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Power Control and Resource Allocation for Delay-Constrained Communications

Permanent Link: http://ufdc.ufl.edu/UFE0024302/00001

Material Information

Title: Power Control and Resource Allocation for Delay-Constrained Communications
Physical Description: 1 online resource (168 p.)
Language: english
Creator: Li, Xiaochen
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: delay, optimization, packet, power, qos, resource
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: Real-time applications such as streaming multimedia will be supported in the next generation wireless networks. Services required by these applications are different from file transfer services in that they expect low transmission delay, i.e., delay-constrained communications. Providing quality of service (QoS) guarantees to multimedia applications poses a significant challenge for the design of wireless networks. This dissertation focuses on the power and resource allocation schemes for delay-constrained communications, with statistical QoS requirements characterized by the triplet of data rate, delay bound, and delay bound violation probability. We study the optimal power control and resource allocation schemes to provide statistical QoS guarantees, which are more challenging than providing average delay guarantees, since statistical QoS imposes constraints on the distribution of transmission delay. In the first part of the dissertation, we study the throughput maximization problem subject to the delay bound violation probability and average power constraint, for a single-user, single-channel system. The buffer size is assumed to be infinite and the delay bound is relatively large. This problem is actually the effective capacity maximization problem, which is defined as the maximum data rate a system can sustain under the statistical QoS constraint, in large delay regime. We propose a simple cross-layer suboptimal power control scheme which significantly increases the effective capacity comparing to the optimal channel-gain-based power control scheme. We also investigate the impact of delayed channel state information on the performance of power control schemes. Finally, we study the joint power and channel allocation scheduler for a multi-user, multi-channel system, based on the effective capacity and reference channel approach. The scheduling algorithm explicitly guarantees users' statistical QoS requirements while minimizing the resource usage. In the second part of the dissertation, we study the dual problem, minimizing the delay bound violation probability, subject to an average power constraint and throughput constraint. The transmission buffer size is assumed to be finite (small delay regime). Therefore the delay bound violation probability translates to buffer fullness probability, or packet drop probability. The queuing behavior with a finite size buffer is quite different from that of an infinite size buffer. We analyze the fundamental limit of power control performances over continuous wireless channels for finite size buffer models. Dynamic programming techniques, which are used to address the control of queueing systems under discrete channel models, will result performance degradation due to quantization. Our method is to decompose the original optimization problem into three sub-problems, and sequentially solve the three sub-problems. We prove that the two problems have the same optimal solution. By solving the sub-problems, we provide structural information about the optimal solution. The optimal cross-layer power control scheme is combined with adaptive modulation technique in a variable-rate, variable-power system, where both packet drop probability and decoding error probability are considered.
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 Xiaochen Li.
Thesis: Thesis (Ph.D.)--University of Florida, 2009.
Local: Adviser: Wu, Dapeng.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0024302:00001

Permanent Link: http://ufdc.ufl.edu/UFE0024302/00001

Material Information

Title: Power Control and Resource Allocation for Delay-Constrained Communications
Physical Description: 1 online resource (168 p.)
Language: english
Creator: Li, Xiaochen
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: delay, optimization, packet, power, qos, resource
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: Real-time applications such as streaming multimedia will be supported in the next generation wireless networks. Services required by these applications are different from file transfer services in that they expect low transmission delay, i.e., delay-constrained communications. Providing quality of service (QoS) guarantees to multimedia applications poses a significant challenge for the design of wireless networks. This dissertation focuses on the power and resource allocation schemes for delay-constrained communications, with statistical QoS requirements characterized by the triplet of data rate, delay bound, and delay bound violation probability. We study the optimal power control and resource allocation schemes to provide statistical QoS guarantees, which are more challenging than providing average delay guarantees, since statistical QoS imposes constraints on the distribution of transmission delay. In the first part of the dissertation, we study the throughput maximization problem subject to the delay bound violation probability and average power constraint, for a single-user, single-channel system. The buffer size is assumed to be infinite and the delay bound is relatively large. This problem is actually the effective capacity maximization problem, which is defined as the maximum data rate a system can sustain under the statistical QoS constraint, in large delay regime. We propose a simple cross-layer suboptimal power control scheme which significantly increases the effective capacity comparing to the optimal channel-gain-based power control scheme. We also investigate the impact of delayed channel state information on the performance of power control schemes. Finally, we study the joint power and channel allocation scheduler for a multi-user, multi-channel system, based on the effective capacity and reference channel approach. The scheduling algorithm explicitly guarantees users' statistical QoS requirements while minimizing the resource usage. In the second part of the dissertation, we study the dual problem, minimizing the delay bound violation probability, subject to an average power constraint and throughput constraint. The transmission buffer size is assumed to be finite (small delay regime). Therefore the delay bound violation probability translates to buffer fullness probability, or packet drop probability. The queuing behavior with a finite size buffer is quite different from that of an infinite size buffer. We analyze the fundamental limit of power control performances over continuous wireless channels for finite size buffer models. Dynamic programming techniques, which are used to address the control of queueing systems under discrete channel models, will result performance degradation due to quantization. Our method is to decompose the original optimization problem into three sub-problems, and sequentially solve the three sub-problems. We prove that the two problems have the same optimal solution. By solving the sub-problems, we provide structural information about the optimal solution. The optimal cross-layer power control scheme is combined with adaptive modulation technique in a variable-rate, variable-power system, where both packet drop probability and decoding error probability are considered.
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 Xiaochen Li.
Thesis: Thesis (Ph.D.)--University of Florida, 2009.
Local: Adviser: Wu, Dapeng.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0024302:00001


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Firstofall,myspecialgratitudegoestomyadvisor,ProfessorDapengOliverWu,forhisgreatinspirationandexcellentguidancethroughoutthisdissertationandmyPh.D.educationatUFL.Hisenthusiasmanddeepthoughtssparkmyinterestinacademicresearch.Iamgratefultohimforhisinsightfulguidanceandstricttrainingoncreativethinking,rigorousanalyzing,andeectivewritingskills.Mydeeplyappreciationgoestomycommitteemembers:ProfessorLiuqingYang,JaniseMcNairandShigangChen,fortheirinterestinmyworkandthevaluablefeedbacksonmyresearch.IwouldliketothankProfessorJianboGao.Ihavelearntalotfromhissignalprocessingclassesandelaboratelydesignedcourseprojects.IwouldliketothankProfessorP.OscarBoykinformanyusefuldiscussionsaboutthequeueingtheory.IwouldliketothankmyMasteradvisorProfessorBingliJiao,heguidedmeintotheworldofwirelesscommunications.Iwouldliketothankmylab-matesintheMultimediaCommunicationsandNetworkingLaboratory(MCN)hereinUF.Iamfortunatetobeamemberofthisfriendlyandfamily-likegroup.IwouldliketothankXihuaDong,forthehelpfuldiscussionsontheresearchandcooperationofmanypapers;BingHan,WenxingYe,JunXu,ZhifengChen,TaoranLu,YiranLi,YunzhaoLi,andmyseniorlab-mateDr.JieyanFan,fortheirconstantsupportsandsincerefriendship,andIcherisheveryminutewehavespenttogether;ShanshanRen,ZiyiWangandLinZhang,forhostingthepartiesandaddingtheelementoffuntomyPh.D.life.IhavespentwonderfulfouryearsinGainesville.Withoutthem,itisnotevenpossible.IwouldalsoliketothankZongruiDing,LeiYang,QianChen,JiangpingWang,YakunHu,QinChen,QingWang,YounghoJoandChrisPaulson.WishyouallhavesuccessinyourPh.D.studies.Iwouldliketothankmyparentsfortheendlessloveandconstantsupportthey'veprovidedduringmywholelife.ThanksfortheencouragementforeverytinyprogressthatIhaveevermade.Withoutthem,Iwouldhaveneverbeenabletoaccomplishwhat 4

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page ACKNOWLEDGMENTS ................................. 4 LISTOFTABLES ..................................... 9 LISTOFFIGURES .................................... 10 ABSTRACT ........................................ 13 CHAPTER 1INTRODUCTION .................................. 15 1.1WirelessFadingChannels ........................... 16 1.2RelatedWorksonDelay-ConstrainedCommunications ........... 19 1.2.1PhysicalLayerModel .......................... 21 1.2.2Link-PHYlayerModel ......................... 25 1.3OutlineoftheDissertation ........................... 32 2HIERARCHICALQUEUE-LENGTH-AWAREPOWERCONTROL ...... 35 2.1SystemDescription ............................... 36 2.1.1StructureofDataSourceandTransmitter .............. 36 2.1.2MarkovChainModel .......................... 37 2.2HierarchicalQueue-Length-AwarePowerControlScheme .......... 39 2.2.1HierarchicalQueue-Length-AwarePowerControlScheme ...... 41 2.2.2SteadyStateQueueLengthDistribution ............... 42 2.2.3AveragePower .............................. 45 2.2.4EectiveCapacitywithPowerControl ................ 47 2.2.5PeakPowerConstraint ......................... 47 2.3SimulationResults ............................... 49 2.3.1SteadyStateQueueLengthDistribution ............... 49 2.3.2EectiveCapacity ............................ 50 2.3.3PowerGainin3GEnvironment .................... 52 2.3.4HQLAwithAdaptiveModulation ................... 55 2.3.5PeakPowerConstraint ......................... 57 2.4SteadyStateAnalysisforVariable-RateArrivalProcessandCorrelatedChannel ..................................... 57 2.4.1Correlatedchannel ........................... 57 2.4.2Variable-RateArrivalProcess ..................... 61 2.5Summary .................................... 64 3QOS-DRIVENPOWERALLOCATIONFORMULTI-CHANNELCOMMUNICATIONSUNDEROUTDATEDCHANNELSIDEINFORMATION ............ 65 3.1Introduction ................................... 65 6

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.................................. 67 3.3OptimalPowerAllocationScheme ....................... 68 3.4SuboptimalPowerAllocationScheme ..................... 71 3.5SimulationResults ............................... 75 3.6Summary .................................... 76 4JOINTPOWERANDCHANNELALLOCATIONINWIRELESSNETWORKS 79 4.1Introduction ................................... 79 4.2ReferenceChannelApproach .......................... 80 4.3SystemDescription ............................... 81 4.4SimulationResults ............................... 87 4.4.1SimulationSetting ............................ 87 4.4.2PerformanceEvaluation ......................... 89 4.5Summary .................................... 92 5JOINTQUEUE-LENGTH-AWAREPOWERCONTROL ............ 93 5.1SystemModel .................................. 96 5.2SeparateQLAPowerControl ......................... 102 5.3JointQLAPowerControl ........................... 106 5.4StructureOfTheOptimalPowerControlScheme .............. 113 5.4.1ConvexityoftheObjectiveFunction .................. 114 5.4.2SolutionfortheConstraint-RelaxedOptimizationProblem ..... 116 5.4.3OnlyOneNegativeColumnin^pi;j 118 5.4.4ArbitraryNumberofNegativeColumnsin^pi;j 123 5.4.5StructureoftheOptimalPowerControlScheme ........... 124 5.5SimulationResults ............................... 125 5.5.1SQLAPowerControl .......................... 125 5.5.2JQLAPowerControl .......................... 127 5.6Summary .................................... 129 6POWERCONTROLWITHADAPTIVEMODULATION ............ 134 6.1AdaptiveModulationOverview ........................ 135 6.2AdaptiveModulationinCrossLayerDesign ................. 137 6.3JQLAwithAdaptiveModulation ....................... 138 6.4SimulationResults ............................... 141 6.5Summary .................................... 143 7CONCLUSIONS ................................... 147 APPENDIX ......................................... 150 APROOFS ....................................... 150 A.1ProofofLemma 3.1 ............................... 150 A.2ProofofLemma 3.2 ............................... 151 7

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5.1 ............................... 152 A.4ProofofLemma 5.2 ............................... 153 A.5ProofofLemma 5.3 ............................... 154 A.6ProofofLemma 5.4 ............................... 155 A.7ProofofLemma 5.5 ............................... 157 A.8ProofofLemma 5.6 ............................... 157 A.9ProofofLemma 5.7 ............................... 158 A.10ProofofLemma 5.8 ............................... 159 REFERENCES ....................................... 160 BIOGRAPHICALSKETCH ................................ 168 8

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Table page 2-1Parametersfor3Genvironmentsimulation. ..................... 53 2-2Parametersfor3Genvironmentsimulationwithadaptivemodulation. ...... 56 3-1Comparisonofcomputationalcomplexity. ..................... 75 5-1Congurationoff(g). ................................. 103 5-2Constructingpi;jfrom^pi;j. ............................. 124 5-3Constructingyjfrom^yj. .............................. 126 5-4SimulationparametersforSQLA. .......................... 127 5-5Simulationresults. .................................. 127 5-6SimulationparametersforJQLA. .......................... 128 5-7SimulationresultsforJQLA. ............................. 129 9

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Figure page 1-1Typeoffadingchannels. ............................... 17 1-2Physicallayerandlink-PHYlayersystemmodels ................. 20 2-1Structureofdatasourceandtransmitter. ...................... 37 2-2Updateofthequeuelength. ............................. 39 2-3Markovpropertyofthequeuelength. ........................ 39 2-4Hierarchicalqueue-length-awarepowercontrolscheme. .............. 41 2-5Hierarchicalqueue-length-awarepowercontrolschemewithpeakpowerconstraint. 41 2-6ProbabilitymassfunctionofHQLA/CONST. ................... 50 2-7ProbabilitymassfunctionofHQLA/TDWF. .................... 51 2-8DelayboundviolationprobabilityofHQLA/TDWF. ............... 51 2-9EectivecapacityofHQLA/CONST. ........................ 52 2-10EectivecapacityofHQLA/TDWF. ........................ 52 2-11EectivecapacityofHQLA/OPT. .......................... 53 2-12PowergainofHQLA/CONSToverCONSTPC. .................. 54 2-13PowergainofHQLA/TDWFoverTDWFPC. ................... 54 2-14PowergainofHQLA/TCIoverTCIPC. ...................... 55 2-15PowergainofHQLA/TCIoverTCIPCwithadaptivemodulation,voicedata. 56 2-16Dmaxvs.averagepowerwithxedand. .................... 57 2-17Delayboundviolationprobabilityat20mph. .................... 60 2-18Delayboundviolationprobabilityat80mph. .................... 60 2-19Anexampleofvariable-ratearrivalprocess. .................... 62 2-20QueuelengthdistributionofTCIPCwithvariable-ratearrivalprocess. ..... 63 2-21QueuelengthviolationprobabilityofTCIPCwithvariable-ratearrivalprocess. 63 3-1Systemdiagram. ................................... 68 3-2EectofCSIdelayontheeectivecapacity. .................... 77 10

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........................................ 78 4-1QoSprovisioningarchitectureinabasestation. .................. 82 4-2Queueingmodelusedformultiplefadingchannels. ................ 87 4-3PerformancegainLc(K;N)vs.averageSNR. ................... 90 4-4PerformancegainLp(K;N)vs.averageSNR. ................... 90 4-5PerformancegainLe(K;N)vs.averageSNR. ................... 91 5-1Systemmodel. .................................... 98 5-2Diagramofstatesupdate. .............................. 98 5-3ExampleofPq(g),q=0,=4. ........................... 109 5-4Anexampleoffadingregionsoftheoptimalpowercontrolschemewhenall^pi;j0. ............................................ 125 5-5Anexampleoffadingregionsoftheoptimalpowercontrolschemewhensomeofthe^pi;j<0. ..................................... 126 5-6SQLA,=25,M=50. ............................... 128 5-7SQLA,=5,M=50. ................................ 129 5-8TCIandTDWFpowercontrol. ........................... 130 5-9JQLApowercontrol,=25,M=50. ....................... 130 5-10JQLApowercontrol,=10,M=50. ....................... 131 5-11JQLApowercontrol,=5,M=50. ........................ 131 5-12Packetdropprobabilityv.s.averagepower.=25,M=50. ........... 132 5-13Packetdropprobabilityv.s.averagepower.=10,M=50. ........... 132 5-14Packetdropprobabilityvs.averagepower.=5,M=50. ............ 133 6-1A(K)anditscurvetting .............................. 141 6-2Constantpowercontrol,M=10,=5,PER=103. .............. 142 6-3TDWFpowercontrol,M=10,=5,PER=103. ............... 143 6-4PDRvs.PER.=1,M=10. ........................... 144 6-5PDRvs.PLR.=1,M=10. ........................... 144 11

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........................... 145 6-7PDRvs.PER.=5,M=10. ........................... 145 12

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Real-timeapplicationssuchasstreamingmultimediawillbesupportedinthenextgenerationwirelessnetworks.Servicesrequiredbytheseapplicationsaredierentfromletransferservicesinthattheyexpectlowtransmissiondelay,i.e.,delay-constrainedcommunications.Providingqualityofservice(QoS)guaranteestomultimediaapplicationsposesasignicantchallengeforthedesignofwirelessnetworks.Thisdissertationfocusesonthepowerandresourceallocationschemesfordelay-constrainedcommunications,withstatisticalQoSrequirementscharacterizedbythetripletofdatarate,delaybound,anddelayboundviolationprobability.WestudytheoptimalpowercontrolandresourceallocationschemestoprovidestatisticalQoSguarantees,whicharemorechallengingthanprovidingaveragedelayguarantees,sincestatisticalQoSimposesconstraintsonthedistributionoftransmissiondelay. Intherstpartofthedissertation,westudythethroughputmaximizationproblemsubjecttothedelayboundviolationprobabilityandaveragepowerconstraint,forasingle-user,single-channelsystem.Thebuersizeisassumedtobeinniteandthedelayboundisrelativelylarge.Thisproblemisactuallytheeectivecapacitymaximizationproblem,whichisdenedasthemaximumdatarateasystemcansustainunderthestatisticalQoSconstraint,inlargedelayregime.Weproposeasimplecross-layersuboptimalpowercontrolschemewhichsignicantlyincreasestheeectivecapacitycomparingtotheoptimalchannel-gain-basedpowercontrolscheme.Wealso 13

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Inthesecondpartofthedissertation,westudythedualproblem,minimizingthedelayboundviolationprobability,subjecttoanaveragepowerconstraintandthroughputconstraint.Thetransmissionbuersizeisassumedtobenite(smalldelayregime).Thereforethedelayboundviolationprobabilitytranslatestobuerfullnessprobability,orpacketdropprobability.Thequeuingbehaviorwithanitesizebuerisquitedierentfromthatofaninnitesizebuer.Weanalyzethefundamentallimitofpowercontrolperformancesovercontinuouswirelesschannelsfornitesizebuermodels.Dynamicprogrammingtechniques,whichareusedtoaddressthecontrolofqueueingsystemsunderdiscretechannelmodels,willresultperformancedegradationduetoquantization.Ourmethodistodecomposetheoriginaloptimizationproblemintothreesub-problems,andsequentiallysolvethethreesub-problems.Weprovethatthetwoproblemshavethesameoptimalsolution.Bysolvingthesub-problems,weprovidestructuralinformationabouttheoptimalsolution.Theoptimalcross-layerpowercontrolschemeiscombinedwithadaptivemodulationtechniqueinavariable-rate,variable-powersystem,wherebothpacketdropprobabilityanddecodingerrorprobabilityareconsidered. 14

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Thegrowingdemandondataservicesdrivestheevolutionofwirelesscommunicationsystems.Thewirelesscommunicationtechnologieshavebeendevelopedtoanewstagethatreal-timeapplications,suchasstreamingmultimedia,onlinegamesandremotemedicalmonitoringanddiagnosis,canbeexpected[ 1 ].Thesereal-timeapplications,orsocalledqualityofservice(QoS)guaranteedapplications,aredierentfrombest-eortapplicationsinthattheyaresensitivetotransmissiondelay[ 2 ].Therealizationofreal-timeapplicationsreliesontheadequatedatarateprovidedbythephysicallayertechnologies,aswellastheelaboratelydesignedprotocolsoftheupperlayerssuchthatreservedthroughputs,boundsondelaysandlossratesaremet.Inthephysicallayer,bytheuseofbroadband,multi-carriermodulation(MCM)suchasorthogonalfrequency-divisionmultiplexing(OFDM)[ 3 ],multiple-inputmultiple-output(MIMO)[ 4 ]antennas,thedatatransmissionratewillbeashighastensofmegabitspersecond[ 5 ].Inthelinklayer,whichutilizestheservicesprovidedbythephysicallayerdirectly,howtoschedulethephysicallayerresources(power,bandwidth,codeetc.)toprovidesatisfactoryQoSguaranteesbecomesabigchallenge[ 6 ]. Physicallayerperformances,e.g.,capacityanderrorrate,arehighlydependentonchannelconditions.Wirelesschannelsaresharedmedia,whicharevulnerabletointerferenceandsubjecttotime-,frequency-andlocation-dependentattenuations.Section 1.1 introducesthecharacteristicsofwirelesschannelsandthechallengestheyimposeonthesignalingdesign.Wewillrestrictourattentiontosingleinputsingleoutput(SISO)atslowfadingchannel,whichisfundamentaltothestudyofothercomplicatedchannelmodels.Delay-constrainedcommunicationshavebeenwidelystudiedinthepastdecade.Althoughalltheseworkscanbecategorizedas\delay-constrained",themodelsofthesystemandtheproblemformulationsarequitedierent.Section 1.2 reviewsthemajorresultsonthistopic.Section 1.3 outlinesthedissertation. 15

