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Utilizing Multiuser Diversity in Multicast Transmissions and Geographic Communications

Permanent Link: http://ufdc.ufl.edu/UFE0042537/00001

Material Information

Title: Utilizing Multiuser Diversity in Multicast Transmissions and Geographic Communications
Physical Description: 1 online resource (100 p.)
Language: english
Creator: CHOI,BYONGHYOK
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2011

Subjects

Subjects / Keywords: GEOGRAPHICTRANSMISSION -- MULTIUSERDIVERSITY -- NETWORKCODING -- OPPORTUNISITCRECEPTION -- SUPERPOSITIONCODING -- WIRELESSMESHNETWORK
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: Multipath propagation is a unique characteristic of wireless communication channels that causes signal level fluctuations called fading. Initially, the fading was considered an impairment to communications, but it has recently been shown that fading instead can be exploited to improve performance, especially in wireless networks. For example, in network with many communicators, there exist multiple communication links between radio nodes, and the different links experience different fading gains. At any instant time, it is likely that there is a pairs of radios that has a good channel quality. The probability of having such links increases with the number of radios in the network, thus achieving \emph{multiuser diversity} or \emph{network diversity}. We propose to develop new approaches to improve the performance by exploiting network diversity or multiuser diversity over a wireless fading channel. We propose the use of superposition coding that can be applied for the downlink transmission and a geographic transmission scheme for the uplink of wireless mesh or sensor networks. We first propose the use of superposition coding (SPC) over network coding for reliable multicast over time-varying fading channels. Two-level SPC is utilized in conjunction with two network-coded versions of the packets in order to take advantage of the diversity of fading gains that can exist during each message transmission. Through the use of SPC, a receiver who has good channel conditions can recover more copies of the network-coded packet. This approach can be utilized for the downlink transmission in wireless mesh network to improve the throughput performance. We compare the performance of reliable multicasting using network coding with and without 2-SPC. When the transmission rates of both messages in 2-SPC are equal to the transmission rate without SPC, and the rates are independent of the channel SNR, it is shown that 2-SPC may provide significant gains. However, when the communication parameters are optimized to maximize the multicasting throughput, 2-SPC shows little performance improvement over network coding without SPC. The results indicate that SPC is useful to improve the performance of network coding for reliable multicast if the transmission rates for the all of the message were fixed, and the channel statistics are not known exactly. Next, we consider the use of simulcasting by employing 2-SPC to deliver a mix of multicast and unicast traffic to receivers over fading channels when the transmitter has channel state information (CSI), which may be delayed. The CSI allows the transmitter to adapt the parameters of the SPC to provide additional messages to the receiver who is expected to have a better channel condition in the next time slot. We show that simulcasting can provide additional performance gains over using just network coding for several different cases where the source has exact or delayed knowledge of the channel state. In the third part of this work, we consider the uplink of wireless mesh or sensor networks. When the channels from the mobile radios or sensors, hereafter called ``nodes'', to the infrastructure nodes (the access points (APs) or sinks) suffer from fading, packet transmissions may need to be relayed through other nodes since direct transmissions to the APs may have a high probability of failure. We propose a geographic approach that can improve performance by using opportunistic reception, in which a relay is selected from those nodes that can receive the packet correctly and move it toward the AP. We assume that the packet may be delivered in at most two hops. We consider the design of a scheme to select which nodes should compete to relay the packet and how they should compete in a time-slotted protocol. We then show that this problem of relay selection can be cast as an optimization problem. The resulting protocol is called Geographic Transmission with Optimized Relaying (GATOR), we show that GATOR provides better performance gains than direct transmission, fixed routing, and other geographic transmission schemes. Finally, we study the use of multi-hop GATOR to improve throughput and energy efficiency for the uplink transmission in mesh networks in which APs are spare and the dimension of the network is large that the packet may need to be delivered in multiple hops between the source and the AP. We propose two multi-hop GATOR with fixed and non-fixed hop distance, and compared those performances with ones of 2-hop GATOR, multi-hop routing, and direct transmission. We show that the multi-hop GATOR with fixed optimal hop distance offers large performance gains over 2-hop GATOR, multi-hop routing, or direct transmission, especially when the dimension of the network is large and and APs are sparse.
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 BYONGHYOK CHOI.
Thesis: Thesis (Ph.D.)--University of Florida, 2011.
Local: Adviser: Shea, John M.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2011
System ID: UFE0042537:00001

Permanent Link: http://ufdc.ufl.edu/UFE0042537/00001

Material Information

Title: Utilizing Multiuser Diversity in Multicast Transmissions and Geographic Communications
Physical Description: 1 online resource (100 p.)
Language: english
Creator: CHOI,BYONGHYOK
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2011

Subjects

Subjects / Keywords: GEOGRAPHICTRANSMISSION -- MULTIUSERDIVERSITY -- NETWORKCODING -- OPPORTUNISITCRECEPTION -- SUPERPOSITIONCODING -- WIRELESSMESHNETWORK
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: Multipath propagation is a unique characteristic of wireless communication channels that causes signal level fluctuations called fading. Initially, the fading was considered an impairment to communications, but it has recently been shown that fading instead can be exploited to improve performance, especially in wireless networks. For example, in network with many communicators, there exist multiple communication links between radio nodes, and the different links experience different fading gains. At any instant time, it is likely that there is a pairs of radios that has a good channel quality. The probability of having such links increases with the number of radios in the network, thus achieving \emph{multiuser diversity} or \emph{network diversity}. We propose to develop new approaches to improve the performance by exploiting network diversity or multiuser diversity over a wireless fading channel. We propose the use of superposition coding that can be applied for the downlink transmission and a geographic transmission scheme for the uplink of wireless mesh or sensor networks. We first propose the use of superposition coding (SPC) over network coding for reliable multicast over time-varying fading channels. Two-level SPC is utilized in conjunction with two network-coded versions of the packets in order to take advantage of the diversity of fading gains that can exist during each message transmission. Through the use of SPC, a receiver who has good channel conditions can recover more copies of the network-coded packet. This approach can be utilized for the downlink transmission in wireless mesh network to improve the throughput performance. We compare the performance of reliable multicasting using network coding with and without 2-SPC. When the transmission rates of both messages in 2-SPC are equal to the transmission rate without SPC, and the rates are independent of the channel SNR, it is shown that 2-SPC may provide significant gains. However, when the communication parameters are optimized to maximize the multicasting throughput, 2-SPC shows little performance improvement over network coding without SPC. The results indicate that SPC is useful to improve the performance of network coding for reliable multicast if the transmission rates for the all of the message were fixed, and the channel statistics are not known exactly. Next, we consider the use of simulcasting by employing 2-SPC to deliver a mix of multicast and unicast traffic to receivers over fading channels when the transmitter has channel state information (CSI), which may be delayed. The CSI allows the transmitter to adapt the parameters of the SPC to provide additional messages to the receiver who is expected to have a better channel condition in the next time slot. We show that simulcasting can provide additional performance gains over using just network coding for several different cases where the source has exact or delayed knowledge of the channel state. In the third part of this work, we consider the uplink of wireless mesh or sensor networks. When the channels from the mobile radios or sensors, hereafter called ``nodes'', to the infrastructure nodes (the access points (APs) or sinks) suffer from fading, packet transmissions may need to be relayed through other nodes since direct transmissions to the APs may have a high probability of failure. We propose a geographic approach that can improve performance by using opportunistic reception, in which a relay is selected from those nodes that can receive the packet correctly and move it toward the AP. We assume that the packet may be delivered in at most two hops. We consider the design of a scheme to select which nodes should compete to relay the packet and how they should compete in a time-slotted protocol. We then show that this problem of relay selection can be cast as an optimization problem. The resulting protocol is called Geographic Transmission with Optimized Relaying (GATOR), we show that GATOR provides better performance gains than direct transmission, fixed routing, and other geographic transmission schemes. Finally, we study the use of multi-hop GATOR to improve throughput and energy efficiency for the uplink transmission in mesh networks in which APs are spare and the dimension of the network is large that the packet may need to be delivered in multiple hops between the source and the AP. We propose two multi-hop GATOR with fixed and non-fixed hop distance, and compared those performances with ones of 2-hop GATOR, multi-hop routing, and direct transmission. We show that the multi-hop GATOR with fixed optimal hop distance offers large performance gains over 2-hop GATOR, multi-hop routing, or direct transmission, especially when the dimension of the network is large and and APs are sparse.
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 BYONGHYOK CHOI.
Thesis: Thesis (Ph.D.)--University of Florida, 2011.
Local: Adviser: Shea, John M.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2011
System ID: UFE0042537:00001


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UTILIZINGMULTIUSERDIVERSITYINMULTICASTTRANSMISSIONSANDGEOGRAPHICCOMMUNICATIONSByBYONGHYOKCHOIADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOLOFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENTOFTHEREQUIREMENTSFORTHEDEGREEOFDOCTOROFPHILOSOPHYUNIVERSITYOFFLORIDA2011

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c2011ByonghyokChoi 2

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Tomyparentsandmywife. 3

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ACKNOWLEDGMENTS IamthankfultoaenrichingexperienceandpeoplehavinginspiredmeduringmyPh.D.attheUniversityofFlorida.Especially,IwouldliketoexpressmysincerestthankstomyadvisorDr.JohnM.Shea,forhisguidance,expertise,andcontinuedsupportandencouragement.Iamverygratefulfortheopportunitytohaveworkedwithhim.IthankDr.Wong,Dr.McNair,andDr.Barooahfortheirguidance,suggestionsandinterestinmywork.IthankmyfriendswhomademystayinGainesvilleenjoyable.SpecialthankstoRyanWongforthevaluablediscussions,andformakingmydaysatWINGmuchmoreenjoyable.Idedicatethisworktomyparentswhohavesupportedandtrustedme,andmywifewhohasbeenaconstantsourceofinspirationinmylife. 4

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TABLEOFCONTENTS page ACKNOWLEDGMENTS .................................. 4 LISTOFTABLES ...................................... 7 LISTOFFIGURES ..................................... 8 ABSTRACT ......................................... 11 CHAPTER 1INTRODUCTION ................................... 14 1.1SuperpositionCodingandLinearNetworkCodingforReliableMulticastoverFadingChannels ............................. 15 1.2SuperpositionCodingandNetworkCodingforMixedMulticast/UnicastTrafconaTime-varyingChannel ...................... 16 1.3GeographicTransmissionwithOptimizedRelaying(GATOR)fortheUplinkinMeshNetworksLimitto2-hop ....................... 17 1.4Multi-hopGeographicTransmissionwithOptimizedRelaying(GATOR)fortheUplinkinMeshNetworks ....................... 17 1.5OutlineofDissertation ............................. 18 2SUPERPOSITIONCODINGANDLINEARNETWORKCODINGFORRELIABLEMULTICASTOVERFADINGCHANNELS ..................... 20 2.1IntroductionofSuperpositionCodingandLinearNetworkCoding ..... 20 2.2MotivatingExample:Two-receivermulticastnetwork ............ 21 2.3SystemModel ................................. 23 2.4ReliableMulticastingwithFixedTransmissionRates ............ 26 2.4.1NetworkCodingWithoutSPC ..................... 26 2.4.2NetworkCodingwith2-SPC ...................... 26 2.4.3SimulationResults ........................... 29 2.5ReliableMulticastingwithOptimumTransmissionRates .......... 30 2.5.1ThroughputUnderNetworkCodingwithoutSPC .......... 32 2.5.2ThroughputUnderNetworkCodingwith2-SPC ........... 33 2.5.3SimulationsResults .......................... 34 2.6Summary .................................... 35 3SUPERPOSITIONCODINGANDNETWORKCODINGFORMIXEDMULTICAST/UNICASTTRAFFICONATIME-VARYINGCHANNEL .................... 36 3.1IntroductionofSuperpositionCodingandNetworkCodingforMixedMulticast/Unicast 36 3.2MotivatingExample .............................. 37 3.3SystemModel ................................. 39 5

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3.4SimulcastingandNetworkCodingtoReceiverswithDifferentChannelGains ...................................... 41 3.5SimulcastingandNetworkCodingovertheTwo-StateMarkovChannel .. 43 3.5.1CommunicationwithNoFeedback .................. 44 3.5.2CommunicationwithFeedbackwithNoDelay ............ 45 3.5.3CommunicationwithFeedbackDelayedbyOneTimeSlot ..... 45 3.5.4SimulationResults ........................... 47 3.6Summary .................................... 49 4GEOGRAPHICTRANSMISSIONWITHOPTIMIZEDRELAYING(GATOR)FORTHEUPLINKINMESHNETWORKS .................... 52 4.1IntroductionofGeographicTransmission ................... 52 4.2NetworkModel ................................. 54 4.3GeographicTransmissionwithOptimizedRelaying(GATOR) ....... 56 4.3.1OptimalRelayRegionsforaSingleSource ............. 58 4.3.2ExtensiontoMultipleSourcesandAPs ................ 64 4.4ComparisonTransmissionSchemes ..................... 65 4.4.1ConventionalSchemes ......................... 66 4.4.2GeographicTransmissionSchemes .................. 66 4.5SimulationResults ............................... 68 4.6Summary .................................... 76 5MULTI-HOPGEOGRAPHICTRANSMISSIONWITHOPTIMIZEDRELAYING(GATOR)FORTHEUPLINKINMESHNETWORKS ............... 78 5.1IntroductionofMulti-hopGeographicTransmission ............. 78 5.2NetworkModel ................................. 79 5.3Multi-hopGeographicTransmissionwithOptimizedRelaying(GATOR) .. 80 5.3.1Multi-hopGATORwithFullDesignDistance(mhGATOR-FDD) ... 82 5.3.2Multi-hopGATORwithIntermediateDesignDistance(mhGATOR-IDD) 84 5.4SimulationResults ............................... 86 5.5Summary .................................... 93 6CONCLUSIONS ................................... 94 REFERENCES ....................................... 96 BIOGRAPHICALSKETCH ................................ 100 6

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LISTOFTABLES Table page 4-1Parametersusedforcalculatingthroughputpenaltyofroutingandgeographictransmissionrelativetodirecttransmission. .................... 68 7

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LISTOFFIGURES Figure page 2-1Two-usermulticastnetworkwithandwithoutSPC. ................ 22 2-2MulticastnetworkwithKreceivers. ......................... 23 2-3ExpectednumberoftransmissionsforsuccessfulreceptionofapacketwithB=16. ........................................ 30 2-4ExpectednumberoftransmissionsforsuccessfulreceptionofapacketwithK=16. ........................................ 31 2-5Throughputcomparisoninamulticastnetwork. .................. 34 3-1Two-usersimulcast/multicastnetworkwithandwithoutSPC. .......... 38 3-2MulticastnetworkwithKreceivers. ......................... 39 3-3Two-stateAWGNchannel. .............................. 40 3-4Bestachievablethroughputsfortransmissionofmulticastandunicasttrafctotworeceiverswithdifferent,knownchannelstatistics. ............. 43 3-5Throughputgainof1-delayedfeedbackovernofeedbackforthevaluesofpgandpb. ........................................ 48 3-6Throughputcomparisoninasimulcastnetworkwith/withoutfeedbackchannelstateinformationwhenpg=pb. ........................... 49 3-7Throughputcomparisoninasimulcastnetworkwith/withoutfeedbackchannelstateinformationwhenpg6=pb. ........................... 50 4-1Exampleofmeshnetworklayoutwith9accesspoints.Ai=i-thaccesspoint. 55 4-2Structureofonetimeframefortheprotocolsinthischapter. ........... 56 4-3Pictorialdescriptionofoptimalforwardingresolutionprotocolingeographictransmission.Sr=sourcenode.A=accesspoint. ................ 63 4-4Throughputvs.numberofaccesspointsforvariousnumbersofforwardingregions,M.TheaverageSNRisS0=10dB,andthenumberofcarrier-reservationmini-slotsusedbysourcesisK=16.ForS-GeRaF,thebestcombinationofthenumberofforwardingregions(M=8)andthenumberofRTS/CTSslots(N=10)wasusedsee Figure4-5 ........................ 70 4-5ThroughputofS-GeRaFvs.numberofaccesspointsforvariousnumbersofforwardingregions,M,andRTS/CTSslots,N,forthecollisionavoidanceprotocol.TheaverageSNRisS0=10dB,andthenumberofcarrier-reservationmini-slotsusedbysourcesisK=16. .............................. 71 8

