrangetotallydiersforeachrandomnetworktopology.Hence,thestatisticalestimationfortheoptimalcarrier 41

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Inthenumericalanalysis,weconverttherawchannelratesintotheeectivedataratesbyconsideringthePHYandMACoverhead.Theeectivedataratescanbesupportedare32.0,24.5,14.3,5.4Mbps.Thenetworksizeis500m500mwith20nodes.Thereare10sourceswith10ows.Eachsourcerandomlyselectsanothernodeasdestination.Figure 2-7 showsboththesimulationresultandthenumericalresultfortheaggregatelinkthroughput.Theproposedapproachisabletoprovideanimprovedaggregatelinkthroughput.Wealsoobservethattheoptimalcarriersensingrangeshavecoveredtheonesobtainedfromthesimulation( 16 ). 2.4.2.1Pathcapacitywithoptimalcarriersensingthreshold 42

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Impactofnetworktopologytotheoptimalcarriersensingthresholdsforaggregatelinkthroughput Figure2-7. Comparisonbetweennumericalandsimulationresultsforaggregatelinkthroughput Figure2-8. Impactofthenumberofhopsofpathsontheoptimalcarriersensingthresholdsforend-to-endpathcapacity First,wexthehopdistancetobe220minachaintopologyandshowtheend-to-endthroughputforpathswithdierenthopcounts.InFigure 2-8 ,whenthereisonlyone-hoppath,theend-to-endthroughputtotallydependsonthehopdistance. 43

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Wethendiscusstheimpactofhopdistanceontheoptimalcarriersensingthreshold.Westillusechaintopology.Eachpathconsistsof10hops.Thehopdistanceissettobe220m,330mand440m.AsshowninFigure 2-9 ,theoptimalcarriersensingrangeforthepathwith220mhopdistanceisfrom450mto650m,whiletheoptimalcarriersensingrangefortheonewith320mhopdistanceisfrom580mto850m.Withcarriersensingrangeof450m,thepathof220mhopdistanceachievestheoptimalthroughputwhilethepathof320mhopdistancehasnothroughputatall.Thelongerthehopdistancethepathuses,thelowertheend-to-endthroughputissincebecausethemaximumdatarateofthelinkislimitedbythehopdistance.Forexample,thecarriersensingrangeshouldbelargeenoughtoseparatethetransmissionswhichwouldresultincollision.Anditshouldnotbetoolargetotakeadvantageofthespatialreuse.Inthissetting,wealsoconcludethatacarriersensingrangeof2timesto3timesofthehopdistanceisagoodchoiceforpathsofdierenthopdistances. 44

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Impactofhopdistanceontheoptimalcarriersensingthresholdsforend-to-endpaththroughput Figure2-10. Impactofthenumberofowsontheoptimalcarriersensingthresholdsformultiowaggregatethroughput Figure2-11. Impactofthesizeoftopologiesontheoptimalcarriersensingthresholdsformultiowaggregatethroughput networksizeof500m500m.Weincreasethenumberofowsfrom4to16.AccordingtotheFigure 2-10 ,thenetworkwith16owsreachestheoptimalthroughputwhenthecarriersensingrangeis160mwhiletheonewith4owsreachestheoptimalthroughput 45

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Second,weanalyzetheimpactofthesizeofthetopologyontheoptimalcarriersensingthreshold.Thereare15nodesinthenetworksofdierentsizesofthetopology.AsshowninFigure 2-11 ,theoptimalcarriersensingrangeforthenetworkwiththesizeof100m100mbeginsatthedistanceof125mwhiletheoptimalcarriersensingrangeforthenetworkwiththesizeof400m400mbeginsatthedistanceof400m.Thelargerthenetworksizeis,theearlierthenetworkreachestheoptimalaggregateend-to-endowthroughputasthecarriersensingrangeincreases.Itisbecausethatthelargernetworkwiththesamenumberofowshasasmallernetworkdensityandlongerhopdistance.Carriersensingrangehastobelargeenoughtoseparateadjacenttransmissions. 15 )( 18 )tocalculatetheabovenetworkperformancemetrics,itassumesthattheoptimalvalueisachievedwhenthenonaggressivelinkschedulingisused.Thenonaggressiveschedulingmaynotallowallthenodeswhichareseparatedfarfromeachothertobeabletotransmit.Inthisway,itmayavoidthecollisionwithinthemaximumconcurrenttransmissionsetandthepossiblyachievedthroughputmightbegreaterthanamaximalconcurrenttransmissionset.However,theaggressiveschedulingcanbeimplementedbysimplyfollowingthecarriersensing 46

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Impactofnumberofowsontheoptimalcarriersensingthresholdswithnonaggressivetracformultiowaggregatethroughput mechanismwhilethenonaggressiveschedulingneedsmorecomplicatedmechanismotherthancarriersensingmechanismtocoordinatethetransmissions.Inotherwords,theaggressiveschedulingbettercapturestheeectofcarriersensingmechanismthannonaggressivescheduling. Inthissubsection,weinvestigatethecasewithnonaggressiveschedulingwhichusesalltheconcurrenttransmissionsetstondtheoptimalend-to-endthroughputofmultipleowsandthecorrespondingcarriersensingthresholds.FromFigure 2-12 andFigure 2-13 ,wecanseethatthedecreasingtrendoftheend-to-endthroughputwhenincreasingthecarriersensingrange.Withnonaggressivescheduling,ahigheraggregateend-to-endowthroughputisobtainedbuttheschedulingincorporatesthemixedeectofseveralfactors,suchasbackomechanism,otherthanthecarriersensingmechanism.Thus,usingourapproach,wecanonlygetthepointofcarriersensingrangewheretheperformanceisgoingtodecreaseratherthanthewholeoptimalcarriersensingrangeforthenonaggressivetraccase. 2-2 .Thedistancebetweenthetransmittersisequalto200m.Thedatarate1MbpsisusedanditsSINRrequirementis10dB.Thelinklengthis100 47

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Impactofsizeofthetopologyontheoptimalcarriersensingthresholdswithnonaggressivetracformultiowaggregatethroughput Figure2-14. Impactofdierentsetsofcarriersensingrangesonaggregatelinkthroughput 2-14 ,wecouldseethatthesetswithindices4,5,and6givetheoptimalaggregatelinkthroughput.Letusrstexamineset4forexample,thecarriersensingrangesarechosentobef240;160;160gm.Inthiscase,transmitter1andtransmitter2willtransmitconcurrentlyanditachievestheoptimalaggregatelinkthroughput2Mbps.Forset5,thecarriersensingrangesaref240;160;240gm.Theoptimalaggregatelinkthroughputcanbeachievedbyschedulingthel1rstandl2second.Forset6,itisthesymmetricalcaseforset5.Herewecouldseethemaximalorderedconcurrent 48

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Accordingtothenumericalandsimulationresults,itwouldnotbereasonabletoclaimanycommonoptimalcarriersensingthresholdforallthenetworks,orevenfornetworkswherebothnodedensityandtracfollowthesameprobabilitydistributions.Thus,awayofgettingtheoptimalcarriersensingthresholdsforanygivennetworkisindeedneededandourapproachendeavorstoachievethisgoal. Moreover,ourapproachtakesintoaccountthedistinctcarriersensingthresholdsinasinglenetworkandndsasetofoptimalcarriersensingthresholdsfordierentnodes.Weclearlyshowthatproperlyusingdierentcarriersensingrangesachieveshighernetworkthroughputthanusingauniquecarriersensingrangeoverthewholenetwork. 49

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Inthispaper,wefocusononemajorQoSmetric,i.e.,availablebandwidth.Beforeadmittingamultimediaow,itisparamounttoknowwhetherapathcanprovideenoughbandwidthfortheow.Inthepreviouswork( 15 ),wehavedevelopedatheoreticalmodeltocalculatepathcapacitywithoutconsideringbackgroundtrac.However,thisproblembecomesmoredicultwhentherearesomebackgroundtracbecausetheinterferencebetweenanewowandexistingtracishardtoestimateandcontrol. Previousworkshavefocusedonestimatingnodes'availablebandwidthandapplyingtheresulttoestimatinglinks'andpaths'availablebandwidthinQoSrouting,admissioncontrolandowcontrol( 24 { 30 ).Awidelyusedapproachistomeasurethechannelidletimeandaccordinglycalculateanode'savailablebandwidth.Toobtainapath'savailablebandwidth,interferencehastobetakenintoconsideration.Nodesinthesameneighborhoodorineachother'sinterferencerangesharethesamewirelesschannel.Totalthroughputoflinksinterferingwitheachotheralongapathcannotexceedthechannelbandwidthorthelocalavailablebandwidth. Therearealsomanyworksusingowcontentiongraphandcliqueconstraintstoconstructnecessaryandsucientconditionsorderivelowerandupperboundsofpaths'throughputtobenetresourceallocation,QoSrouting,andowcontrol( 18 )( 31 )( 32 ).Intheseworks,acliqueisoftenreferredtoasasetoflinkssatisfyingthateverytwoof 50

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Twosimpletopologies theminterferewitheachother.Thecliqueconstraintissimplythatthetotalfrequencyoflinksinacliqueisnotlargerthanone,whereafrequencyofalinkisdenedasthelink'sthroughputdividedbythechannelbandwidth. Inthispaper,westudythepathavailablebandwidthproblemwithbackgroundtracinmultirateandmultihopwirelesssensornetworks( 16 )inasystematicway.Weassumethatthereexistsaglobaloptimallinkschedulingandcalculatethemaximumavailablebandwidthofpathsforanygivenbackgroundtrac.Forexample,athreelinktopologyisshownintheScenarioIofFigure 3-1 .Theproblemhereistondthemaximumavailablepathbandwidthalongaone-hoppathoverlinkL3.SupposelinkL1andL2donotinterferewithorheartransmissionfromeachother,butlinkL3interfereswithandhearboththetransmissionsoverL1andL2.ThebackgroundtracoverL1andL2occupythesametimesharebuttheirtimesharesdonotoverlapwitheachother.IfthecontentionbasedIEEE802.11MACprotocol(( 6 ))isusedandL3'sdemandrequiresatimeshareof1,L3cansuccessfullyoccupyatimeshareof1aftersometime,andthetimesharesofL1andL2willcompletelyoverlapwitheachother.However,usingthemechanismofchannelidletimetoestimateavailablebandwidth,theowoverL3isonlyadmittedifitoccupiesatimesharenotlargerthan12.Inthispaper,byassumingthataglobaloptimallinkschedulingexists,wewillcorrectlycalculatethemaximumavailablebandwidthoverlinkL3. Weformulatethepathavailablebandwidthproblemusinglinearprogrammingandproposetheconceptsofindependentsetsandcliquestotakeintoconsiderationoftheadvantagesoflinkadaptation.Anindependentsetandacliquearenotonlyspeciedbya 51

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WealsoextendthepathavailablebandwidthproblemintoajointdesignofQoSroutingandlinkschedulingtondpathswithhighavailablebandwidth. Therestofthispaperisorganizedasfollows.InSection 3.2 ,wedevelopatheoreticalmodeltocalculateavailablepathbandwidth.WethenstudyupperboundsandlowerboundsderivedfromcliquesandindependentsetsinSection 3.3 .InSection 3.4 ,severalroutingmetricsareproposed.WeevaluatetheperformanceofdierentQoSroutingmetricsandavailablebandwidthestimationmetricsusingtheproposedmodelsinSection 3.5 .Finally,Section 3.6 concludesthispaper. 3.2.1AvailableBandwidthProblem GivenanewpathPK+1,wewanttondouthowmuchmoretracthatthenetworkcouldsupportoverPK+1.LetfK+1denotethethroughputoverpathPK+1.TheproblembecomesmaximizingthroughputfK+1overpathPK+1whileguaranteeingthedeliveryofthroughputxi(1iK)overpathPi(1iK),respectively.BeforewestudythefeasibleconditionoftheK+1ows,werstintroducethemultiratecapabilityandstudyindependentsetswithmultiplediscreteratesinthefollowingsubsections. 52