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TheimpactoftheseimpedimentstotheEMwaveistwo-folded.First,therearecreatingmultiplepropagationpathsfromthetransmittertothereceiver;dierentpathshavedierentpropagationdelay.Second,theamplitudeandphaseoftheEMwaveofeachpathisattenuatedseverely.Atthereceiverside,themultipathsthatexperiencesimilardelay(thedelaydierenceisrelativelysmallcomparingtotheinverseofthesignalbandwidth)areunresolvable.Thesemultipathcomponentsareconstructivelyordestructivelycombinedtogetherandusuallyexhibitfastvariations.Themultipaths(orcombinedmultipaths)whichexperiencedelaylongerthantheinverseofthesignalbandwidthmakethechanneltimedispersive.Asinglepulsetransmittedfromthetransmitterwillinduceasequenceofpulsesatthereceiver.Inthefrequencydomain,atimedispersivechannelischaracterizedbyitsunevenfrequencyresponses.Therearedeepfadingsatsomefrequencylocations,makingthechannel\selective"inthefrequencydomain.Coherentbandwidthisthestatisticalmeasureofafrequencyselectivechannel;thefrequencyresponseofthechannelishighlycorrelatedwithinthecoherentbandwidth. Despitethedispersivepropertyintimedomain,wirelesschannelsarealsodispersiveinthefrequencydomainduetoDopplershiftinducedbythemovementofthetransmitter/receiver 16

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Typeoffadingchannels. antennas,andobstaclesinbetweenthepropagationpath.Thedynamicenvironmentaccountsforthetime-varyingandunpredictablenatureofwirelesschannels.Similartothetimedispersiveproperty,thefrequencydispersivechannelisstatisticallymeasuredbythecoherenttime,withinwhichthechannelhascorrelatedfading. Dependingontherelativevalueofthecoherenttimeandtheinverseofcoherentbandwidthtothesymbolduration,awirelesschannelcanbecategorizedasatfastfading,atslowfading,frequencyselectivefastfadingandfrequencyselectiveslowfading.AsillustratedinFig. 1-1 ,achannelundergoesatfading(resp.,frequencyselectivefading)ifthesymboldurationislonger(resp.,smaller)thantheinversecoherentbandwidth,andundergoesslowfading(resp.,fastfading)ifthesymboldurationissmaller(resp.,larger)thanthecoherenttime. WewillstudytheQoSprovisioningproblemforatslowfadingchannels.Althoughfrequencyselectivechannelsaretypicalinbroadbandcommunicationsystems,thestudyonatfadingchannelsismorefundamental.Thefrequencyselectivechannelcanbeviewedasmultipleparallelnarrowbandsub-channels,andeachofthemundergoesaatfading.ThisisexactlytheideabehindOFDMsystems,whichhavebeenadoptedinvariousindustrystandards,e.g.,IEEE802.11a/g/n,LTEandWiMAX.Typically,thediversityinherentinmultiplechannelswillsubstantiallyimprovetheQoSprovisioningperformance[ 7 ]. 17

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8 ].Inapilotaidedsystem,thepilotsymbolsareperiodicallymultiplexedwiththeinformationbearingsymbolsandusedtotrackingthevariationofthefadingchannel.Blindchannelestimation,whichdonotneedpilotsymbols,ismorebandwidthecientthanpilotaidedschemes[ 9 ].Howeverthepilotaidedschemesarefavorableinindustryduetoitssimplicityandaccuracyinfadingstateestimation.Theyhavebeenadoptedinmanymobilewirelessstandards,e.g.,WiMAX[ 10 ]andLTE.ForaWiMAXsystemoperatingat2:5GHz,avehiclemovingonthehighwayat70mphwillexperienceatime-varyingchannelwithcoherenttimeapproximately1:6ms[ 11 ,page204].ThesymboldurationofWiMAXsignalis0:1ms,andthepilotsymbolsareinsertedeverytwosymbols,whichismuchsmallerthanthecoherenttime. Theatslowfadingchannelcanbemodeledbyblock-fadingadditivewhiteGaussianchannel(BF-AWGN)[ 12 ],whichbelongstoageneralclassofblock-interferencechannelsintroducedbyMcElieceandStark[ 13 ].InBF-AWGNmodel,theatfadingchannelhasbandwidthWHz.ThefadingstateisassumedtobexedwithinoneblockofdurationTbsec,andvariesfromoneblocktoanother.Thefadingprocessisrepresentedbyrealsequencefgng,gn0,wherenistheindexfortheblock.Dependingonthemodelofthefadingprocess,thevalueofgncanbetakenfromanitesetorspanoverthewholenon-negativerealaxis.Thefadingprocessmayhavememory,i.e.,fgngisnotnecessarytobeindependent,identically,distributed(i.i.d.).Forexample,thefadingprocesscanbemodeledasaMarkovchain.Thedistributionofgn+1conditionedonthepreviousfadingstategnis,ingeneral,dierentforeachgn.Inthefollowing,wewillrefertognasfadinggain,fadingstateorchannelgaininterchangeably. Despitethefadingprocess,thechannelitselfismemoryless.Thisisthedirectconsequenceofatfadingassumption.Thechanneloutputonlydependsonthecurrent 18

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wherewnistherealGaussianrandomvectorwithzeromeananddiagonalcovariancematrixI. 1-2 illustratesthetwodelay-constrainedsystemmodels.Therstmodelisapurephysicallayermodelwherequeue(orbuer)isexcluded.Thetransmissiondelay,i.e.,codingdelay,isstrictlyrestrictedwithinMblocks,andeachblockhasNchanneluses,asdescribedintheprevioussection.ReliabletransmissionisachievedbyencodingtheinformationbitswithinMblockstoaverageouttheGaussiannoiseandfadingeect. Thesecondmodelisalink-PHYlayermodel.Theincomingpacketsarestoredinthetransmissionbueruntiltheyareservedordropped.Boththearrivalprocessandfadingprocesscontributetothedynamicsofthesystem.Hencethelink-PHYlayermodelismorecomplicatedtostudy.Thetransmissiondelayconsistsoftwoparts:oneisthequeuingdelayinthebuer,andtheotheroneisthecodingdelayinthephysicallayer. Forbothofthetwomodels,thechannelsideinformation(CSI)isassumedtobeperfectlyknownatthereceiversideandthetransmitterside.Hencethepowerorratecontrolcanbeperformedtooptimizethesystemperformance.Thefadingprocessisassumedtobestationaryandergodic. 19

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B Physicallayerandlink-PHYlayersystemmodels. A .Physicallayermodel; B .Link-PHYlayermodel. 20

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14 ].Webrieyreviewthecapacitynotionsoffadingchannelsandthepowercontrolschemesthatachievethemaximumcapacities. 13 ]thatwithperfectCSI,thecapacityisindependentofN.UndertheaveragepowerconstraintP0,thecapacityis wherethepowercontrolP(g)satisestheaveragepowerconstraint TheoptimalP(g)thatmaximize( 1{2 )istime-domainwaterlling(TDWF)[ 15 ] Twocodingschemescanbeappliedtoachievethiscapacity.Oneisthevariable-rate,variable-powercode.Thewholecodewordismultiplexedbycodewordsselectedfromdierentcodebooks.Eachcodebookisparticularlydesignedforaspecicfadingregionwithdistinctrateandaveragepower.Thecodewordselectedfromonecodebookspanoveralltheblocksthatfallintothefadingregionofthatcodebook[ 15 ].SinceM=1,anymultiplexedcodewordhasinniteduration.Anothercodingschemeusessinglecodebookandcanbecharacterizedasconstantrate,variablepower.Therateofthecodematchestheergodiccapacityin( 1{2 )andhasunityaveragepower.Thesymbolsofcodeword 21

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16 ].Theconstant-ratecodewordspansoveralltheblocks,whichleadstoinnitecodingdelay. isattainableforeachblock,wherePisthepowerofthecodeword.AGaussiancodebookwitheachsymbolindependentlydrawnfromnormaldistributionN(0;1)andscaledbyp CSIisavailabletothetransmitterintwoways,causaloracausal.Inthecausalcase,thetransmitteratthen-thblockknowsthefadinggainofallthepreviousblocksandthecurrentblock.Intheacausalcase,fadinggainsofallMblocksareknowntothetransmitteratthebeginningofthetransmission.Theacausalcaseispossibleifthetransmitterhasaccesstomultipleparallelchannelsandthefadinggainofeachchannelisperfectlyknown[ 17 ][ 18 ][ 19 ].WedenotefP(n;g(c))gthepowercontrolschemeforthen-thblock,whereg(c)denotethesetfg1;:::;gcg.IfCSIiscausallyknown,c=n,whileifCSIisacausallyknown,c=M. Similartoergodiccapacity,theexpectedcapacityisdenedas Theoptimalcausalpowercontrolschemessubjecttobothshort-andlong-termaveragepowerconstraintsaregivenin[ 20 ].Short-termpowerconstraintimposesaupperboundonthetotaltransmissionpowerofeachMblocks,whilethelong-termconstraintonlyimposestheupperboundontheaverage.Theoptimizationproblemissolvedbybackwarddynamicprogramming.Thealgorithmperformsanexhaustivesearch.Theoptimalpower 22

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1{4 ).Anditresultshighercapacitythanoptimalshort-termpowercontrolsincetheconstraintislessstringent.Theoptimalacausalpowercontrolschemeundertheshort-termpowerconstraintisstudiedin[ 21 ]. Toachieveexpectedcapacity,wecanconcatenatethecodewordthatachievetheinstantaneouscapacityforeachblock.Eachcodewordspansoneblockandthetransmissionisvariable-rate,variable-power. Motivatedbythedemandforconstant-ratedelay-limitedapplicationssuchasVoIP[ 10 ],anotherdelay-constrainedcapacity,outagecapacity,wasintroduced[ 22 ],[ 23 ].AninformationoutageoccursiftheinstantaneouschannelcapacityissmallerthanatargetdatarateR.Outagecapacityisthemaximumerror-freedataratethatachannelcansupport,providedthattheinformationoutageprobabilitydoesnotexceedapre-denedthreshold, Theoptimalpowerallocationschemeforoutagecapacityisstudiedin[ 24 ]underacausalCSIassumption,subjecttoshort-andlong-termaveragepowerconstraints.TheproblemissolvedbasedonLagrangiantechniques.Theoptimalpowerallocationschemeisdeterministicforcontinuouschannelgainandprobabilisticfordiscretizedchannelgain.InaspecialcaseM=1,theoptimalpowercontrolschemeistruncatedchannelinversion(TCI) whereRisdeterminedbyandg0isdeterminedbytheaveragepowerconstraint.Itisshownin[ 24 ]thattheoutagecapacitycanbeachievedbyusingasinglerandomGaussiancodebook.Theconstant-ratecodewordspansovertheMblocks.Andthesymbolsofthecodewordtransmittedthroughthen-thblockisscaledbyp 23

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20 ]bydynamicprogrammingapproach.Forlong-termaveragepowerconstraint,thecausalityofCSIsubstantiallydegradestheoutagecapacityatlowoutageprobability.Similartotheacausalscenario,singlerandomGaussiancodebookachievestheerror-freeoutagecapacitywhenN!1.TheupperboundofrandomcodingerrorprobabilityisderivedforniteN.TheerrorprobabilityapproachestheoutageprobabilityasN!1forallratesmallerthantheoutagecapacity. ForamorestringentQoSrequirement,noinformationoutageisallowed,i.e.,=0.Theoutagecapacityturnstobethedelay-limitedcapacityintroducedin[ 25 ][ 26 ].Delaylimitedcapacityisthemaximumerror-freedataratethatthechannelcansustainregardlessoftherealizationofthefadingprocess.Hencewithoutpowercontrol,delaycapacityisactuallythe\worstcase"channelcapacity.Ifpowercontrolisavailable,forsinglechannelcase,theoptimalstrategyistotalchannelinversion g;(1{9) whereisobtainedbytheaveragepowerconstraint Eg( g)=P0:(1{10) Andthedelay-limitedcapacityis Ifthechannelcannotbeinvertedwithniteaveragepower,e.g.,Rayleighfadingchannel,thedelaylimitedcapacityiszero.Asintheoutagecapacity,theoptimalpowercontrolschemeresultsconstant-ratetransmissionoverallMblocks.Henceasinglecodebook,variable-powercodingschemeachievesthedelay-limitedcapacityinthelimitingcaseN!1.Ifthepowercontrolisconsideredasapartofthechannel,thetransmitterisactuallydealingwithanAWGNchannel.WhenNisnite,thecodewordspansM

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27 ][ 28 ][ 29 ][ 30 ]. Forreal-timeapplicationsthatconsistofbothtime-variantandtime-invariantdatastreams,bothexpectedQoSandoutagecapacity(delay-limitedcapacityasaspecialcase)arenotadequatetodescribethecapacitydemands.Avariable-ratetransmissionschemeisstudied[ 31 ]whichmaximizestheexpectedcapacitysubjecttoaninformationoutageprobability(ofabasicrate)constraintandalong-termaveragepowerconstraint.Thesoobtainedcapacityislargerthanoutagecapacitysincethetransmissionrateisallowedtouctuate.Itisshown[ 31 ]thatwhenM=1,theoptimalpowercontrolschemeisacombination(multiplexing)ofwater-llingandchannelinversion,forcontinuousfadingdistributions.ThisworkisextendedtoM>1,acausalCSIscenariobythesameauthors[ 32 ].TheoptimizationproblemissolvedbasedongeneralizedKarush-Kuhn-Tuckerconditions[ 33 ].Asin[ 24 ],theoptimalpowercontrolschemeisdeterministicforcontinuousfadingdistributionsandprobabilisticfordiscretizedfadingdistributions. 25

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Thusthephysicallayermodelactuallysolvesasetofdelay-constrainedproblems:ecientlytransmittingBinformationbitswithaveragepowerP0withinMblocks,andtheBinformationbitsarereadyatthetransmittersideatthebeginningofthetransmission.Thecapacitymaximizationprobleminsection 1.2.1 maximizesBsubjecttoconstraintP0.Thedualproblem,xingBwhileminimizingP0isstudied[ 34 ]. Thephysicallayermodeldoesnotsuitableformorecomplicatedproblemssuchas(weuseterm\packet"insteadof\bit"intherestofthischapter) Theseproblemsarecommoninpacketswitchingnetworks. Essentially,theaforementioneddicultystemsfromthefactthatinformation-theoreticalapproachesonlycapturethevariationofthechannelbutleavethevariationofdatasourceunconsidered.Thereforethelink-PHYlayermodelisneededtostudybothofthetwofactors[ 35 ]. Considerthelink-PHYlayermodelillustratedinFig. 1-2 .ThebuercanaccommodateKpackets.Wedenotea(n),c(n)ands(n)thenumberofpacketsthatarriveinthenthblock,themaximumnumberofpacketsthatcanbetransmittedinthenthblock,andtheactualnumberofpacketsthatistransmittedinthatblock.Hereweimplicitlyassumethats(n)c(n),hencec(n)representsthecapabilityofservicefacilities.Ineachblock,s(n)packetsareencodedbyonecodewordthatspansthewholeblockandtransmitted.IfweassumeNissucientlylarge,c(n)isjusttheinstantaneouschannelcapacityofthatblock,measuredbythenumberofpackets,andthetransmissioniserror-free.Thesequencefa(n)g,fs(n)gandfc(n)garerefereedtoasarrivalprocess,departureprocess,andserviceprocess,respectively. 26

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Whenoneispickedastheobjective,theothersbecomeconstraintstothesystem. Despitethenumberofpacketsizerepresentationofprocessfa(n)g,fc(n)gandfs(n)g,thereareotherinterpretations[ 36 ].Wewillfocusonthenumberofpacketrepresentation.Itisshownin[ 37 ]thatproblemsthatbasedondierentinterpretationscanbesolvedbyauniedapproach. 38 ]studiedthecasewhereallthepacketshavethesamedeadline,underAWGNchannel.Theoptimalstrategyisthe\lazy"schedulingwherethelowestratethatcanmeetthedeadlineareemployed.Thisworkisextendedtothediscrete-statesBF-AWGNchannel[ 34 ]withbothcausalandacausalCSIassumptions.Thesamedeadlineconstraintisalsoextendedtoindividualdeadlineconstraint.Eachpacketisassumedtohavethesamelifetimelblocks.Andthedeadlineofapacketisitsarrivaltimeplusthelifetime.ThecasualCSIproblemis 27

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In[ 39 ],theaforementionedoptimizationproblemisgeneratedtoBTproblem,i.e.,transmittingBpacketswithintimeT,andeachpacketmayhavedierentarrivaltimeandlifetime.OptimalsolutionisgivenforthecasewhereallBpacketsarriveatthebeginningandhavethesamedeadline,overcontinuous-timediscrete-stateMarkovianfadingchannelmode.Suboptimalsolutionsaregivenforarbitraryarrivalprocessesandlifetimeconstraints.In[ 40 ]optimalsolutionforarbitraryBTproblemsisgivenforAWGNchannel,andwithacausalknowledgeofarrivalprocess. Strictaveragedelayboundisconsideredin[ 41 ],wheretheschedulingalgorithmguaranteesthattheaveragepacketdelayissmallerthanathreshold.Anearoptimalstrategybasedon\criticalbacklog"policiesisproposedforON-OFFchannelmodel(Gilbert-Elliottchannel).Byexploitingtheschedulingalgorithm,thequeuelengthdriftsaroundatargetvalue,whichisoptimizedtominimizetheaveragepower. Berryetal.studiedtheoptimaldeterministicpowercontrolschemeforaqueueingsystemwithinnitebuer(nopacketdropping)[ 37 ].Thepowercontrolpolicydeterminesthetransmissionpowerbasedonthesystemstatuswhichisdenedasatripletofnumberofarrivalpackets,fadinggainandqueuelengthofthecurrentblock.ThefadingprocessismodeledasaMarkovchain.Twoconictobjectivesareconsidered,minimizingaveragetransmissionpowerandminimizingaveragedelay.Intuitively,transmittingwithalowerraterequireslesspowerbutincreasestheaveragedelayandviceversa.Thusthetwoobjectivescannotbeminimizedsimultaneously.Thiskindofproblemsisconsideredas 28

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Theaveragepower/delaycurveforanitebuerwithoccupancyKpacketsisstudiedin[ 42 ],forAWGNchannel.Thepowercontrolschemesstudiedtherebelongtotheclassofzero-outage,probabilisticpowercontrol.Sincethebuersizeisnite,itispossiblethatarrivingpacketsndafullbuerandsomeofthepacketshavetobedropped.Thezero-outagepropertyimpliesthatallthepacketswillbedeliveredandnoneofthemwillbedroppedduetonitebuerconstraint(forAWGNchannelthisisachievable).Probabilisticpowercontrolismoregeneralthandeterministicpowercontrol.Foragivensystemstate,aprobabilisticpowercontrolchoosesonepowerlevelfrommultiplepossiblechoices,accordingtoacertainprobability.Fordeterministicpowercontrol,thereisonlyonepowerlevelassociatedwitheachsystemstate.Itisshownthatdeterministicpowercontrolsformthebasisofprobabilisticpowercontrols,andtheoptimaldeterministicpowercontrolformtheboundaryofachievablepower/delayregion. Asin[ 37 ],theoptimaldeterministicpowercontrolisfundbydynamicprogramming.Andthemethodiseasilyextendedtonite-stateMarkovianBF-AWGNchannel,orreplaceaveragedelayconstraintbyaboundeddelayconstraint.Noticethatinthiscasethestate-spacegrowsexponentiallywiththedelayboundandusuallyprohibitsitspracticeuse. Theconceptofzero-outagepowercontroliscloselyrelatedtodelay-limitedcapacity.Andthustheysuerthesamelimitationfromthevariationofchannel.Ifthechannelcan 29