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4-6Throughputvs.numberofaccesspointsforvariousnumbersofcarrier-reservationmini-slotsusedbysources,K.TheaverageSNRisS0=10dB,andthenumberofforwardingregionsisM=32. ........................... 72 4-7Probabilityofpacketdropfromsourcereachingmaximumnumberoftransmissions(Ntx=4)vs.maximumdistancefromaccesspoint.NumberofAPsis4,theaverageSNRisS0=10dB,andthenumberofcarrierreservationmini-slotsusedbysourcesisK=16,thenumberofRTS-CTSslotsusedbyS-GeRaFis10,thenumberofforwardingregionsforS-GeRaFis8,andthenumberofforwardingregionsforGATORandGATOR-GBRRis32. ............. 73 4-8Probabilityofpacketdropfromsourcereachingmaximumnumberoftransmissions(Ntx=4)vs.numberofaccesspoints.TheaverageSNRisS0=10dB,andthenumberofcarrier-reservationmini-slotsusedbysourcesisK=16,thenumberofRTS-CTSslotsusedbyS-GeRaFis10,thenumberofforwardingregionsforS-GeRaFis8,andthenumberofforwardingregionsforGATORandGATOR-GBRRis32. ......................................... 74 4-9Throughputvs.numberofaccesspointsfordifferentvaluesoftheaverageSNRS0.Thenumberofcarrier-reservationmini-slotsusedbysourcesisK=16,andthenumberofforwardingregionsforGATORandGATOR-GBRRisM=32. 75 4-10Throughputvs.numberofaccesspointsfordifferentvaluesofthedensityofon-nodes,.TheaverageSNRisS0=10dB,thenumberofcarrier-reservationmini-slotsusedbysourcesisK=16,andthenumberofforwardingregionsforGATORandGATOR-GBRRisM=32. ....................... 76 4-11Energypersuccessfulpacket,Ep,vs.numberofaccesspoints.TheaverageSNRisS0=10,thenumberofcarrier-reservationmini-slotsforsources'transmissionisK=16,thenumberofRTS-CTSslotsusedbyS-GeRaFis10,thenumberofforwardingregionsforS-GeRaFis8,andthenumberofforwardingregionsforGATORandGATOR-GBRRis32. ........................ 77 5-1Structureofonetimeslotfortheprotocolsinthischapter. ............ 80 5-2Depictionofmulti-hopGATORwithFullDesignDistance(mhGATOR-FDD). .. 83 5-3Depictionofmulti-hopGATORwithIntermediateDesignDistance(mhGATOR-IDD). 85 5-4Depictionofmulti-hoproutingschemewithintermediatedesigndistance. ... 86 5-5ThroughputofGATORvs.dimensionofnetworkwithparameterdhop.S0=10dB,K=16,M=32,andNtx=8 ............................... 89 5-6Throughputofroutingvs.dimensionofnetworkwithparameterdhop.S0=10dB,K=16,andNtx=8 ................................... 90 5-7Throughputvs.dimensionofnetworkwhenS0=10dB,K=16,andNtx=8.ForGATOR,M=32 .................................... 90 9

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5-8Energypersuccessfulpacket,Epvs.dimensionofnetworkwhenS0=10dB,K=16,andNtx=8.ForGATOR,M=32 ....................... 91 5-9Averagenumberofhoppersuccessfulpacketvs.dimensionofnetworkwhenS0=10dB,K=16,andNtx=8.ForGATOR,M=32 .................. 92 10

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AbstractofDissertationPresentedtotheGraduateSchooloftheUniversityofFloridainPartialFulllmentoftheRequirementsfortheDegreeofDoctorofPhilosophyUTILIZINGMULTIUSERDIVERSITYINMULTICASTTRANSMISSIONSANDGEOGRAPHICCOMMUNICATIONSByByonghyokChoiMay2011Chair:JohnM.SheaMajor:ElectricalandComputerEngineering Multipathpropagationisauniquecharacteristicofwirelesscommunicationchannelsthatcausessignalleveluctuationscalledfading.Initially,thefadingwasconsideredanimpairmenttocommunications,butithasrecentlybeenshownthatfadinginsteadcanbeexploitedtoimproveperformance,especiallyinwirelessnetworks.Forexample,innetworkwithmanycommunicators,thereexistmultiplecommunicationlinksbetweenradionodes,andthedifferentlinksexperiencedifferentfadinggains.Atanyinstanttime,itislikelythatthereisapairsofradiosthathasagoodchannelquality.Theprobabilityofhavingsuchlinksincreaseswiththenumberofradiosinthenetwork,thusachievingmultiuserdiversityornetworkdiversity.Weproposetodevelopnewapproachestoimprovetheperformancebyexploitingnetworkdiversityormultiuserdiversityoverawirelessfadingchannel.Weproposetheuseofsuperpositioncodingthatcanbeappliedforthedownlinktransmissionandageographictransmissionschemefortheuplinkofwirelessmeshorsensornetworks. Werstproposetheuseofsuperpositioncoding(SPC)overnetworkcodingforreliablemulticastovertime-varyingfadingchannels.Two-levelSPCisutilizedinconjunctionwithtwonetwork-codedversionsofthepacketsinordertotakeadvantageofthediversityoffadinggainsthatcanexistduringeachmessagetransmission.ThroughtheuseofSPC,areceiverwhohasgoodchannelconditionscanrecovermorecopiesofthenetwork-codedpacket.Thisapproachcanbeutilizedforthedownlink 11

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transmissioninwirelessmeshnetworktoimprovethethroughputperformance.Wecomparetheperformanceofreliablemulticastingusingnetworkcodingwithandwithout2-SPC.Whenthetransmissionratesofbothmessagesin2-SPCareequaltothetransmissionratewithoutSPC,andtheratesareindependentofthechannelSNR,itisshownthat2-SPCmayprovidesignicantgains.However,whenthecommunicationparametersareoptimizedtomaximizethemulticastingthroughput,2-SPCshowslittleperformanceimprovementovernetworkcodingwithoutSPC.TheresultsindicatethatSPCisusefultoimprovetheperformanceofnetworkcodingforreliablemulticastifthetransmissionratesfortheallofthemessagewerexed,andthechannelstatisticsarenotknownexactly. Next,weconsidertheuseofsimulcastingbyemploying2-SPCtodeliveramixofmulticastandunicasttrafctoreceiversoverfadingchannelswhenthetransmitterhaschannelstateinformation(CSI),whichmaybedelayed.TheCSIallowsthetransmittertoadapttheparametersoftheSPCtoprovideadditionalmessagestothereceiverwhoisexpectedtohaveabetterchannelconditioninthenexttimeslot.Weshowthatsimulcastingcanprovideadditionalperformancegainsoverusingjustnetworkcodingforseveraldifferentcaseswherethesourcehasexactordelayedknowledgeofthechannelstate. Inthethirdpartofthiswork,weconsidertheuplinkofwirelessmeshorsensornetworks.Whenthechannelsfromthemobileradiosorsensors,hereaftercallednodes,totheinfrastructurenodes(theaccesspoints(APs)orsinks)sufferfromfading,packettransmissionsmayneedtoberelayedthroughothernodessincedirecttransmissionstotheAPsmayhaveahighprobabilityoffailure.Weproposeageographicapproachthatcanimproveperformancebyusingopportunisticreception,inwhicharelayisselectedfromthosenodesthatcanreceivethepacketcorrectlyandmoveittowardtheAP.Weassumethatthepacketmaybedeliveredinatmosttwohops.Weconsiderthedesignofaschemetoselectwhichnodesshouldcompetetorelay 12

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thepacketandhowtheyshouldcompeteinatime-slottedprotocol.Wethenshowthatthisproblemofrelayselectioncanbecastasanoptimizationproblem.TheresultingprotocoliscalledGeographicTransmissionwithOptimizedRelaying(GATOR),weshowthatGATORprovidesbetterperformancegainsthandirecttransmission,xedrouting,andothergeographictransmissionschemes. Finally,westudytheuseofmulti-hopGATORtoimprovethroughputandenergyefciencyfortheuplinktransmissioninmeshnetworksinwhichAPsarespareandthedimensionofthenetworkislargethatthepacketmayneedtobedeliveredinmultiplehopsbetweenthesourceandtheAP.Weproposetwomulti-hopGATORwithxedandnon-xedhopdistance,andcomparedthoseperformanceswithonesof2-hopGATOR,multi-hoprouting,anddirecttransmission.Weshowthatthemulti-hopGATORwithxedoptimalhopdistanceofferslargeperformancegainsover2-hopGATOR,multi-hoprouting,ordirecttransmission,especiallywhenthedimensionofthenetworkislargeandandAPsaresparse. 13

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CHAPTER1INTRODUCTION Wirelessmeshnetworks,designedtoprovidewirelesslast-mileaccess,haveseveraladvantagesincludinglowcost,robustness,andeasyandincrementaldeployment.Theseadvantagesmakeitoneoftheessentialtechnologiesinnextgenerationwirelesscommunicationnetworks.Wirelessmeshnetworkscanbeviewedasspecialcasesofwirelessadhocnetworks.Ontheotherhand,wirelesssensornetworks,composedofalargenumberofsensorsthataredenselydistributedtomonitoraphenomenon,havedrawnincreasingattentionduetotheirvarietyofapplicationsandlowcostsolutions. Werstconsidertechniquesthatcanbeappliedforthedownlinkofwirelessmeshorsensornetworks.Here,thedownlinkreferstoinformationowfromtheinfrastructurenodesorAPstotheothernodes.Forasensornetwork,thiscanbedeliveryofsensorcontrolinformationfrominfrastructurenodes(theinformationsinkscanservethisfunctionality)tothesensornodes.Forameshnetwork,thiscanbethedeliveryofdatafromAPs(base-stations)tothemobilenodes.Thedownlinktransmissionmayincludetrafctobemulticasttoagroupofnodesaswellasunicasttrafcintendedforspecicnodes. Inwirelessnetworks,sincethechannelsvaryrandomlybecauseoffadingandshadowing,whendownlinktransmissionsarebroadcastoverawirelesschannel,fadingcanresultinthemessagesonlybeingreceivedbyasubsetoftheintendednodes.Ithasbeenshownthatlinearnetworkcoding[ 1 2 ]canbeusedtoofferprotectionagainsttransmissionfailuresbyextractingdiversityacrossthenodesinthenetwork[ 3 5 ],whichwecallnetworkdiversity.Weproposesimpletwolevelsuperpositioncoding(2-SPC)alongwithlinearnetworkcodingtofurtherimprovetheperformancebytakingadvantageofthediversityoffadinggainsthatcanexistduringeachdownlinkmulticasttransmission.Inaddition,weproposetheuseofsimulcastingtodeliveramixofmulticastandunicasttrafctonodesbyemploying2-SPC.Inthislatterapproach, 14

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2-SPCsimulcastsmulticastmessagestoagroupofnodesandunicastmessagestoaspecicnodesimultaneously. Wenextfocusonuplinktransmission,inwhichagroupofnodeshavetheirowninformationtotransmittooneormoreAPs(orsinks).Wirelessmeshnetworkspresentchallengingproblemsinthedesignofnetworkprotocols:thefadingrateofthewirelesschannelsisusuallyhigherthantherateatwhichnetworkstateinformationisexchangedamongthenodes,andfornetworkswithmorethanafewtensofnodes,thenetworktopologymaychangeatafasterratethantheroutinginformationcanbepropagatedthroughthenetwork.Inadditiontotheseproblems,anothersevereproblemisthat,asthesizeofthenetworkgrows,theamountofprotocolinformationforatroutingincreasesquickly,andthuscontrolinformationdominatesthetrafcinsuchnetwork.Thus,conventionalroutingprotocolsthatarebasedonpre-determinedlinksandroutesexperiencehighratesofpacketfailure.Weproposethegeographictransmissionapproachesthatcanroutepacketsusinglocationinformation,evenwhentheunderlyingtopologyofthenetworkisrapidlychanging.Geographictransmissioncanalsoreducetheamountofcontrolinformationthatneedstobedistributedacrossthenetwork,andachievemultiuserdiversityagainstfading,becauseforwardingnodesforapacketareopportunisticallyselectedfromamongthosethatreceivethepacket.Previousschemesforselectingtheforwardingnode(orarelay)havebeenadhoc.Weformulatetherelay-selectionprobleminatime-slottedprotocolasanoptimizationproblemandnditssolution. 1.1SuperpositionCodingandLinearNetworkCodingforReliableMulticastoverFadingChannels Inmanywirelessnetworkapplications,communicationmessagesmustbemulticasttoagroupofreceivers.Whenthesetransmissionsarebroadcastoverawirelesschannel,fadingcanresultinthemessagesbeingreceivedbyonlyasubsetoftheintendedreceiversonanygiventransmission.Theconventionalapproachof 15

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retransmissionviaautomaticrepeatrequest(ARQ)resultsintheperformancebeingdominatedbythesinglereceiverthatexperiencestheworstpropagationconditionsforeachbroadcastpacket.Recently,ithasbeenshownthatlinearnetworkcodingcanbeusedtoreducetheaveragenumberoftransmissionsrequiredtodeliverthemulticastmessagebymakingitpossibleforareceivertorecoverBpacketsthatarecodedtogetheraftercorrectlyreceivinganyBtransmissions. InChapter 2 ,weproposetheuseofSPConthedownlinkofameshnetwork.Weconsidertransmissionofpacketizeddatainatime-slottedprotocol.Thefadingisassumedtobeindependentamongthereceivingnodesandacrosstimeslots.Thegoalistofurtherimprovetheperformancebytakingadvantageofthediversityoffadinggainsthatcanexistduringeachmessagetransmission.SPCisusedtosimultaneouslytransmitmultiplelinearnetwork-codedversionsofthepacketsduringeachtransmission.Thenumberofcopiesthataparticularreceivercanrecoverdependsonthereceiver'sfadingprocess:thebetterthechannelconditions,themorecopiesofthenetwork-codedpacketcanberecovered.WeshowthatbyappropriatelychoosingtheparametersoftheSPC,theaveragenumberoftransmissionscanbereducedincomparisontopreviousapproachesinsomescenarios. 1.2SuperpositionCodingandNetworkCodingforMixedMulticast/UnicastTrafconaTime-varyingChannel InChapter 2 ,weconsiderwhethertheadditionofsuperpositioncodingtolinearnetworkcodingcanimprovethethroughputofreliablemulticastdeliveryoverfadingchannels. InChapter 3 ,weconsidertheuseofsimulcastingwithlinearnetworkcodingtotransmitmixedmulticastandunicasttrafcoveraRayleighfadingchannelwithaverageSNRdeterminedbyatwo-stateMarkovchain.Weevaluatetheeffectoffeedback(withorwithoutdelays)ontheabilitytoimprovethethroughputofcombinedmulticastingandunicastingtoallowthesimulcastingsignalconstellationtobeoptimizedbasedon 16