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Asuccessfultransmissionalsorequiresthatthesignaltointerferenceplusnoiseratio(SINR)belargerthanacertainthreshold.AhigherratealsorequiresahigherSINR.LetSINR(k)denotetherequirementofSINRofraterk.Therefore,asuccessfultransmissionsatisestwoconditions: Pinf+PnSINR(k);(3{1) wherePristhereceivedpower,PinfistheinterferencepowerandPnisthenoisepower. AlinkschedulingScanbedescribedasmultiplesetsoflinksandeachsetisscheduledinonetimeslot.Eachsetisreferredtoasaconcurrenttransmissionlinksetthereafter.LetMbethetotalnumberofdierentsetsoflinksinthelinkscheduling,Ei(1iM)betheithsetoflinks,andibethelengthoftimeslotscheduledforlinksinEitotransmit,istheperiodthatSrepeatsitself,!Ri=fri1;ri2;:::;riLgisathroughputvectorifEiisscheduledfortransmission,rijisachievablethroughputoverlinkLjifEiisscheduledfortransmission.Apparently,rij=0ifLj=2Ei.!fisfeasibleifand 53

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IneachconcurrenttransmissionlinksetEi,giventransmissionpoweratalllinksintheset,wecancalculatethesignaltointerferenceplusnoiseratio(SINR)SINRijateachlinkLjasfollows, wherePrkjisthereceivedinterferencepoweratlinkLjduetothetransmissionoverlinkLk,PrjjisthereceivedsignalpoweroftransmissionoverlinkLj,andPNisthenoisepower. Let!RidenotethemaximumlinkratevectorofEi,and!Ri=frijj1jLg,whererij=0iflinkLj=2Ei.rijdenotesthemaximumsupportedlinkrateatlinkLjinEi,anditisdeterminedbyPrjjandSINRijaccordingtoEquation 3{1 .NoticethatalinkLjinEimaybeabletochoosearate0
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3{2 ,weonlyneedtoconsiderthoseconcurrenttransmissionsetswitharatevector!Ri=frij(1jL)gwhererij>0foranylinkLj2Ei. Noticethatinmultiratenetworks,wherelinksareallowedtotransmitwithdierentratesatdierenttime,amaximumindependentsetmaybeasubsetofanotherindependentset,however,thereareatleastonelinkintheformeronewithahighermaximumratethanitinthelatterone.Thisisnottrueforsingle-ratenetworksormultiratenetworkswithaxedrateassignment. FromProposition2,onlyindependentsetsarenecessarytobeconsideredinthefeasibleconditionEquation 3{2 .FromProposition1,foreachindependentset,onlythemaximumsupportedlinkratesarenecessarytobeconsideredinthefeasiblecondition.Actually,onlymaximalindependentsetswithmaximumsupportedratevectorsarenecessarytodeneafeasiblecondition.ThisistheProposition3. 55

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isequivalentto Proofisomittedhereduetothespacelimit. FollowingthenotationweusedinSection 3.2.1 ,wedeneP=SiPi.InP,werstndallmaximumindependentsetsE(1cM)andcalculatethemaximumsupportedratevectors!RforeachEofP.LetI(Pk)bearowindicatorvectorinRjPj,and ThentheproblemtondthemaximumthroughputoverpathPK+1canbeformulatedas MaximizefK+1Subjectto:cMP=1RKPk=1xkI(Pk)fK+1I(PK+1)0;cMP=11;0(1cM);fK+10;(3{6) whichcanbesolvedbysomestandardlinearprogrammingapproach.IfthesolutionofthisoptimizationproblemfK+1islargerthanorequaltotheow'sdemandxK+1,thenewow'sdemandcanbesupportedoverthepathPK+1withoutaectingthebandwidthrequirementsofbackgroundtrac. Theaboveformulationcanalsobeextendedintothecaseswheretherearemorethanoneowwithcorrespondingdemandsjoiningthenetworksimultaneously. 56

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Inthispaper,acliqueCisdenedasasetofmultiplecouplesofalinkanditstransmissionrate(Li;ri),andC=f(Li;ri)g8i.ForanytwolinksLiandLj(i6=j)inacliqueC,notbothtransmissionswillbesuccessfulifLitransmitsdatawitharateriandLjtransmitsdatawitharaterjatthesametime.ThisphenomenonisalsoreferredasthatLiwithrateriinterfereswithLjwithraterj. AmaximalcliqueCisdenedasacliquewhichsatisesthatC[f(Li;ri)gisnotacliqueforanycouple(Li;ri),whereLi=2CandriisapositiverateifLitransmitsalone.AmaximalcliquewithmaximumratesisdenedasamaximalcliqueCwhichsatisesthatCwillnotbeamaximalcliquebyreplacing(Li;ri)with(Li;r;i)foranyLi2Candr;i>ri,wherer;iisanachievablerateoverLiifLitransmitsalone. Forexampleinafour-linkchaintopologyasshowninFigure 3-1 ,weassumethatalllinkscanonlysupport36and54Mbpsifeachofthemtransmitsalone.Wealsoassumethatanytwooflinks1,2,and3interferewitheachotherwhicheverratestheyusefortransmission,andthesameforlinks2,3,and4.Links1and4interferewitheachotherif 57

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Apparently,ifonlylinksareconsidered,amaximalcliquecouldbeasubsetofanothermaximalclique.Thiscannothappeninsingle-ratenetworksorinmultiratenetworkswhereeachlinkalwaysusesaxedrate. Inasingleratewirelessnetwork,severalwork( 18 )( 32 )haveshownthatthetotaltimeshareforsuccessfultransmissionsoveralllinksinacliquecannotexceedoneorthemaximumavailabletimeshare.Thus,XLi2Cyi N;whereristhelinkrateandNisthesizeoftheclique. In( 15 ),weshowedasimilarresultformultiratewirelessnetworkwhereeachlinkselectsaxedratefrommultiplechoicesandusedthecliquetransmissiontimetoderiveanupperboundofthroughput.Letri(1iN)denotethelinkrateoverlinkLiinacliquewithNlinks.Wecanhave:XLi2Cyi

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^T;(3{7) where^Tisdenedasthecliquetransmissiontimeforoneunitoftracin( 15 ). However,anupperboundderivedfromagivenratevectorisnotnecessarilyanupperboundforanetworkwhereeachlinkmaychooseadierenttransmissionrateatdierenttime,whichisatypicalcasewithsomeappropriatelinkadaptationscheme. Nowletusanalyzetheupperboundofthroughputinawirelessnetworkwhereeachlinkisallowedtousedierentratesatdierenttime.Let!Y=fy1;y2;:::;yLgbethedemandvectoroflinksLi(1iL).Cij(1jMi)isthejthcliquegivenaratevector!Ri=fri1;ri2;:::;riLg,andMiisthetotalnumberofdierentcliquesfor!Ri.Let!ICijbeanindicatorvectorforcliqueCij,and!ICij(k)=8><>:1;Lk2Cij0;Lk=2Cij;Lk2P: 59

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Acounterexampleisthefour-linkchaintopologyinFigure 3-1 andisanalyzedinSection 3.5 Therefore,itisnoteasytoderiveanupperboundforthefeasiblethroughputvector!Ybydirectlyapplying!Yovercliques.Hereweuseupperboundsforachievablelinkthroughputvectorsoverindividual!Ritoconstructanupperboundof!Y.Thenanupperboundisgivenbythefollowingoptimizationproblem. MaximizefK+1Subjectto:LPk=1gik Therstconstraintconsidersallcliqueconstrainsforall!Ri.Thesecondconstraintsatisesthelinkdemandsrequiredbytheend-to-endthroughputxi(1iK)andfK+1. IfthetotalnumberofdierentratesisZ,canbeaslargeasZL1,i.e.,ZL1.Foreachi,thetotalnumberofdierentcliquesMialsoincreasesquicklywithL.Though 60

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Toreducethecomputationcomplexityoftheaboveproblem,wecanuseasmallnumberofcliquesforeachitoderivealooseupperboundof!gi,anddevelopsomealgorithmstoremovesomeunnecessaryratevectors!Ri.Theseareleftforfuturestudies. Indistributedwirelessnetworks,itisoftennotfeasibletotimelyobtainthegloballinkschedulinginformationandaccordinglycalculateaccurateavailablebandwidthofanewpath.Therefore,itisimportanttodevelopadistributedalgorithmtondapathandestimatetheavailablebandwidthofthatpathwithbackgroundtracinmind. Toobtaininformationofbackgroundtrac,eachnodeisrequiredtoobservethechannelutilization.Thiscanbedonebycarriersensing.Anodeassumesthatitcantransmitduringchannelidleperiods,andnototherwise.Itcalculatesachannelidlenessratioidle1,i.e.,theratioofthelengthoftimeitsensesanidlechanneltothetotalsensingtime.AlinkLiassumesthatitcantransmitnewtracforatimeshareiindicatedbythesmallervalueidleofitstwoendnodes,and 61

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Toestimateavailablebandwidthofapath,westillneedtoconsidertheinterferenceamonglinksofthatpath.Weheredenealocalinterferencecliqueforapath.Alocalinterferencecliqueisacliqueandalllinksinthecliqueareinasequenceonthepath.Wefollowtheapproachinpaper( 15 )tondthelocalinterferencecliques.ForacliqueC=fL1;L2;:::;LjCjg,andthecorrespondingidletimeratiofortheselinks,!=f1;2;:::;jCjg,wehave ri1:(3{11) Wecanfurtherhave Thisactuallyprovidesanupperboundoftheavailableend-to-endbandwidthofapathPgiventheratevector!R=fr1;r2;::;rjPjgandthelinkidlenessvector!. Theaboveestimationassumesthatanytwolinks'idletimearenotoverlapped.Itmaygivealooseupperbound.AconservativeestimationistoaddanotherconstraintbyassumingthatthetimeshareioflinkLiissharedbyalllinksinacliquewiththeirindividualtimesharelessthani,whichboundsthethroughputforanyklinksinCby:kXi=1f rimax1iki: rji(1ijCj);fmini:1ijCji iPj=11 WeproposetousetheminimumvalueofestimatedavailablebandwidthcalculatedbyEquation 3{11 3{12 or 3{13 forall(local)maximalcliquesasroutingmetricsandaswellasmetricstoestimatethepathavailablebandwidth.Eachintermediatenodeonapath 62

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Intraditionalroutingalgorithmswithoutconsideringbackgroundtrac,severalworkssuchas( 15 )haveshownthatbothend-to-endtransmissiondelay(E2ETD)andlocalcliquetransmissiontime(LCTT)aregoodroutingmetricstondapathwithahighend-to-endpathcapacity.Here,wedesigntworoutingmetricsbasedonE2ETDandLCTTtoconsiderthebackgroundtrac.WeknowthatlinkLi'savailablethroughputfiislessthanorequaltoiri,andhencetheaveragedelayforoneunitoftracislargerthanorequalto1 SimilartoEquation 3{7 whichusescliquetransmissiontimetoconstructanupperbound,hereweproposeanewestimateofavailablebandwidthbyconsideringbothcliqueconstraintandbackgroundtracforgiven!Rand!,i.e., maxC:cliquePLi2C1 3-1 andtheparametershasbeenexplainedinSection 3.3.1 .SupposethereisamultihopowtravelingthroughlinksL1,L2,L3,andL4,andrequiresthesamethroughputoverthesefourlinks,i.e.,f=y1=y2=y3=y4