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Beawareofthedicultyinprovidingzero-outagedelayboundguarantee(alsoknownasdeterministicQoSguarantee),WuandNegistudiedstatisticalQoSprovisioningprobleminafadingchannelenvironment[ 43 ]forlargedelayboundconstraint.Thebuerisassumedtobeinniteandthereisnopacketdropping.StatisticalQoSrequirementisspeciedbythetripletofthesourcedata-rate,thepacketdelayboundDmax,andthedelayboundviolationprobability(theoutageprobability).SatisfyingthestatisticalQoSrequirementimpliesthatthedelayboundviolationprobabilityissmallerthan whereD(1)denotestherandomvariableofpacketdelaywhenqueueentersthestablestatus.ThemaximumarrivaldataratethatasystemcansustainunderthestatisticalQoSconstraintisderivedin[ 44 ],termedaseectivecapacity whereuistheQoSexponentwhichrelatestheDmaxand.Infact,accordingtothelargedeviationtheory,theprobabilityofsteadystatequeuelengthq(1)exceedingthethresholdQmaxsatises[ 45 ][ 46 ] Prob[q(1)Qmax]'euQmax;(1{14) 30

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1{14 )canberewrittenas Prob[D(1)Dmax]'euDmax;(1{15) whereDmax=Qmax=.From( 1{15 )and( 1{12 ),leteuDmax=,thestatisticalQoSrequirementcanbesatised.And Ifthearrivalprocesshasvariablerate,thelinearrelationshipbetweenDmax=Qmax=doesnotholdandonlyqueuelengthviolationprobability( 1{14 )canbeguaranteed[ 47 ]. EectivecapacitycharacterizesthestatisticalQoSprovisioningcapabilityinlargedelayboundregime.Forsmalldelayboundornitebuerwherepacketdropduetofullbuermayoccur,theapproximationderivedfromlargedeviationtheory( 1{14 )and( 1{15 )donothold.Withinnitebuersize,thequeuelengthq(n)updatesas InanitebuerofsizeL, Themaxminstructuremakesthequeuingbehaviorcomplicatedandtheelegantexponentialdecaypropertyofthetaildistributionofpacketlength(andalsothepacketdelayifthearrivalisconstant)vanishes. ProvidingexplicitstatisticalQoSguaranteesforavariable-ratearrivalprocessandnitebuersizeisnotaneasytask.PeopleresorttoanotherQoSmeasure,thepacketlossprobability.Packetlossincludesthepacketsdroppingatthetransmitterbecauseofafullbueranderroneouslydecodingatthereceiverduetonoisychannel.NoticethatmanyaforementionedworksassumethatN!1andthetransmissioniserrorfree,orkept 31

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QoSprovisioningproblemintermsofpacketlossprobabilityforanitebuerisstudiedin[ 48 ]andthereferencestherein.Theoptimalrateandpowercontrolschemeareobtainedwhichminimizethepacketdroppingprobabilitysubjecttoaxedpacketerrorprobability,orminimizethetotalpacketlossprobability.Thechannelmodelisstillnite-stateMarkovianBF-AWGN.Andtheoptimizationproblemissolvedbydynamicprogramming,asin[ 37 ]and[ 42 ]. 2 studiesthequeue-length-aware(QLA)powercontrol(PC)schemewhichmaximizestheeectivecapacitysubjecttolong-termaveragepowerconstraint.Thepowercontrolschemesthataimatoptimizingphysical-layerperformancemeasures,adaptthetransmissionpowertothechannelgain;wecallthese\channel-gain-based"(CGB)PC,suchasTDWFandTCIdescribedinsection 1.2.1 .ItisshownthatCGB-PCisnotoptimalinlink-PHYlayermodelswherethequeueisincorporated[ 37 ].TheoptimalCGB-PCthatmaximizestheeectivecapacityisproposedin[ 49 ]and[ 7 ].ThestructureoftheoptimalCGB-PCdependsonthedelaybound.Attwoextremes,i.e.,delayboundapproachestoinniteandzero,theoptimalCGB-PCapproachesTDWFandTCI,respectively.Tofurtherimprovetheperformance,weproposethehierarchicalqueue-length-aware(HQLA)powercontrolwhichisasimpleschemebutsubstantiallyincreasetheeectivecapacityovertheoptimalCGB-PCschemeinmoderateQoSrequirementsregime. Chapter 3 investigatestheimpactofimperfectCSItotheoptimalpowercontrolscheme.TheCSIisassumedtobeperfectlyestimatedatthereceiversidebutdeliveredtothetransmittersideafternblocks.TheoutdatedCSIdegradestheeciencyoftheoptimalpowercontrolschemegreatlysinceitreliesontheaccuracyofCSI.Toaddressthisproblem,atwo-stepsuboptimalpowerallocationschemeisproposedfora 32

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Chapter 4 addressestheproblemofprovidingexplicitstatisticalQoSguaranteesforamulti-user,multi-channelsystem.Thejointpowerandchannelallocationalgorithmisstudied,andtheQoSprovisioningcapabilityisensuredbyexploitingeectivecapacityandreferencechannelapproach.Weassumethetransmitter(thebase-station)hastheperfectCSIknowledgeaboutthechannels.Ateachtransmissionslot,aschedulerallotsthetransmissionpowerandchannelaccesstoalltheusersbasedonapre-determinedreferencechannel.Threeallocationschemesareproposed,whichutilizebothmultiuserdiversityandfrequencydiversity.Theproposedschemessubstantiallyreducetheresourceusagewhileexplicitlyguaranteeingtheusers'QoSrequirements. Chapter 5 andChapter 6 studyoptimalpowercontrolschemethatminimizespacketlossprobabilitysubjecttolong-termaveragepowerconstraint.InchapterChapter 5 ,weassumeN!1andthepacketlossprobabilityreducestopacketdropprobability.InChapter 6 ,weconsideramorepracticalscenario,i.e.,Nisniteandpacketlossprobabilityconsistsofbothpacketdropandpacketerror.Thisworkiscloselyrelatedto[ 48 ].Thedierenceisthechannelmodelbeenused.In[ 48 ]andmostrelatedworks,theBF-AWGNchannelismodeledasFSMC.ThustheoptimizationproblemcanbeformulatedasaMarkovdecisionproblemandsolvedbydynamicprogramming.ThisapproachisnotsuitableforsolvingcontinuouschannelmodelproblemssuchasRayleighfadingchannel,sincethequantizationofcontinuouschannelresultsperformancedegradationandcomputationalcomplexitygrowsexponentiallyasthenumberofchannel 33

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Chapter 7 summarizesthedissertation. 34

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ExistingPCschemesfallintotwocategories,namely,CGB-PCandQLA-PC.CGB-PCsuchasTDWFadaptsthetransmissionpowerbasedonthechannelgain(physical-layerinformation),whichaimsatoptimizingcertainphysical-layerperformancemeasuressuchasphysicallayerdatarate,biterrorrate(BER),orsignal-to-noiseratio(SNR);QLA-PCadaptsthetransmissionpowerbasedonthequeue-length(link-layerinformation)andpossiblythechannelgain(physical-layerinformation),withtheaimofoptimizingcertainlink-layerperformancemeasuressuchaslink-layerdatarateanddelayboundviolationprobability. Inthischapter,weshowthatCGB-PCschemesachievepoorlink-layerdelayperformance.Toimprovetheperformance,QLA-PCisneeded.ExistingQLA-PCschemes[ 50 ]aimatminimizingthetransmissionpowerundertheconstraintontheaveragedelay.Butaverage-delayguaranteemaynotsatisfytherequirementsofdelay-sensitiveapplications;e.g.,usingahandhelddevicetowatchmobileTVoverWiMAX,requirescertaindelayboundviolationprobability,whichcannotbespeciedbyaveragedelaysinceaveragedelaycannotspecifythe(tail)probabilitydistributionfunction;e.g.,foragivendelaybound(say,1second),twosystemswiththesameaveragedelayof500mscouldhavequitedierentdelayboundviolationprobabilities,e.g.,40%vs.0.1%.Dierentfromguaranteeingaveragedelay,weconsidersstatisticaldelayguaranteesorstatisticalQoS,i.e.,thetripletofdatarate,delaybound,anddelayboundviolationprobability,whichismoregeneralandchallengingthanguaranteeingaveragedelay,sinceweneedtobeabletoguaranteethedelayboundviolationprobability(ordelaydistribution). WefocusonQLA-PCschemesthataimatmaximizingthethroughputsubjecttothestatisticalQoSguarantees.Specically,weproposeanovelschemecalledhierarchicalqueue-length-aware(HQLA)PC.ThekeyideaistocombinethebestfeaturesofthetwoPCschemes,i.e.,agivenCGB-PCschemeandtheclear-queue(CQ)PCscheme;here,the 35

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Theremainderofthischapterisorganizedasfollows.Section 2.1 describesthesystemstructureandtheMarkovchainmodelofthesystem.Section 2.2 introducestheproposedHQLA-PCandanalyzeitsperformance.Section 2.3 presentsthesimulationresults.Section 2.4 extendstheresultstocorrelatedchannelandvariable-ratearrivalprocess.Section 2.5 summariesthechapter. 2-1 .Adatasourcegeneratesbitstreamataconstantrate~bits/sec.Thebitstreamisrststoredinthesourcebuerwheredataprocessingisperformed.Thisproceduremayinvolveblockprocessingsuchasfrequencydomainvideocoding,blockcodingorformattingthebitsstreamintoapacket.Ingeneral,theoutputofthesourcebuerisnolongerconsecutive.Withoutlossofgenerality,assumethattheoutputofthesourcebuerisblockeddata 36

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Structureofdatasourceandtransmitter. withaconstantrate.Eachblockcontainsbits,whereisanintegerand~Tb.TheequalitytakesplacewhenthereisnoextradataaddedinthedataprocessingprocedureandaproperchosenTbsuchthat~Tbisaninteger.Thelaterconditioniseasytomeetforlarge~.Theblockeddataisfedintothetransmissionbueratthebeginningofeachblockandisserved(transmitted)inarst-in-rst-out(FIFO)fashion.Weassumethatthecapacityofthetransmissionbuerisinnite,thereforeallthebitscanbeservedeventually.Sinceforthetransmitter,onlytheblocksizematters,wewillusetodenotethearrivalrateanddiscard~inthefollowingdiscussions. Inourmodeldescribedabove,thetransmissiondelayissimplythewaitingtimeinthetransmissionbuerplusoneblockofcodingdelay.Foraconstantarrivalrate,thetransmissiondelay(countinblocks)isequivalenttothequeuelength(countinbits)uptoascalarandafraction.Infact,denoteqthequeuelengthinthebuerwhenacertainbitistransmitted,thetransmissiondelayofthisbitrangesfrombq=ctobq=c+1,wherebxcndsthelargestintegerthatisnotgreaterthanx.Thereforebystudyingthequeuelengthdistributionofthesystem,thestatisticalmeasureofthetransmissiondelaycanbeobtained.Inthefollowingsections,wedemonstratethatthequeuelengthformsaMarkovchain,andinsection 2.2.1 thesteadystatequeuelengthdistributionisobtainedbysolvingequilibriumequationofMarkovchain. 37

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Letq(n)denotesthequeuelengthatthebeginningofthen-thblock,orontheotherwords,itisthenumberofbitswaitinginthetransmissionbuerbeforethearrivalofthenewblockandthetransmissionofthatblock;s(n)denotesthenumberofbitsthatwillbetransmittedduringthen-thblock.AsillustratedinFig. 2-2 .thequeuelengthupdatefunctionis where[x]+istheLindley'soperatorwhichmeansmax(x;0). Therelationshipbetweenq(n+1),g(n),q(n)isillustratedinFig. 2-3 .Noticethatq(n)isthequeuelengthatthebeginningofthen-thblock,itisindependentofg(n).Sincefg(n)garei.i.d.byassumption1),ifq(n)isknown,thevalueofq(n+1)isuniquelydeterminedbyg(n)andisirrelevanttothepreviousqueuelengthq(k),k
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Updateofthequeuelength. Markovpropertyofthequeuelength. Asmentionedinsection 1.2.2 ,forreal-timeapplications,becausethedatatobetransmittedisgeneratedonthey,itispossiblethatthecapacityprovidedbytheCGBPCschemeexceedsthebackloginthebuer.Toschedulethetransmissionpowermoreeciently,weneedtodesignaPCschemewhichconsidersboththechannelgainandthequeuelength.Withoutlossofgenerality,denotethetransmissionpoweras~P(n)=~P(g(n);q(n)).TheoptimalPCschemeshouldmaximizethethroughputwhilesatisesthestatisticalQoSconstraint. ThestatisticalQoSrequirementissatisedmeansthatforacertainconstantarrivalrate,theprobabilitythatthedelayboundDmaxisviolatedisnotgreaterthan 39

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(2{5)s:t:Prob[D(1)Dmax]0; AsillustratedinFig. 2-4 ,theproposedHQLAPCschemeconsistsoftwocomponents,theCGBPCandtheCQPC.TheCGBPCpartcouldbeanyPCschemewhichdeterminesthetransmissionpoweronlyaccordingtothecurrentblockchannelgain,i.e.,TDWF.TheCQPCndstheminimumpowerneededtoclearthecurrentblockqueue.Thetwopartsworkindependently.Aftereachofthetwopartsdeterminesthetransmissionpower,thesmalleroneischosen.ThehierarchicalstructureiseasytobeimplementedorupgradedfromtheexistingCGBPCsystem. 40

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Hierarchicalqueue-length-awarepowercontrolscheme. Hierarchicalqueue-length-awarepowercontrolschemewithpeakpowerconstraint. Inpractice,thereisalwaysapeakpowerconstraint.Athirdcomponent,thepeakpowercomponent,shouldbeaddedintotheHQLAPCscheme,asinFig. 2-5 .Thethreecomponentsformadecisiontree.Ateachnode,thesmalleroneischosen. Insection 2.2.1 ,wediscusstheproposedHQLAPCschemeindetail.Insection 2.2.2 weanalyzethesteadystatequeuelengthdistributionoftheproposedscheme.Theaveragepowerisgiveninsection 2.2.3 .Section 2.2.4 discussestheeectivecapacitywithpowercontrol.TheHQLAwithpeakpowerconstraintisdiscussedinsection 2.2.5 From( 2{1 ),s(n)shouldnotexceedq(n)+becausethemaximumnumberofbitsthatcanbetransmittedduringoneblockisthenumberofbitsremainedinthebuerplusthe 41

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When( 2{7 )isviolated,theactualtransmissiontimeTactualwillbesmallerthantheblocklengthTs;whileifthetransmissiontimeissettobeTs,thetransmissionpowercanbereducedto BTs1 OnecanalsouseotherpairoffT;P(n)g,TactualTTs,P0(g(n);q(n))P(n)f(g(n))toschedulethetransmissionunderthissituation.ObviouslythepairfTs;P0(g(n);q(n))gminimizesthepower.ChoosingtransmissiontimeequaltotheblocktimeTscanbealsoviewedasthelazyschedulingwithinoneblock,whichminimizesthetotalenergyofatransmissionwithanarbitraryarrivalpatternandadeadlineconstraint.Lazyschedulingalwaysschedulesthecurrentworkloadevenlybetweenthecurrenttimeandthedeadline.InourcasealltheworkloadscomeatthebeginningoftheblockandthedeadlineisTssecafterthat.ThereforethepairfTs;P0(g(n);q(n))gminimizesboththepowerandtheenergywithinoneblock.TheseleadtoourHQLAPCstrategy:whenthepowerdeterminedbyf(g(n))cannotclearthequeue,keepP(n)=f(g(n))unchangedotherwisereducethepowerfromf(g(n))toP0(g(n);q(n)) ~P(n)=min"f(g(n));2q(n)+ BTs1 42

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Asdescribedinsubsection 2.1.2 ,thesequenceq(n)formsadiscrete-timediscrete-stateMarkovchain.Sinceweassumethebuerhasinnitecapacity,thedimensionofthestatesspaceisinnite.Denotetheinnitedimensionrowvectorx=[x0;x1;:::]thesteadystatedistributionofthequeuewhere InanirreducibleandaperiodichomogeneousMarkovchainthesteadystatedistributionalwaysexistsandisindependentoftheinitialstateprobabilitydistribution.Eitherxi=0foralli,wherethereexistsnostationarydistribution,orxi>0foralliandthevalueofxiareuniquelydeterminedthroughtheequilibriumequation[ 51 ,page29] wheretheinnitedimensionmatrixPistheonesteptransitionprobabilitymatrix,withitselementpi;jtheonesteptransitionprobabilityfromstateitostatej. InthefollowingdiscussionweshowthattheMarkovchainq(n)ishomogeneousundertheproposedHQLAPCschemeandthei.i.d.channelassumption.ThenthetransitionprobabilitymatrixPiscalculatedfromthemarginaldistributionofg(n).TheirreducibleandaperiodicpropertycanbeeasilyobtainedfrommatrixP. Bycontradiction,supposetheMarkovchainisnothomogeneous.Denotepi;j(n)theonesteptransitionprobabilityfromstateitostatejatblockn,pi;j(n)=Prob[q(n+1)=jjq(n)=i];i0;j0=Prob[[i+s(n)]+=j]=Prob[bBTslog2(1+~P(n)g(n))c=i+j]: 43

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2{9 ),~P(n)isafunctiononlyofg(n)whenthecurrentqueuelengthq(n)isknowntobei.Thereforethemarginaldistributionofthechannelgaing(n)uniquelydeterminespi;j(n).Wheng(n)isi.i.d.,pi;j(n)=pi;jandP(n)=Pareirrelevanttotheblockindexn.HencetheMarkovchainq(n)ishomogeneous. Obviouslypi;j=0forj>i+.Whenj=0,thequeueiscleared.Accordingto( 2{9 ),f(g(n))P0(g(n);q(n))becauseP0(g(n);q(n))istheminimumpowerneededtoclearthequeue.Thereforepi;0=Prob[f(g(n))P0(g(n);q(n))] (2{14)=Prob[f(g(n))g(n)2i+ BTs1]: BTs1f(g(n))g(n)<2i+j+1 DeneasetofbymatrixfAig,fBig,i=0;1;2;:::.Thek-throwandl-thcolumnelementofmatrixAiandBiare(Ai)k;l=pk+i;l+; 44

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AllthestatesareconnectedhencetheMarkovchainisirreducible.Ifthechainstartsatstatei,itcanreturntostateiafterarbitrarysteps.Thereforethechainisaperiodic. SincetheMarkovchainq(n)isirreducible,aperiodicandhomogenous,wecansolveforxby( 2{11 )and( 2{12 ).IfthetransitionprobabilitymatrixPhastheformin( 2{18 ),theeigenvectorproblem( 2{11 )canbesolvedbythematrix-geometricmethoduptoascalar,whichcanbeobtainedbythenormalizationfunction( 2{12 ).Partitiontheinnitedimensionrowvectorxintoasetof1rowvectorsxi=[xi;xi+1;:::;x(i+1)1],i0.Accordingtothematrix-geometricmethod, whereRisthesolutionof andx0isthesolutionof Bothequation( 2{20 )and( 2{21 )canbesolvedinaniterativeway,see[ 52 ]fordetaildiscussions.FinallyapplythenormalizationconstraintP1i=0xi=1togetthesteadystatequeuelengthdistribution. 45

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Assumingchannelgaing(n)isi.i.d.Rayleighdistributedwithprobabilitydensityfunctionfch(g)=eg.From( 2{14 )and( 2{15 ),thetransitionprobabilityforCONSTfpci;jgis:pci;0=e P(2i+ BTs1) P(2i+j BTs1)e P(2i+j+1 ForTDWF,therearetwosituationsthataccounttotheeventq(n+1)=q(n)+.OneisthesameasCONST,thetransmissionpowerissosmallthats(n)issmallerthanone;anothersituationisg(n)
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2{29 )isomittedbecauseatsteadystate,bothchannelgainandqueuelengtharestationary.( 2{29 )canbenumericallyevaluated. 1.2.2 fordetails).Itisadualproblemofeectivebandwidth,wherethedepartureprocessisconstantandthearrivalprocessisrandom.Thevalidityofeectivebandwidthrequiresthatthearrivalprocessbestationary[ 46 ,page291].Analogously,thevalidityofeectivecapacityrequiresthatthevirtualdepartureprocess(thecapacityprovidedbythechannel)bestationary.NoticethattheHQLAPCdoesnotchanges(n)comparingtoitscorrespondingCGBPC.AndforCGBPC,thedepartureprocesss(n)isdeterminedbythechannelgaing(n).Iffg(n)gisstationary,fs(n)gisalsostationary.Therefore,theeectivecapacityisvalidforCGBPCandHQLAPC(exceptforchannelinversionPCwhereP/1=g,s(n)becomesadeterministicvariable. ~P(n)=min"Ppeak;min[f(g(n));2q(n)+ BTs1 DeneacombinedCGBPCschemefpeak(g(n))=min[Ppeak;f(g(n))],~P(n)canberewrittenas ~P(n)=min"fpeak(g(n));2q(n)+ BTs1 Theconclusionandresultinsubsection 2.2.2 and 2.2.3 canbedirectlyappliedtothissituation,providedthatthetransitionprobabilitymatrixPisre-calculatedaccordingtofpeak(g(n)). 47