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thechannelconditionsofreceivers.Weshowthatsimulcastingcanprovideadditionalperformancegainsoverusingjustnetworkcodingforseveraldifferentcaseswherethesourcehasreliableknowledgeofthechannelstatewithorwithoutdelays. 1.3GeographicTransmissionwithOptimizedRelaying(GATOR)fortheUplinkinMeshNetworksLimitto2-hop InChapter 4 ,weconsidercommunicationintheuplinkofawirelessmeshnetwork.AgroupofnodeshaveinformationtotransmittooneormoreAPs.WhenthechannelsfromthenodestotheAPssufferfromfading,thenthedirecttransmissionstotheAPsmayhaveahighprobabilityoffailure,andpacketsmayneedtoberelayedthroughothernodes.Undertheconventionalroutingapproach,inwhichtherelayingnodeispre-selected,fadingmayalsocauseahighprobabilityoffailureattherouter.Geographicapproacheshavebeenproposedthatcanimproveperformancebyusingopportunisticreception,inwhicharelayisselectedfromthosenodesthatcanreceivethepacketcorrectlyandmoveittowardtheAP.Existinggeographictransmissionschemesuseanadhocdesignfortheprotocolthatselectstherelaynode.Inthiswork,weproposeGeographicTransmissionwithOptimizedRelaying(GATOR),whichprovidesamathematicaldesignforrelayselectioninatime-slottedgeographiccommunicationschemeontheassumptionthatthepacketmaybedeliveredinatmosttwohops.WeevaluatedtheperformanceofGATORintermsofthroughput,energyefciency,andprobabilityofpacketdropbyreachingmaximumnumberofallowedtransmissions,andcomparedtheperformanceofGATORtodirecttransmission,routing,andothergeographictransmissionschemes. 1.4Multi-hopGeographicTransmissionwithOptimizedRelaying(GATOR)fortheUplinkinMeshNetworks InChapter 4 ,westudiedGATORschemeinmeshnetworks,butlimitedthemaximumnumberofhopuntilapacketisdeliveredtoanAPfromasourcetotwo.However,inapracticalmeshnetwork,therelaymaynotbestillnearenoughtohaveareasonableprobabilityofdeliveringthepackettothedestinationAPinoneadditional 17

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transmission,andthenthemultipletransmissionapproachhastobeconsidered.Forthemulti-hopapproach,geographictransmissionmayneedtobedesignedtomaximizesomemeasureofefciencyintransmittingtheinformationtotheultimatedestination.Therearemanypossiblemeasuresthatcanbeusedforthispurpose.Theseincludetransmissiondistance,transportcapacity[ 6 ],expectedforwardprogress[ 7 ],informationefciency[ 8 ],andresidualdistancetothedestination.Moreover,anypracticalgeographictransmissionschememayneedtotakeintoaccounttheenergyexpendedinreceptionbythepotentialrelays. InChapter 5 ,weconsideredtheuseofGATORintheuplinktransmissionforameshnetworkwithtimevaryingfadingchannelsinwhichAPsarespareandthedimensionofthenetworkislargethatthepacketmayhavetobeforwardedinmultiplehopsbetweenthenodeanddestinationAP.Weintroducetwomulti-hopGATORprotocols:oneisusingaxedhopdistanceinwhichthehopdistanceisselectedforbalancingtheforwardprogressandnumberofpossiblepotentialrelays,andtheotherisusingnon-xedhopdistancetominimizetheresidualdistancebyachievingthemultiuserdiversity.Wecomparedtheperformanceofmulti-hopGATORtomulti-hoprouting,directtransmission,and2-hopGATORandroutingaswell. 1.5OutlineofDissertation Therestofthedissertationisorganizedasfollows.InChapter 2 ,wepresenttheproposedSPCapproachesfordownlinkmulticasttransmission.Werstconsidernetworkcodingforreliablemulticastoverfadingchannels,wherethefadingisunknown.Weproposetheuseof2-SPCtofurtherimprovetheperformance.Followingtheapproachin[ 3 4 ],werstconsidertheperformanceforxedtransmissionratesandevaluatetheexpectednumberoftransmissionsrequiredtotransmitnetwork-codedpacketsreliablytoallofthereceiversinthemulticastnetwork.Wethenanalyzetheperformancewiththetransmissionparametersoptimizedtomaximizethethroughput. 18

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InChapter 3 ,wepresentSPCapproachestodeliveramixofmulticastandunicasttrafcfordownlinktransmission.WeconsidertheuseofSPCwithnetworkcodingtoreceiversoverfadingchannelswithdifferentchannelstatistics.Inparticular,weconsiderRayleighfadingchannelsinwhichtheaveragesignal-to-noiseratioatareceiverchangesovertime.Weevaluatetheperformancewhenthesourceknowsthechannelstateandwhenithasonlydelayedknowledgeofthechannelstate.Weconsidermixedmulticast/unicasttrafcandcomparethethroughputoftheproposedtechniquetotheuseoftimesharingbetweenthemulticastandunicasttrafc. WedevelopthegeographictransmissionschemeintheuplinktransmissionforameshnetworkinChapter 4 .WeconsiderascenarioinwhichtheAPsaredistributedinspacewithasufcientdensitythatpacketshaveahighprobabilityofreachingtheAPintwohopsformostnodes.Wepresentthe2-hopGATORprotocolandderivetheoptimalrelayselectionschemeforGATORwhencommunicationisoveraRayleighfadingchannel.Theperformanceof2-hopGATORschemeiscomparedtotwoconventionalschemesandtwogeographictransmissionschemes.TheuseofGATORinthemulti-hopuplinktransmissionforameshnetworkisstudiedinChapter 5 ,whereweintroducetwomulti-hopGATORprotocolsandcomparedtheperformancestomulti-hoprouting,directtransmission,and2-hopGATORandrouting.Finally,wepresentourconclusionsinChapter 6 19

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CHAPTER2SUPERPOSITIONCODINGANDLINEARNETWORKCODINGFORRELIABLEMULTICASTOVERFADINGCHANNELS 2.1IntroductionofSuperpositionCodingandLinearNetworkCoding SincetheseminalworkbyAhlswedeetal.[ 1 ],networkcodinghasreceivedconsiderableattentionfromtheresearchcommunity.Recently,networkcodingtechniqueshavebeenproposedtoimprovecommunicationefciencyinwirelessnetworks[ 9 15 ].Inwirelessnetworks,atransmittingnodecanexploitthebroadcastnatureofthemediumalongwithaprioriknowledgeoftheinterferencetocombineseveralpacketsatthenetworklayerintoanetwork-codedpacket.Thenodesreceivingthenetwork-codedpacketusetheknowledgeoftheinterferingpacketsavailableatthenetworklayertorecoverthepacket.Thisincreasesthespatialre-useandthroughputinmultihopwirelessnetworks. Mostoftheexistingworkonapplyingnetworkcodingtowirelesscommunicationsfocusesonunicasttrafc[ 9 14 ],whichisintendedforasingledestination.However,multicasttrafcisincreasinginimportance,particularlyformilitarycommunications.In[ 3 ],theauthorsevaluatetheperformanceofnetworkcodingforreliablemulticasting.Theauthorsanalyzetheperformanceofseveralreliablemulticastingtechniquesinatreenetwork,wherethebranchesofthetreeareunreliablecommunicationchannels.Thenumericalresultsin[ 3 ],indicatethatnetworkcodingcansignicantlyreducethenumberofretransmissionsinthenetworkcomparedtoschemeslikeratelesscoding,link-by-linkARQandend-to-endARQ. Theauthorsextendtheirworkin[ 4 ]toprovideasymptoticboundsonthereliabilitygainofnetworkcoding,whichismeasuredintermsoftheexpectednumberoftransmissionsperpacketforanaccesspointtocommunicatepacketstoagroupofKreceiversoverawirelesschannel.AsKgoestoinnity,thereliabilitygainofnetworkcoding,comparedtoARQ,is(logK).Then,byemployingtheaccesspointmodelasabuildingblockinatreetopology,itisshownthatwhenthenumberofreceiversis 20

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large,networkcodingachievesthebestperformanceintermsoftheexpectednumberoftransmissions,comparedtoschemeslikeregularARQandforwarderrorcorrection(FEC)schemes. Onecommonsourceofunreliablechannelsisduetomultipathfading.Infadingchannels,theperformanceofthenetworkisdictatedbythechannelgain(s)oftheuser(s)inthecurrenttransmissionduration.Inmanyapplications,thechannelgainmaynotbeknownpriortotransmission.In[ 16 ],ShamaiproposedtheuseofSPCasawaytoimprovecommunicationperformanceforchannelswithrandomandunknownchannelgains.ThebasicideaisthatbyusingSPC,theamountofinformationthatisreceivedvariesbasedonthequalityofthechannel.Shamaiconsideredinnite-levelSPC.Themorepracticalcaseoftwo-levelSPC(2-SPC)wasconsideredin[ 17 ]andshowntoprovideperformanceclosetoinnite-levelSPC. Inthischapter,weconsidernetworkcodingforreliablemulticastoverfadingchannels,wherethefadingisunknown.Weproposetheuseof2-SPCtofurtherimprovetheperformance.Followingtheapproachin[ 3 4 ],werstconsidertheperformanceforxedtransmissionratesandevaluatetheexpectednumberoftransmissionsrequiredtotransmitnetwork-codedpacketsreliablytoallofthereceiversinthemulticastnetwork.Wethenanalyzetheperformancewiththetransmissionparametersoptimizedtomaximizethethroughput.Webeginbyprovidingamotivatingexampleinthenextsection. 2.2MotivatingExample:Two-receivermulticastnetwork Inthissection,weillustratetheadvantagesofemployingSPCinconjunctionwithnetworkcodingformulticastingtotworeceivers,asshowninFig. 2-1A .ConsiderascenarioinwhichAlicewishestomulticastablockofthreedatapacketstobothBobandCharlie.SupposethatthechannelsfromAlicetoBobandCharlieareindependent,quasi-staticRayleighfadingchannelswithindependentfadinggainsacrossthetime-slots.Ineachtransmissioninterval,Alicetransmitsanetwork-codedpacket 21

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ATwo-usernetworkcodedmulticastnetwork. BTwo-usernetworkcodingmulticastnetworkwithSPC. Figure2-1. Two-usermulticastnetworkwithandwithoutSPC. thatisalinearcombination(usingcoefcientsinsomeGaloiseld)ofthethreedatapackets.Onceareceiverrecoversanythreeofthenetwork-codedpackets,itwillbeabletorecoverallthreedatapackets.TransmissionisterminatedwhenbothBobandCharliecanrecoverthethreedatapackets. ConsiderrstthescenarioinwhichnetworkcodingisusedwithoutSPC.IntimeslotT0,Alicetransmitsanetwork-codedpacketP1toBobandCharlie.ThechannelgainofBobisverygood,whichpermitsthereceptionofthepacketP1.However,Charliehasapoorchannelgainandcannotreceivethepacket(packetlossisdenotedby;.)Inthesecondtime-slot,whenAlicetransmitsP2,thechannelgainsofBobandCharliearesuchthatCharliecanreceoverthepacketP2,whereasBobdoesn'treceivethepacket(denotedby;).BothBobandCharliereceivethepacketsP3andP4inthethirdandfourthtime-slots,respectively.Sincebothhaverecoveredthreenetwork-codedpackets,thetransmissionisterminatedaftertimeslotT3. Nowconsiderthesamenetwork,butwithSPCasillustratedinFig. 2-1B .Inthersttime-slot,AliceusesSPCtotransmittwonetwork-codedpacketsP01,andP02.The 22

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Figure2-2. MulticastnetworkwithKreceivers. channelgainofBobisverygood,whichpermitsthereceptionofboththenetwork-codedpacketsP01andP02.ContrastthistotheT0slotof Fig.2-1A ,inwhichBobcanreceiveatmostonepacketregardlessofhischannelquality.Intime-slotT1,Charlie'schannelgainpermitsthereceptionofonlyonenetwork-codedpacketP03,whereasBobdoesn'treceiveanypackets(denotedby;).Intime-slotT2,bothreceiversrecoverbothofthenetwork-codedpackets,P05andP06.SincebothBobandCharliereceivedatleastthreenetwork-codedpackets,thetransmissionisterminated.Inthisexample,wenotethatSPCwithnetworkcodingrequiredthreetime-slotsforthetransmissionofthreenetwork-codedpackets,whereasnetworkcodingrequiresfourtimeslots.ThisgaininperformanceisduetotheabilityofSPCtotakeadvantageofthediversityinfadinggains. In section2.3 ,weanalyzetheperformancegainsof2-SPCintermsoftheexpectednumberoftransmissionsrequiredforthesuccessfulreceptionofpacketsinamulticastnetworkforxedvaluesofpacketlossonalink,wheretheallocationofpowerbetweenthebasicandadditionalmessagesisoptimizedtothelinkconditions.In section2.5 ,wendthetransmissionrates,powerallocation,andnumberofpacketstobelinearlycombinedinthenetworkcodingtomaximizethethroughputofnetworkwithandwithout2-SPC. 2.3SystemModel ConsiderabroadcastchannelwithasourceSandKreceivers1,2,,Kasdepictedin Figure2-2 .SuseslinearnetworkcodingonablockofBdatapackets. 23

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ConsiderrsttheoperationwhenSPCisnotused.Thenineachtransmissioninterval,Screatesanewuniquelinearcombinationofthedatapacketsandbroadcastsittothereceivers.ThisisrepeateduntilallKreceiverssuccessfullyreceiveatleastBpackets,atwhichtimeallofthereceiverswillbeabletorecovertheoriginalBdatapackets. TheprocedureissimilarifSPCisused.However,SPCcansimultaneouslydelivermultiplestreamsofinformationwithdifferentsignal-to-noiseratio(SNR)requirementsfortheirreception.Inthiswork,weconsideronly2-SPC,asitisthemostpracticalscheme,butourresultscanalsobeextendedtohigher-orderSPCschemes.For2-SPC,wecallthemessagethathasthelowerSNRrequirementthebasicmessageandthemessagethathasthehigherSNRrequirementtheadditionalmessage.Thus,when2-SPCisused,Screatestwonewnetwork-codedpacketsineachinterval.Asbefore,thepacketsareuniquelinearcombinationsofthedatapackets.Thetwonetwork-codedpacketsaretransmittedtothereceiversusing2-SPC.ThereisnodistinctionbetweenthetypesofinformationcarriedinthetwodifferentlevelscreatedbySPC(i.e.,thebasicandadditionalmessage);rather,thetwolevelsprovidetheabilitytodeliverdifferentquantitiesofinformationdependingonthechannelquality. Asin[ 3 4 ],wemodelthechannelsfromStotheKreceiversasbeingindependentbutwithidenticalstatistics.ThereceivedsymbolsatdifferentreceivershavethesameaverageSNRs.Thefadinggainsareunit-energyRayleighrandomvariablesthatareconstantduringeachtransmissionintervalandindependentacrosstransmissionintervals.Moreover,thefadinggainsofdifferentreceiversareindependent.WeassumethatthereisreliableandinstantaneousfeedbackfromthereceiverswhentheyhaverecoveredBnetwork-codedpackets. LetPtdenotethetransmitpower,Wthebandwidthofthesystem,andN0=2isthenoisepowerspectraldensity(PSD).ThentheaverageSNRatallofthenodesis=Pt=N0W.Letfzi,jgbeasetofindependentexponentialrandomvariableswith 24