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TheoptimizationproblemgeneratesthefollowinglinkschedulingS,S=8>>>>>>><>>>>>>>:(1=0:1;E1=fL1;54g);(2=0:3;E2=fL2;54g);(3=0:3;E3=fL3;54g);(4=0:3;E4=f(L1;36);(L4;54)g);f=16:2 Thethroughputfcanbesupportedbythefollowingtworatevectors!R1and!R2,theircorrespondingsupportedthroughputvectors!f1and!f2,andtheirtimeshares1and2:!R1=f54;54;54;54g;1=0:1;!f1=f54;0;0;0gC1=f(L1;54);(L2;54);(L3;54);(L4;54)g!R2=f36;54;54;54g;2=0:9;!f2=f12;18;18;18gC2=f(L1;36);(L2;54);(L3;54)gyi=1f1i+2f2i=f=16:2 ItisnotdiculttoshowthecliquewiththemaximumcliquetransmissiontimesharearetheaboveC1andC2forR1andR2,respectively,whosecliqueconstraintsarevalidforindividualthroughputvectorf1andf2,respectively,butnotforthemaximumend-to-endthroughputf:PLi2C1f1i Noticethattheupperboundsofend-to-endthroughputprovidedbycliquesforeither!R1or!R2(refertoEquation 3{7 )islessthanf=16:2:!R1:s11 54=13:5<16:2!R2:s21 36+2 54=108 715:43<16:2 64

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Randomtopology Figure3-3. Availablebandwidth Itclearlyshowsthatthemaximumfeasiblethroughputvectordoesnotsatisfyanycliqueconstraintinthisexample,andhencecliqueconstraintscannotdirectlyprovideanupperboundanymore. Apparently,achievingtheoptimumend-to-endthroughputf=16:2requiressomeappropriatelinkadaptationalgorithm,whichallowsL1totransmitdatawithdierentdataratesatdierenttimetoobtainhigherend-to-endthroughputthananyxedratevectors. Inthesimulation,30nodesarerandomlylocatedina400m600mrectangleareaasshowninFigure 3-2 .Four802.11aratesareused,i.e.,54,36,18,and6Mbps. 65

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33 ).8sourcesandtheirdestinationsarerandomlychosenandeachow'sdemandis2Mbps.Duetospacelimitation,weonlycomparethreeroutingmetrics,hopcount,end-to-endtransmissiondelay(e2eTD),andaverageend-to-enddelay(average-e2eD)(refertoEquation 3{14 ). Inthesimulation,weassumethatowsjointhenetworkonebyone.Thesimulationstopswhenthedemandofoneowisnotsatised.Figure 3-2 alsoshowsthepathsfoundbytheroutingmetricaverage-e2eD,whichareillustratedbysolidarrows.Thee2eTDndsdierentpathsforsomeows,andthedottedarrowsshowsomedierentlinksusedbye2eTD.Figure 3-3 showstheavailablebandwidthofeachow'spathfoundbydierentroutingmetrics.Apparently,theaverage-e2eDcanndpathswiththelargestavailablebandwidthamongthesethreemetrics,anditfailstondapathtosatisfythedemandforthe8thow.Thee2eTDfailstondapathtosatisfythedemandforthe5thow,anditisthe3rdowforthehopcount. 3.4 including\cliqueconstraint(Equation 3{11 )",\bottlenecknodebandwidth(Equation 3{10 )",\minoftheabovetwo(Equation 3{12 )",\conservativecliqueconstraint(Equation 3{13 )",\expectedcliquetransmissiontime(Equation 3{15 )".Weapplythesemetricstothepathsfoundbytheroutingmetricaverage-e2eDintheabovesubsection. FromFigure 3-4 ,wecanobservethat\cliqueconstraint"underestimatestheavailablebandwidthwhenthebackgroundtracislightduetotheignoreoftheadvantagesoflinkadaptation,andoverestimatestheavailablebandwidthwhenthebackgroundtracisheavyduetotheignoreofbackgroundtrac.\bottlenecknodebandwidth"considerstheeectofbackgroundtracbutignorestheinterferenceamongtracalongthenewpath,andhenceoverestimatestheavailablebandwidthespeciallywhenthebackgroundtracis 66

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Estimatedavailablebandwidth light.\conservativecliqueconstraint"considersbothcliqueconstraintsandbackgroundtrac,andperformsthebestamongthesemetrics.\expectedcliquetransmissiontime"obtainslowervaluesofavailablebandwidthandperformsalittleworsethan\conservativecliqueconstraint".Furthermore,allmetricsexcept\cliqueconstraint"underestimatetheavailablebandwidthwhenbackgroundtracisheavy.Thisdemonstratestheshortageofusingchannelidletimetoestimatetheavailablebandwidthandveriesthepreviousresultsinthepaper. Fromthetheoreticalmodelandperformanceevaluationresults,wefurtherhavethefollowingkeyobservationsinmultirateandmultihopnetworks: 67

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68

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Itisimportanttoknowthethroughputcapacitywhenplanninganddeployingthesenetworkssinceexcessivetracloadoftengeneratesmuchlessdeliveredthroughputthanamodestamountoftracload( 34 ). Thereareextensivestudiesonthecapacityofwirelessadhocnetworks.Inarecentlandmarkpaper( 35 ),GuptaandKumarshowedthattheorderofthepernodethroughputcapacityis(n)=(W 36 { 39 )andreferencestherein)alsostudiedtheasymptoticboundsorscalinglawsofpernodecapacitywhenmobility,delay,and/orinfrastructuresupportaretakenintoconsideration. Althoughasymptoticalcapacityboundsareimportanttoguidethedesignofwirelessadhocnetworks,theydonotprovideexactcapacityfornetworkswithgiventopologiesandaremoreappropriateforlarge-scalenetworks.Therearealsolotsofwork( 18 )( 34 )( 40 )( 41 )andreferencetherein)intheliteraturestudyingthenetworkcapacityofnetworkswithgiventopologies.However,mostoftheseworkmodeledthecalculationofnetworkthroughputasNPcompleteproblems,whicharenotcomputationallyfeasibleformanypracticalsizednetworks.WewilldetailsomeoftheirworkinSection 4.2 69

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Inthetheoreticalmodelofthecapacitybounds,wedonotassumeanyspecicinterferencemodel,whichcanbetheprotocolmodel,thephysicalmodel( 35 ),orthediskmodel,aslongaswecandeterminewhethertwoormorewirelesslinkscansuccessfullytransmitdatasimultaneouslyornot.Wealsodonotlimitthelocationandthenumberofsourcesanddestinations,orthevalueofcapacityallocationvectoramongows.Whenallnodesaresourcesandrandomlychooseadestination,andallofthemhavethesamethroughput,i.e.,thecapacityallocationvectorisanall-onevector,thecapacitybecomesthepernodethroughputcapacitystudiedin( 35 ). Withthesecomputationalfeasibleandaccuratebounds,wefurtherdemonstratehowtheycouldbeusedtoevaluatetheperformanceofroutingmetricsandverifytheasymptoticboundsproposedintheliterature. Therestofthispaperisorganizedasfollows.InSection 4.2 ,wedescribesomerelatedwork.WethenproposethenetworkmodelandillustratethethroughputcapacityofnetworkswithgiventopologiesisNPcompleteinSection 4.3 .InSection 4.4 andSection 4.5 ,wederivethelowerandupperboundsofthroughputcapacity,respectively.We 70

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4.7 .Finally,Section 4.8 concludesthispaper. Li.etc.( 34 )usedns2simulationstoexamineinteractionsofthe802.11MACandadhocforwardingandtheeectoncapacityforseveralsimplecongurationsandtracpatternsinnetworkswithgiventopologies.TheauthorsalsoprovidedtheoreticalanalysistoshowthatpernodecapacityisasymptoticallyupperboundedbyO(1=p Tondexactcapacityofwirelessadhocnetworks,ToumpisandGoldsmith( 40 )studiedcapacityregionsforwirelessadhocnetworks,wherethecapacityregionsdescribethesetofachievableratecombinationsbetweenallsource-destinationpairsinthenetwork.However,asthenumberofnodesincreases,thenumberofbasicratematricesincreasesfactoriallyifmultihoproutingandspatialreuseareallowed.Therefore,theauthorsalsoindicatedthattheirMATLAB/Croutinestodeterminethecapacityregionsbecomeimpracticalfornetworkswithmorethanvetofteennodesevenwithasinglexedrate. Jainetc.( 18 )studiedtheimpactofinterferenceonnetworkthroughputofwirelessadhocnetworksusingaconictgraph.Theyformulatedmaximizationofthethroughputofasinglesource-destinationpairasamax-owproblemandstudiedthethroughputofmultiplesource-destinationpairsusingamulticommodityowformulation.Theyusedindependentsetstoconstructconstraintstondathroughputlowerbound,and 71

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Balakrishnan( 41 )proposedtouseamaximumDistance-2matching(D2EMIS)problem,whichisNPcomplete,tomodelthemaximumnumberofpossibleconcurrenttransmissiontoestimatethemaximumMAClayercapacity.TheyproposedapproximationalgorithmstosolveD2EMISproblembasedondiskgraphstocomputeanupperboundonthisnumberandprovidesolutionsthatarewithinasmallconstantfactor(typically2to3)oftheoptimalsolution. Comparedtothesework,weproposelowerandupperthroughputboundsofnetworkcapacity,whichcanbecomputedbypolynomial-timealgorithms.Ourmodeldoesnotlimitthenumberofsourcenodesorows,andcanbeusedtocalculatecapacityforanycapacityallocationvectoramongows.Thelowerboundisveryclosetotheupperbound,andbothofthemarecomputationallyfeasibleforpracticalsizednetworks.Therefore,theycouldbeusedtoevaluateperformanceofanypracticalsizednetworkswithanygiventopologiesandtracpatterns. 4.3.1DenitionofNetworkCapacity 72

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73

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MaximizeSkSubjectto:P1A1P1ARSkP1kKfkI(Pk)=00(1A);Sk0(4{1) whereAisthenumberofallindependentsetsforthelinksetP=[1iKPi,R=fre:e2PgistheratevectorforthethindependentsetEandre=0ife=2E,isthetimeshareallocatedforlinksinEtotransmitdata,jPjisthenumberofdierentlinksinP,I(Pk)isanrowindicatorvectorinRjPj,andIe(Pk)=8><>:1;ife2Pk0;otherwise Tofacilitatethestudy,werstintroduceseveralconcepts.Linkinterferenceset(LIS)ofalinklinalinksetPisdenedasasetofalllinksinterferingwithlinP,whichisreferredasLIS(P;l)andLIS(P;l)P.Toincludelitselfinthisset,weassumethatlinterfereswithitself.WetreatPasapath,andhence\in"Pisthesameas\on"P.ForanygivenorderoflinksinP,linksappearingrstintheorderare\upstream"linksoflinksappearinglaterintheorder,andthelatteronesare\downstream"linksofthe 74

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Theorem1:Inasingle-ratenetwork,perlinkcapacityCPsatises Proof: ToproveRe 75