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NoticethattheHQLAPCschemewithCGBPCpartf(g(n))actuallyhasthesamequeuelengthdistributionasf(g(n)).BecauseHQLAonlyreducethetransmissionpowerwhenf(g(n))canclearthequeueandthereducedpowerisstillcapableofclearingthequeue.Thereforetheeectivecapacitycalculatedby( 1{13 )isalsotrueforHQLAPCschemewiththesamef(g(n)).Fori.i.d.channelgain,(u)=1 48

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Solvefor gettheparameteroftheCGBPCscheme,i.e.,PforCONSTandCforTDWF,forthecriticalstate.IfasmallerPorlargerCisused,thequeuewillbeunstable,andallthestatesaretransient.Atthecriticalstate,thequeueisrecurrentnull,themeanrecurrencetimeis1andthereisnostationarydistribution.Thereforeastimegoesby,theprobabilitythatthequeuelengthreturntozeroiszero.Underthissituation,theHQLAPCschemeisequivalenttotheCGBPCschemebecausetheprobabilitythatthequeuecanbeclearediszero.ThereforeEg;q[~P(g;q)]=Eg[f(g)].Thelowerboundofaveragepoweris wheretheparameteroff(g)isobtainedby( 2{34 ). 2.3.1SteadyStateQueueLengthDistribution 2-6 andFig. 2-7 showtheprobabilitymassfunctionforHQLA/CONSTandHQLA/TDWFrespectively.Forallthesimulations,=1,BTs=100,=50andP=1.Thecomputersimulationhas106runs.Theanalyticalresultsmatchthesimulationresultsverywell.ThequeuelengthdistributionbehavesdramaticallydierentfordierentCGBPCcomponents.ThedistributionofHQLA/CONSTdecayssmoothly 49

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ProbabilitymassfunctionofHQLA/CONST. andexponentiallywhenthequeuelengthislarge.ThedistributionofHQLA/TDWFhaspeaksatqueuelengthequaltoK,K=0;2;:::.AndtheamplitudeofthepeakdecreasesasKincreases.ThisisbecauseforHQLA/TDWF,whenthechannelgainissmallerthanthecutothreshold,thetransmitterstopstransmitting.WhenKsuchblockssuccessivelyoccur,theincensementofthequeuelengthwillbeK.TheprobabilitydecreasesexponentiallywithK.Fig. 2-8 showsdelayboundviolationprobabilityofHQLA/TDWFwiththesamesimulationparameters.ForlargeDmax,theviolationprobabilityisapproximatelyexponentiallydistributed,whichveriesthevalidityofthetheoryofeectivecapacitywithpowercontrol. Sincetheanalyticalresultmatchesthesimulationresultverywell,inthefollowingsubsections,onlytheanalytical(numerical)resultswillbeshown. 49 ]astheCGBpart,whichmaximizestheeectivecapacityamongalltheCGBPCscheme.Fig. 2-9 ,Fig. 2-10 andFig. 2-11 illustratetheeectivecapacityoftheHQLA/CONST, 50

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ProbabilitymassfunctionofHQLA/TDWF. Figure2-8. DelayboundviolationprobabilityofHQLA/TDWF. HQLA/TDWFandHQLA/OPTrespectively.InFig. 2-9 andFig. 2-10 ,theeectivecapacityofOPTisalsoillustratedasareference.Inthesimulation,=1,BTs=100,theaveragepowerE[~P]=1.Forthesameaveragepower,theeectivecapacityofHQLA/TDWFandHQLA/CONSTPCschemeissignicantlyincreasedcomparingtothecorrespondingchannelgainbasedPCscheme.HQLA/OPTbooststheeectivecapacityformoderateu.Forlargeu,allofthethreeHQLAPCschemesapproachtheOPTPC 51

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EectivecapacityofHQLA/CONST. Figure2-10. EectivecapacityofHQLA/TDWF. scheme.HQLA/TDWFandHQLA/OPTperformalmostthesameandarebothsuperiortoOPT. 2-12 throughFig. 2-14 showsthepowergaininatypical3GWCDMAenvironment[ 6 ].Theperformancegainisdenedastheratiooftheaveragepowerrequiredbythe 52

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EectivecapacityofHQLA/OPT. Table2-1. Parametersfor3Genvironmentsimulation. Dmax 12:2Kbps 50msec 103 144Kbps 50msec 103 3:84MHz CarrierFrequency 1:9GHz CGBPCschemeandthatoftheproposedHQLAPCschemetofullthe3GQoSrequirement. Twotypesofservicesareconsideredinthesimulation,voicedataandvideodata.ThesimulationparametersarelistedasinTable 2-1 Wesimulatethreetypicalmovingspeeds,3mphwalkingspeed,35mphlocaldrivingspeedand70mphhighwayspeed.ThemovementoftheterminalcausesDopplerfrequencyshiftfm.Intimedomain,thecoherenttimeisTc=p 53

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PowergainofHQLA/CONSToverCONSTPC. Figure2-13. PowergainofHQLA/TDWFoverTDWFPC. 54

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PowergainofHQLA/TCIoverTCIPC. 53 ].DenotektheminimumSINRofmodulationschemek,andBkthenumberofbitsthatcanbetransmittedduringoneblockifmodulationschemekisapplied.Forconvenient,let0=B0=0,andK+1=BK+1=1whereKisthemaximummodulationscheme.ForCGBPC,themodulationschemetcischosesuchthattcf(g(n))g(n)
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Parametersfor3Genvironmentsimulationwithadaptivemodulation. SpreadingFactor 64 CodingRate 1=3 K 6 PowergainofHQLA/TCIoverTCIPCwithadaptivemodulation,voicedata. Thefactor1:1inaddressesthesignalingoverhead.f(g(n))=min[6=g(n);Pmax]wherePmaxisthepeakpowerconstraint.ThedelayconstraintisfullledbyturningPmax.Thereceiverestimatesandchannelgainandsendsanchannelgainadjustmentindicatorbacktothereceiverwhichtakesvalueof1dB.Thetransmitterupdatesthechannelgainbytheindicatorateachblockanddeterminesthemodulationscheme.Thepowergainissignicantatlowspeedandapproachesunitathighspeed.Thatisbecauseathighspeed,thecoherenttimebecomesshorter,andtheeectivecapacityincreases.ThereforelessPmaxisneededtofullltheQoSrequirement.Accordingly,tcissmallerandthepossibilitythattpissmallerthantcdecreases. 56

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2-16 .Inthesimulation,=1,BTb=200,=120,Ppeak=1,=103.Asindicatedinsection 2.2.5 ,HQLA/TDWFandHQLA/CONSThavethesameaveragepowerattheminimumachievableDmax,thetwocurvesjointattheleftmostpoint.AsDmax!1,theaveragepowerapproachestothelowerboundindicatedby( 2{35 ). 2.4.1Correlatedchannel h(n)=h(n1)+u(n);(2{37) 57

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11 ,page165] 16fm;(2{38) wherefmisthedopplerfrequency,andthecoherencetimeisdenedasthetime,overwhichthetimeauto-correlationfunctionofthefadingprocessisabove0.5;2)computethecoecientby Then,wenormalizeh(n)andobtainh(n)by Thechannelgainisthenobtainedbyg(n)=jh2(n)j. ItispossibletocalculatethetransitionprobabilityofthechannelgainProb[g(n+1)=yjg(n)=x];x;y0.Sequencefg(n)gformsacontinuous-statesMarkovchain,whilethesequenceofqueuelengthfq(n)gisnolongeraMarkovchain.Toapplythemethodinsection 2.2.2 ,weneedtoextendthestatesparameterfromscalerq(n)tovector[q(n+1);g(n)].Additionally,wealsoneedtopartitionthestatespaceofchannelgainintonitebinssincethestatespacemustbediscrete.Denotefr0;r1;:::;rK;rK+1gthechannelgainpartition,wherer0=0,rK+1=1,r1r2:::rK.AndletsetRi=[ri;ri+1),i=[0;:::;K]denoteeachbin.Thevalueoffrig,i=[1;:::;K]canbedeterminedasthe 2{39 ). 58

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BTb1:(2{41) Theelementoftransitionprobabilitymatrixis Prob[q(n+1)=j;g(n)2Ryjq(n)=i;g(n1)2Rx]=Prob[q(n+1)=jjg(n)2Ry;q(n)=i;g(n1)2Rx] (2{42) wherej;k=1whenj=k,j;k=0whenj6=k,andkisthenumberofbitsthatcanbetransmittedwheng(n)=y,q(n)=i.k=i+BTbblog2(1+~P(y;i)y)c.Itiseasytoseethatthetransitionprobabilitymatrixstillhastherepetitiveformrequiredbythematrix-geometricmethod.ThedimensionoffAig,fBigis(K+1)(K+1). Fig. 2-17 andFig. 2-18 illustratethedelayboundviolationprobabilityat20mphand80respectively.=75bits/block,B=120KHz,Tb=2=3ms,centralfrequency1:9GHz.Allthesimulationhas106runs.ThePCisHQLA/TCI.ThecutothresholdofTCIischosensuchthattheaveragepowertosatisfythestatisticalQoSconstraintf=75bits/block;Dmax=20blocks;=103gisminimized.ForTCI,thechannelhasonlytwostates,\ON"and\OFF".Whenthechannelgainissmallerthanthecutothreshold,thetransmissionpoweriszero,asinthe\OFF"state;whilewhenthechannelgainislargerthanthecutothreshold,thetransmissionrateisconstant,asinthe\ON"state.AsanrstorderapproximationoftheAR(1)model,onlytwobinsarenecessary.AscanbeseeninFig. 2-18 ,athighspeed,thisapproximationgivesagoodestimationofthedelayboundviolationprobability.Atlowspeed,thisapproximationisnotaccurateenough.However,wecanfurtherpartitioneachstateintosub-statetoimprovetheaccuracy.Foreachgure,thedelayboundviolationprobabilitiesofthei.i.d.channeland 59

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Figure2-17. Delayboundviolationprobabilityat20mph. Figure2-18. Delayboundviolationprobabilityat80mph. 60

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Denotea(n)thenumberofbitsthatarrivesatthen-thblock.a(n)isanintegerandboundedby0a(n).Themarginaldistributionofa(n)ischaracterizedbypa(m)=Prob[a(n)=m],0m.Thetransitionprobabilitymatrixstillhastherepetitiveformrequiredbythematrix-geometricmethod.Considertheelementoftheithrowandjthcolumnofthetransitionprobabilitymatrix (2{44) =Prob[q(n+1)=q(n)+a(n)s(n)=jjq(n)=i] (2{45) =Prob[a(n)s(n)=ji]; Whenj=0,thequeueiscleared, (2{47) =Xk=0pa(k)Prob[P0(g(n);i;k)f(g(n))]; where BTb1 istheminimumpowertoclearthequeuewhenq(n)=i,a(n)=k; 61

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pi;j=pi;im =Xk=0pa(k)Prob[s(n)=k+m] (2{51) =Xk=0pa(k)Prob[k+mBTblog2(1+f(g)g)+i,pi;j=0. Fig. 2-19 illustratedanexampleofaccumulatedarrivalprocessanddepartureprocess.Themarginaldistributionofarrivalprocessfa(n)gisuniformlydistributedintherange[0;60].=1,BTs=80,P=1,=0:818. Figure2-19. Anexampleofvariable-ratearrivalprocess. 62

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2-20 andFig. 2-21 showthequeuelengthdistributionandthequeuelengthviolationprobabilityoftheabovefa(n)gwithTCIPCrespectively.Thesimulationresultmatchesthetheoreticalnumericalresultverywell. Figure2-20. QueuelengthdistributionofTCIPCwithvariable-ratearrivalprocess. Figure2-21. QueuelengthviolationprobabilityofTCIPCwithvariable-ratearrivalprocess. 63

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64

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2 ,westudiedtheecientpowercontrolschemeforanodetonodecommunicationsystemwithstatisticalQoSguaranteesunderaveragepowerconstraint.Thenodetonodecommunicationsystemcanbeconsideredasasingleuser,singlechannelsystem.Inthischapter,wefocusonthestatisticalQoSprovisioningproblemforasingleuser,multi-channelsystem.Multi-channelsystemshavebeenwidelyusedinwidebandwirelesscommunications,e.g.,OFDMandMIMOsystems.Insuchsystems,asingleusermayoccupymultipleparallelchannels.Theaveragepowerconstraintisimposedonthetotalpowerofalltheparallelchannels. AnoptimalCGBpowerallocationschemehasbeenproposedforsingleuser,multi-channelsystems,whichmaximizestheeectivecapacityundertheassumptionthattheCSIisperfectlyknownatthetransmitterside[ 7 ].HowevertheperfectCSIassumptionisnotfeasibleinmostpracticalsystems.Firstly,thechannelestimationandfeedbackprocedurewillinducedelay.ThetransmittercanonlyhaveadelayedversionofCSI.Secondly,theCSImaynotbepreciselyestimated.Thethermalnoiseandinterferencesfromotheruserswillaecttheaccuracyoftheestimation.Inthischapter,weassumetheCSItothetransmitterisaccuratebuthasprocessingdelay.ThemorerealisticscenariowheretheCSIisbothimpreciseanddelayedwillbethefutureresearchinterest. TheimpactsofimperfecttransmittersideCSIontheadaptivesystemswhichoptimizethephysicallayerperformancesuchasBER,spectraleciencyhaveattractedmuchattention.TheimpactsofchannelestimationerroranddesignissuesforSISOsystemarestudiedin[ 54 ],[ 55 ],andMIMOsystemsin[ 56 ]and[ 57 ].TheeectofdelayedCSIontheaverageBERperformanceofanadaptivesystemwithoutdelay-constrainedisstudiedin[ 58 ].Thedistributionofdelayedchannelgainconditionedonthecurrent 65

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59 ],avariable-rate,variable-powerQAMsystemisanalyzedanddesignedwithconsiderationofbothCSIestimationerroranddelayforMIMObeamformingsystems.ThespectraleciencyismaximizedsubjectanaveragepowerandBERconstraint.AsintheSISOcase,thesmallCSIdelaycausesneglectableperformancedegradation.In[ 60 ],bothuncodedandcodedadaptiveMQAMadaptivesystemsarestudiedwithincorporationofdelayedCSIwithouttheknowledgeofDopplerfrequencyandexactshapeoftheautocorrelationfunctionofthechannelfadingprocess.Largethroughputgainisfoundoverthenonadaptiveschemes. InthischapterweconsidertheimpactofdelayedCSItoadelay-constrainedsystemandproposeasub-optimalpowerallocationschemewhichislesssensitivetotheCSIdelay.NeithertheDopplerfrequencynortheautocorrelationfunctionofthechannelgainsarerequiredfortheproposedpowerallocationscheme.Theestimationofthesetwoparametersisnotaneasytaskandrequirearelativelylongtimesincethedopplerfrequencyistypicallymuchlowerthanthedatarate[ 61 ].Theproposedpowerallocationprocedureincludestwosteps.Intherststep,themulti-channelsystemistreatedasasingle-channelsystemandthetransmissionpowerisdeterminedbythesummationofchannelgainsofallthechannels.Thesummationofchannelgains,onaverage,haslessuctuationthansinglechannelduetotheaverageeect.Inthesecondstep,thetransmissionpowerdeterminedintherststepareallocatedtoallthechannels. Therestofthechapterisorganizedasfollows:Section 3.2 andsection 3.3 describethesystemmodelandoptimalpowerallocationschemerespectively;Section 3.4 presentstheproposedsub-optimalpowercontrolscheme.Section 3.5 illustratesthesimulationresults.Section 3.6 concludesthechapter. 66

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3-1 .Thedatasourcegeneratesinformationbitsataconstantrate.Thebitstreamisstoredinthetransmissionbuerinarst-in-rst-out(FIFO)fashion.Thebuersizeisassumedtobeinniteandthereforeallthebitswillbetransmittedultimately.Ateachtransmissioncycle,acertainnumberofinformationbitsfromtheheadofthebuerareparsedintoNsub-streams,whereNisthenumberofchannels.Eachsub-streamisencodedandmodulated,thentransmittedthroughoneoftheNchannels.Eachchannelexperiencestime-variantfrequency-atfading.WeadoptBF-AWGNmodeltocharacterizethetime-varianceofthechannels.TheBF-AWGNmodelpartitionstime-domainintoblocks.EachblockhasdurationTb.Weassumeaslowfadingchannel,wherethechannelgainwithinoneblockisconstant,andvariesfromoneblocktoanother.Andthechannelgainofdierentblocksarei.i.d.distributed.ThischannelmodelcanbefundinmobileTDMA/TDDsystemswheretheperiodbetweenblocksthatareallocatedtoasingleuserislongerthanthecoherenttime. Thereceiverdetects,demodulatesanddecodessignalsfromeachchannelandcombinedthemintoonedatastream.ThereceiveralsoestimatesthechannelgainforeachchannelandfeedsthembacktotheTransmitter.Thedelaybetweentheactualchannelgainandthechannelgainfedbackfromthereceiverisnblocks,whichincludesthetimeforchannelgainestimation,transmission(atthereceiverside),anddetection(atthetransmitterside).Thetransmitterusesthedelayedchannelgaintodeterminethetransmissionrateandmodulationcodingscheme(MCS)ofeachchannel. WeassumeoptimalMCSexistssuchthatinstantaneouschannelcapacityisachievablewithzeroBERwithinoneblock.Denotegi(n),i=1;2;:::;Ntheactualchannelgainforthei-thchannelofthen-thblock,Pi(n)thetransmissionpowerforthei-thchannelofthen-thblock.Thetransmittedsignalxi(n)andreceivedsignalyi(n)arerelatedby 67

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Systemdiagram. wherewi(n)isthecomplexwhiteGaussiannoise,wi(n)CN(0;1).AssumingunitarysignalpowerE[jxi(n)j]2=1,thereceivedsignaltonoiseratio(SNR)is Thenumberofbitsthatcanbetransmittedbythei-thchannelinthen-thblockis: NTblog2(1+Pi(n)gi(n));(3{3) whereBisthetotalbandwidth.Thetotalnumberofbitstransmittedinthen-thblockis 68

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Prob[D(1)Dmax]:(3{5) whereD(1)denotestherandomvariableofthewaitingtimeofthebitsinthebuerwhenthequeueenterssteadystate, Accordingtothelargedeviationtheory[ 44 ],foraqueueingsystemwithconstantarrivalandarbitrarydepartureprocess,thefollowingapproximationholds Prob[D(1)Dmax]eDmax;(3{7) whereistheparametercalledQoSexponent[ 62 ],whichisdeterminedbythearrivalanddepartureprocessofthequeuingsystem. Substituting( 3{7 )into( 3{5 ),weconverttheconstraintondelayboundviolationprobabilityintotheconstraintonQoSexponent, Dmax:(3{8) TheconceptofeectivecapacityisusedtomeasuretheQoSprovisioningcapabilityofthetransmissionsystemmentionedabove.Theeectivecapacityisdenedasthemaximumconstantarrivalratethatasystem(specically,thedepartureprocess)cansupportunderthestatisticalQoSconstraint.Itisthelogarithmmomentgeneratingfunctionofthedepartureprocess.Denotetheaccumulateddepartureprocessfortherstnblocksas Theeectivecapacityis: 69