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unitenergy.ThentheSNRatreceiveriduringtransmissionintervaljisi,j=zi,j.Forsimplicityofnotation,wedropthetimeindexjinwhatfollows. Weusechannelcapacitytodeterminetheachievabletransmissionratesandoutageprobabilitiesfornetworkcoding(withorwithout2-SPC).Without2-SPC,thecapacityoftheGaussianchannelisgivenby ri(zi)=log(1+zi).(2) With2-SPC,thecapacitiesachievedforthebasicandadditionalmessagesdependon,zi,andalsoontheallocationofpowerbetweenthebasicandadditionalmessages.Let,2[0,0.5],bethepowerallocationparametersuchthat(1)]TJ /F7 11.955 Tf 12.12 0 Td[()istheproportionoftotaltransmitpowerassignedforthebasicmessage,andistheproportionofthetotalpowerassignedtotheadditionalmessage.Thenthecapacitiesforthebasicandadditionalmessagesare[ 18 ] ri,b(zi)=log1+(1)]TJ /F7 11.955 Tf 11.95 0 Td[()zi 1+zi,andri,a(zi)=log(1+zi), (2) respectively.Ifasignalistransmittedatarater0,thenthepacketislost(i.e.,outageoccurs)ifthechannelcapacity,givenbyeitherri,ri,b,orri,aislessthanr0.ForinstanceifSPCisnotusedandthemessageistransmittedatrater0,thentheoutageprobabilityis p=Pr[log2(1+zi)
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2.4ReliableMulticastingwithFixedTransmissionRates Werstcomparetheperformanceofnetworkcodingwithandwithout2-SPCforasysteminwhichthetransmissionrateofboththemessagesin2-SPCisequaltothetransmissionratewithoutSPC.Tocompareourresultswiththosein[ 3 4 ],wereportourresultsforxedvaluesofthelinkoutageprobabilityforthesystemwithoutSPC.Notefrom( 2 )thatdependingonthetransmissionrate,theoutageprobabilitycorrespondstodifferentaverageSNRs,whichresultindifferentperformancewhen2-SPCisutilizedinconjunctionwithnetworkcoding.Thus,weprovideafamilyofcurvesatdifferentaverageSNRsforthesystemusingnetworkcodingwith2-SPC. 2.4.1NetworkCodingWithoutSPC TheperformanceofnetworkcodingwithoutSPChasbeenanalyzedin[ 3 ]anddependsonlyontheoutageprobability,p.Forreferenceinthenextsection,letr0bethetransmissionrateand0betheSNRthresholdbelowwhichoutageoccurs;i.e.,themessageisnotreceivedifzi<0(cf.( 2 )). TheexpectednumberoftransmissionsforthesuccessfulreceptionofBpacketsbyallKreceiversis E[NncK]=1Xn=01)]TJ /F3 11.955 Tf 11.95 0 Td[(FNncK(n),(2) wheretheprobabilitythatallKreceiversreceiveatleastBpacketswithinntransmissionsisgivenby FNncK(n)=Pr(NncKn)=(nXk=Bnk(1)]TJ /F3 11.955 Tf 11.96 0 Td[(p)kpn)]TJ /F5 7.97 Tf 6.59 0 Td[(k)K.(2) 2.4.2NetworkCodingwith2-SPC Let1and2,12,bethechannelgainssuchthatifzij,j=1,2,receiveriiscapableofreceivingatleastjpacketsinthattransmissioninterval.Weconsider2-SPCinwhichthebasicandadditionalmessagesarebothtransmittedattherater0thatprovidesthespeciedoutageprobabilitypforthesystemthatusesnetworkcodingwithoutSPC.From( 2 ),thevaluesof1and2thencanbeexpressedasfunctionsof 26

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theaverageSNR,,andtheproportionofpowerallocatedtotheadditionalmessage,,as 1()minz:(1)]TJ /F7 11.955 Tf 11.96 0 Td[()z 1+z0,and2()minfz:z0g. (2) Considerrsttransmissiontoasinglereceiver.TheexpectednumberoftransmissionsrequiredforthesuccessfulreceptionofBnetworkcodedpacketis E[Nsct]=1Xn=dB=2e1)]TJ /F3 11.955 Tf 11.95 0 Td[(FNsct(n),(2) whereFNsct(n)isthecumulativedistributionfunction(cdf)ofthenumberoftransmissionsrequiredforsuccessfulreceptionofBcodedpacketsunder2-SPC.WeonlyneedtoevaluatethecdfFNsct(n)inordertoevaluatetheexpectednumberoftransmissions,E[Nsct].Towardsthatendweintroducethefollowingnotation.LetYndenotethenumberofmessagessuccessfullyreceivedafterthenthtransmission,whichisthesumofnindependentincrements.LetXi2f0,1,2gdenotethevalueoftheithincrement,whichisthenumberofmessagessuccessfullyreceivedontheithtransmission.Letpj=Pr(Xi=j),j2f0,1,2g.Thenp0=1)]TJ /F3 11.955 Tf 11.96 0 Td[(e)]TJ /F14 7.97 Tf 6.59 0 Td[(1(),p1=e)]TJ /F14 7.97 Tf 6.58 0 Td[(1())]TJ /F3 11.955 Tf 11.96 0 Td[(e)]TJ /F14 7.97 Tf 6.58 0 Td[(2(),andp2=e)]TJ /F14 7.97 Tf 6.58 0 Td[(2(). Fortransmissiontoasinglereceiver,thenumberofrequiredtransmissionsisgivenbyNsct=minfn:YnBg.ThecdfofNsctisthengivenby FNsct(n)=nXk=dB=2ePr(Nsct=k),(2) 27

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wheretheprobabilitymassfunction(pmf),Pr(Nsct=n)isgivenbyPr(Nsct=n)=Prf(Yn)]TJ /F6 7.97 Tf 6.59 0 Td[(1=B)]TJ /F4 11.955 Tf 11.96 0 Td[(1,Xn=1) (2)[(Yn)]TJ /F6 7.97 Tf 6.59 0 Td[(1=B)]TJ /F4 11.955 Tf 11.96 0 Td[(2,Xn=2)[(Yn)]TJ /F6 7.97 Tf 6.59 0 Td[(1=B)]TJ /F4 11.955 Tf 11.95 0 Td[(1,Xn=2)g, whereYn)]TJ /F6 7.97 Tf 6.59 0 Td[(1representsthenumberofpacketssuccessfullyreceivedaftertherstn)]TJ /F4 11.955 Tf 12.54 0 Td[(1transmissions,andXnisthenumberofpacketssuccessfullyreceivedinthenthtransmissionduration.BynotingthatthethreeeventsaremutuallyexclusiveandtheXiarei.i.d.,( 2 )canbewrittenasPr(Nsct=n)=Pr(Yn)]TJ /F6 7.97 Tf 6.58 0 Td[(1=B)]TJ /F4 11.955 Tf 11.96 0 Td[(1)Pr(Xn=1)+Pr(Yn)]TJ /F6 7.97 Tf 6.59 0 Td[(1=B)]TJ /F4 11.955 Tf 11.96 0 Td[(2)Pr(Xn=2)+Pr(Yn)]TJ /F6 7.97 Tf 6.59 0 Td[(1=B)]TJ /F4 11.955 Tf 11.96 0 Td[(1)Pr(Xn=2). ThepmfofYcanbeevaluatedfromthepmfofXusingtheFourierinversionformula, Pr(Yk=y)=1 2Z)]TJ /F14 7.97 Tf 6.59 0 Td[(fYk(!)ge)]TJ /F5 7.97 Tf 6.59 0 Td[(j!yd!=1 2Z)]TJ /F14 7.97 Tf 6.59 0 Td[(kXi(!)e)]TJ /F5 7.97 Tf 6.59 0 Td[(j!yd!,(2) wherekXi(!)=E[ej!Xi]=p0+p1ej!+p2e2j!,isthecharacteristicfunctionofX,andYk(!)isthecharacteristicfunctionofY. Themultiuserscenarioisastraight-forwardextensionofthesingleusercase,bynotingthatFNscK(n)=FNsct(n)K,whereFNscK(n)isthecdfofthenumberoftransmissionsrequiredforthesuccessfulreceptionofatleastBcodedpacketsatalloftheKreceiverswhenthesourceSemploys2-SPC.Theoptimalvalueofthatminimizestheexpectednumberoftransmissionunder2-SPCcanbeevaluatednumerically. 28

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2.4.3SimulationResults Wecomparetheperformanceofnetworkcodingforreliablemulticastingwithandwithout2-SPC.Theperformanceisevaluatedforsystemsusingthesametransmissionrates(i.e.,thebasicandadditionalmessagesforthesystemusing2-SPCaretransmittedatthesamerateasthemessagesforthesystemthatdoesnotuseSPC).Weevaluatetheperformancebasedontheexpectednumberoftransmissionsrequiredtodeliverapacket.Inordertocomparetheresultswiththosein[ 3 ],weindexourresultsbasedonthelinkoutageprobabilityforthesystemthatdoesnotuseSPC. Theexpectednumberoftransmissionsforsuccessfulreceptionofapacket(normalizedbytheblocksize,B)withandwithout2-SPCinanetwork-codedmulticastnetworkareshowninFigs. 2-3A and 2-3B ,asfunctionofthenumberofreceiversinthesystem,forseveralvaluesofandforoutageprobabilitiesp=0.05andp=0.2.Theblocksize,B,foralloftheseresultsis16.Aspreviouslymentioned,for2-SPC,theperformancealsodependsontheaverageSNR,,sotheperformanceisshownforseveralvaluesof. Whenp=0.05,2-SPCalongwithnetworkcodingoutperformsnetworkcodingforallvaluesoftransmitpower,,andnumberofreceiversK.Forinstance,whenK=32,and=15dB,2-SPCrequires52%fewertransmissionsthannetworkcoding.However,theperformanceadvantageofnetworkcodingwith2-SPCdependssignicantlyonthetransmissionrate(andhencetheaverageSNR).Forexample,whenp=0.2,theminimumexpectednumberoftransmissionsof2-SPCconvergestotheexpectednumberoftransmissionsofnetworkcodinginthehighSNRregime.Thus,inthisscenario,2-SPCprovidesnosignicantadvantageovernetworkcodingwithoutSPC. Figure2-4 showstheexpectednumberoftransmissionswithandwithout2-SPCasafunctionofblocksizeB,forseveralvaluesofaverageSNR,.Thenumberofreceivers,K,is16.AsBincreases,theexpectednumberoftransmissionsperpacketdecreases,buttherateofdecreasebecomessmallasBbecomeslarge.Forp=0.05, 29

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Ap=0.05 Bp=0.2 Figure2-3. ExpectednumberoftransmissionsforsuccessfulreceptionofapacketwithB=16. and=15dB,2-SPCwithnetworkcodingrequires59%fewertransmissionscomparedtoasystememployingnetworkcoding.Whenp=0.2,astheaverageSNRincreases,theperformancegaindueto2-SPCbecomesnegligible. 2.5ReliableMulticastingwithOptimumTransmissionRates Intheprevioussection,weevaluatedtheperformanceofreliablemulticastingwithandwithoutSPCforcommunicationatpredeterminedxedtransmissionrates. 30

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Ap=0.05 Bp=0.2 Figure2-4. ExpectednumberoftransmissionsforsuccessfulreceptionofapacketwithK=16. Inthissection,weconsideroptimizationofthetransmissionrateforthesystemthatdoesnotemploySPCandoptimizationofthetransmissionratesofthebasicandadditionalmessages,aswellasthepowerallocationamongthemessagesforthesystemthatemploys2-SPC.Sincevaryingthetransmissionratesvariestheamountofinformationdelivered,wecomparetheperformancebasedontheachievable 31

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multicastingthroughput,whichwedeneastheaveragerateofinformationdeliveredpertransmissioninterval. 2.5.1ThroughputUnderNetworkCodingwithoutSPC Considerrstthesinglereceiverscenario.LetR(z)betheratesuccessfullyreceivedbythereceiverwhenthechannelpowergainisz.BlocksofrateBR(z)bitsarenetworkcoded,whereBdoesnotneedtobeaninteger.ARQisemployedinthefollowingmanner.Ifattimen,theratereceivedexceedsBR(z),thenthemessagescanbedecoded,andanACKissentbacktothetransmittertostoptransmissionsofthatnetworkcodingblock. FortransmissionwithoutSPCatrater0,therequiredchannelgainforapackettobesuccessfullyreceivedisz0=(2r0)]TJ /F4 11.955 Tf 11.96 0 Td[(1)=. ThethroughputofnetworkcodingonblocksofBpacketsfortransmissiontoasinglereceiverisgivenby Tnc=1Xn=1r0B nPr(Nnct=n)=r0B1Xn=1FNnct(n) n(n+1), (2) wherePr(Nnct=n)=0ifn
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Thevaluesofz0andBthatoptimizethethroughputcanthenbefoundvianumericalsearch. 2.5.2ThroughputUnderNetworkCodingwith2-SPC AsinthecaseofnoSPC,considerrstnetworkcodingtoasinglereceiver.Consider2-SPCwiththebasicandadditionalmessagestransmittedatratesrbandra,respectively,andwithproportionofthetotaltransmissionpowerallocatedtotheadditionalmessage.Thentherequiredchannelgainthresholdsforcorrectdecodingofthebasicandadditionalmessagescanbecomputedfrom( 2 )tobez1=2rb)]TJ /F4 11.955 Tf 11.96 0 Td[(1 (1)]TJ /F7 11.955 Tf 11.95 0 Td[(2rb),andz2=(2ra)]TJ /F4 11.955 Tf 11.96 0 Td[(1)=, respectively. Thethroughputunder2-SPCcanbecomputedas Tsc=R(Z)B1Xn=1FNsct(n) n(n+1),(2) wherePr(Nsct=n)=0ifn
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Figure2-5. Throughputcomparisoninamulticastnetwork. 2.5.3SimulationsResults Thethroughputofnetwork-codedmulticasttransmissionwithandwithoutSPCisdepictedin Figure2-5 .TheblocksizeBis16,andthenumberofreceiversKis2.Weobservethat,whenthesourcetransmitswithoutSPCatthetransmissionrate,r0,thatmaximizesthethroughput,thereisnosignicantgainbyemployingSPC.WeobservedthistrendoverawiderangeofvaluesofBandK.Onepossibleexplanationforthisisthattheperformanceisdominatedbythereceiverwiththeworstchannelconditions,andsothetransmissionschemeshouldbedesignedfortheworstchannels.SPCsplitstheenergybetweentwotransmissionsinthehopeofgettingadditionalthroughputingoodchannelconditions,whilepenalizingtheperformanceofthebasicmessageinbadchannelconditions.Thus,fornetworksinwhicheverynodemustreceivethesamemulticastinformation,networkcodingplusSPCprovideslittlebenetovernetworkcodingalone. 34

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2.6Summary Inthischapter,westudiedtheuseof2-SPCinanetwork-codedsystemtoimprovetheefciencyofreliablemulticastingbytakingadvantageofdiversityinfadingchannels.Wecomparedtheperformanceofreliablemulticastingusingnetworkcodingwithandwithout2-SPCintwoscenarios.Intherst,thetransmissionratesforallofthemessageswereequal,xedvaluesthatwereindependentofthechannelSNR.Forthisscenario,weshowthat2-SPCmayprovidesignicantgains.Inthesecondscenario,weoptimizedthecommunicationparameterstomaximizethemulticastingthroughput.Inthissecondscenario,2-SPCshowedlittleperformanceimprovementovernetworkcodingwithoutSPC.TheresultsindicatethatSPCmaybeusefultoimprovetheperformanceofnetworkcodingforreliablemulticastifthechannelconditionsarenotknownexactly.Also,SPCmaybeusefulifitisusedtoincludemessagesotherthanthosefromthemulticastingstream,whichweconsiderinChapter 3 35