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First,divideatimeperiodintoM=jLISjtimeslotswiththesamelength.LetSi(1iM)denotethesetoflinksscheduledfortransmissionintimesloti.ThereforeascheduleScanberepresentedbyS=fS1;S2;:::;SMgandthescheduleSrepeatseveryMtimeslots.SisfeasibleifandonlyiftherearenotwoormorelinksinterferingwitheachotherinanySi(1iM).SsatisesthegloballyfairdemandvectorifandonlyifalllinksappearsthesametimesinS.Forsimplicity,weonlyneedtondanSwhereeachlinkappearsexactlyonce.NowletusconstructanStoachievethelowerboundRe First,ndanLISandinsertalllinksinLISintoSi(1iM)sothateachSihasexactlyonelinkfromLIS.Thereafter,foranylinklnotinanySi,ndanisuchthatthereisnolinkinSiinterferingwithlandinsertlinSi.Ifthereisalinkl;,whichcannotbeinsertedintoanySi(1iM),thereisalinkl;iineachSi(1iM)interferingwithl;.Therefore,LIS(P;l;)fl;;l;1;l;2;:::;l;MgandjLIS(P;l;)jM+1>jLISj.ThiscontradictsthedenitionofLISinEquation 4{2 .ThusalllinkscanbeinsertedinsomeSi(1iM).Afterinsertingalllinks,SisafeasiblescheduleandeachlinkappearsexactlyonceinS. Therefore,eachlinkwillbescheduledfortransmissioninexactonetimesloteveryMtimeslots.ThethroughputofalllinksarethesameandequaltoRe WeuseasimilarproceduretoconstructafeasiblescheduleStoachievethetighterlowerboundsRe

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WeinsertlinksintoSi(1iMF)intheorderthattheyappearsonPfromthedestinationtothesource.InsertlintoonlyoneSi,whichhasnolinksinterferingwithl.Fortherstlinkl;whichcannotbeinsertedinanySi(1iMF),thereisalinkl;iinterferingwithl;ineachSi(1iMF).Sincealll;iaredownstreamlinksofl;,FIS(P;l;)fl;;l;1;l;2;:::;l;MFgandjFIS(P;l;)jMF+1>jFISj,whichisacontradictiontothedenitionofFISinEquation 4{3 .Therefore,everylinkinPcanbeinsertedinsomeSi(1iMF)andtheresultingschedulingS=fS1;S2;;SMFgisfeasible,whereeachlinkappearsexactlyonce. SinceinP,eachlinkisscheduledfortransmissioninexactonetimesloteveryMFtimeslots,thethroughputofalllinksisthesameandequaltoRe Followingthesamewayasabove,ifweinsertlinksintoSi(1iMB)intheordertheyappearsfromthesourcetothedestination,wecanndafeasibleschedulingS=fS1;S2;:::;SMBg,whereeachlinkappearsexactlyonce,toachievethelowercapacityboundRe 77

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Thelinkinterferencesettransmissiontime(ITT)TLIS;lisdenedasthesummationoftransmissiontimeofapacketoveralllinksinthesetLIS(P;l).ForFISandBIS,wedeneTFIS;landTBIS;linthesameway. whereTmisthetransmissiontimeforapacketoverlinkm,andTLIS,TFIS,andTBISarethemaximumITTofallLIS,FIS,andBIS,respectively.LetLPdenotethelengthofpayloadinapacket. Theorem2:Inamultiratenetwork,perlinkcapacityCPsatises Proof: Sametotheprooffortheprevioustheorem,weneedtoconstructafeasiblelinkschedulingStoachievetheselowerbounds. Timeisstilldividedintotimeslotswithequallength.AlinkschedulingS=fS1;S2;:::;SMg.Si(1iM)isasetoflinks.Intimesloti(1iM),alllinksinSiarescheduledfortransmission.SrepeatseveryMtimeslots.Sisfeasibleifandonlyif,inanySi,anylinkdoesnotinterferewithanyoftheothers.Tosatisfythegloballyfairdemandvector,wherealllinkshavethesamethroughput,thenumberofSi(1iM)includingthesamelinklisMl,andMl Tl=Mm Tmforalll;m2P. 78

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Let0denotethesetoftimeslotswhichhaveatleastonelinkinterferingwithl,andj0j+Ml>M.Fromonetimeslotin0,choosealinkdenotedasl1,whichinterfereswithl.Removeallthetimeslots,inwhichl1isscheduledfortransmissionfrom0.Theresultedsetisdenotedas1,andthenumberofremovedtimeslotsisdenotedas1,and1Ml1

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4{4 Therefore,alllinkscanbescheduledfortransmissionusingtheaboveprocedure.TheresultinglinkschedulingSisfeasible,andeachlinkisscheduledfortransmissioninMltimeslots.Thethroughputfofalllinksisthesameandequaltof=Re;lMl 80

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4{4 ,thiscompletestheproof.2 Intheaboveproof,wedonotspecifythelengthofbutweassumeeachlinkkeepstransmittingpacketsintheslotswhichthelinkisscheduledfortransmission.Wemustnoticethatpacketsaretransmittedoneaftertheother,andthepackettransmissionwillfailifthetransmissionisinterruptedattheslotboundary.Therefore,inanyslot,allthelinksscheduledfortransmissioninthatslotneedtotransmitexactlyanintegernumberofpackets.Thisrequiresthat'slengthisanintegertimesofthelengthsofalllinktransmissiontime. Forapracticalscheduling,wealsorequirethatMandMli(1iN)areallintegers.LetAbethesmallestvaluesatisfyingthatATLISandATli(1iN)areallintegers.ThenM=ATLISandMli=ATli. Forexample,iftheprecisionofapackettransmissiontimeismicrosecond,wecanrepresenteachlinktransmissiontimebyanintegerwiththeunitofmicrosecond.Normally,thisprecisionisaccurateenoughforthe802.11system,whichhasratesequaltoseveralMbps.Foranerprecision,wecanalwaysuseasmallerunit,likenanosecond.Accordingly,couldbetheleastcommonmultipleofTli(1iN),AcouldbethereciprocalofthegreatestcommonfactorofTLISandTli(1iN). 81

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Toderivethelowerboundsofminimumlinkcapacity,werstdenethe\equivalent"interferencelinksettransmissiontimeforLIS,FISandBIS,respectively,asfollows, ^TLIS(P;l)=Pm2LIS(P;l)f;mTm^TFIS(P;l)=Pm2FIS(P;l)f;mTm^TBIS(P;l)=Pm2BIS(P;l)f;mTm^TLIS=maxl2P^TLIS(P;l)^TFIS=maxl2P^TFIS(P;l)^TBIS=maxl2P^TBIS(P;l)(4{6) 82

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Proof:WetaketherstlowerboundLp Tondafeasibleschedulingtoachievetherstlowerbound,werstdeneT;l=f;lTl.FollowingthesameprocedureintheprevioussubsectionbutreplacingTlwithT;l,wewillndafeasibleschedulingSwhereeachlinklwillbescheduledT;l whereI(Pi)=fIl1(Pi);Il2(Pi);:::;IljPj(Pi)g(1iK)isrowindicatorvectorforpathPiasdenedinSection 4.3.2 .Fromtheorem3,wehave 83

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andthenetworkcapacitySCsatises Proof:SimilartotheproofofTheorem3,weonlyprovetherstlowerboundheretosavespace.Othertwocanbeprovedusingalmostthesameprocedure. FromtheproofofTheorem3,weknowthatwecanndafeasiblelinkschedulingStoobtainthroughputf;iLp ForagivenorderoflinksinP,alocalinterferenceclique(LIC)oflinklisdenedasacliqueincludinglinwhichalllinksarenexttoeachotheronpathP.Wedene 84

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Inthispaper,weintroducetwomorenewconceptsforagivenorderoflinksinP.Theforwardinterferenceclique(FIC)oflinklonpathPisdenedasfollows.FirstletFIC=flg.Checkeverylinkfromthedownstreamlinksoflintheorderthattheyappearfromltothedestination.IfalinkinterfereswithalllinksinFIC,insertitintoFIC.TheresultingsetoflinksiscalledtheforwardinterferencecliqueFICoflinklonpathP,whichisreferredasFIC(P;l).Thebackwardinterferenceclique(BIC)oflinklonpathP,orBIC(P;l),isdenedinthesamewayexceptthatBICchecksallupstreamlinksinsteadofdownstreamlinksofl. Wedenethemaximuminterferencecliquetransmissiontime(MCTT)TIC,TLIC,TFIC,andTBICforIC,LIC,FIC,andBIC,respectively,asfollows. Fromtheabovedenitions,itiseasytoshowthefollowingrelationshipsbetweenthesevariables: Similartothelowerboundofnetworkcapacity,wehavethefollowingtheoremsfornetworkscapacity. 85

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insingle-ratenetworks,andinmultiratenetworks,itsatises Givenalinkcapacityallocationvector!F=ff;i(1ijPj)g,wedenethe\equivalent"MCTTasfollows ^TIC=maxallICsPlm2ICf;mTm^TFIC=maxl2PPlm2FIC(P;l)f;mTm^TBIC=maxl2PPlm2BIC(P;l)f;mTm^TLIC=maxl2PPlm2LIC(P;l)f;mTm 4{12 ,wehave ^TIC^TFIC^TLIC,and^TIC^TBIC^TLIC(4{15) Theorem6:Givenalinkcapacityallocationvector!F=ff;i(1ijPj)g,theminimumlinkcapacityCPsatises 86

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wherethe\equivalent"MCTTsarecalculatedusingEquation 4{8 and 4{15 Forpathcapacity,itisnotdiculttoshowthatCPLp 4{12 andthatsingle-ratenetworksarespecialcasesofmultiratenetworks,itiseasytoproveTheorem5.SimilartotheproofsofTheorem3and4basedonTheorem2inthepreviousSection,wecanproveTheorem6and7accordingtoTheorem5. AsndingamaxmumcliqueisanNPcompleteproblem,itisnoteasytocalculatejMICjandTIC.Fortunately,wehavepolynomial-timealgorithmtocalculateTFIC,TBIC,TLIC,^TIC,^TIC,and^TICasshowninthefollowingsection. 4-1 ,weshowapolynomialalgorithmtoderivetheM,MF,MB,TLIS,TFIS,andTBISforagivenorderoflinksinP.Apparently,thealgorithmcomplexityisO(jPj2)asdenotedinthenotesofTable. 87

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Intheproofofthelowerboundofperlinkcapacityinsingle-ratenetworks,werstusetheO(jPj2)algorithmshowninTable 4-1 tondaLIS.ForeachlinklbeforeitisinsertedintheschedulingS,thecomparisonofinterferencerelationshipsisexecutedatmostjSjtimes,wherejSjisthenumberoflinksalreadyscheduledintheschedulingS.Therefore,thetotalnumberofcomparisonsofinterferencerelationshipsisatmostP2ijPji1=jPj(jPj1) 2andthereareatmostjPjtimessetinsertions.ThealgorithmasawholeisanO(jPj2)algorithm. Intheproofofthelowerboundofperlinkcapacityinmultiratenetworks,werstusetheO(jPj2)algorithmshowninTable 4-1 tondaLISwhichhastheinterferencesettransmissiontimeequaltoTLIS.ForthejthlinkinsertedintotheschedulingS,thecomparisonsofinterferencerelationshipsisexecutedatmostX1i
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Interferencesettransmissiontimeandinterferencecliquetransmissiontime Similarly,wecanprovethatwecanusepolynomial-timealgorithmstodevelopthelinkschedulingtoachievethelowerboundsofperlinkcapacitybasedonFISandBIS.FromtheproofsofTheorem3and4,weknowthatthealgorithmstodevelopthelinkschedulingtoachievethelowerboundsofminimumlinkcapacityandminimumowcapacityhavethesamecomplexitywiththatforperlinkcapacity. Herewegiveasucientbutnotnecessaryconditionwhenthelowerboundsareequaltotheupperbounds:givenanorderoflinksinP,foranytwolinks,iftheyconictwitheachother,alllinksbetweenthemonPinterferewithbothofthem.Ifthisconditionissatised,anytwolinksinterferingwitheachother,togetherwithalllinksbetweenthem 89