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44 ].Therefore( 3{8 )isequivalentto Dmax):(3{11) Equation( 3{11 )relatestheeectivecapacitytothestatisticalQoSconstraint.GivenadepartureprocessandstatisticalQoStriplet,wecancheckwhetherornotthestatisticalQoScanbeguaranteed. Thedepartureprocesss(n)isastochasticprocesscontrolledbythechannelgainfgi(n)gandtransmissionpowerfPi(n)g.ByadaptingfPi(n)gtofgi(n)g,wecanchangethedepartureprocesss(n)andincreasetheeectivecapacity.Substituting( 3{9 )and( 3{4 )into( 3{10 ),theeectivecapacityofmulti-channelsystemwithblockfadingchannelmodelis Theexpectationistakenoverthechannelgain. Ifthetransmitterhastheperfectknowledgeofchannelgain,theoptimizationproblemofmaximizingeectivecapacitycanbeexpressedas maxfPi(k)gEC()=limsupn>11 whereP0istheaveragepowerforeachblock.TheoptimalsolutionfPopti(n)gtoequation( 3{13 )isgivenin[ 7 ,eq.(22)-(25)].Thesolutionisoptimalinthesensethatthetransmitterknowsthecurrentchannelgain.DenoteEOptC()thisoptimaleectivecapacity.Ifthechannelgainavailableatthetransmittersidehasnblocksdelay,thetransmissionpowerobtainedforthen-thblockisactuallyPopti(nn),andtheeective 70

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NTfnPk=1NPi=1log2(1+Popti(kn)gi(k))]:(3{14) ConsiderPopti(kn)asanotherpowercontrolscheme,itiseasytoseethatEC(;n)EOptC().InthenextsectionweproposeasuboptimalpowerallocationschemefordelayedCSIscenario,whichresultssimilareectivecapacityasin( 3{14 )whilereducesthecomputationalcomplexitysignicantly. 3{13 )intotwosteps.Intherststep,wetreatthemulti-channelsystemasasinglechannelsystemandusesthesummationofthechannelgainsastheequivalentchannelgain: Thetotaltransmissionpowerofthen-thblockPtotal(n)isdeterminedbygeq(n)bysolvingthesinglechanneleectivecapacitymaximizationproblem maxfPtotal(k)gEC=limsupn>11 Thesolutionto( 3{16 )isgivenin[ 49 ], +1eq(n)1 71

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+1eq1 wherep(geq)istheprobabilitydensityfunctionofgeq.Whenallthechannelsexperiencesi.i.d.Rayleighfading,geqfollowschi-squaredistributionwithdegree2N, wheregistheexpectationofchannelgainofonechannel. 53 ,page214].InthesecondstepweassignthetotalpowerPtotal(n)toeachchannelbysolvingthefollowingoptimizationproblem maxfPi(k)gEC=limsupn>11 wherePtotal(k)ispre-calculatedby( 3{17 ).SincePtotal(k)isuniquelydeterminedbytheinstantaneouschannelgainsandtheirmarginaldistributions,wecantreatPtotal(k)asaconstantandunchangedparameterforanyk.Thetotalpowerconstraintconditioncanbewrittenas: whereisanarbitraryconstant.Ateachblock,werstcalculatePtotal(k)by( 3{17 ),andthensolve( 3{20 )withtotalpowerconstraintconditionreplacedby( 3{21 ),andnallysubstituteinthesolutionwithPtotal(k). Tosolve( 3{20 ),weconsidertwoscenarios: 72

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3{20 )reducesto: maxfPi(1)gEC=1 Inthefollowingdiscussion,weomitthetimeindexkforsimplicity. 3{16 )is 3.1 ,seeAppendix A.1 .Thesolutionisactuallythefrequencydomainwaterlling[ 53 ,page116].Theactivechannelset=1canbefoundbythefollowingLemma. ForaproofofLemma 3.2 ,seeAppendix 3.2 73

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3.2 suggestsaniterationalgorithmfornding=1.Atbeginning,=0containsallthechannelsandN0=N.Acutothresholdisobtainedassumingthatallthechannelsareallowedtotransmit.However,theso-obtainedthresholdmaybegreaterthanthechannelgainofsomechannels.FromLemma 3.2 ,thosechannelsdonotbelongtotheactiveset=1.Thereforewecandiscardthosechannels.Theremainingchannelsformthenew=0setandthecutothresholdC(N0)isrecalculated.TheiterationrepeatsuntilthechannelgainsofalltheremainingchannelsaregreaterthanC(N0). 49 ]. Theoverallalgorithmissummarizedasfollows:Forblockn: Step1:Obtain=Ptotal(n)by( 3{17 ),ifPtotal(n)=0,setPi(n)=0foralli,algorithmends. Step2:Let=0=[1;2;:::;N],N0=j=0j. Step3:ObtainC1(N0)by( 3{26 ). Step4:Lete==fmjg1m>C1(N0)g.Ifje=j=0,let=1=e=,gotoStep6. Step5Let=0==0ne=,wherendenotessetsubstraction.N0=j=0j.GotoStep3. Step6:ObtainPi(n)by( 3{23 ).Algorithmends. Comparetotheoptimalsolution,theproposedsub-optimalpowerallocationschemereducesthecalculationcomplexityintwoaspects.First,inoptimalsolution,thecalculationofcutothresholdinvolveseveralcoupledN-foldintegrationin.Insub-optimalsolution,wehavetwocutothresholds.OneisforPtotal(n)andanotheroneforPi(n).ThecalculationofthresholdforPtotal(n)involvesonlyone-foldintegration.ThethresholdforPi(n)isobtainedbysimplesummationandmultiplication.Secondly,forbothofthetwopowerallocationschemes,thesearchfortheactivechannelsetneediterationprocedure.Ineachiteration,theoptimalschemeneedtocalculatetheproductofthenon-integerpowerofthechannelgains,whilethesub-optimalschemeonlyneedstocalculatethe 74

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Comparisonofcomputationalcomplexity. Operation Optimal Suboptimal None1-foldIntegration None 1Non-integerpowerofthechannelgains NoneReciprocalofthechannelgains N N summationofreciprocalofthechannelgains.ThesummaryofcomplexitycomparisonislistedinTable 3-1 11 ,page220].Fig. 3-2 illustratestheeectofCSIdelayandDopplerfrequencyshiftonthetwopowerallocationschemesrespectively.Thedelayis0,2,5blocks,andtheDopplerfrequencyfdis5Hzand10Hz,respectively.Forbothofthetwopowerallocationschemes,theeectivecapacitydegradesslightlyinsmallregime.Thesmallregimecorrespondstoloosedelayconstraintsystems.Thisresultisconsistentwiththatindelayconstraintfreesystems,wheresmallCSIdelaycausesneglectableperformancedegradation.Forlargewhichcorrespondstostringentdelayconstrainthowever,theeectivecapacitydecreasesdramaticallywhenCSIdelayoccurs.AndlargerDopplerfrequencyshiftresultsmoredegradationduetofasterchangingofthechannelstatus.ThedelayconstraintsystemsaremoresensitivetoCSIdelay. Fig. 3-3 illustratestheratiooftheeectivecapacityachievedbythesuboptimalschemetothatoftheoptimalscheme.IntheperfectCSIscenario,thisratiodecreaseswiththeincreaseof.Thisisbecauseofthenatureofsolvingmethodologyofthetwoschemes.Theoptimalsolutionisexpectedtohavebetterperformancethanthesub-optimalsolution.Itisworthnotingthatevenatveryhighregime,thesuboptimal 75

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76

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B EectofCSIdelayontheeectivecapacity. A .Optimalsolution; B .Suboptimalsolution. 77

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B Ratioofeectivecapacityachievedbythesuboptimalsolutiontotheoptimalsolution. A .MaximumDopplerfrequency5Hz; B .MaximumDopplerfrequency10Hz. 78

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Muchworkhasbeendoneontheresourceallocationschemesforwirelessnetworks(see[ 43 ]forasurvey).ToprovisionQoSguaranteesforreal-timeapplications,admissioncontrol,resourceallocation,andschedulerareneeded.Atthebeginningofeachtransmission,theresourceallocationalgorithmcomputestheamountofresourcethatisneededtosupporttheuser'sQoSrequirementbasedonthestatisticalinformationofthenetwork.Admissioncontrolcheckstheavailabilityoftherequest.Fortheadmitableuser,theresourcecalculatedbytheresourceallocatorisreservedforitsfutureuse.Theschedulerdecidestheactualresourceassignmentsforalltheadmittedusers,ateachtransmissioninterval,basedontheinstantaneousnetworkstatus.Thetotalresourceassignedbytheschedulershouldnotexceedwhathasbeenreservedatthebeginningofthetransmission. Inatraditional(weighted)roundrobin(RR)scheduler,eachuserisallocatedaxedportionofachannelduringthelifetimeofitsconnection.Thismethodensuresthateachuserinthesystemhastheequalchancetotransmitdata,butitdoesnotutilizemultiuserdiversity[ 63 ],resultinginloweciency.Toutilizemultiuserdiversity,KnoppandHumblet[ 64 ]proposedaschedulingscheme(calledK&Hscheduler)thatallows,atanytimeslot,onlytheuserwiththebestchanneltotransmit.TheK&Hschedulermaximizesthetotalergodiccapacitybyutilizingthemultiuserdiversitybutitdoesnotprovideanydelayguarantee.Auserinadeepfadeofanarbitrarilylongperiodwillnot 79

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Toaddressthelimitationoftheschedulingalgorithms,i.e.,inabilityofprovisioningexplicitQoS,thejointK&H/RRscheduler[ 44 ]isproposed.ThejointK&H/RRschedulingsimpliesthetaskofexplicitprovisioningofQoSguaranteeswhileachievingeciencyinutilizingwirelesschannelresources(duetomultiuserdiversity).Specically,thedesignoftheschedulerisbasedontheK&Hscheduling,andshiftstheburdenofQoSprovisioningtotheresourceallocationmechanism,suchthatthedesignoftheschedulerissimplied.Thispartitioningwouldbemeaninglessiftheresourceallocationproblemnowbecomescomplicated.However,itispossibletosolvetheresourceallocationproblemecientlyusingthemethodofeectivecapacity.Eectivecapacitycapturestheeectofchannelfadingonthequeueingbehaviorofthelink,usingacomputationallysimpleyetaccuratemodel,andthus,isthecriticaldeviceweneedtodesignanecientresourceallocationmechanism.ComparedtotheRRscheduling,thejointK&H/RRschedulingcansubstantiallyincreasethestatisticaldelay-constrainedcapacity(a.k.a.,eectivecapacity)ofafadingchannel,whendelayrequirementsarenotverytight.Forexample,inthecaseoflowsignal-to-noise-ratio(SNR)andergodicRayleighfading,thejointK&H/RRschedulingcanachieveapproximatelyPKk=11 Theremainderofthischapterisorganizedasfollows.Section 4.2 introducesthereferencechannelapproach.Section 4.3 describestheproposedPCandschedulingschemes.Section 4.4 presentsthesimulationresults.Section 4.5 summarizesthechapter. 65 ].Duetothefrequencydiversity 80

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44 ],whendelayrequirementsarelooseormoderate.However,whenusers'delayrequirementsarestringent,thejointK&H/RRreducestotheRRscheduling,andsothehighcapacitygainduetomultiuserdiversityassociatedwiththeK&Hscheduling,vanishes.Toextractmorecapacityinthiscasewithtightdelayrequirements,itisdesirabletohaveascheduler,whichateachinstant,dynamicallyselectsthebestchannelamongmultiplechannelsforeachusertotransmit,soastoobtainfrequencydiversity.Inotherwords,thisschedulermustndachannel-assignmentschedule,ateachtime-slot,whichminimizesthechannelusagewhileyetsatisfyingusers'QoSrequirements.Thisschedulingproblemisformulatedasalinearprogram,inordertoavoidthe`curseofdimensionality'associatedwithoptimaldynamicprogrammingsolutions.Thekeyideabehindthisiswhatiscalledthereferencechannelapproach,whereintheQoSrequirementsoftheusers,arecapturedbyresourceallocation(channelassignments).ThereferencechannelapproachallowsustoobtaincapacitygainundertightQoSconstraints,byutilizingfrequencydiversity. TheschedulersmentionedaboveonlyconsiderchannelassignmentswithoutPC(i.e.,thetransmissionpoweriskeptconstant).Ifthechannelgainsareknownatthetransmitterside,itisdesirabletoadaptthetransmissionpoweraccordingtothechannelvariationssoastoachievehighercapacityunderaveragepowerconstraints.Inthischapter,weaddresstheproblemofoptimumPCandchannelassignmentfordelaysensitiveapplicationsoveramulti-channel,multi-usersystem.Ourproposedschedulerallocatesbothpowerandchannelamongtheusers.TheobjectiveistominimizetheresourceusagewhilesatisfyingtheQoSrequirementsofusers. 4-1 showstheQoSprovisioningarchitectureofthedownlinkofawirelessnetwork,whereabasestationtransmitsdataoverNparallel,time-slottedfadingchannelstoKreal-timemobileusers,eachofwhichrequirescertainQoSguarantees.Thechannel 81

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WeadoptBF-AWGNmodelforeachparallelchannel,whichassumesthatthechannelgainsareconstantoveratimedurationoflengthTb,andTbissmallenoughthatthechannelgainsareconstant,yetlargeenoughthatidealchannelcodescanachievecapacityoverthatduration.Wefurtherdivideeachblockintoinnitesimaltimeslots,andassumeauidmodelforthepackettransmission,whichmeansthatthesamechannelncanbesharedbyalltheusers,inthesameblock.Thesystemdescribedabovecouldbe,forexample,anidealizedFDMA-TDMAsystem,wheretheNparallel,independentchannelsrepresentNfrequencies,whicharespacedapart(FDMA),andwheretheblockofeachchannelconsistsofTDMAtimeslotswhichareinnitesimal. Figure4-1. QoSprovisioningarchitectureinabasestation. Thus,eachuserkhastime-varyingchannelpowergaingk;n(t)andtransmissionpowerPk;n(t),foreachoftheNindependentchannelsduringablock.Heren2f1;2;:::;Ngreferstothen-thchannel.Thebasestationisassumedtohavetheperfectknowledgeoftheinstantaneouschannelgain.Thecapacityofthen-thchannelforthek-thuserattimetis 82

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ToprovideQoSguarantees,weemploythreemechanisms,namely,admissioncontrol,resourceallocation,andscheduling.Uponthearrivalofanewconnectionrequest,werstusearesourceallocationalgorithmtocomputehowmuchresourceisneededtosupporttherequestedQoSunderaweightroundrobinscheduler.Specically,theresourceallocationalgorithmwillcalculatethexedchannelassignmentfractionfk;ng(fk;ngarerealnumbersintheinterval[0,1])ofchanneln,touserk,forthedurationoftheentireconnectiontime.BecausethePCdependsontheinstantaneouschannelgainandthesystemiscausal,attheresourceallocationphase,theallocatorwillnotknowthetransmissionpowerforeachtimeslotandthereforetheresourceallocationalgorithmassumesthatalltheusersusethesameandconstantpowerP0fortransmissionoverallthechannels.Thischannelassignmentfk;ngsatisesthatthetime-varyingcapacityofuserkintimet where wouldbesucienttofullltheQoSrequirements.Thechannelassignmentfractionfk;ngiscalculatedusingthejointK&H/RRschemepresentedin[ 65 ].Undertheassumptionofhomogeneoususers,theresourceallocatorwillcalculatetwoparametersf;gaccordingtousers'QoSrequirementtriplets,andthechannelassignmentfractionfk;ngisthengivenby wherek(n;t)istheuserwhohasthehighestchannelgainofchanneln,inblockt;and1()isanindicatorfunctionsuchthat1(k=a)=1ifk=a,and1(k=a)=0ifk6=a.f;gsatisfyK+1.Noticethatwhen=0,thejointK&H/RRschemereducesto 83

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65 ]showsthatwhenthedelayconstraintisloose,!0,thejointK&H/RRapproachesK&H;whenthedelayconstraintisstringent,!0,thejointk&H/RRapproachesRR.SinceWeconsiderthedelaysensitiveapplicationsinthispaper,whichimpliesthatthedelayconstraintisstringent,wewilluseRRschemetocalculatefk;ngforsimplicity. Thischannelassignmentfk;ngandpowerP0laterwillbethereferencechannelorbenchmarksystemfortheschedulerthatweuseinthispaper.Noticethatfk;ngonlyrepresentsthechannelresourcesreservedfortheusers,ratherthantheactualfractionsoftheNchannelblocksusedbytheusers,whichwillbecalculatedbytheschedulerduringeachblock. Afterexecutingtheresourceallocationalgorithm,theadmissioncontrolmodulecheckswhethertherequiredresourcecanbesatised.Ifyes,theconnectionrequestisaccepted;otherwise,theconnectionrequestisrejected.Foreachadmittedconnections,thebasestationestablishesabuerforit.Weassumethatthebuersizeisinnitesothatnopacketwouldbelostduetothetransmissiondelay.Thearrivalpacketsofeachconnectionsqueueupinthebuerinarstinrstoutmanner.Theschedulerdecides,ineachblock,howtotransmitthepacketsintheoutputportofeachbueroverthemultiplechannels.Specically,theschedulercalculatestheactualchannelassignmentfwk;n(t)g,whichisthefractionofchannelnusedbyuserk,andpowerassignmentfPk;n(t)gforbasedonlyonthechannelgainsfgk;n(t)gofthecurrentblockandtheamountofchannelreservedforeachuserfk;ng.Weproposethreeschemesforscheduling,whichareformulatedasthreeoptimizationproblemsforPCandchannelassignment.Weexpectourschedulerwouldecientlyutilizeboththemultiuserdiversityandthefrequencydiversityinherentinthemulti-user,multi-channelsystem,andthereforewould 84

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Sinceweusetheresourcesreservedduringtheresourceallocationphaseasareference,wecalltheresultingschedulerasreference-channel(RC)scheduler.Inaddition,sinceweadaptthetransmissionpoweraccordingtothechannelvariations,wefurthercalltheschedulerasadaptive-power-controlbasedreference-channel(APC-RC)scheduler.WeformulateourAPC-RCschedulersinthreeoptimizationproblemsbasedonthreedierentobjectivefunctions(namely,channelusage,powerconsumption,andenergyconsumption)asbelow. 1)Minimizethetotalchannelusage(APC-RC/c). minfwk;n(t)gfPk;n(t)gPKk=1PNn=1wk;n(t) (4{5) s.t.PNn=1wk;n(t)ck;n(t)PNn=1k;nc0k;n(t);8k Theconstraint( 4{6 )representstheQoSconstraintssincetheinstantaneouschannelcapacityspeciedby( 4{2 )[righthandsidein( 4{6 )]isenoughtosatisfytheQoSrequirements.Theconstraint( 4{7 )arisesbecausethetotalusageofanychannelncannotexceedunity.Theconstraint( 4{10 )ensuresthatthetotalpowerusedbytheschedulerwillnotexceedthatusedbythebenchmarksystem.Theintuitionoftheformulation( 4{5 )through( 4{10 )isthat,thelessisthechannelusageinsupportingQoSfortheKrealtimeusers,themoreisthebandwidthavailableforusebyotherdatatransmission,suchasbest-eorttrac. 85

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minfwk;n(t)gfPk;n(t)gPKk=1PNn=1Pk;n(t) (4{11) s.t.PNn=1wk;n(t)ck;n(t)PNn=1k;nc0k;n(t);8k 3)Minimizethetotalenergyconsumption(APC-RC/e). minfwk;n(t)gfPk;n(t)gPKk=1PNn=1wk;n(t)Pk;n(t) (4{17) s.t.PNn=1wk;n(t)ck;n(t)PNn=1k;nc0k;n(t);8k TheconstraintsinAPC-RC/pandAPC-RC/earethesamewiththatinAPC-RC/c.Theonlydierencebetweenthethreeschedulersistheobjectivefunction.TheAPC-RC/cschedulerminimizesthetotalchannelusagesuchthattheremainingchannelresourcecanbeallocatedtothebesteortusers.TheAPC-RC/pscheduleraimsatreducingthetransmissionpower,whichwouldbedesirableinthesenseofreducingtheco-channelinterference(betweencells)andadjacentchannelinterference.Theminimizationproblems( 4{5 )through( 4{22 )canbesolvedbynonlinearprogrammingmethods[ 66 ]. 86

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4.4.1SimulationSetting 4-1 ,inwhicheachconnection 4-2 .InFigure 4-2 ,thedatasourceofuserkgeneratespacketsataconstantrater(k)s.Generatedpacketsarerstsenttothe(innite)bueratthetransmitter.Thehead-of-linepacketinthequeueistransmittedoverNfadingchannelsatdataratePNn=1rk;n(t).Eachfadingchannelnhasarandompowergaingk;n(t).Weuseauidmodel,thatis,thesizeofapacketisinnitesimal.Inpracticalsystems,theresultspresentedherewillhavetobemodiedtoaccountfornitepacketsizes. Figure4-2. Queueingmodelusedformultiplefadingchannels. Weassumethatthetransmitterhasperfectknowledgeofthecurrentchannelgainsgk;n(t)inblockt.Therefore,itcanuserate-adaptivetransmissions,andidealchannelcodes,totransmitpacketswithoutdecodingerrors.Undertheroundrobinscheduling,thetransmissionraterk;n(t)ofuserkoverchanneln,isgivenasbelow, 87