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CHAPTER3SUPERPOSITIONCODINGANDNETWORKCODINGFORMIXEDMULTICAST/UNICASTTRAFFICONATIME-VARYINGCHANNEL 3.1IntroductionofSuperpositionCodingandNetworkCodingforMixedMulticast/Unicast Multicasttrafcisimportantinmanymilitaryapplications,andsuchtrafcshouldbebroadcastatthephysicallayertotakeadvantageofthewirelessmulticastadvantage[ 19 ].Thischapterfocusesonphysical-layermulticasting(hereafter,simplymulticasting),whichisthedeliveryofmulticastinformationviabroadcastoverawirelesschannel.Forreliablemulticastdelivery,ithasbeenshownin[ 3 4 ]thatlinearnetworkcodingoffersasignicantperformanceadvantageoverconventionalapproaches,suchasARQorratelesscoding.Theresultsin[ 3 4 ]areapplicabletomanychannelmodels,includingfadingchannels,wherethefadingcoefcientsareunknownatthetransmitter.Forunicastcommunicationoverfadingchannelswithunknowngainsatthetransmitter,superpositioncoding(SPC)hasbeenshowntoofferhighertransmissionratesthanconventionalsingleratetransmission[ 16 17 ].InChapter 2 ,weconsideredtheuseofSPCinconjunctionwithlinearnetworkcodingtotakeadvantageofthechannelvariabilityformulticastingoverRayleighfadingchannels.Two-levelSPC(2-SPC)isshowntoimprovetheperformancewhenthecommunicationparametersarenotoptimizedtothechannelstatistics.However,theadditionof2-SPCofferslittleperformancegainovernetworkcodingalonewhentheparametersofthenetworkcodingand2-SPCareoptimizedtothechannelstatistics.Thereasonforthisisintuitive:theperformanceofthemulticasttransmissionisdominatedbytheworstchannelconditions,andsuperpositioncodingonlyprovidesbenetsforchannelswithbetterconditions. Inthischapter,weconsidertheuseofSPCwithnetworkcodingtoreceiversoverfadingchannelswithdifferentchannelstatistics.Inparticular,weconsiderRayleighfadingchannelsinwhichtheaveragesignal-to-noiseratioatareceiverchangesover 36

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time.Weevaluatetheperformancewhenthesourceknowsthechannelstateandwhenithasonlydelayedknowledgeofthechannelstate.Weconsidermixedmulticast/unicasttrafcandcomparethethroughputoftheproposedtechniquetotheuseoftimesharingbetweenthemulticastandunicasttrafc.Webeginbyprovidingamotivatingexample. 3.2MotivatingExample AsinChapter 2 ,webeginwithanexampletomotivatetheschemethatweinvestigate.Here,weillustratetheadvantagesofemployingSPCovernetworkcodingforsimultaneousdeliveryofmulticastandunicasttrafctotworeceivers.ConsiderascenarioinwhichAliceneedstomulticastablockofthreedatapacketstobothBobandCharlie.AlicealsohasunicastpacketsforbothBobandCharlie.SupposethatthechannelsfromAlicetoBobandCharlieareindependentchannels,eachofwhichcanbeinoneoftwostates,agoodstateGandabadstateB:forexample,thenoisevarianceinstateGismuchsmallerthaninstateB.Forthisexample,assumethatAliceknowsBob'sandCharlie'schannelsstates. ConsiderthescenarioinwhichAlicemulticastspacketstoBobandCharliewithoutSPC,asshowninFig. 3-1A .Ineachtimeslot,atleastoneofthechannelsisintheBstate.TosuccessfullymulticasttobothBobandCharlie,Alicemusttransmitatarateatwhichthemessagecanberecoveredovertheworseofthetwochannels.Thus,ineachtimeslot,Alicetransmitsexactlyonemulticastmessageatthesamerate.IntimeslotT1thechanneltoBobisintheGstate,andthusBobcouldreceiveinformationtransmittedatahigherrate.Similarly,forCharlieinslotT2. Nowconsiderthesamenetwork,butwithSPCusedtosimultaneouslytransmitamulticastmessageandaunicastmessageswhenareceiverisintheGstate,asillustratedinFig. 3-1B .IntimeslotT0,bothchannelsareintheBstate,soAlicemulticastsapacketM1tobothBobandCharliewithoutSPC.Intime-slotT1,thechanneltoBobisinstateG.IftheSNRinstateGissignicantlyhigherthaninstateB,thenAlicecanuseSPCtotransmitaunicastmessagetoBobsimultaneouslywiththe 37

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ATwo-usernetworkcodedmulticastnetwork. BTwo-usernetworkcodedsimulcastnetworkwithSPC. Figure3-1. Two-usersimulcast/multicastnetworkwithandwithoutSPC. transmissionofthemulticastmessagetobothBobandCharlie,withlittledegradationintherateofthemulticastmessageorasmallamountofadditionalenergyinthetransmission.Asin[ 20 ],wecallthissimulcasting,whichistheuseofphysical-layertechniquestosimultaneouslydelivermessageswithdifferentSNRrequirementsfortheircorrectreception.Thus,intimeslotT1,Aliceuses2-SPCtosimulcastthemulticastpacketM2andtheunicastpacketU1(whichisintendedforBob).The2-SPCschemeischosensothatbothBobandCharliecanreceiveM2,butonlyBobcanrecoverU1becausehischannelisbetterthanCharlie's.Similarly,intimeslotT2,AlicesimulcaststhemulticastpacketM2andtheunicastpacketU2(whichisintendedforCharlie).BothreceiverswillrecoverM3,whileonlyCharliewillrecoverU2. Thus,byusing2-SPCforsimulcasting,twoadditionalunicastpacketscanbedeliveredinadditiontothethreemulticastpacketsdeliveredinthethreetimeslots.However,thechannelconditionsatthereceiversareoftennotknownexactly,andtheinclusionofaunicastpacketreducestherateavailableforthemulticastpackets.Intherestofthischapter,weevaluatetheuseofsimulcastingoverRayleighfadingchannels, 38

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Figure3-2. MulticastnetworkwithKreceivers. wheretheaverageSNRsatBobandCharliemaybedifferent,maychangeovertime,andmaynotbeknownexactlyatAlice. 3.3SystemModel WeconsidercommunicationfromasourceStoKreceivers,asdepictedin Figure3-2 .ThechannelssufferfromadditivewhiteGaussiannoiseandRayleighfading,whichisassumedtobeconstantovereachtimeslot.LetZiandSidenote,respectively,thefadinggainandthechannelstateofreceiveri.Thefadinggainsatdifferentreceiversareindependent,buttheaverageSNRsmayvaryacrossreceiversandacrosstimeslots,asdescribedfurtherbelow. Toachievereliablemulticastdeliveryoverthefadingchannel,linearnetworkcodingisemployedasdescribedin[ 3 5 ].ThesourceuseslinearnetworkcodingonBpacketsatatime.ThesourcetransmitsalinearcombinationoftheBpacketsineachtimeslotuntileachoftheKreceivershasrecoveredBofthelinearcombinations.Atthatpoint,eachreceivercanrecovertheoriginalBdatapackets,andthesourcewillusenetworkcodingtodeliverthenextBpackets. Weconsidertheuseofsuperpositioncodingtosimulcastbothmulticastandunicastmessages.Inthiswork,weconsideronly2-SPC,asitisthemostpracticalscheme,butourresultscanalsobeextendedtohigher-orderSPCschemes.For2-SPC,wecallthemessagethathasthelowerSNRrequirementthebasicmessageandthemessagethathasthehigherSNRrequirementtheadditionalmessage.Consider2-SPCtotwo 39

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Figure3-3. Two-stateAWGNchannel. receiversthathavedifferentaverageSNRs.Totakeadvantageofdifferentchannelqualitiesatthereceivers,weemploy2-SPCtosimulcastmulticastmessagesandunicastmessagessuchthatthebasicmessagecarriesthemulticastmessageandtheadditionalmessagecarriesaunicastmessage.Weevaluatetheperformanceintermsofthebestachievablecombinationsofmulticastthroughputs,asdeterminedusingthecapacityforthebroadcastchannel[ 21 ]. In section3.5 ,weconsiderascenarioinwhichtheaverageSNRsofthechannelsvaryaccordingtoahomogeneousnite-stateMarkovchain[ 22 23 ].Thechannelstateisxedduringeachtimeslot,andthechannelstatesatdifferentreceiversareindependent.Inthischapter,werestrictouranalysistothecaseoftwostates,labeledGandB(forgoodandbad,respectively).TheaverageSNRinstateGishigherthantheaverageSNRinstateB.WedenotetheprobabilityoftransitioningbetweenthestatesbyP(GjB)=pgP(BjG)=pb, andthestatetransitionprobabilitiesareillustratedinFig. 3-3 .Thestateprobabilitiesatsteadystateare(G)=pg pg+pb,and(B)=pb pg+pb. Weassumethatthereceiverscanestimatethechannelstateandfeedthisinformationbacktothesource.Weconsidertwocasesofchannel-stateinformationatthesource.In 40

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therst,thesourceknowstheexactchannelstateforthecurrentslot.Inthesecond,thetransmitterknowsonlythechannelstateforthepreviousslot. 3.4SimulcastingandNetworkCodingtoReceiverswithDifferentChannelGains Werstconsidertransmissonofmulticastandunicastpacketstotworeceivers(1and2),wheretheaverageSNRsatthereceiversaredifferent(butxedandknown).Withoutlossofgenerality,weletreceiver1bethereceiverwiththehigherSNR.Wecomparethethroughputofsimulcastingwith2-SPCtothatoftimesharingtodistributethe(networkcoded)multicastandunicastpackets. Letiand idenote,respectively,theinstantaneousandaverageSNRsatreceiveri.Consider2-SPCwiththebasicandadditionalmessagestransmittedatratesrbandri,a,respectively.Notethatthemulticastmessageissentatasinglerate,whileweallowdifferenttransmissionratesfortheunicastmessagestodifferentreceivers(indifferenttimeslots).Weallocateaproportion2[0,1]ofthetotaltransmissionpowertotheadditionalmessageforunicastingand1)]TJ /F7 11.955 Tf 12.28 0 Td[(tothebasicmessageformulticasting.Letzi,bandzi,a,zi,bzi,a,denotetherequiredfadinggainthresholdsforcorrectdecodingofthebasicandadditionalmessagesatreceiveri,respectively.Thecapacitiesforthebasicandadditionalmessagesare[ 18 ] ri,b(zi,b)=log1+(1)]TJ /F7 11.955 Tf 11.96 0 Td[()izi,b 1+izi,b,andri,a(zi,a)=log(1+izi,a). (3) WeconsidersimulcastingblocksofBmulticastpacketsandtransmissionofadditionalunicastpacketswith2-SPCtotworeceivers.Weconsidertwodifferentapproachesforhowthesourcehandlesthetransmissionofunicastdata.Intherstapproach,thesourcemaximizestheunicastthroughputbyalwayssendingtheunicastdatatothereceiverwiththebetterchannel.ThentheachievablecombinationofmulticastandunicastthroughputsisgivenbythetupleT=(Tmulti,Tuni),whereTmultidenotesthethroughputachievedbymulticastingablockofBpacketstotworeceivers 41

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asabasicmessage,andTuniisthethroughputachievedbyunicastingadditionalmessagestothereceiverwiththebestchannel.ThemulticastthroughputcanbecalculatedasinChapter 2 ,andtheunicastthroughputfollowsdirectlyfrom( 3 ), T= 1Xn=BrbB nPr(Nt=n),r1,aPr(Z1z1,a)!.(3) Here,NtisthetotalnumberoftransmissionsrequiredforthesuccessfulreceptionofBmulticastpacketsbybothreceivers. Thesecondapproachthatthesourcecanusefortheunicastdataistoalternateunicasttransmissionsbetweenthetworeceiverstoprovidetime-sharefairness.Forthisapproach,thethroughputisT=(Tmulti,Tuni)= 1Xn=BrbB nPr(Nt=n),1 2hTuni+~Tunii!, (3) where ~Tuni=r2,aPr(Z2z2,a)(3) istheexpectedthroughputofunicastinginaslottothereceiverwiththeworsechannel.NotethatthevalueofTmultiisthesameasTmultiforagiven,butthesameisnottrueforTuniandTuni.Theoptimalchoicesoffzi,bgandfzi,agforagivenvalueofcanbefoundnumerically. Themulticastthroughputandtheunicastthroughputof2-SPCiscomparedtothatoftimesharingbetweenmulticastingandunicastinginFig. 3-4 fortwosetsofaveragereceivedSNRs,f ig.TheblocksizeBis16,andthenumberofreceivers,K,is2.Foreachvalueofthemulticastthroughput,weoptimizetheunicastthroughputof2-SPC.WeomittheTvaluesfornetworkcodingtomaketheothercurveseasiertodistinguish,andbecausethischannelisnottheemphasisofthischapter. 42

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Figure3-4. Bestachievablethroughputsfortransmissionofmulticastandunicasttrafctotworeceiverswithdifferent,knownchannelstatistics. Simulcastingusing2-SPCoutperformstimesharingforallcombinationofmulticastingandunicasting(exceptforpuremulticastingorpureunicasting).Moreover,asthedifferencebetweentheaveragereceivedSNRsofthetworeceiversincreases,simulcastingusing2-SPCprovidesmorethroughputimprovementovertimesharingbetweenmulticastingandunicasting.Themulticastthroughputisdominatedbythereceiverwiththeworstchannelconditions,butsimulcastingusing2-SPCachievesadditionalunicastthroughputbytakingadvantageofthechannelwiththehigheraverageSNR. 3.5SimulcastingandNetworkCodingovertheTwo-StateMarkovChannel Inthissection,weconsidertheuseof2-SPCtosimulcasttoreceiversthathaveaverageSNRsdeterminedaccordingtoidenticaltwo-stateMarkovchains,asdescribedin section3.3 .Asintheprevioussection,weconsidertransmissionfromasourcetotworeceivers.LetSidenotethechannelstateofreceiveri.Thenthecombinedchannel 43

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stateisthetuple(S1,S2),andwecanrefertoaparticularchannelstateatsometimebythetupleofvalues,suchas(G,B). Wecomparethethroughputperformanceforthreedifferentcasesofchannel-statefeedback:nofeedback,feedbackwithnodelay,andfeedbackdelayedbyonetimeslot.Whenthereisnofeedback,westillalternatetheunicasttransmissionsbetweenthetworeceiversinordertoprovidetimefairness.However,whenthereisfeedbackandthechannelsareindifferentstates,theunicasttransmissionistargetedtothereceiverwiththebestchannel.Thus,thehigherthroughputTuniisachievedinsteadofTuni(see Figure3-4 ).Sincethesteady-stateprobabilitiesarethesameforthetworeceivers,thereisnolossoflong-termfairnessunderthisapproach. 3.5.1CommunicationwithNoFeedback Ifnochannelinformationisprovidedtothesource,thesourceneedstoxthecommunicationstrategy.Thepossibleoptimalcommunicationstrategiesarebasedonthepossiblechannelcombinations:(G,G),(G,B)or(B,G),or(B,B).Thus,theoptimalthroughputis TnoFB=max TGG, TGB, TBB, where Ts1s2istheexpectedthroughputofmulticastandunicastachievedwhenthesignalisdesignedforchannelstate(s1,s2),si2fG,Bg.Thesevaluescanbecalculatedusingthesteady-stateprobabilitiesas TGG=2(G)TGG+2(G)(B)(0,Tuni=2) TGB=2(G)+(G)(B)TGB+(B)(G)+2(B)TGB,multi,~Tuni=2 TBB=TBB. Intheabove,Ts1s2denotestheachievableunicastandmulticastthroughputforknownchannelstates(s1,s2),whichisgivenby( 3 ).TuniistheunicastthroughputthroughchannelstateG.Ts1s2,multidenotesthemulticastthroughputofTs1s2,and~Tunidenotes 44