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TheaboveconditionimpliesthatifwecouldplacelinksinterferingwitheachotherclosetoeachotherintheorderoflinksinP,wecouldmakethelowerboundsverycloseorevenequaltotheupperbounds.Linksclosetoeachotheringeographicallocationsofteninterferewitheachother,andlinksfarawayfromeachotheroftendonotinterferewitheachotherforpowerlimitedtransmissions.Therefore,wecouldorderlinksinPaccordingtotheirgeographicallocations.ThisresultsinthefollowingalgorithmtoorderthelinksinP.Firstndageographicallocationor\point'inthetopology,aroundwhichthereisthehighestdensityoflinksinP.Thenorderthelinksbythedistancetothatpoint.Herethedistanceofalinktoonepointisdenedastheaveragedistanceofthetwoendnodesofthatlinktothepoint.This\point"canbeoftenestimatedbythecenterpointinatopologysincepathsoftentravelthroughthecenterpartofatopology.Wewillusethecenterpointandsomerandompointstoevaluatehowtheorderoflinksimpactsonthecapacityboundsinthenextsection. Unlessotherwiseindicated,thereare400nodesrandomlyanduniformlylocatedina1500m3000mtopology.Eachnoderandomlychoosesanothernodeasitsdestination.Inthegures,thelowerboundisequaltoLpmin1iKfi 90

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15 )). 4.6.3 .Wealsoevaluatetheperformanceof30randomordersofthelinksinP. Weplotthe\equivalent"linkinterferencesettransmissiontimeandthe\equivalent"linkinterferencecliquetransmissiontimeinFigure 4-1 .Itisclearfromthegure,byorderingthelinksindistancefromaxedlocation,wecangetmuchlowervaluesof^TFISand^TBISwhichcontributetomuchbetterlowerbounds.Therandomordersoflinkshavealittlerbettervaluesof^TFICand^TBIC,whichcontributetoalittlebetterupperbounds.Thegurealsoshowsthatthecapacityboundsarenotaectedmuchiflessnumberofdierentordersarechecked. Figure 4-2 showsthecapacityboundsfor30randomtopologies.Therearetwoimportantobservations.First,theupperboundisveryclosetolowerbound,andthedierenceisfrom13:2%to28:8%and21:5%onaverage.Second,theperformanceusingthecenterpointandonerandomorderisalsogoodenoughcomparedtheperformanceusing30pointsand30randomorders,andthedierenceisonly0:0%3:12%and0:5%onaverageforthelowerbound,and0:6%8:19%and3:23%onaveragefortheupperbound. 4-3 showsthepernodecapacityboundsforvedierentrouting 91

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Capacitybounds metrics.Itiseasytoobservethathopcountleadstoaverylownetworkcapacityduetotheignoranceofmultiplerates,whileETTandLCTTachievethehighestnetworkcapacityamongalltheroutingmetrics.DierentfromasinglepathwhereLCTTalmostalwaysresultsinhigherend-to-endthroughputthanETTasshownin( 15 ),LCTTisnotnecessarybetterthanETTintermsofnetworkcapacitywhenmultipleowscoexist.TheratioofthelowerboundobtainedbyLCTTtothatobtainedbyETTrangesfrom0.90to1.06and0.97onaverage.Theratiofortheupperboundrangesfrom0.92to1.19and1.01onaverage.ComparedwithLCTTandhopcount,thelowerboundobtainedbyLCTTisonaverage5.00timesthatobtainedbyhopcount,andtheupperboundobtainedbyLCTTisonaverage6.42timesthatobtainedbyhopcount. 4-4 demonstratesthatperowcapacitydecreasesingeneralwhenthenumberofowsincreases.Itdecreasesslowlywhenthenumberofowsissmall,anddeceasesas(1=n)whenthatnumberislarge.Figure 4-5 showstheaggregateow 92

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Pernodecapacity Figure4-4. Perowcapacitywithdierent#ofows capacity.Theaggregateowcapacitynormallyincreasesalongwiththenumberofowandbecomesstablewhenthenumberofowsislarge. 4-6 ,weobservethattheper-nodecapacitydecreasesmuchfasterthan(1=p 93

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Networkcapacitywithdierent#ofows Figure4-6. Pernodecapacity nodesissmall.Onlywhenthenumberislargerthan500inthestudiedtopologies,itapproximatelyfollowstheasymptoticbounds(1=p 35 ). 94

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95

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Algorithmtondlinkinterferenceset(LIS)andmaximumITT(TLIS)andthemaximumsizeofLIS(M) PathP=fl1;l2;:::;ljPjg(intheorderfromsourcetodestination) 1M=0,TLIS=0 2fori=1tojPj-1 3forj=i+1tojPj 7;Mj=Mj+1 8ifmax(Mi;Mj)>M 11ifmax(TLIS;i;TLIS;j)>TLIS 13j=(TLIS;i>TLIS;j)?i:j 15end 16end 17end Note:5;,6;,and7;areonlynecessaryforLIS.Without5;,6;,and7;,itndsthecorrespondingparametersforFIS.IfwesortlinksinPintheorderfromdestinationtosource,wegettheseparametersforBISinsteadofFIS. ComplexityisO(jPj2):thealgorithmhasatmostjPj(jPj1) 2timesofseveralcomparisons,setinsertions,andadditions. 96

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55 )( 56 )( 57 ).Theexistenceofmultiplechannelsandmultipleradioshasgreatlyexpandedmanageableresourcespace,i.e.,channel,radio,user,andtime,toimprovethenetworkperformance.Thequestionofhowtoecientlyusetheavailableresourcesinmultiradiowirelessnetworksisofgreatimportance.Inthispaper,theproposedopportunisticmultiradioMAC(OMMAC)isdesignedtoexploitmulti-radiodiversityinordertoenhancethethroughputperformance. Opportunistictransmissionschemesingeneralcanbeperceivedasawaytoutilizethephysical-layerfeedbackfrommultiplesourcestoimproveperformancethroughmediumaccesscontrol( 54 ),packetscheduling( 53 ),andrateadaptation( 42 ).TheproposedOMMACcanberegardedasanaturalintegrationofthesethreeapproachestomaximizetheextentofexploitingresourcediversities.Notonlyresponsibleforgrantingmediumaccesstopackets,OMMACalsoconsidersthetotalthroughputofallradiosonanode,whichschedulesthetransmissiononper-channelbasis,i.e.,selectingthebesttransmissionpairforeachchannel,ratherthanper-packetbasiswhichselectsthebestchannelfortransmissioneverytimeapacketgainsaccesstothemedium( 44 ).Duetodierentinterferencelevel,channelfadingstatistics,andgeographicaldierenceofusers,variablemaximumdataratescanbesupportedondierenttransmissionlinkswhichisconsideredbyOMMACwhenoptimizingthelocalspectralusage.Thechannel-basedpacketschedulingonlytakesadvantageoftheone-hopinformation,thustheroutingandabovelayersremainunchanged. Inordertoexploitmulti-radiodiversity,OMMACusesmulti-castRTSandvirtualmulti-CTStocollectreceiver-measuredchannelqualityinformationoverseveralcandidatetransmissionlinks.Theabovementionedtechniquesmakeitpossibletomeasureseveral 97

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6 ),thusOMMACdoesnotgenerateexclusivecommunicationoverheadforextracontroltraccomparedtoIEEE802.11. OMMACiscloselyrelatedtotwocategoriesofresearchwork.Oneismulti-channelmulti-radioMACdesign,theotheroneisMACprotocolsexploitingresourcediversities.Duetothetechnicallimitationofthenumberofradiosoneachhost,manypreviousworksfocusonhowtoecientlyusemultiplechannelswithoneortwotransceivers( 48 )( 49 )( 50 )( 51 )( 52 ).Noneofthemcanbeeasilytailedtoachievethegoalofschedulingmultipletransmissionsamongseveralavailableradiosonasinglenode.Forpracticalmulti-radioMACschemesinmulti-hopadhocwirelessnetworkswiththeaimatimprovingnetworkthroughput,A.Adyaetal.( 45 )proposedamulti-radiounicationMACprotocoltocoordinatetheoperationofmultiplewirelessnetworkcards.However,thechannelassignmentisxed,whichlimitstheextentofusinglocalspectrum.OMMACpushesforwardtheideaofimprovinglocalspectralusageeciencybyconsideringthedynamicchannelselectionforseveralavailableradiossimultaneously.Anothersetofrelatedresearchistheopportunisticrateadaptationschemes.OneofthetypicalexampleisOAR( 42 ).OARachievessignicantperformanceimprovementbytakingtheopportunityofgoodchannelconditiontosendmultiplepacketsatthesametransmissionduration.InMOAR( 44 ),V.Kanodiaetal.furthershowtheperformancegainbyexploringthefrequencydiversityoverOARwithasinglechannel.Whendirectlyapplyingthesingle-radioopportunistictransmissionschemetomultiradiowirelessnetworks,theproblemofecientlysharingavailablechannelpoolisnotaddressed.OneofthemajorcontributionoftheOMMACissuccessfullycoordinatingmultipleradiosinutilizingthesamechannelpoolandprovidingimprovedper-radiothroughputbyleveragingthemultiradiodiversitycomparedwithOARandMOARasshowninns2simulations. 98

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5.2 ,weintroducethekeyideasforOMMAC.SecondinSection 5.3 ,wedescribethedetailedprotocoldesignissues.Third,wetheoreticallyanalyzetheperformanceimprovementofOMMACinSection 5.4 .Theperformanceevaluationthroughns2isgiveninSection 5.5 .Finally,wedrawtheconclusioninSection 5.6 5.2.1MultipleMACDiversityIssues 5-1 LinkDiversity:Givenachannelonaxedfrequency,thelinkdiversityexistsinthescenarioinwhichthereareseveralpotentialreceiversfortransmission.Atatime,thequalityofalinkbetweenacertainsourceanditsnext-hopneighborisbetterthanothers.Forexample,thelinksetflisa,lisb,liscgcanrepresentasourceoflinkdiversity,wherelisaisdenedasthelinkbetweenSandnext-hopAonchanneli.Wedenoteitasalinkdiversityset. ChannelDiversity:Givenseveralavailablechannelsonorthogonalfrequenciesorcodes,severaltransmissionscanbecarriedoutsimultaneouslyondierentchannelswithoutinterferingwitheachother.Forexample,thelinksetfl1sa,l2sa,l3sagcanrepresentasourceofchanneldiversity.Wedenoteitasachanneldiversityset. Multi-radioDiversity:Givenseveralavailablechannelsandmorethanoneradioonasinglenode,themulti-radiodiversityarisesinthescenariowheredierentgeographicallylocatedusersexperiencedierentlinkqualities.Forexample,thelinksetflisj:j2(a;b;c);i2(1;2;3)gcanrepresentasourceofmulti-radiodiversity.Wedenoteitasamulti-radiodiversitylinkset.Fromthedenition,itiscleartoseethatthemulti-radiodiversitysetistheouterproductofthelinkdiversitysetandthechanneldiversityset,thusprovidingalargerspaceforexploitingthediversitiesinthenetwork. 99

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Illustrationforlinkdiversity,channeldiversity,andmulti-radiodiversity.NodeSisthesourcenode,nodeA,nodeB,nodeCarereceivers.ThereisanongoingtransmissionbetweennodeDandnodeEonchannel3.Thegureshowsdierencesingeographicallocationandinterferencelevelwhichgiverisetomultiplediversities. Formulti-channelmulti-radiowirelessnetworks,thefreedomofexploitingdierenttypesofdiversitieshasbeengreatlyincreased.Sinceseveralradioscanworksimultaneouslyondierentchannels,bothlinkandchanneldiversitycanbeexploitedsimultaneouslybetweenanodeanditsneighboringnodes,whichgivesrisetomulti-radiodiversity. 5-1 forinstance.SupposetherearepacketsfPa,Pb,PcgintheoutgoingqueueofnodeS.ThecurrentlinkqualitiesaredescribedinFigure 5-2 .IfSselectsthebestchannelwheneverapacketgetstheaccessfortransmission,Shastoselectlinkl1sa,l2sbandl3scsequentiallyforpacketsPa,PbandPc.ThetotalthroughputfornodeSatthattimeis78Mb/s.We 100