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Ontheotherhand,forthecombinationofroundrobinandRCscheduling,thetransmissionraterk;n(t)ofuserkoverchanneln,isgivenasbelow, where andfwk;n(t)gandfPk;n(t)garesolutionstooneoftheminimizationproblemsspeciedby( 4{5 ),( 4{11 ),or( 4{17 ). TheaverageSNRisxedineachsimulationrun.DenetheaverageSNRby=E[gk;n(t)P0=2]=P0=2,wheretheexpectationisoverthemarginaldistributionofgk;n(t).Thevalueofisindependentofkandnsincefgk;n(t)garei.i.d.overkandn;thevalueofisalsoindependentoftimetsincetheexpectationisoverthemarginaldistributionofgk;n(t)ratherthanajointdistributionovergk;n(t1)andgk;n(t2),wheret1andt2aretwodierentepochs.AssumethatthetransmissionpowerP0andnoisevariance2areconstantandequalforallusers,inasimulationrun,fortheroundrobinscheduler.WesetE[gk;n(t)]=1inallthesimulations.From( 4{24 )and( 4{26 ),itcanbeseenthatthebandwidthBccanbecanceledoutonthebothsidesof( 4{6 ),( 4{12 ),and( 4{18 ).SothereisnoneedtospecifythevalueofBc. Thesampleinterval(blocklength)Tbissetto1milli-second.WegeneratechannelgainsbyAR(1)modelasdescribedinsection 2.4 .Foreachkandn,thetimesequencefgk;n(t)gformsanindependentAR(1)process.Inthesimulations,weset=0:8,whichroughlycorrespondstoaDopplerrateof58Hz. 88

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65 ]showsthatthevalueoffk;ngincreaseswiththeincreaseofthesourcerate.Byproperlychoosingthesourcerate,wecanhavek;n1=K,whichmeansthatalloftheNchannelsarereservedbytheresourceallocatorandareevenlysharedbyalltheusers.Forafaircomparison,wextheratiofN=KgsothateachuserisallottedthesameamountofchannelresourcefordierentfK;Ngpairs.Wesimulatedthreecases: 1)K=N=2,2)K=N=4,3)K=N=8.ToevaluatetheperformanceoftheAPC-RCschedulingalgorithms,weintroducethreemetrics,expectedchannelusagegainLc(K;N),expectedpowerconsumptiongainLp(K;N)andtheexpectedenergyconsumptiongainLe(K;N)denedasbelow, Averagetotalchannelallocatedbythescheduler=N Averagetotalpowerallocatedbythescheduler=NKP0 1 Averagetotalenergyallocatedbythescheduler=NK(1 1 89

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Fig. 4-3 throughFig. 4-5 showstheperformanceofLc(K;N),Lc(K;N)andLc(K;N)withdierentfK;Ngpairsrespectively. Figure4-3. PerformancegainLc(K;N)vs.averageSNR. Figure4-4. PerformancegainLp(K;N)vs.averageSNR. 1)Allofthethreegainsaregreaterthan1,whichindicatesthatourAPC-RCschedulersaresuperioroverthebenchmarkRRscheduler. 90

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PerformancegainLe(K;N)vs.averageSNR. 2)AllofthethreegainsincreasewithN.ThisisbecauseourAPC-RCapproachutilizesfrequencydiversity.WiththeincreaseofchannelnumberN,thedegreeoffrequencydiversityincreases.Thereforeweobservelargergains. 3)TheexpectedchannelusagegainLc(K;N)monotonicallydecreaseswiththeincreaseoftheaverageSNR.Intuitively,thisiscausedbytheconcavityofthecapacityfunctionc=log2(1+g),wheregisthechannelpowergain.ForhighaverageSNR,ahigherchannelgaindoesnotresultinasubstantiallyhighercapacity.Thus,forahighaverageSNR,schedulingbychoosingthebestchannels(withorwithoutQoSconstraints)doesnotresultinalargeLc(K;N),unlikethecaseoflowaverageSNR.Inaddition,Fig. 4-3 showsthatthegainLc(K;N)fallsmorerapidlyforlargerN.ThisisbecausealargerNresultsinalargerLc(K;N)atlowSNRwhileathighSNR,Lc(K;N)goesto1nomatterwhatNis. 4)TheexpectedpowerconsumptiongainLp(K;N)monotonicallyincreaseswithaverageSNR.Thereasonisthefollowing.ForRayleighfadingchannels(usedinoursimulations),thechannelpowergaingisexponentiallydistributed.Asincreases,theaveragechannelpowergaingalsoincreases,leadingtotheincreaseoftheprobability 91

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4{12 ),takesasmallvalue.Hence,E[PKk=1PNn=1Pk;n(t)]reduces,whichtranslatesintotheincreaseofLp(K;N). 5)TheexpectedenergyconsumptiongainLe(K;N)decreaseswithforsmallandincreaseswithforlarge.Theoptimizationproblemofminimizingthetotalenergyconsumptioncanbeviewedasthecombinationofminimizingthetotalchannelusageandminimizingthetotalpowerconsumption.Forsmall,theeectofminimizingthetotalchannelusagedominateswhileforlarge,theeectofminimizingthetotalpowerconsumptiondominates. 92

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InChapter 2 and 3 ,wefocusontheoptimalpowercontrolschemeswhichmaximizetheeectivecapacity.Eectivecapacitystemsfromthelargedeviationtheory,whichgivesagoodapproximationofthequeuelengthdistributionatlargequeuelengthregime.Toapplylargedeviationtheory,thequeuingsystemmustsatisfythefollowingtwoconditions, 1. Thetransmitterbuerhasinniteoccupancy(largequeuelengthregime) 2. Nopacketsdropduetodelayboundviolation.Allthearrivalpacketswillbetransmitted. Theabovetwoconditionsarenotrealisticinpracticalsystemsdesignedforreal-timeapplications.Inpractice,thetransmitterbueralwayshasnitecapacity.Itispossiblethatnewarrivalpacketsndafullbuer.Inthiscase,someofthepacketsmustbedropped,eitherthenewarrivalpacketsorthepacketsthathavealreadybeenwaitinginthebuer.Thesecondstrategyisnotecient,sinceforreal-timeapplications,theinformationreceivedafterthedelayboundwillbeconsideredofnouse.Forexample,inastreamingmultimediaapplication,aframewhicharriveaftertheplaytimewillnotbeplayedeveniftheyaresuccessfullytransmitted.Theecientstrategyistodiscard(drop)thepacketswhosewaitingtimeislongerthanthedelaybound. Inthefollowingtwochapters,weadoptamorerealisticqueuingmodel.Thedierencesfromthepreviouschaptersare 1. Thetransmitterbuerhasnitesize. 2. Thepacketswhosewaitingtimeislongerthanthedelayboundwillbedropped. Inthischapter,westilluseBF-AWGNchannelmodel,andthefadingprocessisassumedtobei.i.d..ineachblock.ThechannelgainofeachblocktakescontinuousvalueanditsmarginaldistributionischaracterizedbyfCH(g),g2[0;1).Wealsoassumetheinstantaneouschannelcapacitycanbeachievedduringoneblock.Underthisassumption, 93

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whereW,P,gdenotethebandwidth,transmissionpowerandchannelgain(thenoisevarianceisabsorbeding),respectively.Underthisassumption,thepowercontrolisactuallyequivalenttoratecontrol.Oncethetransmissionpowerisdetermined,thetransmissionrateisalsodetermined. Theinstantaneouschannelcapacityassumptionimpliesthatallthetransmittedpacketscanbereliablydelivered.Theonlyinformationlossisduetopacketdrop.Byproperlychoosingthetransmissionbuersizeandpacketdropstrategy,wecanguaranteethatallthetransmittedpacketshavetransmissiondelaysmallerthanthedelaybound.DenotethebuersizeasM(Dmax).Thedroppedpacketscanberegardedashavinginnitedelay.Thus,thedelayboundviolationprobabilityisequivalenttothepacketdropprobability.ThestatisticalQoSconstraintf;Dmax;gisequivalenttof;M(Dmax);Pdropg,wherePdropdenotesthepacketdropprobability. Inthischapter,westudythepower(rate)controlproblemtominimizethepacketdropprobability.Theoptimizationproblemcanbeformulatedas minP(n)Pdrops:t:AveragePowerP0P(n)0=0M=M(Dmax);(5{2) 94

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5{2 )isthedualproblemofthecapacitymaximizationprobleminchapter 2 maxP(n)s:t:AveragePowerP0P(n)0Prob[D(1)>Dmax]M=M(Dmax):(5{3) Inchapter 2 ,weshowthatincrosslayermodel,thepowercontrolschemeshouldtakeintoconsiderationofbothchannelgainandqueuelength.Thereforethetransmissionpowerofthen-thblockshouldhavethegeneralform TheHQLApowercontrolschemeproposedinchapter 2 isasuboptimalscheme.Thetransmissionpowerischosenastheminimumpoweroff(g(n))andthepowerneededtoclearthequeue.HQLAworksforanychannelgainbasedpowercontrolschemef(g(n)),butdoesnotprovideanyguidanceindesigningf(g(n)).Inaddition,itdoesnotaectthequeuingbehavior.ThequeuelengthdistributionobtainedbyapplyingHQLAisthesameasthatbyapplyingf(g(n))only.ThereforeHQLAisnotanecientpowercontrolscheme(althoughitisbetterthanf(g(n))). InthisChapter,weinvestigatetwomethodstosolve( 5{2 ).Thepowercontrolschemesderivedbythetwomethodsintentionallycontrolthequeuingbehaviortominimizethepacketdropprobability.Therstmethodisaparametricmethod.Weassumethechannelgainandthequeuelengthaectthetransmissionpowerindependently.Theresultingpowercontrolschemeiscalledseparatequeue-length-aware(SQLA)powercontrol.SQLAhastheformP(g(n);q(n))=f(g(n))h(q(n)),andf(g(n))=f(g(n);a),whereaaretheparametersoff(g(n)).TheoptimizationoverP(n) 95

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5{2 ),sinceweimposeformulationassumptionsonthesolution. Thesecondmethoddoesnotimposeanyassumptionsontheformulationofthepowercontrolscheme.Theresultingpowercontrolschemeiscalledjointqueue-length-aware(JQLA)powercontrol.WithoutspecicformulationofP(n),( 5{2 )isnotsolvable,becauseofthelackofexplicitrelationbetweenP(n)andthepacketdropprobability.ThereforeweseekotheroptimizationparametersinsteadofthetransmissionpowerP(n).Theparametersmustfullycharacterizethequeueingbehaviorofthesystemandhasnitedimension.Thetransitionprobabilitymatrixturnsouttobeagoodchoicewhichsatisestheabovetworequirements.Wedecomposetheoriginaloptimizationproblemintotwooptimizationproblems,onerelatesthetransitionprobabilitymatrixwiththepacketdropprobability,andtheotheronerelatesthetransitionprobabilitymatrixwiththetransmissionpower. Thereminderofthischapterisorganizedasfollows:subsection 5.1 introducesthesystemmodel.Section 5.2 andsection 5.3 describetheSQLAandJQLArespectively.Section 5.4 investigatesthestructuralinformationabouttheJQLApowercontrolscheme.Section 5.5 presentsthesimulationresults.Section 5.6 summarizesthechapter. 5-1 .Thedatasourcegeneratesblockeddataataconstantratepacketsperblock.EachpacketcontainsLbits.Asinpreviouschapters,theblockisthesmallesttimeunitduringwhichthetransmitterconductspowerandratecontroloperations.Thepowerandratecontrolmoduledeterminethetransmissionpowerandrate(thenumberofpacketsthatwillbetransmittedduringoneblock)basedontheinformationofthetransmitterbueroccupancyandtheinstantaneouschannelgain,whichisassumedtobeperfectlyknownbythetransmitter.Theencoder 96

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ThetimingdiagramisthesameasFig. 2-2 .Thepacketsarriveatthetransmissionbueratthebeginningofeachblock.Ifthebuercannotaccommodateallthearrivalpackets,someofthepacketswillbedropped.Therearetwostrategiesforpacketsdropping,discardsomeofthearrivalpacketsordiscardthepacketsthathavealreadybeenwaitinginthetransmissionbuer.Fordelayconstrainedcommunications,thebeststrategyistoaccommodateallthearrivalpacketsanddiscardfromtheheadofthebuer.Denoteq(n)thenumberofpacketsinthebuerbeforethenewarrivalofthen-thblock,Mthebuersize,s(n)thenumberofpacketsthatwillbetransmittedduringthen-thblock.ThedelayboundDmaxiscountedinthenumberofblocks.Supposeforblockn,Mq(n)<,i.e.,notallthenewarrivalpacketscanbeaccommodated.Denoted(n)=(Mq(n))thenumberofpacketstobedropped.ChoosingM=Dmax,therstd(n)packetsinthebuerhaswaitedDmaxblocks,andshouldbedropped.Theremainingpacketsarepushedaheadandemptytheroomatthetailofthebuerforaccommodatingthenewarrivals.Afterthenewpacketsbeenstored,certainnumberofpackets(determinedbytheratecontrol)areremovedformtheheadofthebuerandbetransmitted. Ingeneral,d(n)canbeexpressedby Andthenumberofpacketsremaininthebuerbeforethetransmissionis 97

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Systemmodel. AsillustratedinFig. 5-2 ,thesystemupdatefunctionis, Figure5-2. Diagramofstatesupdate. Thesequencefq(n)gformsahomogeneous,irreducible,andaperiodicMarkovChain.TheproofisthesameasinChapter 2 .ThesteadystatequeuelengthdistributioncanbeobtainedfromtheonesteptransitionprobabilitymatrixP.SincethebuerhasnitecapacityM,Pisasquarematrixofsize(M+1)(M+1).Thei-throwj-thcolumnof 98

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Substitute( 5{7 )into( 5{8 ), Tocalculatepi;jforeachpairoffi;jg,weconsidertwosituations. 1)0i
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thetransitionprobabilitymatrixcanberepresentedas: Thesteadystatequeuelengthdistributionisgivenby where=[0;1;:::;M]isa1(M+1)rowvector.Theelementiistheprobabilityofqueuelengthequaltoiwhenthequeueentersthesteadystate, Knowingthesteadystatequeuelengthdistribution,wecannowderivethepacketsdropprobability.Thepacketdropprobabilityisdenedastheratioofthenumberofthepacketsbeendroppedtothenumberoftotalarrivalpackets, 100

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Thepacketdropprobabilityis Whenthequeueenterssteadystate, whered(1)q(1)denotethenumberofpacketdropandqueuelengthwhenqueueentersthesteadystate,respectively. Similarly,theaveragetransmissionpoweris, Step(a)holdsbecauseg(n)andq(n)areindependent.Inthefollowingdiscussionswewillneglectblockindexn,sincethechannelgainsarei.i.d.,andthequeuelengthdistributiondoesnotchangeinthesteadystate, 101

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5{21 ),( 5{22 ),( 5{4 )into( 5{2 ),weobtaintheoptimizationfunctions, minP(g;q)Pdrop=1 Theconstraint=(P(g;q))impliesthatthesteadystatequeuelengthdistributionisafunctionofpowercontrolP(g;q),whichisdeterminedbyequations( 5{12 )through( 5{17 ). 5{24 )isnotaneasytask.BecausewithoutknowingtheexactformofP(g;q),theprobabilityin( 5{12 )cannotbederived.ThereforewedonotknowtheexplicitexpressionoffigasafunctionofP(g;q).Comparingtotheoptimizationproblemin( 3{13 ),theoptimizationvariableP(g)isexplicitlyincludedintheobjectivefunction.HencetheLagrangianmethodcanbeappliedtondtheoptimalsolution. Inthissection,weintroducetheparametricmethodtosolvetheoptimizationproblem( 5{24 ).ThekeystepistondtheexplicitrelationshipbetweenP(g;q)andfig.Theparametricmethodisasub-optimalmethod.Likelinearminimum-mean-square-error(MMSE),whichonlygivesoptimalsolutioninthelinearsub-space,weassumeP(g;q)hascertainstructure,andsolve( 5{24 )inthatsub-space. Werstassume 102

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Thechannelgaingiscontinuous,withoutknowingtheexactexpressionoff(g),westillcannotndtheprobabilitiesin( 5{12 ).Thereforeweneedtomakeassumptionsabouttheformoff(g).f(g)isexpectedtohaveoptimalperformancefordelayconstrainedcommunications.Considertwoextremecases,Dmax=1(M=1)andDmax=0(M=0).TheTDWFandTCIpowercontrolareknowntobeoptimalinthesetwocases,respectively.f(g)shouldhaveageneralformwhichincludesTDWFandTCI.Thereforeweassume where=[1;2;g0]T.Byproperlychoosingparameters1,2,g0,f(g;)in( 5{26 )canbeconguredintothreewidelyusedpowercontrolschemes,i.e.,TDWF,TCIandCONST,aslistedinTable 5-1 Table5-1. Congurationoff(g). 0 0 CONST TDWF 0 TCI Changingthevaluesof1,2andg0givesafamilyofpowercontrolschemeswhichliebetweenTDWFandTCI.Substituting( 5{25 )into( 5{23 ),theaveragepowerconstrainedis 103

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Averagef(g)overggives where0(x)istheupperincompletegammafunctiondenedas 0(x)=Z1xet ThenonnegativeconstraintP(g;q)0impliesH0andf(g;)0.Thecutothresholdg0isalwaysgreaterthanorequaltozero.Solvingforf(g;)0yields Noticethatwhen2<0,12 NowwewillderivetransitionprobabilitymatrixPasafunctionofHand,denotedasP(H;).Substitute( 5{26 )and( 5{25 )into( 5{13 )(assumeg0=0),andrewritesasafunctionofgandq, Llog2(ea1(q)g+ea2(q))c;(5{33) 104

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5{33 )isanincreasingfunctionofg.Theminimumchannelgainfortransmittingxpacketsis ~a1(q)(2xL TbB~a2(i))00,thechannelgainboundariesofkixareamendedaccordingtotherelativevaluebetweeng0andfb(i)xg Substituting( 5{36 )into( 5{15 )and( 5{16 ),weobtainthetransitionprobabilitymatrixP(H;). 105

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minH;Pdrop=1 Thenumericalsolutioncanbefoundbysequentialquadraticprogramming(SQP)method[ 67 ,page576].ThesimulationresultsofSQLAaredemonstratedinsection 5.5 106

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minfP(g;q)gMXq=0qEg[P(g;q)] (5{38a)s:t:=P (5{38c)P(g;q)0: TheconstraintM=Dmaxand=0areomittedsincetheparameterMandcanbeviewasxedparameters.Theconstraint( 5{38c )isrelatedtothetransmissionpowerby( 5{12 ),( 5{13 ),and( 5{14 ). Noticethatthequeuelengthqtakesonlydiscretevalue,thetransmissionpowerP(g;q)canberepresentedbyasetofcontinuousfunctionsfPq(g)g,q=0;1;:::;M.Theobjectivefunction( 5{38a )canberewrittenas ForagiventransitionprobabilitymatrixP,thesteadystatequeuelengthdistributionfqgisuniquelydetermined.ThereforefqgcanbeviewedasxedparametersasP.Inaddition,thei-throwofPisuniquelydeterminedbyPi(g)andisirrelevanttoPk(g),k6=i.Thereforeminimizingthesummationin( 5{39 )isequivalenttoindependentlyminimizingEg[Pq(g)]foreachq2[0;1;:::;M], minfPq(g)gEg[Pq(g)]s:t:pi;j=Prob[q(n+1)=jjq(n)=i]Pq(g)0:(5{40) DenotePq(g)thesolutionof( 5{40 ).Noticethateachtransmissionpowerisassociatedwithonemaximumtransmissionrate(packetsperblock)andviceversa. 107

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~Pi(g)=A(i) whereA(i)=2iL WTb1,i0.Pq(g)mustbeacombinationofregionsof~Pi(g),i=[0;1;:::;min(q+;M)].Asetof~Pi(g)curvesandanexampleofPq(g)areshowninFig. 5-3 DenotefR(q)igthefadingregionswherethetransmissionrateisipacketsperblockandthequeuelengthequalstoq.R(q)iTR(q)j=fori6=j,andSmin(q+;M)i=0R(q)i=[0;+1).Pq(g)canberepresentedby where1(x)=1iftheconditionxistrue,and1(x)=0otherwise.Substituting( 5{42 )intoEg[Pq(g)],theaveragepoweris From( 5{7 ),thetransitionprobabilityp(q;j)is 108