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theunicastthroughputthroughchannelB.NotethatTs1s2,multiisnotachievedunlessallreceivershavesuccessfullyreceivedthemulticastpacket. 3.5.2CommunicationwithFeedbackwithNoDelay Ifthesourceknowsthechannelstatewithnodelay(i.e.,itknowstheaverageSNRtoeachreceiver,butnottheinstantaneousSNRs),thesourcethencanoptimizethetransmissionratestotheaverageSNRsineachtimeslot.Forchannels(G,B)and(B,G),thesourcealwaystransmitstheunicastpackettothereceiverwiththebetterchannel.Thus,thethroughputwithnofeedbackdelayisgivenbyT0)]TJ /F5 7.97 Tf 6.59 0 Td[(dFB=2(G)TGG+2(G)(B)TGB+2(B)TBB. 3.5.3CommunicationwithFeedbackDelayedbyOneTimeSlot Ifthesource'sknowledgeofthechannelsstateisdelayedbyonetimeslot,thesourcecanoptimizeitstransmissionparameterstomaximizethethroughputbasedonitsknowledgeoftheprobabilitiesofthecurrentstategiventhepreviousstate.Weagainconsiderthattheunicasttransmissionistargetedonlytothereceiverwiththebetterchannelwhenthechannelispredictedtobe(G,B)or(B,G).LetSt)]TJ /F6 7.97 Tf 6.59 0 Td[(1bethepreviouschannelstatesatreceivers1and2.TheoptimalsignalinthecurrentstatewillbeasignaldesignedforoneofthefourpossiblestatesfGG,GB,BG,BBg,andwelet^Stdenotethisstate.(Forthepurposeofdiscussion,wecantreatthisastheestimatedcurrentstate.)Thethroughputwith1-delayedfeedbackchannelstateinformationis T1)]TJ /F5 7.97 Tf 6.58 0 Td[(dFB=XSt,^StPr(St,^St)TSt,^St,(3) wherePr(St,^St)isthejointprobabilitythattheactualcurrentstatesareSt=st,andtheestimatedstatesare^St=st.TSt,^Stisthecorrespondingthroughputoftheevent(St=st,^St=st).Forsimplicityofnotation,let(st,^st)=(St=st,^St=st)inwhatfollows. 45

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Wegiveabriefexampleofhowthethroughputtermsin( 3 )canbecalculated.Considerthosesummationtermswhere^St=GB;therearefoursuchevents:(GG,^G^B),(GB,^G^B),(BG,^G^B),and(BB,^G^B).ThosetermsinthesummationcanbecalculatedasXSt,^St=GBPr(St,^St=GB)TSt,^St=GB=nPr(GG,^G^B)+Pr(GB,^G^B)oTGB+nPr(BG,^G^B)+Pr(BB,^G^B)o(TGB,multi,0). Sincethechannelstatesareindependentacrossreceivers,thejointprobabilityPr(St,^St)=Pr(S1,t,^S1,t)Pr(S2,t,^S2,t).Letpandqbetheconditionalprobabilityofestimatingthecurrentstateto^St=GgivenpreviousstatesSt)]TJ /F6 7.97 Tf 6.59 0 Td[(1=GandSt)]TJ /F6 7.97 Tf 6.59 0 Td[(1=B,respectively,as pPr(^St=GjSt)]TJ /F6 7.97 Tf 6.59 0 Td[(1=G)qPr(^St=GjSt)]TJ /F6 7.97 Tf 6.59 0 Td[(1=B). Forsimplicityofnotation,let(^sj~s)=(^St=sjSt)]TJ /F6 7.97 Tf 6.59 0 Td[(1=s).ThejointprobabilityPr(St,^St)cannowbewrittenintermsofthetransitionprobability,steady-stateprobability,p,andq,accordingtothelawoftotalprobability.Forinstance,Pr(G,^G)=Pr(G,^G,~G)+Pr(G,^G,~B)=Pr(Gj~G)Pr(^Gj~G)Pr(~G)+Pr(Gj~B)Pr(^Gj~B)Pr(~B)=(1)]TJ /F3 11.955 Tf 11.95 0 Td[(pb)p(G)+pgq(B). Thethroughputwith1-delayedfeedbackchannelstateinformationcannowbefoundbyoptimalchoiceofpandq,as T1)]TJ /F5 7.97 Tf 6.58 0 Td[(dFB=maxp,q2f0,1gXSt,^StPr(St,^St)TSt,^St. 46

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3.5.4SimulationResults Foralltheresultspresentedinthissection,theaverageSNRsforthetwostatesare G=15dBand B=5dB.Wepresentresultsforthethreecasesofchannel-statefeedbackdiscussedabove:nofeedback,feedbackwithnodelay,andfeedbackdelayedbyonetimeslot.TheblocksizeBusedinlinearnetworkcodingis16,andthenumberofreceiversKis2. In Figure3-5 ,weshowthethroughputgainachievableoverachannelwithfeedbackdelayedbyonetimeslotincomparisontoachannelwithnofeedback,asafunctionofpgandpb.Here,thethroughputgainisdenedasE[T1)]TJ /F5 7.97 Tf 6.59 0 Td[(dFB)]TJ /F17 11.955 Tf 12.47 0 Td[(TnoFB].Intheregions0pg,pb0.5and0.5pg,pb1,thethroughputgainofhaving1-delayedfeedbackcanbesignicant.However,intheotherregion,T1)]TJ /F5 7.97 Tf 6.59 0 Td[(dFBgivesalmostthesamevalueasTnoFB.Inthisregion,oneoftwoscenariosoccur:eitherthetransitionprobabilitiesarecloseto0.5andthusnothelpfulinestimatingthenextstate,oroneofthestatetransitionprobabilities,pgorpbismuchlargerthantheotherandthechannelstaysinaspecicstatemostofthetime. InFig. 3-6A ,wecomparethemaximumachievablethroughputsforseveraldifferentscenarios.Eachsubgraphisforadifferentcombinationofpgandpb.Ineachsubgraph,wecomparetheperformanceofthethreexedtransmissionstrategies(thebestpossibleperformancewithnofeedbackistheupperenvelopeofthese),simulcastingwithnofeedbackdelay(T0)]TJ /F5 7.97 Tf 6.58 0 Td[(dFB)andonetime-slotfeedbackdelay(T1)]TJ /F5 7.97 Tf 6.59 0 Td[(dFB),andtimesharingbetweennetworkcodingandunicastingwithonetime-slotfeedbackdelay(T1)]TJ /F5 7.97 Tf 6.59 0 Td[(dFBofNWC). Thebenetoffeedback(evenwithadelay)isclearlyshowninFig. 3-6A forpg=pb=0.1.Furthermore,thebenetofthesimulcastingapproachcanbeseen.Forexample,byreducingthemulticastthroughputfrom1.12bits/s/Hzto0.95bits/s/Hz,unicasttransmissionatrate0.5bits/s/Hzcanbeachieved,evenwithafeedbackdelayofonetimeslot.Bycontrast,iftime-sharingisusedtodividethechannelbetween 47

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Figure3-5. Throughputgainof1-delayedfeedbackovernofeedbackforthevaluesofpgandpb. multicastingandunicastingandthesamemulticastthroughputistobeachieved,thentheunicastrateisonly0.28bits/s/Hz.Thus,simulcastingachievesovera75%higherunicastingrate.Ifthefeedbackdelayiseliminated,thenthesimulcastingthroughputincreasestoapproximately0.7bits/s/Hz. AsseeninFigs. 3-7A and 3-6B ,thebenetofdelayedfeedbackgreatlydecreasesasthefeedbackinformationbecomeslessreliable(pgandpbcloserto0.5).However,simulcastingstillprovidesasmallgainoftimesharingbetweenmulticastingandsimulcastinginthesecases.Whenpg=0.8andpb=0.4,thereisnegligiblethroughputgainforeitheroftheschemeswithfeedbackdelayedbyonetimeslotoversimulcastingwithnofeedback,asshowninFig. 3-7B .Infact,xedtime-sharingbetweenmulticastingandunicastingcanachievethesameperformanceassimulcastingwithfeedbackdelayedbyonetimeslot.ThereasonisthatthesteadystateprobabilitiesaredominatedbytheGstate.WhenthefeedbackindicatesthatthepreviousstateisB,thecurrentstateislikelytobeG;however,thisislikelywithoutthefeedback.Ontheotherhand, 48

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Apg=pb=0.1 Bpg=pb=0.5 Figure3-6. Throughputcomparisoninasimulcastnetworkwith/withoutfeedbackchannelstateinformationwhenpg=pb. whenthepreviousstateisG,thenextstateisalmostequallylikelytobeBorG,andsothedelayedfeedbackisagainnothelpful.Insuchacase,onlyfeedbackwithnodelaycanstillproducesignicantgains,asalsoshowninFig. 3-7B 3.6Summary Inthischapter,westudiedtheuseofsimulcastingtotransmitmulticastandunicastinformationonaRayleighfadingchannelwithaverageSNRdeterminedby 49

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Apg=0.2,pb=0.4 Bpg=0.8,pb=0.4 Figure3-7. Throughputcomparisoninasimulcastnetworkwith/withoutfeedbackchannelstateinformationwhenpg6=pb. atwo-stateMarkovchain.Weevaluatetheeffectoffeedback(withorwithoutdelays)ontheabilitytoimprovethethroughputofcombinedmulticastingandunicastingtoallowthesimulcastingsignalconstellationtobeoptimizedbasedonthechannelconditions.Knowledgeofthechannelstatesallowssimulcastingtotakeadvantageofdifferencesinchannelconditionsbetweenthereceivers.Wecomparedthethroughputofsimulcasting2-SPCwithtime-sharingbetweennetworkcodingandunicasting, 50

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wherelinearnetworkcodingisusedtotransmitthemulticastdataefcientlyovertheunreliablefadingchannel.Weshowedthatwhenthesourcehasareliableestimateofthechannelstate,thensimulcastingcansignicantlyoutperformtimesharingbetweenmulticastingandunicasting.Ifthefeedbackisdelayed,theperformanceincreaseoveraxedtransmissionschememaybegreatlyreduced(dependingonthestatetransitionprobabilities).Thus,simulcastingshowsthegreatestpotentialforchannelsthatchangerelativelyslowlyincomparisontotherateoffeedback. 51

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CHAPTER4GEOGRAPHICTRANSMISSIONWITHOPTIMIZEDRELAYING(GATOR)FORTHEUPLINKINMESHNETWORKS 4.1IntroductionofGeographicTransmission Wirelessmeshandsensornetworkspresentchallengingproblemsinthedesignofnetworkprotocols.Thereasonisthatthefadingrateoftheradiochannelsisusuallyhigherthantherateatwhichnetworkstateinformationisexchangedamongradios.Thus,conventionalprotocolsthatarebasedonpre-determinedlinksandroutesexperiencehighratesofpacketfailureduetooutage.Inaddition,fornetworkswithmorethanafewtensofnodes,thenetworktopologymaychangeatafasterratethantheroutinginformationcanbepropagatedthroughthenetwork.Again,conventionalproactiveandreactiveroutingprotocolswilloftenhavesevereproblemsbecausetheroutinginformationchangesfasterthannewroutinginformationcanbedistributedthroughthenetwork.Thedifcultiesinprotocoldesignarefurtherenhancedifthenodesalsouserandomsleepingprotocolstoconserveenergy.Thus,intheuplinkofwirelessmeshandsensornetworks,theperformanceisoftenlimitedbyfadingchannelsandsleepingnodes,bothofwhichresultinpacketfailures. Geographictransmissionschemescanovercometheseproblemsbytakingadvantageofopportunisticreception(OpRx),inwhichasenderbroadcastsapackettomultiplereceiversandaforwardingagentisselectedfromthosereceiversthatcorrectlyrecoverthemessage[ 24 32 ].OneoftherstOpRxschemesdescribedintheliteratureisalternaterouting[ 33 ,Sec.IV.D],inwhichapacketthatexperiencestoomanytransmissionfailurestothenodeselectedbytheroutingtablemaythenbeforwardedbyanalternatenode.Asimilarschemecalledselectiondiversityforwarding(SDF)isproposedin[ 24 ]and[ 34 ].InSDF,anacceptablelistofforwardingagentsispre-determinedusingchannelstateinformationfedbackfromneighboringnodes.Opportunisticmulti-hoprouting(ExOR),proposedin[ 31 ],issimilar,withcandidateforwarderschosenbasedonclosenesstothedestination.Astochasticforwarding 52

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approachissuggestedin[ 32 ],whereaforwarderisrandomlychosenfromalistaccordingtoanoptimaldistribution. Takentotheirextreme,theuseofpre-determinedroutesiseliminated,andgeographicrouting[ 25 27 35 39 ]canbeused,inwhichpacketsareforwardedinthedirectionofthedestination.Mostworkongeographicroutinghasfocusedonallowingroutinginhighlydynamicnetworksandonreducingtheroutingoverhead(forinstance,tableupdatesoroodedrouterequestpackets).AgeographicapproachthatprovidesdiversitywithrespecttorandomsleepschedulesofthepotentialforwardersisGeographicRandomForwarding(GeRaF)[ 25 26 ].Oneproblemidentiedin[ 25 ]and[ 26 ]ishowtodesignapracticalschemetoselectanodetobethenext-hopforwarderforapacket.In[ 25 ,Sec.4],theauthorspresentanadhocschemebasedonpartitioningthesetofpotentialrelaysintopriorityregionsbasedondistancefromthedestination.Thisschemeisthenshowntoofferperformanceclosetotheidealcaseinwhichthebestrelayisalwayschosen.Forfadingchannelswithachannelcoherencetimethatisontheorderofthepacketlength,geographicroutingwillprovidebetterperformancethanconventionalroutingprotocolsbecausepre-determinedrouteswilloftenperformpoorlybecausethespeciedlinkswilloftenbeindeepfades.In[ 27 ],theGeRaFschemeisextendedtofadingchannels,withthesameapproachtondingpriorityregions.In[ 40 ],Rossietal.provideanadaptiveframeworkfornext-hoprelayselectionthatcanaccommodatevariouscostfunctionsbutrequiresnumericaloptimization.In[ 41 ]and[ 42 ],node-activationprobabilitiesareoptimizedtoimprovemeasuressuchastransmissiondistance.In[ 43 ],theauthorsconsidertheselectionofanenergy-efcientrouterinaNakagamifadingchannelbyconsideringboththemaximumforwardingdistanceandthepacket'ssuccessfultransmissionprobabilityonatime-correlatedchannel. RelatedtoOpRx,opportunistictransmission(OpTx)canalsotakeadvantageofvariationsinthewirelesschannelbytransmittingtoanodethathasagoodchannel 53

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gain(cf.[ 44 46 ]),thusachievingmultiuserdiversity.OpTxschemes,suchasthosein[ 8 47 49 ],arebasedontheapproachin[ 44 ],inwhichtheentiresystembandwidthisallocatedtotheuserwiththebestchannelgainateachtimeandthepowerissimultaneouslyadaptedtomaximizethesum-ratecapacity.AnothertypeofOpTxisproposedin[ 50 ],inwhichmobilityisusedtomovepacketsclosertotheirdestinations.However,OpTxschemesaredependentonhavingpacketsavailableformanynext-hopradios,havingaccuratechannel-stateinformationforthenext-hopradios,andhavingpacketsthatcantolerateadditionallatency.Infadingwirelesscommunicationchannels,thechannelstatemaychangetoofasttoallowforaccurateupdatesinwirelessmeshandsensornetworks.Furthermore,manytypesoftrafccannottoleratesuchdelays,andtheavailabilityofappropriatepacketsisoftenlimitedbytransport-layerprotocols(cf.[ 51 ]). Inthischapter,wedevelopageographictransmissionprotocolthatcanachievediversitythroughopportunisticreception.Weconsideratime-slottedscheme,whichallowsustooptimizethewayinwhichpotentialrelayscontendtobecometheforwarderforapacket.Thus,wecallourschemeGeographicTransmissionwithOptimizedRelaying(GATOR).In section4.2 ,weintroducethenetworkmodelthatweconsider.In section4.3 ,wepresenttheGATORprotocolandderivetheoptimalrelayselectionschemeforGATORwhencommunicationisoveraRayleighfadingchannel.Section 4.4 describesthetransmissionschemesthatweuseforperformancecomparisons,and section4.5 providesperformanceresults.Thechapterisconcludedin section4.6 4.2NetworkModel Weconsiderawirelessmeshorsensornetwork,withxedAPsplacedonaregulargridinasquareareaofdimensionDkm,asshownin Figure4-1 .TheAPsaresurroundedbynodesthatwishtotransmitinformationontheuplinktotheAPs.WeassumethatthenodesknowtheirownlocationsandthoseoftheAPsandalwayssendinformationtothenearestAP.WeconsiderascenarioinwhichtheAPsaredistributedin 54