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Illustrationforlocalizedoptimization.Foreachnext-hopaddress(corrspondingtoapacket),thelinkqualityondierentchannelmaybedierent.Foreachchannel,thelinkqualitywithdierentreceiversmaybedierent.FromFigure 5-1 ,duetotheongoingtransmission,themaximumsupportabledatarateonl3scisonly6.Thehorizontalellipserepresentspacket-basedscheduling,whileverticalellipserepresentschannel-basedscheduling. refertoitaspacket-basedpacketscheduling.InOMMAC,withtheobjectiveofimprovinglocalspectralusageeciency,theoptimalpacketschedulingpolicywouldbethelinksubsetfl1sb,l2sc,l3sagorfl1sb,l2sc,l3sbg.Inthiscase,thetotalthroughputis132Mb/s.Wecallitchannel-basedpacketscheduling.InFigure 5-2 ,itiscleartoseethatchannel-basedpacketschedulingisoptimizedforeachchannel,whilepacket-basedpacketschedulingisdoneforeachpacket.Whenapplyingthepreviousmulti-channelschemes( 43 )( 47 )( 48 )( 49 )( 51 )( 52 )directlyintomulti-radiosystems,theyusuallyfallintothecategoryofpacket-basedscheduling. Wouldlocalthroughputoptimizationhelpimproveaggregatethroughputinmulti-hopwirelessnetwork?Itisbelievedthatlocaloptimizationwouldnotnecessarilyleadtotheglobaloptimization.However,solvingglobaloptimizationofthethroughputofnetworkrequiresperfectknowledgeoftracpattern,networktopologyandinterferencedistribution.Evenwithalltheknowledgeoftheabove,theproblemitselfisNPhard( 45 ).Thus,toourbestknowledge,almostalltheMACprotocolshavenotachievedtheglobaloptimalsolutiontotheproblemofmaximizingthethroughputinwirelessmultihopnetworks.Insomesense,alloftherelatedresearchworkssuchas( 42 )( 44 )( 45 )attempttoimprovethelocalthroughputinstead.Manyshowtheperformanceimprovementin 101

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TimelineforOMMAC.Assumethecurrenttransmissionuses4radiosatonetime.DuringtheprocessofRTSC-RTSD-CTS,thesenderisabletocollectchannelinformationon9linksifthenegotiationprocessissuccessful. networkthroughputthroughexperimentsorsimulations.WewillshowtheperformanceevaluationofOMMACinSections 5.4 and 5.5 102

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44 )( 46 ).Thetransmissionpoweristhesameforeachtransmitter.Weassumethatchannelisstationaryduringeachtransmissionperiod( 42 ).Thequeueateachnodeisinnite. Thechannellistisconstructedaccordingtoalocalchannelusagelist.InOMMAC,eachnodemaintainsalocalchannelusagelistwhichrecordstheinformationwhichchannelisavailableinthetransmissionrangeofthenode.Italsorecordstheusageofradios.LetCdenotethetotalchannelsetinthenetwork.LetCadenotethesetofthelocalavailablechannels.LetRadenotethesetofthelocalavailableradios.ThetransmitterchecksCaandRawhenthebackotimerstarts.ThenmchannelsarerandomlyselectedbythetransmitterfromitsavailablechannelsetCatoformthechannellistinRTSC.Thenumberofchannelsthatthenodewillusefordatatransmissionisatmostmin(jCaj;jRaj).LetCtdenotethechannelsinthechannellist. Theotherimportantdataeld,thenexthoplistH,containstheaddressesofcandidatereceivers.Inordertofullyexploitthemulti-radiodiversityasmuchaspossible,thetransmitterchoosesasmanypacketswithdierentnext-hopaddressesaspossibleundertheconstraintofthemaximumnumberofpacketstoscheduleisdme.Inthecaseof>1,thereareseveralcandidatereceiverswaitingonthesamechanneltosendback 103

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UponreceivingtheRTSC,candidatereceiverstunetheiravailableradiostoasetofchannelsonthechannellist.Denotethechannelsetthattheithreceiverinthenext-hoplistofRTSCisabletomeasureasCri.Apparently,CriCt.Ifthenumberofavailableradiosattheithreceiver,denotedasMri,isequaltothelengthofthechannellistinRTSC,thenCri=Ct.Otherwise,receiverhastochooseasubsetofchannelsinCttolistento.TherstpriorityisgiventoCcts.Thesecondpriorityisgiventothechannelsthattheavailableradiosarealreadysittingon.Fortherestoftheavailableradios,thereceiverrandomlytunestheradiostochannelswhichareinthechannellistinRTSC. RTSDissentontheselecteddatachannelsaccordingtothechannellistafteranSIFSintervalfollowingthetransmissionofRTSC.EachRTSDcontainssourceaddressandthenext-hoplistwhichisthesameinRTSC.RTSDisusedasaprobingmessagetoenablethechannelmeasurementatthecandidatereceivers.Themulti-castpropertyofRTSDenablesthemeasurementofchannelqualityatdierentreceiverswhichmayexperiencedierentlinkqualitiesondierentchannelsoratdierentlocations.NoticethateachRTSDcontainsacopyofthenext-hoplist.InthecasethatalegitimatereceivermaynothearRTSCbuthappentohearRTSDononeorseveraldatachannels,thereceiverwill 104

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EventhoughwemakesurethateachreceiverrsttunesoneofitsavailableradiostoCcts,itisstillpossiblethatthelinkqualityonCctsissopoorthatRTSDcannotbeheard.Thenifitisthecase,thereceiverisgoingtoskipchannelCctsandswitchtheradiotothekthchannelinthechannellistinRTSCwherek=(Ccts+1)modjCtj.Afterashortsensingtime(20s),ifthechannelisidle,thenthereceiverwillsendCTSthroughthatchannel.Otherwise,itswitchtheradiotothekthchannelinthechannellistinRTSC.ThemaximumnumberofchannelswitchingisaparametercapturingthetradeobetweenCTSwaitingtimeandtheamountofinformationthesenderwishestoget.Accordingtothechannelswitchingrulehere,receiversarecoordinatedtotransmitondistinctchannelseveniftheyneedtotransmitCTSonthechannelsotherthanchannelCcts.IncasethereisnosuccessfulRTSD-CTSexchangeforareceiveronthedatachannel,thechannelisnotusedfordatatransmission.Thetransmittersendsupdatedinformationabouttheavailabilityofthechannelonthecommonchannel(seealsoin 5.3.4 )aftertimeout. 105

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maxXi(Xjxijqij)s:t:XiXjxijm;8i2Ct;j2H;XixijjCrjj;8j2H;Xjxij1;8i2Ct;Xixijyj;xij2f0;1g;8i2Cs;j2H; whereqijisthemaximalsupportabledatarateonlinklisjandxijisthepacketschedulingpolicyforthejthreceiverontheithchannel.Thevaluesofxijareeither0or1,with1forschedulingthetransmissionontheithchannelforpacketstothejthreceiverinthenexthoplist.yjisthenumberofpacketswiththejthaddressinthenexthoplistinthequeueofthetransmitter.HisthenexthoplistinRTSC.Thustheobjectivefunctionistomaximizetheoverallthroughputofavailableradiosattimet.Therstconstraintdescribesthefactthatpacketschedulingisconnedbythenumberofavailablechannelsatthenode.ThesecondconstraintcomesfromtherequirementthatthereceivercanacceptpacketsatonetimeuptothenumberofitsownavailableresourcesjCrij,whichisthenumberofchannelsthereceiverisabletomeasure.Thethirdconstraintlimitsonetransmissionperchannelatatime.Thefourthconstraintisthatthenumberofthepacketsscheduledforthejthreceiverinthenexthoplistcannotexceedthenumberofpacketswiththejthaddressinthequeueofthetransmitter.Ifadditionalconcernsaregiventothetracloadateachnode,weneedtocomparethetracloadforthejthreceiver,denotedbypj,andallthetracrateqij.Sincesomenodesmayhavetracloadpj
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.Replacingqijintheobjectivewithmin(qij;pj)solvesthementionedproblemsusuallyinthenetworksfordierentiatedservices. Theaboveformulationisacombinatorialoptimizationproblem.Anupperboundofthisproblemisusingtheverticesofxij=1forthemaximalqijamongalljforeachi,i.e.,selectingthebestlinkqualityforeachchannelandschedulingthecorrespondingtransmissionwiththemaximaldatarateqij.Althoughtheoptimalsolutionmaynotbeattheverticesoftheabovementionedupperbound,thephilosophyofsolvingtheproblemremainsthesamedespitethelimitationofthenumberofavailablechannels,radiosandpackets.Theopportunisticchannel-basedpacketschedulingiscarriedoutaccordingtothesolutionoftheaboveoptimizationproblem.Itisdierentfromtheapproachmanymulti-channelschemesadopt,whichistoselectarelativelygoodchannelforeachtransmissionpair.AsexplainedearlierinSection 5.2.2 ,theapproachweuseheretakesbetterusageofallavailablespectralusage. Sincethenumbersofchannelsandradiosaresmall,therecursivebrute-forcesearchcansolvetheprobleminshorttime1.Thealgorithmisexecutedbythesendertodeterminethepacketschedulingstrategy. 107

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Fromtheabove,itshouldbeclearthatOMMACisabletoexploitmulti-radiodiversityasmuchaspossiblethroughmulti-castRTS,virtualmulti-CTS,RSV,andlocalchannel-basedpacketschedulingwhilekeepingthecommunicationoverheadlow. 5-1 .SupposeS,A,B,Carethenodeswith3availableradiosfordatachannels.InsourceS'soutgoingqueue,therearepacketswithnext-hopaddressesA,B,C.ForStoinitiateatransmission,SrstmulticastsaRTSCframeonthecommonchannel.TheRTSCframeincludesthechannellistindicatingthatch1,ch2,ch3arechosenfromtheavailablechannelsbyS.Italsoincludesthenext-hopaddresslistconsistingofA,B,Cforthepacketsinitsqueue.ThroughthecoordinationofRTSC,nodesA,BandCswitchtheirradiostolistentoallthesethreechannelsch1,ch2andch3.BylisteningtothefollowingRTSDonthethreedatachannels,Aisabletomeasuretheinstantchannelqualitiesforlinksetfl1sa;l2sa;l3sagandsendsbackasinglevirtualmulti-CTSwiththechannelqualitiesforseverallinksononeofthechannelsamongfch1;ch2;ch3g.SodonodesBandC.Inthisway,thelinkinformationcollectedbynodeScouldbeinFigure 5-2 .AsexplainedinSection 5.2.2 ,thelocalspectralusageismaximizedbycarryingoutthechannel-basedpacketschedulingresultinginsubsequentdatatransmissiononthelinksfl1sb,l2sc,l3sagorfl1sb,l2sc,l3sbg.ThenRSVissentonthecommonchanneltoinformothernodesintheneighborhoodtoupdatetheirlocalchannelusagelists.SincethereceiversA,B,Chavealreadytunedtheirradiosonchannelsindicatedby 108