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5{40 )isturnedintooptimizationovertheregionsfR(q)ig Figure5-3. ExampleofPq(g),q=0,=4. Withoutlossofgenerality,theregionR(q)imaynotbecontinuous.Forexample,R(q)i=[3;5)S[7;10).Weprovethatintheoptimalsolution,eachregionfR(q)igisacontinuousset,andtheregionsspanfromlefttorightontherealaxisastheregionindexigrowsfrom0tomin(q+;M). 109

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P(j;i)ifijand0g1
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FromLemma 5.1 ,ifwealterthesub-regionsuchthat[g1;g02)2Rj,[g2;g3)2Ri,theaveragepowerwillbereduced.Thenewregionsetcontainssub-regions[g1;g02)2Rj,and[g02;g3)2Ri.From( 5{50 ),pq;iandpq;jremainsunchanged.Thereforethenewregionsetisafeasiblesolutionandyieldssmalleraveragepower.Thiscontradictstheassumptionthattheoriginalregionsetistheoptimalsolution.Thereforealltheregionsarecontinuousandspanfromlefttorightonthepositiverealaxisastheregionindexincreases. Iftheprobabilityofsub-region[g1;g2)issmallerthan[g2;g3),sameresultcanbeobtainedbyndingg02betweeng2andg3,whichsatises Therestoftheproofisthesameasintherstcaseandisomittedhere. Sinceallthefadingregionsarecontinuousandspanfromlefttorightonthepositiverealaxisastheregionindexincreases,eachfadingregioncanberepresentedbyR(q)i=[g(q)i;g(q)i+1)and0=g(q)0g(q)1:::gqmin(q+;M)gqmin(q+;M)+1=1.Using( 5{44 ), Proposition 5.1 givesthesolutiontotheoptimizationproblem( 5{40 ).NowwedenotetheoptimalsolutionasfPq(g;P)gtoemphasisthatthepowercontroldependsonthetransitionprobabilitymatrixP. 111

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5{24 ),thefeasibleregionisasubspaceofpowercontrolschemeP(g;q).Allthepowercontrolschemesinthefeasibleregionsatisfytheaveragepowerconstraint.Inthissection,westudytheoptimizationprobleminthespaceoftransitionprobabilitymatrixes.Themappingfromthetransitionprobabilitymatrixspacetothepowercontrolspaceisnotonetoone.Aswehaveseeninthepreviousproofs,multiplepowercontrolschemesmayresultthesametransitionprobabilitymatrix.However,thosepowercontrolschemeshavedierentaveragepowers.Nowweneedtomapthefeasibleregionfromthepowercontrolschemespacetothetransitionprobabilitymatrixspace,andsearchfortheoptimaltransitionprobabilitymatrixwhichminimizesthepacketdroppingprobabilitywithinthefeasibleregion.Thisisthefunctionofthesecondsub-problem, minPPdrop=1 (5{53a)s:t:MXl=0lEg[Pl(g;P)]P0 Thelastthreeconstraints( 5{53d ),( 5{53e ),( 5{53f )aretheconstraintsonthevalidityofthetransitionprobabilitymatrix.Therstconstraint( 5{53b )givesthefeasibleregion,i.e.,atransitionprobabilitymatrixisfeasibleifthepowercontrolschemewhichyieldsthesmallestaveragepowersatisestheaveragepowerconstraint.ThefollowingLemmaprovesthat( 5{53 )isequivalentto( 5{24 ). 112

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5{24 ),Ptheoptimalsolutionto( 5{53 ).ThenthepowercontrolschemefPq(g;P)gyieldsthesamepacketdropprobabilityasP0(g;q). 5.2 ,seeAppendix A.4 Asinsection 5.2 ,thesecondsub-problemissolvedbytheSQPmethod. 5{53 )isontheorderofO(M2).AndthenumberofelementsintheHessianmatrixisontheorderofO(M4).ForlargeM,thecomputationalcomplexityinSQPmethodistoohigh.Inaddition,exceptforthenumericalresults,wedonotknowanystructuralinformationaboutthepowercontrolscheme.Tothisend,weusethesteadystatequeuelengthdistributionastheoptimizationparameter,insteadofP,andre-solve( 5{24 ).Thestrategyissimilarasinsection 5.3 .Theoriginaloptimizationproblemisdecomposedintothreesub-problems.Therstoneisthesameas( 5{38 ),foragiventransitionprobabilitymatrixP,ndtheoptimalpowercontrolschemePq(g;P)whichminimizestheaveragepower.Thesecondsub-problemndstheoptimaltransitionprobabilitymatrixP,foragivensteadystatequeuelengthdistribution,whichminimizestheaveragepower, minPMXi=0iEg[Pi(g;P)] (5{54a)s:t:=P DenoteP()thesolutionto( 5{54 ). 113

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minPdrop=1 Denotethesolutionto( 5{55 ).TheoptimalpowercontrolisfPq(g;P())g.UsingthesamestrategyasinprovingLemma 5.2 ,wecanprovethatfPq(g;P())gyieldsthesamepacketdropprobabilityasP0(g;q).ThusfPq(g;P())gistheoptimalsolutionto( 5{24 ). Therstproblemhasbeensolvedinsection 5.3 ,andthethirdproblemcanbenumericallysolvedbySQPmethod.Wewillfocusonsolvingthesecondproblem. 5{54d )and( 5{54e ) whereL(i)=min(i+;M)isthecolumnindexoftherightmostnonzeroentryofthei-throwofP.TherearetotallyPMi=0L(i)independententriesinmatrixP.DenoteU(j)=max(j;0)therowindexoftheuppermostnonzeroentryofthej-thcolumnofP.ItiseasytondthatU(L(i))=iandL(U(j))=j.Wecanrewrite( 5{54 )as(thedependentparameterspi;0areexcluded) 114

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(5{57c)L(i)Xj=1pi;j1;8i: Thefeasiblesetforpi;j,i=0:::M,j=1:::L(i)islinearandconvex.Nowwewillprovethattheobjectivefunctionisalsoconvexonpi;j,i=0:::M,j=1:::L(i),ifA(k)A(k1)>0,k1. 5.3 ,seeAppendix A.5 5.4 ,seeAppendix A.6 Proof.

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5.2 showsthattheobjectivefunction( 5{57a )isconvex.Thefeasiblesetofpisalsoconvex.WecanuseLagrangianmethodtondtheglobaloptimalsolution.Theboundaryconditions( 5{57c )and( 5{57d )makethesolvingprocedurecomplicated.Werstremovethesetwoconditionsandsolveasimpleoptimizationproblemwithonlyequalconstraint minpPavg(p)=MXi=0iki(pi) (5{60a)s:t:MXi=U(j)ipi;j=j;j=1;2;:::;M: Thenusethesolutiontoconstructthesolutionto( 5{57 ). FormtheLagrangianfunction where=[1;2;:::;M]T.DierentiateJ(p;)w.r.t.pi;jandsetthederivativetozero, @pi;jJ(p;)=iL(i)Xk=L(i)j+1B(k) Weobtain 116

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where0isassumedtobezero.From( 5{48 ), Substituting( 5{65 )into( 5{60b ), Sumupfrombothtwosidesofequation( 5{66 ), Changetheorderofsummation,therighthandsideof( 5{67 )is Substituting( 5{68 )and( 5{64 )into( 5{67 ) where 117

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5{69 ).Wecansolve( 5{69 )foreachk,andgetpi;jby( 5{65 )and( 5{64 ). 5.5 ,seeAppendix A.7 .Let^pi;jbetheoptimalsolution. ^pi;j=FCH(B(L(i)j)yj+1)FCH(B(L(i)j+1)yj):(5{71) Particularly,whenj=M,B(L(i)j)=B(MM)=0.WedonotneedtocalculateyM+1,whichdoesnothavedenitionaccordingto( 5{69 ). Wehavefollowingobservationsabout^pi;j. (2) (3) IfB(k+1)=B(k)=c,k1,wherecisaconstant,^pi;jhasthesamesignforeachcolumnjexceptfortheuppermostelementpU(j);j,j2[;M]. (4) 5.6 ,seeAppendix A.8 5{57 )from^pi;j.FromLemma 5.6 ,( 5{57d )isalwayssatised.Weonlyneedtoconsiderconditionpi;j0;i=0:::M;j=1:::L(i).Werstconstructtheoptimalsolutionforaspecialcasewhereonlyonecolumn^pi;j0<0(exceptfortheuppermostelement^pU(j0);j0).Thengeneralizetheresulttoothercases. 1. Onlyonecolumn^pi;j0<0(exceptfortheuppermostelement^pU(j0);j0). 2.

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5{54 )canbeobtainedasfollows.Letj1=max(j:FCH(B(L(i)j0)^yj0+1)FCH(B(L(i)j+1)^yj)0;j2[1;2;:::;j01]): ToproveProposition 5.3 ,werstproveLemma 5.7 andLemma 5.8 (2) 5.7 ,seeAppendix A.9 (2) 5.8 ,seeAppendix A.10 119

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ProofofProposition 5.3 whereisamatrixwithelementsi;j.Theoptimalsolutionshouldsatisfy @pi;jJ(p;;)=0 (5{77a)MXi=U(j)ipi;j=j (5{77c)i;jpi;j=0 (5{77d)i;j0: FromLemma 5.8 ,pi;j0,( 5{77c )issatised.Alsopi;j=0intheregionR3.Leti;j=0outsideR3,( 5{77d )issatised. DierentiateJ(p;;)w.r.t.pi;jandsetthederivativetozero @pi;jJ(p;;)=iL(i)Xk=L(i)j+1B(k) 120

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5{63 )to( 5{68 ),weobtain where And Satisfying( 5{77a )and( 5{77b )isequivalenttosatisfying( 5{79 )and( 5{81 ). Compare( 5{70 )( 5{67 )with( 5{80 )( 5{79 ),sincei;j=0outsideR3,forj2[1;:::;j1]S[j0+2;:::;M]andalli2[U(j);:::;M] Whenj=j0+1, where(a),(b)and(c)arebecauseof( 5{73 ),( 5{71 )and( 5{82 )respectively.Let 5{81 ).Henceallpi;jinR1,R2andR5(from( A{50 ))satisfy( 5{81 ). InR3,pi;j=0.For( 5{81 )tobesatised,wehave whichyields 121

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(a)holdsbecauseof( A{46 ).Sumup( 5{87 )and( 5{74 ), Compare( 5{88 )and( 5{79 ),wehave Insummary,if 5{77a )and( 5{77b ). Nextwewillprovethatthereexisti;j0,(i;j)2R3fory(i)jgivenin( 5{90 ),suchthat( 5{77e )issatised.Thesei;jwilleecty(i)jinregionR3andy(i)j0+1. From( 5{80 ),for8(i;j)2R4, Whenj=j1+1,substituting( 5{80 )into( 5{90 ), 122

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5{72 ),andLemma 5.7 .( 1 ),for8(i;j)2R4 Thereforei;j1+1>0.Similarly,whenj2[j1+2;:::;j0], NoticethatB(k+1)=B(k)=c,i;j1+1andhenceallotheri;jareirrelevanttoi.Thisisconsistentwith( 5{84 ),whichimplies ^yj0+1+j0j0+1:(5{95) 5.3 givesthesolutionwhenonlyonecolumn^pi;j0<0.Compare^pi;j0andpi;j,onlythecolumnsfromj1toj0arechanged.Theitemsintherestofthecolumnsarekeptunchanged.Werewritethecolumnsj1toj0ofpi;jas whereyj(j0)isobtainedby 123

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Ingeneral,theremaybemorethanonecolumnof^pi;jthataresmallerthanzero.Denotethecolumnindexesasj01j1n,pi;j0i0.Thereforeweonlyneedtoupdatetheremainingcolumnsj0i0,gotostep26.Ends 5.2 ,thelastsub-problemisnumericallysolvedbytheSQPmethod.Withoutknowingtheexactlyexpressionof,wecanstillgetstructuralinformationabouttheoptimalpowercontrolschemefromtheresultofthesecondsub-problem. Werstconsiderthecasewhereall^pi;j>0.Inthiscase,pi;j=^pi;jandtheboundariesoffadingregionsR(i)jisobtainedbyg(i)j=B(j)^yL(i)j+1.WheniM,g(i)jhasthesamevalueforeachj.Thatis,thepowercontrolschemeisthesamewhen 124

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5-4 showsanexampleofchannelgainregionsforM=9,=3.Theaxisofchannelgainisplottedinlogarithmscale.Thelinelinkingg(i)j,g(i+1)j+1,g(i+2)j+2,:::isastraightline. Figure5-4. Anexampleoffadingregionsoftheoptimalpowercontrolschemewhenall^pi;j0. Whennotall^pi;j>0,pi;jisobtainedfrom^pi;jbyalgorithmdescribedinTable 5-2 .Weareinterestedinthefadingregionboundariesg(i)j.Thereforewerewritethealgorithmintermsofy(i)j,asinTable 5-3 .Fig. 5-5 showsanexampleofoptimalfadingregionswhennotall^pi;j>0.Inthisexample,M=9,=3.^y7<^y8=candF(7)=5.Inthiscase,someelementsoftransitionprobabilitymatrixwillbezero. 5.5.1SQLAPowerControl 5-6 andFig. 5-7 illustratetwoexamplesofSQLApowercontrols,forstringentdelayconstraintandloosedelayconstraint,respectively.ThesimulationparametersandtheresultingpacketdropprobabilitiesarelistedinTable 5-4 andTable 5-5 ,respectively.When=25,thedelayboundisM==2blocks,andtheCGBpartofthepowercontrol 125

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Constructingyjfrom^yj. 1.k=M12.If^yk^yk+1=c,forcolumnk,y(i)k=^ykk=k1,gotostep53.Forj2[F(k)+1;:::;k],y(i)j=(yj(k)i2[U(j);:::;U(k)]B(L(i)j0) Figure5-5. Anexampleoffadingregionsoftheoptimalpowercontrolschemewhensomeofthe^pi;j<0. issimilartoTCI.Thequeuelengthdistributiondoesnothaveexponentialdecayproperty.Whilewhen=5,thedelayboundisM==10blocks,andtheCGBpartofthepowercontrolissimilartoTDWF.Thetaildistributionofthequeuelengthisapproximatelyexponential.Asacomparison,theTCIandTDWFpowercontrolfor=25and=5areillustratedinFig. 5-8 .TheyusethesameaveragepowerastheSQLApowercontrolscheme,respectively.Theresultingpacketdropprobabilityare0:07forTCIand0:14for 126

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Table5-4. SimulationparametersforSQLA. M 50 5 0.057 Table5-5. Simulationresults. 5 0.9e-3 1e-3 0.08(TCI) 0.14(TDWF) 5-9 throughFig. 5-11 illustratethreeexamplesofJQLApowercontrols,forstringent,moderateandloosedelayconstraint,respectively.ThesimulationparametersandtheresultingpacketdropprobabilitiesarelistedinTable 5-6 andTable 5-7 ,respectively.Whendelayconstraintisstringent,thepowercontrolschemesfordierentqueuelengthsaresimilarandhaveTCI-likeproperty.Thecutothresholdissmall.Thetransmittertendstotransmitevenisthechannelgainislow.Formoderateandloosedelayconstraint,Pq(g)behavesdierentlyfordierentqueuelengthes.Ingeneral,whenqlengthissmall,Pq(g)issimilartoTDWFandwhenqislarge,Pq(g)issimilartoTCI.Whendelayconstraintisloose,thecutothresholdforsmallqissignicantlylargerthanthatwhendelayconstraintismoderateandstringent.Ittendstowaitforthebetterchannelstatetostarttransmission.LikeSQLA,theJQLApowercontrolsuccessfullysuppressestheprobabilityofthelastqueuestates,henceproducesalowerpacketdropprobability.ComparingTable 5-4 andTable 5-6 ,JQLAismorepowerecientthanSQLA. 127

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B C D SQLA,=25,M=50. A .f(g)ofSQLApowercontrol; B .H(q)ofSQLApowercontrol; C .SQLApowercontrolasafunctionachannelgainandqueuelength; D .QueuelengthdistributionofSQLApowercontrol. Fig. 5-12 throughFig. 5-14 comparethepacketdropprobabilityoftheproposedJQLApowercontrolwithTDWF,TCI,HQLA/TDWF,HQLA/TCI,SQLA,HQLA/SQLArespectively. Table5-6. SimulationparametersforJQLA. M 50 5 10 10 5 0.14 0.046 128

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B C D SQLA,=5,M=50. A .f(g)ofSQLApowercontrol; B .H(q)ofSQLApowercontrol; C .SQLApowercontrolasafunctionachannelgainandqueuelength; D .QueuelengthdistributionofSQLApowercontrol. Table5-7. SimulationresultsforJQLA. 10 5 0.78e-3 1e-3 129

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B C D TCIandTDWFpowercontrol. A .P(g;q)ofTCIpowercontrol,=25; B .QueuelengthdistributionofTCIpowercontrol; C .P(g;q)ofTDWFpowercontrol,=5; D .QueuelengthdistributionofTDWFpowercontrol. B JQLApowercontrol,=25,M=50. A .P(g;q)ofJQLApowercontrol; B .QueuelengthdistributionofJQLApowercontrol. 130

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B JQLApowercontrol,=10,M=50. A .P(g;q)ofJQLApowercontrol; B .QueuelengthdistributionofJQLApowercontrol. B JQLApowercontrol,=5,M=50. A .P(g;q)ofJQLApowercontrol; B .QueuelengthdistributionofJQLApowercontrol. parametersareoptimizedtominimizethepacketdropprobability.SQLAissuboptimalinthatitimposesformulationassumptionsonthepowercontrolscheme.Tondoptimalsolution,wedecomposedtheoriginaloptimizationproblemintothreesub-problems.Insteadofsearchingfortheoptimalpowercontrolschemedirectly(whichisimpossiblebecauseofthelackofclosedformexpressionoftheobjectivefunction),wesequentiallylookfortheoptimalqueuelengthdistribution,transitionprobabilitymatrix,andnallytheoptimalpowercontrol.Itisprovedthattheproposedmethodgivesthesameoptimalsolutionastheoriginalproblem.SQLAandJQLApowercontrolsuccessfullysuppressthe 131

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Packetdropprobabilityv.s.averagepower.=25,M=50. Figure5-13. Packetdropprobabilityv.s.averagepower.=10,M=50. 132

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Packetdropprobabilityvs.averagepower.=5,M=50. probabilityofthelastqueuestates,andhenceproducesalowerpacketdropprobabilitythanCGBpowercontrol.JQLAismoreecientthanSQLAbecauseitdoesnotimposeanyassumptionsontheformulationsofthepowercontrolscheme. 133

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InthischapterweapplyJQLApowercontrolderivedinChapter 5 toapracticalsystemwithadaptivemodulation.ThepowercontrolschemediscussedinChapter 5 minimizesthepacketdropprobabilitybyadaptingthetransmissionpowertothechannelgainandthequeuelengthinthebuer.WeuseShannon'scapacityformulatorelatethetransmissionpowerandrate.UsingShannon'scapacityleadstotwogoodpropertieswhichmaketheanalysissimple 1. Powercontrolisequivalenttoratecontrol. 2. Thepacketerrorrate(PER)duetochannelattenuation,thermalnoiseandinterferencesisassumedtobezero.Packetslossissolelycausedbypacketdrop. However,Shannon'scapacitydenedasthemaximummutualinformationbetweenthetransmitterandreceiverisanidealupperboundontheachievablerate,whichdosenottakeintoconsiderationofanyimplementationissues,suchasthespecicmodulationandcodingschemes.Toachievethismaximumcapacity,onemayneedarbitrarylongcodewordandsophisticateddecodingtechniques.Thearbitrarylongcodewordleadstoarbitrarylongdecodingdelay,whichisnotapplicableforreal-timeapplicationswithstringentdelay.Inaddition,PERcannotbeassumedtobezeroinapracticalsystem.ThevalueofdesirablePERishighlyservice-typedependent.Forexample,thevoiceapplicationscansustainarelativelyhighPERwhileletransferapplicationshaveaverystringentPERrequirement.ThedesignerofapracticalsystemmustincorporatethespecicmodulationandcodingschemeswiththeQoSrequirements. Therestofthechapterisorganizedasfollows.Section 6.1 introducestheadaptivetechniques.Section 6.2 reviewstheadaptivetechniquesintheareaofcrosslayerdesign.Section 6.3 discusseshowtoapplyJQLApowercontrolschemeinapracticalsystemandillustratethesimulationresults.Section 6.5 summariesthechapter. 134