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Figure4-1. Exampleofmeshnetworklayoutwith9accesspoints.Ai=i-thaccesspoint. spacewithasufcientdensitythatpacketshaveahighprobabilityofreachingtheAPintwohopsformostnodes. Timeisassumedtobedividedintoframes,withnodesturningonandofffromframetoframetoconserveenergy.TheAPsarealwayson.Inagivenframe,thedistributionofthenodesthatareon(hereaftercalledon-nodes)followsahomogeneousPoissonpointprocesswithdensitynodesperkm2.Theprocessisassumedtobei.i.d.fromframetoframe.Whenanodeison,itwillgenerateapacketwithprobabilityps.Suchanodeiscalledasource.Ifanon-nodedoesnothaveapackettosend,itwilllistentotransmissionsfromothernodes.Ifitsuccessfullyreceivesapacketfromasource,itmayremainoninthenexttimeframetocontendtorelaythepackettotheAP.Otherwise,itmayturnoffinthenextframe. Wefurtherassumethatthelinkforeachtransmitter-receiverpairisafrequencynon-selective,slowRayleighfadingGaussianchannel.Thefadingeventsforallthelinksareindependentspatiallyandfromframetoframe.Thepath-lossexponentis2.Each 55

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AGeographicTransmissionwithOptimizedRelaying(GATOR). BDirecttransmission. CRouting. DS-GeRaF. Figure4-2. Structureofonetimeframefortheprotocolsinthischapter. nodetransmitsatthesamepower,suchthattheaveragesignal-to-noiseratio(SNR)atareceiverthatis1kmawayisS0.Thus,thereceiveSNRinatimeframeatdistancedkmfromthetransmitterisZS0d)]TJ /F6 7.97 Tf 6.59 0 Td[(2,whereZisanexponentialrandomvariablewithunitenergy.Forsimplicity,wemaketheassumptionthatpowerfulchannelcodingisappliedsuchthatwhenanodesendsapacketwithinformationraterbits/s/HztoanothernodeoranAP,thetransmissionwillbesuccessfulifandonlyiftheinformationrateisbelowthecapacityofthelinkinthatframe.Thatis,transmissionthroughthelinkissuccessfulifandonlyifrd2 Sr. 4.3GeographicTransmissionwithOptimizedRelaying(GATOR) GATORisdesignedformeshnetworksinwhicharelaycanbeemployedifapacketisnotreceiveddirectlybytheAP.Thefocusofourworkisontheproblemofdeterminingwhichnodesshouldcompeteasrelaysandhowtheyshouldcompeteifaxednumberofslotswithineachframeareavailableforcontention.Weassumethatnodesknowtheirlocationsandwhethertheyhavereceivedthepacketcorrectly,buttheydonotknowthechannelfadinggaintotheAP.Thus,weproposeageographicstrategyinwhichnodesusetheirlocationinformationandthatoftheAPindeterminingwhether 56

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andhowtocontendforthechannel.Unlikeconventionalxedrouting,therelayisnotpre-determined.Thus,thisisanopportunisticreceptionschemethatmaybeabletoextractadditionaldiversityfromthechannel. InGATOR,timeisdividedintoconsecutiveframesofequaldurationandstructure.Thestructureforoneframeisshownin Fig.4-2A .Therearetwosetsofmini-slotsatthebeginningofeachframethatareusedtocontendforthechannel.TherstMmini-slotsareusedbypotentialrelaystocontendtoforwardapacketthatwasnotreceivedattheAPinthepreviousframe.TheremainingKmini-slotsareforsourcesthathaveapackettosendtocontendforthechannel.Wedescribetheuseofthesemini-slotsfromasource'sperspectiverst.Relayingisgivenpriority,soasourcewillrstsensethechannelduringtheMmini-slotsbeforecontendingforthechannelintheremainingKmini-slots.IfasourcedoesnotsenseanysignalsintherstMslots,thenthesourcewillselectauniformrandomnumberbetween1andK.Ifasourceselectsi,thenitwillsensethechannelinmini-slots1toi)]TJ /F4 11.955 Tf 12.8 0 Td[(1.Ifacarriersignalisdetectedinthosemini-slots,thenthesourcewillnottransmititsdatainthecurrentframeandwillcompeteforthechannelagaininthenextframe.Ifnocarrierisdetectedinthesemini-slots,thesourcewillsendacarrierinmini-slotitoindicatethatithasacquiredthechannelandwilltransmititspacketintheDataPacketslot.Theremainingslotsintheframearefordatatransmissionandacknowledgments.ApacketmaybedirectlyreceivedbythedestinationAP,inwhichcasetheAPsendsanAP-ACK(AACK).IftheAACKisreceived,thesourcedeletesthesuccessfulpacketfromitsbuffer. IftheAACKisnotreceived,thesourcewillsensethechannelintheMmini-slotsinthenextframe.IfnosignalisdetectedintheMmini-slots,thenthesourcewillassumethatneitherthesourcenoranyrelayreceivedthepacket,anditwillcontendforthechannelagain.IfasignalisdetectedintheMmini-slots,thenthesourcewilllistentothedatapackettoseeifitspacketisbeingrelayed.IftheAPreceivesapacketfromarelayingnode,itwillsendanAACK,andtherelaywillsendaRelay-ACK(RACK)back 57

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tothesource.NotethatweassumethattherateofinformationintheACKsignalsissubstantiallylowerthanthatofthedatapacket.Hencewiththeuseofpowerfulchannelcoding,theACKsignalscanbesuccessfullyreceivedbythesourceevenwhendirectdatapackettransmissionfromsourcetotheAPfails. Nowconsidertheproblemofdeterminingwhichofthenon-sourcenodesshouldcontendtorelayapacket(i.e.,becomepotentialrelays)andhowthosepotentialrelaysshouldusetheMmini-slotstocontendtoforwardapacket.Toavoidcollision,oneandonlyoneoftheon-nodesthathasreceivedthepacketshouldrelayittotheAP.Tomaximizetheprobabilitythattherelay'stransmissiontotheAPissuccessful,itisdesirabletochoosearelaythatisclosetotheAP.However,suchnodesaregenerallyrelativelyfarfromthesource,whichresultsinsuchnodeshavingasmallprobabilityofhavingcorrectlyreceivedthepacket.WewishtooptimizetherelayselectionschemeinGATORtobalancebetweenthesefactors.Formathematicaltractability,wefocusonasinglesourcein subsection4.3.1 .In subsection4.3.2 ,wediscusstheextensionofGATORtomultiplesourcesandAPs,andin section4.5 weusesimulationtoevaluatetheperformancewithmultiplesourcesandmultipleAPs. 4.3.1OptimalRelayRegionsforaSingleSource ConsiderasinglesourcetransmittingtoanAP.Weassumethatafterthissourcesuccessfullycontendsforchanneluse,noothersourcesinthewholenetworkwillsendanypackets.Withoutlossofgenerality,supposethatthesourceislocatedat()]TJ /F3 11.955 Tf 9.3 0 Td[(d,0)andthenearestAPislocatedat(0,0),asshownin Figure4-3 .IfthepackettransmissionfromthesourcedirectlytotheAPfailedintheprevioustimeframe(indicatedbytheabsenceofanAACK),allon-nodesthathavesuccessfullyreceivedthepacketcontendforforwardingittotheAPbasedonthefollowingprotocolinthecurrenttimeframe: 1. Anon-nodethathassuccessfullyreceivedthepacketfromthesourcepicksarandomnumberN(x,y)fromthesetf1,2,...,M,M+1gaccordingtothe 58

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probabilitymassfunction(pmf)pm(x,y)form=1,2,...,M+1,where(x,y)isthelocationofthenode. 2. IfN(x,y)=M+1,thenodewillnotforwardthepacket. 3. IfN(x,y)M,thenthenodesensesthechannelduringmini-slots1toN(x,y))]TJ /F4 11.955 Tf 10.95 0 Td[(1.IfthenodedetectsacarriersignalinanyoftheseN(x,y))]TJ /F4 11.955 Tf 12.2 0 Td[(1mini-slots,itwillnotforwardthepacket.Ifnoothernodestransmitduringthesemini-slots,thenodewillsendacarriersignalinmini-slotN(x,y),andthenforwardthedatapacketinthedataslotoftheframe. Notethatifmorethanoneon-nodesendsacarriersignalinthesamemini-slot,thedatatransmissionsfromthesenodeswillcollide.Thustheoptimalforwardingresolutiondesignprovidesthepmfpm(x,y)thatmaximizestheprobabilityPFoftheeventthatexactlyoneon-nodeforwardstotheAPandsucceedsindoingsointhetimeframeafterthepackettransmissionfromthesource.Forsimplicity,wemaketheassumptionthattherequiredSNRtodetectacarriersignalisverylowsothatallcarriersignalscanbedetectedbyallon-nodesinthenetwork. TocalculatePF,letuspartitiontheplaneintorectanglesofinnitesimalareadxdy.Fortherectangleat(x,y)andanon-nodeinsidethisrectangle,theprobabilitythatthisnodesuccessfullyreceivesthepacketfromthesourceandthenodeselectsN(x,y)=mispm(x,y)e)]TJ /F6 7.97 Tf 6.58 0 Td[([(x+d)2+y2]=Sr.Thustheprobabilitythatnonodeintherectangleat(x,y)forwardsthepackettothedestinationis1Xn=0(dxdy)ne)]TJ /F14 7.97 Tf 6.58 0 Td[(dxdy n!"1)]TJ /F3 11.955 Tf 11.96 0 Td[(e)]TJ /F13 5.978 Tf 7.79 3.86 Td[([(x+d)2+y2] SrmXi=1pi(x,y)#n=exp")]TJ /F7 11.955 Tf 9.3 0 Td[(e)]TJ /F13 5.978 Tf 7.78 3.86 Td[([(x+d)2+y2] SrmXi=1pi(x,y)dxdy#, andtheprobabilitythatexactlyoneon-nodeinthisrectangleselectsanN(x,y)=mandallotheron-nodesinthisrectangleselectN(x,y)>m(thatis,exactlyoneon-nodeinthisrectangleforwards)is1Xn=0(dxdy)ne)]TJ /F14 7.97 Tf 6.58 0 Td[(dxdy n!n1hpm(x,y)e)]TJ /F6 7.97 Tf 6.59 0 Td[([(x+d)2+y2]=Sri"1)]TJ /F3 11.955 Tf 11.96 0 Td[(e)]TJ /F6 7.97 Tf 6.59 0 Td[([(x+d)2+y2]=SrmXi=1pi(x,y)#n)]TJ /F6 7.97 Tf 6.58 0 Td[(1=pm(x,y)e)]TJ /F6 7.97 Tf 6.59 0 Td[([(x+d)2+y2]=Srdxdyexp")]TJ /F7 11.955 Tf 9.3 0 Td[(e)]TJ /F6 7.97 Tf 6.59 0 Td[([(x+d)2+y2]=SrmXi=1pi(x,y)dxdy#. 59

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Thereforetheprobabilitythatexactlyonenodeat(x,y)picksanN(x,y)=mbutnonodeatanylocationpicksanN(~x,~y)m(thatis,exactlyonenodeat(x,y)forwardsbutnonodesatotherlocationsforward)ispm(x,y)e)]TJ /F6 7.97 Tf 6.58 0 Td[([(x+d)2+y2]=Srdxdyexp"ZZ)]TJ /F7 11.955 Tf 9.29 0 Td[(e)]TJ /F6 7.97 Tf 6.58 0 Td[([(~x+d)2+~y2)]=SrmXi=1pi(~x,~y)d~xd~y#=pm(x,y)e)]TJ /F6 7.97 Tf 6.59 0 Td[([(x+d)2+y2]=Srdxdyexp")]TJ /F7 11.955 Tf 9.3 0 Td[(ZZe)]TJ /F6 7.97 Tf 6.59 0 Td[([(~x+d)2+~y2)]=SrmXi=1pi(~x,~y)d~xd~y#. Finally,wehavePF=MXm=1ZZe)]TJ /F6 7.97 Tf 6.59 0 Td[((x,y)pm(x,y)dxdyexp")]TJ /F7 11.955 Tf 9.3 0 Td[(ZZe)]TJ /F6 7.97 Tf 6.58 0 Td[((x,y)mXi=1pi(x,y)dxdy#, where(x,y)=(x+d)2+y2 Sr,\(x,y)=x2+y2 Sr,and(x,y)=(x,y)+\(x,y). WeconsiderthemaximizationofPFsubjecttogm(x,y)=)]TJ /F3 11.955 Tf 9.3 0 Td[(pm(x,y)0form=1,2,...,Mandall(x,y),andg(x,y)=PMm=1pm(x,y))]TJ /F4 11.955 Tf 12.92 0 Td[(10forall(x,y).NotethatPFisconcave,andgm(x,y)andg(x,y)arelinearinfpm(x,y):m=1,2,...,Mandall(x,y)g.ThustheKKTcondition[ 52 ]givestheoptimalchoiceofpm(x,y)necessarilyandsufciently.FirstconsidertheLagrangefunctionasL=PF+MXm=1ZZm(x,y)gm(x,y)dxdy+ZZ(x,y)g(x,y)dxdy. TheelementinthegradientvectoroftheLagrangiancorrespondingtopk(x,y)is@L @pk(x,y)=@PF @pk(x,y)+MXm=1ZZm(x,y)@gm(x,y) @pk(x,y)dxdy+ZZ(x,y)@g(x,y) @pk(x,y)dxdy=(x,y))]TJ /F7 11.955 Tf 11.96 0 Td[(k(x,y)+e)]TJ /F6 7.97 Tf 6.59 0 Td[((x,y)dxdy()]TJ /F5 7.97 Tf 17.15 14.95 Td[(MXm=kZZe)]TJ /F6 7.97 Tf 6.59 0 Td[((x,y)pm(x,y)dxdyexp")]TJ /F7 11.955 Tf 9.29 0 Td[(ZZe)]TJ /F6 7.97 Tf 6.59 0 Td[((x,y)mXi=1pi(x,y)dxdy#+e)]TJ /F6 7.97 Tf 6.58 0 Td[(\(x,y)exp")]TJ /F7 11.955 Tf 9.29 0 Td[(ZZe)]TJ /F6 7.97 Tf 6.59 0 Td[((x,y)kXi=1pi(x,y)dxdy#) 60