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5-3 Forthepathlosscomponent,thereceivedpowerisgivenby: wheredisthetransmitter-receiver(T-R)separationdistance,d0isthereferencedistance,Pr(d0)isthereceivedpoweratd0andisthepathlossexponentwithtypicalvalues25. Forthesmallscalefadingmodel,weuseRiceanfadingdistributionforthereceivedsignalenveloperwhoseprobabilitydensityfunctionisgivenby: 2e(r2+A2) 22I0(Ar whereI0()isthemodiedBesselfunctionoftherstkindandzero-orderwithAasthepeakamplitudeofthedominantcomponent.TheRiceandistributionisoftendescribedintermsofaparameterK.Itisdenedastheratiobetweendeterministicsignalpowerandthevarianceofthemultiplepaths,i.e.,K=A2 109

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where Clearly,thethroughputforeachchanneldependsonthevalueofE(DATA).LetRdenotethesetofavailabledataratesandR=fRiji=1;:::;NRgwhereNRisthenumberofavailabledatarates.Thelargerthedatarateis,thehighertheindexis.ThecorrespondingSignaltoNoiseRatio(SNR)requirementsfordierentdataratesformthesetfiji=1;:::;NRg.LetDdenotethesetoftransmitter-receiverdistancesanddjdenotethedistancebetweenthesourceandthejthreceiver.WewriteD=fdjjj=1;2;:::;Nfg.Letrjdenotethereceivedsignalenvelopeofthereceivedpoweratthejthreceiver.TheSNRatthejthreceiveristhusequalto wherePnisthenoisepower.TheSNRateachreceiverisarandomvariablewhichfollowstheRiceandistribution.ThesetSNRisformedbytheSNRvalueatthereceiver,thatisSNR=fSNRjj1jmfNf;Nrgg.AccordingtoOMMAC,itendeavorstousethebestlinkforeachchannelfordatatransmission.IftheSNRvalueofthebestlinkonthechannelshouldsatisfytheSNRrequirementforRi,thetransmittercanadoptthedatarateRiforthefollowingdatatransmission.LetbethemaximumvalueinthesetSNR. 110

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(5{7) OMMACusesthehighestavailabledataratefortransmission,thustheprobabilityforusingdatarateRibythesourceforeachchannelP(Ri)isasfollows: (5{8) (5{9) Ifweconsiderthespecialtopologywhereeachreceiverisequallyseparated,thedensitydistributionfunctionforSNRateachreceiverisidenticallyindependentlydistributed.Inthiscase,]SNRcanalsorepresentthevalueofSNRateachreceiver.Thustheaboveresultscanbegivenas: (5{10) 111

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(5{11) Theexpectedaveragetransmissionamountofdatais: whereTpreambleisthetransmissiontimeforthephysicallayerpreambleofaDATAframe,andLHisthelengthofpacketheaderwhichmayincludeMAC,IPandTCPheaders. Giventhenumberofnodesncontendingforthetransmissioninwirelessnetworks,thethroughputforeachchannelcanbeobtainedasfollows: (1Ptr)Te+PtrPsTs+Ptr(1Ps)Tc;(5{13) where and 112

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Eachstationtransmitsapacketwithprobability(?).Giventhenumberofcontendingnodesninthewirelessnetworks,Ptristheprobabilitythatthereisatleastonetransmissionintheconsideredslottime,Psistheprobabilitythatthereisexactlyonesuccessfultransmissiononthechannel. TheexpectedaverageamountofdatatransmissionbyusingmiradiosisE(DATAi).LetSibethethroughputoftheithsourceononechannel.SicanbecalculatedbyreplacingE(DATA)withE(DATAi)inEquation( 5{13 ).ThetotalthroughputStonallchannelsisequalto whereAisasetwhichsatisesthefollowingrequirements: InOMMAC,thecommonchannelsaturationproblemismostlyovercomedbyschedulingtransmissionsoverseveralavailablechannelsatatime.ItisenoughtoonlyaccommodateaboutNc=Nr1contentionperiodsduringaDATAtransmissionperiod.Nc=NrdramaticallydecreaseswithNr.Moreover,weadoptthesimilarprocedureofthebursttransmissioninOARtohavethesametransmissiontimeTdataforalldierentrates.Tdataissetlongenoughforatransmissionofapacketatthelowestrate. 113

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Inthenumericalanalysis,forthepathlosscomponent,weusethefreespacepropagationmodelwhenthetransmitter-receiverdistanceislessthanacrossoverdistancedcrossover,andthetwo-raygroundpropagationmodelotherwise. whereboththetransmitterantennagainGtandthereceiverantennagainGraresetasone,theheightofboththetransmitterantennahtandthereceiverantennahraresetas1.5meters,thesystemlossfactorLissetasone,thefrequencyis914MHzandhencethewavelength=0:3282m.Weusethreerates,11,5.5,and2Mbps.Ifonlythepathlosscomponentisconsidered(nochannelfading),theirtransmissionradiiare100,200,and250m,respectively,byappropriatelysettingtheSNRrequirementsandthenoisepower.Channelfadingeectactuallyenlargesthetransmissionrangeaswewillseelater.Therearetotal11non-overlappingchannels.Incase2,thenumberofsourcesis30.Wexthetransmitterandreceiverdistanceasforthedemonstrationpurpose.Wesummarizethemainparametersintable 5-1 Figure 5-4 illustratesthethroughputgainforcase2whenthenumberofradiosforDATAframetransmissionincreasescomparedtothethroughputwithonedataradioforDATAframetransmission.Byexploitingthemulti-radiodiversity,thethroughputincreasesalongwiththenumberofradiosandisuptoaboutmtimeswithmradiosforDATAframetransmissions.Themtimesimprovementoccursatdistantreceiverswherethethroughputisoriginallylow.Weonlydisplaythegureintherangesfrom0300m. 114

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value CWmin 31 numradio 1:10 Tsifs Tdifs Tdata ExperimentParameters Withintherangewearemoreinterested,saylessthan250,normalizedthroughputis1.8times.Wefoundthattheguresforcase1andcase2areverysimilarandthethroughputofcase2isalittleworsethanthatofcase1duetothecontentiononthecontrolchannel.Hereweonlyshowtheperformanceofcase2. Wealsoobservethattheimprovementbroughtbyexploitingthemulti-radiodiversityoccursmainlyatthetransmitter-receiverdistancewherethemaximumsupportedratearemorelikelytochange.ThisissimilartotheimprovementofOARovertheoriginal802.11.Inaddition,OMMACisespeciallyfriendlytotheuserswhichhaveweaksignals.Theimprovementfortheseusersarehuge. Theimprovementbyaddingonemoreradio,i.e.,theper-radiogain,graduallydecreaseswhenthenumberofradiosisincreased.Forexample,thegainof9radiosisclosetothegainsof7and8radios;incontrast,thegainof3radiosismuchlargerthanthegainof2radios.Furtherinvestigationaboutthetradeobetweenthehardwarecomplexityandthenumberofradiosisleftforfurtherwork. Figure 5-5 andFigure 5-6 showtheabsolutethroughputfordierentnumberofradioswhenK=1.Forcase1,thesourcenodeisabletousemoreavailablechannelsforsimultaneoustransmissionsasthenumberofradiosincreases.Forcase2,severalsourcescanshareavailablechannelsandthetotalthroughputislargerevenwiththesamenumber 115

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Throughputgainnormalizedoverthethroughputofonedataradio ofradiosascase1.Thus,aslongastheavailablechannelsareusedupbythesetofnodes,thetotalthroughputisnotincreasingdramaticallyasthecase1.However,OMMACstillmanagestoimprovetheperformanceespeciallyatthedistancewherethemaximumsupportedratearemorelikelytochangewhichisconsistentwithFigure 5-4 Besidestheaboveobservations,itclearlydemonstratesthatOMMACextendsthetransmissionrangeofeachratebyexploitingthemulti-radiodiversity.Thisisreallyimportantinmultihopnetworks,whereroutingalgorithmsghttondtheoptimumtradeobetweentheratesandthecommunicationdistanceswhenchoosingforwardingnodes( 15 ). 16 )andtheRiceanpropagationmodelasinMOAR( 44 ).First,webeginwithsingle-hoptopologiestostudythemainprotocolpropertiesandillustratetheimpactofdierentparameters{thenumberofradiosandthenumberofows-onthroughputperformance.Second,westudymulti-hoptopologiestoverifytheperformanceinwirelessadhocnetwork.WealsocomparetheaggregatethroughputperformanceofOMMACwiththatofMOAR( 44 )anddemonstratethat 116

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ThroughputofOMMACincase1 Figure5-6. ThroughputofOMMACincase2 OMMACsignicantlyimprovesthethroughputbyexploitingthemulti-radiodiversity.Moreover,weshowtheperradiothroughputofOMMACwhichalsooutperformsOARandMOAR.Wedenotethisthroughputas"perradio"throughputinthegures.Inthesimulation,therearetotal11non-overlappingchannels.Threedierentrates,2,5.5,and11Mbps,arestudied.AsinMOAR,theirtransmissionradiiare250,200,and100m,respectively.UDPtracisused.Simulationtimeis50secondsineachrun.Packetsizeis1000bytes. 117

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Single-hopTopology:thesizeoftherectangleis200m200m.Sisthesourcenode. 5-7 tostudytheimpactofdierentparametersontheperformance.Wechangetheparameterssuchasthenumberofradios,thenumberofows,andthechannelfadingparameterinthesimulationtoobservetheirimpactonthroughput. ImpactofTheNumberofRadios:Hereweusedierentnumberofradiostoinvestigatetherelationshipbetweenthenumberofradiosandthethroughput.ThereareeightowsgeneratedfromthesourcenodeStotheothereightnodes.Figure 5-8 illustratesthatthethroughputincreasesalongwiththenumberofradios.ThisindicatesthatOMMAChassuccessfullycoordinatedtheavailableradiosfortransmissiontoimprovethelocalspectralusage. ImpactofTheNumberofFlows:Inthissimulation,wesetthenumberofradiosasfour.FromFigure 5-9 ,weseeadramaticincreaseinthroughputwhenthenumberofowsincreasesfrom1to2,whichresultsfromtheuniquefeatureofpacketschedulinginOMMAC.Whentheoutgoingqueuehasmanypacketswithdierentnext-hopaddresses,themulti-radiodiversityconsistsofalargesetoflinkdiversities,whichgivesOMMACtheopportunitytooptimallyschedulethetransmissionsandimprovethethroughput.Duetothelimitationoftheextentofchannelqualityvariationandthenumberofradios,the 118

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ThroughputofOMMACasafunctionofnumberofradiosinthesingle-hoprectangulartopology Figure5-9. ThroughputofOMMACasafunctionofnumberofowswithdierentRiceanparameterscomparedwiththatofMOARinthesingle-hoprectangulartopology throughputbecomessteadywhenthenumberofowsisclosetothenumberofradios.Alsonoticethattheper-radiothroughputofOMMACisgreaterthanthatofMOAReventhoughthesingle-radioOMMAChasaveragelyfewerchannelstoschedulethetransmissionsthanMOAR,themulti-radiodiversitystilloersperformanceimprovementinper-radioaggregatethroughputinOMMAC. ImpactofTheRiceanParameterK:Hereweusefourradiosineachnode.TherearestilleightowsgeneratedfromthesourceStotheothereightnodes.WetunetheRiceanparameterKfrom0to6.ThelargerthevalueofKis,thesmallervariationthereisinchannelquality.Figure 5-10 showsthroughputofbothMOARandOMMAC.Heretheper-radioaggregatethroughputinOMMACisstillgreaterthanMOAR.SimilarwithMOAR,OMMAC'sthroughputincreaseswhenKincreases. 119