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68 ],[ 69 ],and/orpower[ 70 ],[ 71 ],[ 72 ]accordingtochannelstate.Therearemultiplewaystovarythetransmissionrate,suchaschangingthesymbolrate[ 73 ],constellationsize[ 74 ],codingrate[ 75 ],[ 60 ],oranycombinationsofthem[ 76 ],[ 77 ],[ 78 ],[ 79 ],[ 80 ].Changingthesymbolrateresultsinvariationofbandwidth,whicharisesdesignproblemsformanycommunicationsystemswithxedbandwidth.Thereforechangingtheconstellationsizeandcodingratearemostwidelystudiedandusedtechniques. TheadaptivetechniquewasrstpresentedbyHayes[ 81 ]inlate1960's.Anidealfeedbackchannelisassumedtobeavailablebetweenthereceiverandthetransmitter.Channelstateperfectlyestimatedbythereceiverisconveyedtothetransmitterwithoutdelayanderror.Thetransmitteradjustthepowerlevelaccordingtothechannelstatesuchthattheerrorprobabilityisminimized.Theadaptivetechniquesdidnotholdmuchattractionintheearlyyearsbecauseoftheimplementationcomplexityissues.Forexample,thelackofaccuratechannelestimationtechniquesandreliablefeedbacklinks.Thehardwaredesignisalsochallengingbecauseadaptivetechniquesrequireboththetransmitterandreceiversupportasetofmodulation/codingschemes(andalsorapidlyswitchingbetweenthem),orrequirethatthetransmittercanaccuratelycontrolthepowerlevel.Intherecentyears,therapidlygrowingdemandformobileandpersonaldata-intensiveservicesmakesthespectraleciencyabottleneckforbandlimitedcommunicationsystems.Anon-adaptivesystemmustbeproperlydesignedsuchthatitcansurvivetheworstcasechannelconditions.Inmoderateorbetterchannelconditions,suchsystemswillwastealotofresourcesandbecomeveryinecient.Thereforetheadaptivetechniqueshaveregainedextensiveinterests,especiallyintherecentdecade. 135

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82 ],[ 83 ],WiMAX[ 84 ],[ 85 ],WiFi[ 86 ],3GPPLTE[ 87 ],GeneralSwitchedTelephoneNetworks(GSTN)[ 88 ],AsymmetricDigitalSubscriberLines(ADSL)[ 89 ],VerySmallApertureTerminals(VSAT)[ 90 ],CDMAmobilesatellitelinks[ 91 ]etc.. Asaphysicallayertechnique,AMisprimarilyusedtooptimizephysicallayerperformancessuchasBERorspectraleciency(bits/sec/Hz).ThekeystepinAMCistondtheoptimalsegmentationsofchannelgainandassignappropriatetransmissionrateand/orpowerforeachsegment.In[ 54 ],ajointvariable-ratevariable-powerMQAMmodulationschemeisstudiedtomaximizethespectraleciencysubjecttoaconstantBERconstraint.Thecontinuousspaceofchannelgainispartitionedintoseveralmutualexclusiveregions,calledfadingregions. EachfadingregionisassignedwithasquareQAMconstellationandpowerlevelsuchthataxedtargetBERcanbesatised.Theconstellationsizedeterminesthespectraleciencyofeachfadingregion.Thetotalspectraleciencyisobtainedbyaverageoverallfadingregions.Theadaptationstrategyusedin[ 54 ]isacounterpartofthetheoreticaloptimalpoweradaptationschemederivedin[ 15 ],whichuseShannon'scapacityformulatocalculatethespectraleciency.ThereisanapproximatelyconstantSNRgapbetweenthespectraleciencyachievedbyAMandthetheoreticalcapacitybound.AndthegapisuniquelydeterminedbythetargetBER.Thisnearconstantgapistheperformancedegradationcausedbythespecicmodulationtechniques.ForagiventargetBER,therearemultiplecombinationsofconstellationsizesandpowerlevelstochoose.AMassigntheoptimalcombinationsforeachfadingstate.However,theresearchin[ 79 ]showsthatadaptingonlyoneparameter,eithertransmissionpowerorrate,andxingtheotheronewillachievecomparableperformanceastothejointadaptationsystem.Thisobservationwillgreatlysimplifythecomplexityofanadaptivesystem. 136

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92 ],across-layertechniquecalledNetworkUtilityMaximization(NUM)/AMwasintroducedtointegratethemismatchbetweentheperformanceofphysicallayerandnetworklayer.Theoptimizationparameteristheutilityfunctionwhichcharacterizesthedemandofnetworkprotocolsorapplications.Theoptimaltransmissionrateandpowerpolicythatmaximizethetimeaverageoftheutilityfunctiondiersfromtheirphysicallayercounterpart,TDWF,inthattheratetendstobemoreequalovervaryingfadingconditions. In[ 93 ]theNUM/AMwasextendedtondtheoptimalpolicywithoutexplicitknowledgeofthechanneldistribution.Thetimeaverageutilityfunctionismaximizedoverthearrivalrateandtransmissionpower.TheoptimizationproblemissolvedbytheLagrangemethod.TheLagrangemultipliersareupdatedineachtimeslotbasedontheinstantaneouschannelgain,averagepowerconstraintandstablequeuingsystemconstraint.Byproperlychoosingtheupdatestepsize,theLagrangemultiplierscanbeinterpretedasproportionaltothequeuelengthandaveragepowerconsumption.Andtheywilleventuallyconvergestothesaddlepointandrandomlydriftarounditduetochannelvariations.Theresultingpowercontrolpolicyhasa\waterlling"likeexpression.Itbalancesthetransmissionpowerandqueuelengthbyexploitingatime-varyingthresholdinsteadofaxthresholdasinthephysicallayeroptimalpowercontrolscheme[ 15 ].Thethresholddecreases(thustheprobabilityofceasetransmissionalsodecreases)iftheenergynormalizedqueuelengthislargeandviceversa,matchingintuition. Thesystemmodelusedin[ 93 ]assumesinnitesizebuerandnopacketdrop.Asmentionedinchapter 5 ,buersizeisalwaysniteandpacketdropisinevitable.In 137

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Anitebuersizequeuingmodelisconsideredin[ 94 ],wherethepacketdroprate(PDR)andPERareconsideredsimultaneously.Theadaptivetechniquein[ 94 ]isconstant-power,variate-rate(bychangingtheconstellationofMQAMmodulation).EachtransmissionrateisassociatedwithafadingregionsuchthattheaveragePERwithinthefadingregiondoesnotexceedthetargetPER.ThePDRofthequeuingsystemiscalculatedbyMarkovchainmodelanalysis,similartotheanalysisweusedinthepreviouschapters.EachtargetPERisassociatedwithaPDR.Thetotalpacketlossrate(PLR)is PLR=1(1PDR)(1PER):(6{1) TheoptimalsystemoperatingpointischosenattheminimumPLRpoint.Therate-controlschemeusedin[ 94 ]consideredthetrade-obetweenthePERandPDR,butdoesnotaddressthebalancebetweenthequeuelengthandrateasin[ 93 ].Theratecontrolpolicyisthesameforallthequeuelengths. 94 ]and[ 93 ].AlltheassumptionsinChapter 5 areadoptedexceptforthezeroPERassumption.Nowthepacketlossconsistsofbothpacketdropandpacketerror.Thestrategyweusedinthis 138

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93 ]). Beforegettingintothedetails,weliststwomoreassumptionsaboutthesystem.First,allthepacketerrorscanbedetectedbyCRC.ThisisprovidedtrueifthepacketlengthisrelativelysmallandBERisnottoohigh.Secondly,weassumethereisnoretransmission.Thereasonforchoosingthisstrategyisbasedonthecharacterofreal-timeapplications.Forreal-timeapplications,thepacketswhicharrivebehindthemaximumdelayboundwillbeconsideredofno-use.Forexample,inavideochattingapplication,supposethemaximumdelayis100ms.Apacketarriveswith80msdelayisfoundtobeincorrectbyCRC.Ifwechoosetoretransmitthispacket,itishighlylikelythattheretransmittedpacketwillviolatethe100msmaximumdelaybound.Furthermore,theretransmissionwilloccupyadditionalresourcewhichmayoriginallyusedbythesucceedingpackets.Thiswillincreasethedelayboundviolationprobabilityforthesucceedingpackets.Theno-retransmissionassumptionisalsoutilizedinworks[ 94 ],[ 49 ],[ 93 ]. WeconsiderinstantaneousPERconstraint.Theoptimizationproblemis minP(n)Pdrops:t:AveragePowerP0P(n)0PER(n)D;(6{2) wherePER(n)isthepacketerroratblocknandDisthetargetPER.WeconsiderMQAMmodulationwithconstellationsizeM=2K,whereKisthebitspersymbol.The 139

PAGE 140

53 ,page180] M1)K2;andKiseven4 log2MQ(q M1)K2;andKisodd;(6{3) whereb(n)istheaverageSNRperbit, Solvingfor wegettheminimumtransmissionpowerfortransmittingatKbitspersymbol.Denote(K)bthesolutionfor( 6{6 ),from( 6{4 )theminimumpowerhastheform LetA(K)=K(K)b,comparewith( 5{41 ),wecandirectlyapplythederivationsinchapter 5 OneimportantpropertyweutilizedinthederivationsandproofsinJQLAisB(K+1)=B(K)=c,orequivalentlyA(K)/PKi=1ci.ThisrelationshipisapproximatelysatisedbyA(K).Fig. 6-1 illustratesA(K)anditscurvettingforK=1;2;:::;10,L=100andD=104.A(K)matchesthettedcurveverywellforK2.ForK=1(BPSK),thettedvalueisslightlylowerthanA(1).DenoteA0(K)thettedvalue.WewilluseA0(K)insteadofA(K)tocalculatingfadingregionandpowercalculation.Theactualpowerassumptionwillbeslightlyhigherthanthetheoreticalresult. 140

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Denotef(g)theCGBpowercontrolscheme.Theboundariesoffadingregionforeachmodulationisobtainedbysolvingthefollowingequation(CONSTandTDWF), Fig. 6-2 andFig. 6-3 illustrateoneexampleoftransmissionpowerofCONSTandTDWF,respectively. 141

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whereKristhetransmissionrate(bitspersymbol)andCisthethreshold.Theboundariesoffadingregionis Figure6-2. Constantpowercontrol,M=10,=5,PER=103. Fig. 6-4 throughFig. 6-7 illustratethePDRandPLRasafunctionofPER.Inallthesimulations,WTb=L=1,M=10, 142

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TDWFpowercontrol,M=10,=5,PER=103. PLRforeachpowercontrolschemes.ForallPERvalues,AM-JQLAachievesthelowestPDRandPLR.TDWFandCONSTpowercontrolschemehassimilarperformance.Thisbecausethefadingregionofthetwoschemesaresimilar,whichcanbeseenfromFig. 6-2 andFig. 6-3 .TCIhastheworstperformanceamongallthepowercontrolschemes. 143

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PDRvs.PER.=1,M=10. Figure6-5. PDRvs.PLR.=1,M=10. 144

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PDRvs.PER.=5,M=10. Figure6-7. PDRvs.PER.=5,M=10. 145

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146

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Thisdissertationexplorescross-layeroptimalpowerallocationschemesfordelayconstrainedcommunicationsoverwirelesslinks.Thechannelstateinformationisassumedtobeperfectlyandcausallyknownatthetransmitterside.Andthetransmissionpower(andalsothetransmissionrate)isadaptedtothesystemstatestoprovidedelay-relatedguarantees. Therearetwosystemmodelsfordelay-constrainedcommunications.Inapurephysicallayermodel,theproblemisformulatedastransmittingBbits(orpacket)withinMblocks,wherealltheBbitsinformationarereadyatthebeginningofthetransmission.Inalink-PHYlayermodel,whereatransmissionbuerandqueueareincorporated,thelastrequirementfortheinformationbitsisreleased.Theinformationtobetransmittedarrivesattransmittersidegradually,thusformsaarrivalprocess.Thedelayconstraintalsohasvariousinterpretations.Ingeneral,eachinformationbitmayhaveindividualdeadline,oronlytheaveragedelayareconsidered.Whenthearrivalprocesslastsnitetime,theproblemsofguaranteeingdelay-relatedconstraintsareusuallyreferredtoasschedulingproblem,i.e.,lazyscheduling. Wefocusonthecross-layersystemmodelwithinnitetime-horizon,constant-ratearrivalprocesses.Thesystemstatetowhichthetransmissionpoweradaptsconsistsofinstantaneouschannelgainandqueuelength(bueroccupancy).Thefadingprocessofthechanneliscontinuous.Allthedelay-relatedperformancesaremeasuredwhenthequeueenterssteadystate.Werstconsiderainnitesizebuermodelandthedelayconstraintisdelayboundviolationprobability.Eachbit(packet)isexpectedtobedeliveredwithinthedelayboundafteritsarrival.However,therandomnatureofthewirelesschannelmakesitimpossibleandthedelayboundviolationprobabilitybecomesanimportantQoSmeasure.Westudythepowercontrolschemewhichcanguaranteethedelayboundviolationprobabilitywhilemaximizingthesystemthroughput.Theproposed 147

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TheideabehindHQLApowercontrolisratherintuitivesinceitdoesnotintentionallycontrolthequeuelengthdistribution.ActuallythequeuelengthanddelaydistributionarethesameastheassociatedCGBpowercontrolscheme.Twopowercontrolschemes,SQLAandJQLA,whichintentionallycontrolthequeuelengthdistribution,wereproposedinChapter 5 .Thesystemmodelismodiedtonitesizebuer(buersizeisMpackets),andthedelayboundviolationprobabilityisequivalenttopacketdropprobabilityinthenewmodel.Thismodelismorerealisticsinceinpractice,thebuersizeisalwaysnite.Thetwoproposedpowercontrolschemesaimatminimizingthepacketdropprobabilitysubjecttoanaveragepowerconstraint.SQLAisasuboptimalsolution.ItusesM+4parameterstodescribethepowercontrolscheme,andassumesthatthechannelgainandqueuelengthcontributetothetotaltransmissionpowerseparately.JQLAistheoptimalsolution.Itisfoundbysequentiallysolvingasetofoptimizationproblems.BothSQLAandJQLApowercontrolreducetheprobabilityofthelastqueuestates,andhenceproducealowerpacketdropprobability. InJQLApowercontrol,thefadingregionforthelast+1queuelengthstatesarethesame.Andthebasicrelationshipoftheboundariesofthefadingregionsisg(i+1)j+1=cg(i)j.Thepowercontrolschemevariesfordierentdelayconstraintsandbueroccupancies.Whendelayconstraintisstringent,thepowercontrolschemesfordierentqueuelengthsaresimilarandhaveTCI-likeproperty.Thecutothresholdissmall.Thetransmittertendstotransmitevenifthechannelgainislow.Formoderateandloosedelayconstraints,Pq(g)behavesdierentlyfordierentqueuelengthes.Ingeneral,whenqissmall,Pq(g)issimilartoTDWFandwhenqislarge,Pq(g)issimilartoTCI.When 148

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Intheaforementionedpowercontrolschemes,weassumetheinstantaneouschannelcapacityisachievable,thereforeallthepacketlossesarecausedbypacketdrop.Inapracticalsystem,thepacketerrorduetochanneldistortionisinevitable.WecombineJQLApowercontrolwithadaptivemodulationtechniquesandstudythetotalpacketlossprobabilitysubjecttoinstantaneousPERconstraint,i.e.,theinstantaneousPERiskeptconstantatthereceiverside.AnoptimalinstantaneousPERvalueisfoundnumerically,wherethepacketlossprobabilityachievesitsminimum.TheJQLApowercontroloutperformstheCGBpowercontrolanddemonstratesthesuperiorityofthecross-layerpowercontrolschemes. 149

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3.1 3{22 ),theoptimizationfunctionisequivalentto minfPigEePNi=1Ris:t:NPi=1Pi=P10:(A{1) FormtheLagrangianfunction: Let`=BTb=(Nln2).Wehave ByKKTcondition,theoptimalsolutionmustsatisfy (A{4a)Pm0;m=1;2;:::;N From( A{4a ), whereA=QNi=1(1+iPi)`. 150

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A{4b )and( A{4c ),ifm2=1,thenm=0and Ifm=2=1,thenm0and Comparewith( A{6 ),itiseasytoseethatfor8i2=1and8j=2=1, Thereforewehave whereC=0 A{4d ) whichyields 3.2 3{26 )anddenoteCin( 3{26 )asC(N0),wehave Assume12:::N0(ifitisnot,wecansortthechannelgainsinascendingorder),andthereexistsjsuchthat 151

PAGE 152

From 3.1 ,theactivesub-channelsetcontainsthelargestN1sub-channelsand Noticethat1 From( A{13 ),forallmj1, Hencem=2=1. 5.1 Deneanewfunctionf0CH(x)=fCH(x)=K.f0CH(x)canbeconsideredastheprobabilitydensityfunctionontheregionsR1andR2respectively,because andf0CH(x)0. Denotey1=Rg2g11 and 152

PAGE 153

Substitutingy1;y2intoP(i;j), Sincei
PAGE 154

5{24 ),wehave 1 From( A{26 )and( A{27 ),wehave 1 5.3 DenoteCN=fCNgthesetofallpossibleCN.Supposedet(CN)>0,8CN2CN.ConsideranarbitrarymatrixCN+12CN+1.Subtracttherstcolumnfromthesecondtothe(N+1)-thcolumns,wehave 154

PAGE 155

Wehave det(CN+1)=det(C0N+1)=det(C00N+1)=a1det(eCN);(A{32) whereeCNisthesub-matrixbydeletingtherstrowandrstcolumnofmatrixC00N+1.ItiseasytoseethateCN2CN,thereforedet(CN+1)=a1det(eCN)>0. For8C12C1,det(C1)>0.Thereforedet(CN)>0holdsforallN. Denote(CN)i;jthesub-matrixbydeletingthei-throwandj-thcolumnfrommatrixCN.(CN)i;i2CN1,i2[1;2;:::;N].Thereforedet((CN)i;i)>0,andCNispositivedenite. 5.4 5.1 ,R(i)L(i)=[g(i)j;g(i)j+1).ki(pi)canberewrittenas where(x)=R1xfCH(g) 155

PAGE 156

From( 5{48 ),( 5{56 ) whereFCH(x)=R1xfCH(g)dgisthecomplementarycumulativedensityfunction(ccdf)ofchannelgain.Wehave @pi;m(1L(i)Xk=L(i)j+1pi;k)=1 Substituting( A{37 )into( A{35 ), whereB(j)=A(j)A(j1),j1.WeaddB(0)=0tosequencefB(k)g,whichwillsimplythesubsequentderivations.Denoteh(i)m;nthem-throwandn-thcolumn, 156

PAGE 157

(g(i)j)21(nL(i)j+1) (g(i)j)2fCH(g(i)j):(A{39) Itiseasytoseethath(i)m1;n1=hm2;n2(i)ifmin(m1;n1)=min(m2;n2),andh(i)m1;n1>h(i)m2;n2ifmin(m1;n1)>min(m2;n2).FromLemma 5.3 ,Hispositivedenite.Thereforeki(pi)isaconvexfunctiononpi. 5.5 0fk(x)MXi=U(k)i:(A{41) Because00. 5.6 5{48 ), (2)^pi;L(i)=1FCH(B(1)yj)>0. (3)IfB(k+1)=B(k)=c,fori>U(j),j0ifandonlyifyj+1=yj
PAGE 158

^pi;j=FCH(B(L(i)j)yj+1)FCH(B(L(i)j)cyj)0:(A{44) 5.7 5{66 )-( 5{68 ) Substituting( A{45 )into( A{46 ) (a)holdbecauseof( 5{72 ).Thereforewehave Noticethatfj(0)=0,thesolutionyjexistsand0
PAGE 159

Thereforeyj+10.Whenj=j1,fromLemma 5.7 .( 5.7 ), (a)holdsbecauseofthepropertyofj1.From( 5{72 ), FromLemma 5.7 .( 2 ),itiseasytoverifythatpi;j>0,j2[j1+1;:::;j01]. 159

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XiaochenLireceivedherB.S.andM.E.inelectricalengineeringfromPekingUniversity,Beijing,China,in2002and2005,respectively.ShereceivedherPh.D.inelectricalandcomputerengineeringfromUniversityofFlorida,Gainesville,FLinAugust,2009.Herresearchinterestsareintheareasofoptimalcrosslayerdesign,powercontrol,anddelay-constrainedcommunications. 168