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ThroughputofOMMACasafunctionoftheRiceanparameterKinthesingle-hoprectangulartopology Figure5-11. ThroughputofOMMACasafunctionofnumberofowsinthesinglehoprandomtopologyincomparisonwiththatofMOAR 5-11 .Theincreaseinaggregatethroughputalongwiththenumberofowsagainshowsthebenetofexploitingmulti-radiodiversity.OMMACimprovesthethroughputby2:33timesupto8:91times.Moreover,theper-radioaggregatethroughputinOMMACoutperformsMOARbyaverage1:4times. 120

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ThroughputofOMMACasafunctionofnumberofowsinthemulti-hoprandomtopologyincomparisonwiththatofMOAR AsshowninFigure 5-12 ,OMMACsignicantlyimprovesthethroughputcomparedwithMOAR,andthegainisfrom3:27timesto11:22timeswhenthenumberofowsincreasesfrom2to16.Alsotheper-radioaggregatethroughputinOMMACimprovesasthenumberofowsincreaseandoutperformsMOARwhenthenumberofowsisgreaterthan4.Therstowhaszerothroughputsincetheyaredisconnectedinthesimulatedrandomtopology. Fromalltheresultsabove,wecanseethatOMMACperformswellinexploitingthemulti-radiodiversity.Byexploitingchanneldiversityovermultiplechannels,MOARimprovesthroughputbyupto60%( 44 )comparedtoOAR.Byexploitingthemulti-radiodiversityovermultipleradiosandchannels,MOARfurtherimprovesbothmulti-radioandper-radioaggregatethroughput. 121

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122

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Inthisdissertation,wefocusonthecrosslayerdesignbetweenMACandotherlayersinprotocolstackinwirelessadhocnetworks.OurproposeworkhasaddressedtheproblemofndingoptimalcarriersensingthresholdbystudyingitsimpactonMAClayerlinkschedulingandaggregatethroughputinMAClayer.WealsoaddresstheprobleminroutinglayerbynotonlyndingtherouteswithoptimalpathcapacitybutalsoprovidingafeasibleMAClayerlinkschedulingtoachievethem.SincetheproblemformulationfortheoptimalMAClayerlinkschedulingisusuallyNP-hard,wefurtherstudytheestimatedboundsfornetworkcapacityforwhichweprovidepolynomialsolution.Despiteallthetheoreticalcrosslayerdesign,weendeavortoprovidedistributedsolutionforrealsystemsaswell.OMMACisproposedtoutilizethephysicallayerinformation,specicallymultiradiodiversityinformation,toprovideimprovedaggregatethroughputperformanceinmultichannelmultiradiowirelessadhocnetworks. 123

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Y.Zhu,Q.Zhang,Z.Niu,andJ.Zhu,\Onoptimalphysicalcarriersensing:theoreticalanalysisandprotocoldesign",inProceedingsofIEEEINFO-COM2007. [15] H.zhai,Y.Fang,\Impactofroutingmetricsonpaththroughputinmultirateandmultihopwirelessadhocnetworks",inICNP'06. [16] H.zhai,Y.Fang,\Physicalcarriersensingandspatialreuseinmultirateandmultihopwirelessadhocnetworks",inProceedingsofIEEEINFOCOM2006. [17] A.Akella,G..Judd,P.SteenkisteandS.Seshan,\Selfmanagementinchaoticwirelessdeployments,"inProceedinsofACMMobicom2005. [18] K.Jain,J.Padhye1,VN.PadmanabhanandL.Qiu,\ImpactofInterferenceonMulti-HopWirelessNetworkPerformance",inACMMobicom,September2003. [19] S.Roy,H.Ma,R.Vijayakumar,J.Zhu,\Optimizing802.11WirelessMeshNetworkPerformanceUsingPhysicalCarrierSensing",inUWEETR2006-0005. [20] F.Cali,M.Conti.andE.Gregori,\DynamictuningoftheIEEE802.11protocoltoachieveatheoreticalthroughputlimit",inIEEE/ACMTransactionsonNetworking,8(6):785-799,Dec.2000. [21] K.Jamieson,B.Hull,A.MiuandH.Balakrishnan,\Understandingtherealworldperformanceofcarriersense",inProceedingsofACMSIGCOMM,August.2005. [22] J.Deng,B.Liang,andP.K.Varshney,\TuningthecarriersensingdistanceofIEEE802.11MAC",inProceedingsofIEEEGLOBECOM,Dec,2004. [23] H.Zhai,J.Wang,X.Chen,Y.Fang,\Mediumaccesscontrolinmobileadhocnetworks:challengesandsolution",inWirelessCommunicationsandMobileComputing,Volume6,Issue2,Pages151-170,SpecialIssue:SpecialIssueonAdHocWirelessNetworks,2004. [24] HuaZhu,ImrichChlamtac.Admissioncontrolandbandwidthreservationinmulti-hopadhocnetworks.ComputerNetworks50(11),1653-1674,2006. [25] C.Sarr,C.Chaudet,G.Chelius,andI.Gurin-Lassous.Anode-basedavailablebandwidthevaluationinIEEE802.11adhocnetworks.InternationalJournalofParallel,EmergentandDistributedSystems,2005. [26] S.Shah,K.Chen,andK.Nahrstedt.DynamicBandwidthManagementforSingle-hopAdHocWirelessNetworks.ACM/KluwerMobileNetworksandApplications(MONET)Journal,10(1),2005. [27] Y.YangandR.Kravets.Contention-awareadmissioncontrolforadhocnetworksIEEETransactionsonMobileComputing,4(4),pp.363-377,2005. 125

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H.Wu,X.Wang,Y.Liu,Q.Zhang,andZ.Zhang.SoftMAC:layer2.5MACforVoIPsupportinmulti-hopwirelessnetworksIEEESECON,Sept.2005. [29] H.Zhai,X.Chen,andY.Fang.ImprovingtransportlayerperformanceinmultihopadhocnetworksbyexploitingMAClayerinformation.IEEETransactionsonWirelessCommunications,6(4),2007. [30] K.Xu,K.Tang,R.Bagrodia,M.Gerla,andM.Bereschinsky.AdaptivebandwidthmanagementandQoSprovisioninginlargescaleadhocnetworksIEEEMILCOM,Oct.2003 [31] Y.Xue,B.Li,andK.Nahrstedt.Optimalresourceallocationinwirelessadhocnetworks:Aprice-basedapproach.IEEETransactionsonMobileComputing,5(4),pp.347-364,April2006. [32] Z.FangandB.Bensaou,B.Fairbandwidthsharingalgorithmsbasedongametheoryframeworksforwirelessad-hocnetworksINFOCOM,March2004. [33] J.YeeandH.Pezeshki-Esfahani,UnderstandingwirelessLANperformancetrade-os.CommsDesign.com,Nov.2002. [34] J.Li,C.Blake,D.S.J.D.Couto,H.I.Lee,andR.Morris.Capacityofadhocwirelessnetworks.ACMMobiCom,July2001. [35] P.GuptaandP.R.Kumar.Thecapacityofwirelessnetworks.IEEETransactionsonInformationTheory,46(2):388{404,Mar.2000. [36] M.GrossglauserandD.Tse.Mobilityincreasesthecapacityofad-hocwirelessnetworks.IEEEINFOCOM,2001. [37] A.El.Gamal,J.Mammen,B.Prabhakar,andD.Shah.Throughput-delaytrade-oinwirelessnetworks.IEEEINFOCOM,March2004. [38] B.Liu,Z.Liu,andD.Towsley.Onthecapacityofhybridwirelessnetworks.IEEEInfocom,2003. [39] U.C.KozatandL.Tassiulas.Throughputcapacityofrandomadhocnetworkswithinfrastructuresupport.Mobicom,2003. [40] S.ToumpisandA.J.Goldsmith.Capacityregionsforwirelessadhocnetworks.IEEETransactionsonWirelessCommunications,2(4):736{748,July2003. [41] H.Balakrishnan,C.L.Barrett,V.S.A.Kumar,M.V.Marathe,andS.Thite.Thedistance-2matchingproblemanditsrelationshiptotheMAC-Layercapacityofadhocwirelessnetworks.IEEEJSAC,22(6):1069{1079,Aug.2004. [42] B.Sadeghi,V.Kanodia,A.Sabharwal,E.Knightly,\OAR:anopportunisticauto-ratemediaaccessprotocolforadhocnetworks",inwirelessnetworks,Volume11,Issue1-2(January2005),Pages:39-53,2005ISSN:1022-0038. 126

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J.Mo,H.WilsonSo,J.Walrand,\Comparisonofmulti-channelMACprotocols",inInternationalWorkshoponModelingAnalysisandSimulationofWirelessandMobileSystems,2005. [44] V.Kanodia,A.Sabharwal,andE.Knightly,\MOAR:Amulti-channelopportunisticauto-ratemediaaccessprotocolforadhocnetworks,"inProceedingsofIEEEBROADNETS,2004. [45] A.Adya,P.Bahl,J.Padhye,A.Wolman,andL.Zhou.,\Amulti-radiounicationprotocolforIEEE802.11wirelessnetworks",inProceedingsofIEEEBROADNETS,2004. [46] R.Garces,J.J.Garcia-Luna-Aceves,"Collisionavoidanceandresolutionmultipleaccessformultichannelwirelessnetworks",inProceedingsofIEEEINFOCOM2000,pages595C602,TelAviv,Israel,Mar,2000. [47] A.Nasipuri,J.ZhuangandS.R.Das,\AmultichannelCSMAMACprotocolformultihopwirelessnetworks",inWirelessCommunicationsandNetworkingConference,1999 [48] N.Choi,Y.SeokandY.Choi,\Multi-channelMACprotocolformobileadhocnetworks",inVehicularTechnologyConference,2003. [49] H.Zhai,J.Wang,andY.Fang,"DUCHA:ADual-ChannelMACProtocolforMobileAdHocNetworks,"inIEEETransactionsonWirelessCommunications,vol.5,no.11,Nov.2006. [50] S.L.Wu,C.YLin,Y.C.Tseng,J.-P.Sheu,\ANewMulti-ChannelMACProtocolwithOn-DemandChannelAssignmentforMulti-HopMobileAdHocNetworks",inInternationalSymposiumonParallelArchitectures,AlgorithmsandNetworks(ISPAN'00),2000. [51] JSo,Vaidya,\MultiChannelMACforAdHocNetworks:HandlingMultiChannelHiddenTerminalsUsingASingleTransceive",inMobiHoc,2004. [52] J.Shi,T.Salonidis,EdwardW.Knightly,\Mediumaccesscontrol:Starvationmitigationthroughmulti-channelcoordinationinCSMAmulti-hopwirelessnetworks",inMobiHoc,2006. [53] P.Bhagwat,P.Bhattacharya,A.KrishnaandS.K.Tripathi,\EnhancingthroughputoverwirelessLANsusingchannelstatedependentpacketscheduling",inProc.ofINFOCOM,1996. [54] J.WangandH.Zhai,\OMAR:UtilizingMultiuserDiversityinWirelessAdHocNetworks",IEEETransactionsonmobilecomputing,2006. [55] http://research.microsoft.com/mesh/ [56] http://www.strixsystems.com 127

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http://www.meshdynamics.com/ 128

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FengChenisPh.DstudentinElectricalandComputerEngineeringdepartmentatUniversityofFloridasinceSeptember2005.ShegotdualdegreeofBachelorofEngineeringdegreefrombothDepartmentofElectronicsandInformationEngineeringandDepartmentofComputerScienceandTechnologyatHuazhongUniversityofScienceandTechnology,Wuhan,PRChina,duringSeptember2001CJune2005.SheisatPhilipsResearchNorthAmericaasaninternduringJuly2009-Dec2009.Herresearchinterestisprotocoldesignandcapacityanalysisinwirelessadhocnetworks.SheisIEEEstudentmembersince2006. 129