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fork=1,2,...,Mandall(x,y).DeneK(Ru,Rl)=2e)]TJ /F5 7.97 Tf 6.58 0 Td[(d2=SrZRuRle)]TJ /F6 7.97 Tf 6.58 0 Td[(22=SrI02d SrdL(Ru,Rl)=2e)]TJ /F5 7.97 Tf 6.58 0 Td[(d2=SrZRuRle)]TJ /F14 7.97 Tf 6.58 0 Td[(2=SrI02d Srd, whereI0()=1 2R)]TJ /F14 7.97 Tf 6.58 0 Td[(ecosdisthezeroth-ordermodiedBesselfunctionoftherstkind,andletR1,R2,...,RMbethesolutionofthefollowingsetsofnonlinearequationsoftheLagrangian: e)]TJ /F5 7.97 Tf 6.58 0 Td[(R2M=Sr=K(RM,RM)]TJ /F6 7.97 Tf 6.59 0 Td[(1)e)]TJ /F5 7.97 Tf 6.58 0 Td[(R2M)]TJ /F13 5.978 Tf 5.76 0 Td[(1=Sr1)]TJ /F3 11.955 Tf 11.96 0 Td[(e)]TJ /F5 7.97 Tf 6.59 0 Td[(L(RM,RM)]TJ /F13 5.978 Tf 5.75 0 Td[(1)=K(RM)]TJ /F6 7.97 Tf 6.59 0 Td[(1,RM)]TJ /F6 7.97 Tf 6.59 0 Td[(2)e)]TJ /F5 7.97 Tf 6.58 0 Td[(R2M)]TJ /F13 5.978 Tf 5.76 0 Td[(2=Sr1)]TJ /F3 11.955 Tf 11.96 0 Td[(e)]TJ /F5 7.97 Tf 6.59 0 Td[(L(RM)]TJ /F13 5.978 Tf 5.75 0 Td[(1,RM)]TJ /F13 5.978 Tf 5.75 0 Td[(2)=K(RM)]TJ /F6 7.97 Tf 6.59 0 Td[(2,RM)]TJ /F6 7.97 Tf 6.59 0 Td[(3)...e)]TJ /F5 7.97 Tf 6.58 0 Td[(R21=Sr1)]TJ /F3 11.955 Tf 11.96 0 Td[(e)]TJ /F5 7.97 Tf 6.58 0 Td[(L(R2,R1)=K(R1,0).(4) Thenwehave04=R0R1R2RM<>:1ifR2k)]TJ /F6 7.97 Tf 6.59 0 Td[(1
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k(x,y)=8>>>>>>><>>>>>>>:0ifx2+y2>R2k)]TJ /F6 7.97 Tf 6.59 0 Td[(1e)]TJ /F6 7.97 Tf 6.58 0 Td[((x,y)dxdye)]TJ /F5 7.97 Tf 6.58 0 Td[(L(Rk)]TJ /F15 5.978 Tf 5.75 0 Td[(l,0)ne)]TJ /F6 7.97 Tf 6.58 0 Td[(\(x,y)1)]TJ /F3 11.955 Tf 11.95 0 Td[(e)]TJ /F5 7.97 Tf 6.58 0 Td[(L(Rk,Rk)]TJ /F15 5.978 Tf 5.76 0 Td[(l)ifR2k)]TJ /F6 7.97 Tf 6.58 0 Td[(1)]TJ /F5 7.97 Tf 6.58 0 Td[(l>>><>>>>:0ifx2+y2>R2Me)]TJ /F6 7.97 Tf 6.58 0 Td[((x,y)dxdye)]TJ /F5 7.97 Tf 6.58 0 Td[(L(Rl,0)ifR2l)]TJ /F6 7.97 Tf 6.59 0 Td[(1<>:1ifR2k)]TJ /F6 7.97 Tf 6.59 0 Td[(1
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Figure4-3. Pictorialdescriptionofoptimalforwardingresolutionprotocolingeographictransmission.Sr=sourcenode.A=accesspoint. thepackettransmittedfromthesourcecanusethelocationinformation(locationsofthesourceandAP)inthepackettodetermineinwhichringitlies.Theon-nodesintheringsclosesttothedestinationhavehigherprioritytoforwardthepacketfromthesourcethanthoseon-nodesintheouterrings.Thispriorityisassertedbytransmittingacarriersignalinthepropermini-slot:on-nodesintheringwithouterradiusRiusemini-sloti,whereon-nodesoutsideRMwillnotforwardthepacket.Thus,weevaluatetheperformanceoftheabovePF-maximizingchoiceofpm(x,y)intermsoftheaveragedelayD,measuredintermsofthenumberoftimeframesrequiredtosendthepacketfromthesourcetothedestination,whichisgivenbyD=1Xk=1kPk, wherePkistheprobabilitythatthedestinationsuccessfullyreceivesthepacketinthekthtimeframe.Notethattheprobabilitythatthesourcetransmitstothedestinationdirectlyandsuccessfullyisgivenbye)]TJ /F5 7.97 Tf 6.58 0 Td[(d2=Sr,whichisobtainedfromthenon-outage 63

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event,log(1+ZS0d)]TJ /F6 7.97 Tf 6.58 0 Td[(2)r.Fork=1,2,...,P2k)]TJ /F6 7.97 Tf 6.59 0 Td[(1=1)]TJ /F3 11.955 Tf 11.96 0 Td[(e)]TJ /F15 5.978 Tf 5.76 0 Td[(d2 Sr)]TJ /F4 11.955 Tf 11.95 0 Td[((1)]TJ /F3 11.955 Tf 11.95 0 Td[(e)]TJ /F15 5.978 Tf 5.76 0 Td[(d2 Sr)PFk)]TJ /F6 7.97 Tf 6.59 0 Td[(1e)]TJ /F15 5.978 Tf 5.75 0 Td[(d2 SrP2k=1)]TJ /F3 11.955 Tf 11.96 0 Td[(e)]TJ /F15 5.978 Tf 5.76 0 Td[(d2 Sr)]TJ /F4 11.955 Tf 11.95 0 Td[((1)]TJ /F3 11.955 Tf 11.95 0 Td[(e)]TJ /F15 5.978 Tf 5.76 0 Td[(d2 Sr)PFk)]TJ /F6 7.97 Tf 6.59 0 Td[(11)]TJ /F3 11.955 Tf 11.95 0 Td[(e)]TJ /F15 5.978 Tf 5.76 0 Td[(d2 SrPF. HenceD=1Xk=1(2k)]TJ /F4 11.955 Tf 11.96 0 Td[(1)P2k)]TJ /F6 7.97 Tf 6.58 0 Td[(1+1Xk=12kP2k=2)]TJ /F3 11.955 Tf 11.95 0 Td[(e)]TJ /F5 7.97 Tf 6.59 0 Td[(d2=Sr e)]TJ /F5 7.97 Tf 6.59 0 Td[(d2=Sr+1)]TJ /F3 11.955 Tf 11.96 0 Td[(e)]TJ /F5 7.97 Tf 6.59 0 Td[(d2=SrPF. Thering-basedforwardingresolutionprotocolabovealsominimizestheaveragenumberoftimeslotsneededforapackettotraversefromthesourcetotheAPingeographictransmission.Thisprovestheoptimalityofthepriorityregionsin[ 25 ]and[ 27 ]forsourcesclosetothedestinationwithpath-lossexponent2andRayleighfading,and,moreimportantly,providesasolutiontothedimensionofthepriorityregionswhenthetime-slottedGATORprotocolisused. 4.3.2ExtensiontoMultipleSourcesandAPs InapracticalapplicationofGATOR,therearemultiplesourcesandAPs,asshownin Figure4-1 .Here,wedescribehowwedealwiththeimpactofmultiplesourcesandAPsinGATOR.First,weconsiderthedetectionofcarriersignalsinthecarrier-reservationmini-slots.TheinstantaneousSNRofcarriersignalsreceivedatanyradionodecanbeobtainedbySNRCS= Xip SNRCSicosi!2+ Xip SNRCSisini!2 whereSNRCSidenotesthereceivedSNRofacarriersignalfromanodei,andidenotestherandomphaseofthelinkbetweentransmitternodeiandthereceiver.WeassumethatacarrierwillbedetectedifandonlyifSNRCS>Sth,whereSthisathresholdthatdependsontheSNRparameterS0,thepacketgenerationratepsandthedensityofnodes.Sthischosenbasedonsimulationresultstobalancebetweentheprobability 64

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offalsealarm(dominatedbydetectingcarriersignalsintendedforadifferentAP)andtheprobabilityofmiss(notdetectingacarriersignalintendedforthenearestAPtothereceiver). TheoptimalforwardingregionsdescribedaboveareforanetworkwithasinglesourceataxedlocationandasingleAP.InanetworkwithmultiplesourcesandmultipleAPs,packettransmissionsfrommultiplesourcesandrelaysmayoccurinthesameframe,andthereforeweneedtoconsiderthesignal-to-interference-noiseratio(SINR)ofasource'stransmissiontondtheoptimalforwardingregions,ratherthantheSNR.ThereceivedSINRattheintendedAPisSINRRX=SNRRX PNSi=1SNRi+PNRj=1SNRj+1 whereSNRRXdenotesthereceivedSNRofthepackettransmissionfromthesourcetotheintendedAP,andSNRiandSNRj,respectively,denotethereceivedSNRattheAPofinterferingpackettransmissionsfromtheothersourcesandrelays.HereNSandNRalsodenotethenumberofinterferingtransmissionsfromsourcesandrelays,respectively.TheoptimalforwardingregionswilldependontheSINRattheAPaswellasthedistancefromthesourcetotheAP.ThusforGATORwithmultiplesourcesandAPs,whenasourcegainsaccesstothechannel,weusetheknowndistancetotheAPandthecomputedaverageSINRforthegivensystemparameterstodeterminetherelayingregions(thesecanbeindependentlycomputedateachofthepotentialrelaysthatcorrectlyrecoverapacket). 4.4ComparisonTransmissionSchemes Wehaveselectedtwoconventional(non-geographic)communicationschemesandtwogeographiccommunicationschemesbasedonGeRaFforwhichwewillcomparetheperformancewiththatofGATOR. 65

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4.4.1ConventionalSchemes Therstconventionalschemeisdirecttransmission,inwhichthesourcetransmitstothenearestAPwithnorelayingallowed.Thetimeslotstructureusedforthisprotocolisshownin Fig.4-2B .Sourcescontendforthechannelasdescribedin section4.3 ,andsimplyre-transmitpacketsaftertransmissionfailure. Inthesecondconventionalscheme,xedrouting,weassumethatthereisalwaysarouterplacedmidwaybetweenasourceandthecorrespondingAP.Sincetherouterisoptimallyplaced,thisshouldgivethebestpossibleperformanceamonganyconventionalroutingapproach.Theslotstructureforroutingisshownin Fig.4-2C .SourcescontendforthechannelinthesamewayasinGATOR(cf. section4.3 ).IftheAPcorrectlyreceivesapacketfromasource,itsendsanacknowledgmentintheAACKmini-slot.IftherouterdoesnotheartheAACKsignalandhassuccessfullyreceivedthepacket,itwillsendaRACK.Thentherouterwilltakeoverresponsibilityfordeliveringthepacket.IfeithertheAACKortheRACKisreceived,thesourcedeletesthepacketfromitsbuffer.Allsourcesandroutersemploythechannelcontentionprotocolin section4.3 tocontendforchanneluseorre-transmitpacketsaftertransmissionfailure. 4.4.2GeographicTransmissionSchemes TherstgeographictransmissionschemeisbasedonGeRaF[ 25 27 ]withmodicationstomakeGeRaFutilizeatime-slottedstructure.WerefertothisasSlottedGeRaF(S-GeRaF).TheframestructureusedforS-GeRaFisshownin Fig.4-2D .Therstmini-slotistheRequest-for-Relay(RR)mini-slot,whichisusedbypotentialrelaynodesthathavereceivedapacketfromasourcetocontendtoforwardthepackettotheAP:nodesthathavereceivedapacketfromasourcetransmitacarrierinthismini-slottoreservethechannelforforwarding.IfnocarriersignalisdetectedintheRRmini-slot,sourcescontendforthechannelasdescribedin section4.3 .AsourcethathasacquiredthechannelusestheRTS/CTS-basedcollisionavoidanceprotocol[ 26 ]withtherelayregionsdescribedin[ 27 ]tondasinglerelaynode.TherelayregioncontainsMpriority 66

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regions,andtheithpriorityregion,Bi,isacircularringcenteredonthedestinationwithradiiRi)]TJ /F6 7.97 Tf 6.59 0 Td[(1andRi.TheRi'sareselectedsuchthattheaveragenumberofavailablepotentialrelaysineachpriorityregionisthesame,withtheinitialconditionsthatR0isequaltozero,andRMisequaltothedistancebetweenasourceandthenearestAP.Thus,theRi'ssatisfyZBiP()d=ZBi)]TJ /F13 5.978 Tf 5.75 0 Td[(1P()di=2,...,M, whereP()=P(Z>2 Sr)istheprobabilitythatatransmissionfromasourcetoapotentialrelayatthedistanceawayfromthesourceissuccessful.ThesourcethentransmitsabroadcastRTSmessageandlistensinthesubsequentslotforCTSmessagesfrompotentialrelayslocatedintheinnermostpriorityregion.IfonlyoneCTSmessageisreceived,thesourcewillsendaSTOPmessageandstopthecollisionavoidanceprotocoloperation.IfthesourcereceivesnoCTSs,itwillsendaCONTINUEmessageandlistenagainforCTSsfrompotentialrelayslocatedinthenextpriorityregion.Ifthesourcehearsasignalbutisnotabletodetectthemessage,itwillassumethataCTScollisionoccurs,andwillsendaCOLLISIONmessagewhichwillinitiateacollisionresolutionalgorithm[ 26 ].Tolimitthedurationofthecollisionavoidanceprotocol,itterminatesiftheCTScollisionisnotresolvedwithinNRTS/CTSslots.IfthesourcereceivesaCTSmessagefromonlyonepotentialrelaynodewithinNRTS/CTSslots,thesourcetransmitsthepackettotherelayintheDataPacketslot.ApacketmaybedirectlyreceivedbythedestinationAP,inwhichcasetheAPsendsanACK.IftheACKisreceived,thesourcecandeletethesuccessfulpacketfromitsbuffer.IftheACKisnotreceived,thesourcewillsensethechannelintheRRmini-slotinthenextslot.Ifnosignalisdetected,thenthesourcewillassumethatneithertheAPnortherelayreceivedthepacket,anditwillcontendforthechannelagain.AsourcethatdidnottransmitinapreviousslotwillalsosensethechannelintheRRmini-slot.IfacarriersignalisdetectedintheRRmini-slot,thesourcewilltransmitneitheracarriernora 67

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Table4-1. Parametersusedforcalculatingthroughputpenaltyofroutingandgeographictransmissionrelativetodirecttransmission. ParameterDefaultvalue Bandwidth1MHzDatarate1MbpsData1,000bytesACKdata50bytesRTS/CTSdata50bytesControlmessagedata50bytesPLCPheader16bytesMACheader34bytestdata(PLCPheader+MACheader+data)8,400stACK(PLCPheader+MACheader+ACKdata)800stRTS=CTS(PLCPheader+MACheader+RTS/CTSdata)800stCNT(PLCPheader+MACheader+controlmessagedata)800stmini)]TJ /F6 7.97 Tf 6.58 0 Td[(slot(Slottime)20s RTSmessage,andthesourcewilllistentothedatapackettoseeifitspacketisbeingrelayed.IftheAPreceivesapacketfromarelaynode,itwillsendanACKtothesource,andthesourcewilldeletethepacketfromitsbuffer. ThesecondgeographictransmissionschemeusestheprotocolofGATORbutwiththerelayregionsofGeRaF.WerefertothisasGATORwithGeRaF-basedrelayregions(GATOR-GBRR). 4.5SimulationResults Inthissection,wecomparetheperformancesofGATORandthecomparisonprotocolsspeciedin section4.4 inameshnetwork,asshownin Figure4-1 .Foralloftheresultspresented,thedimensionofthenetworkis24km24km,andr=1bits/s/Hz.Exceptfortheresultsin Figure4-9 and Figure4-10 ,thenodedensityis=10nodes=km2andtherate-normalizedSNRis10.Toavoidtheedgeeffectcausedbyhavinganitesimulationeld,weallowtheboundariestowraparound,suchthatthetopandbottomedgesbecomeadjacent,asdotheleftandrightedgesofthegrid.Foreachprotocol,weconsiderthebestperformanceoverallofferedloadsbyndingthevalueofpsthatmaximizesthethroughputofthenetwork,wherethe 68

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throughputisdenedastheaveragetotalnumberofpacketssuccessfullydeliveredtotheAPspertimeslot.Sincethedifferentprotocolsrequiredifferentnumbersofmini-slots(protocoloverhead),weplotnormalizedthroughputsrelativetothedirecttransmissionschemewithnocontentionslots(i.e.,justData+ACK).Thenormalizedthroughputisthethroughputperslotdividedbythelengthoftheslotrelativetodirecttransmission.Thethroughputreductionisbasedontheparametersin Table4-1 .Forinstance,whenK=16andM=16,theslottimeforGATORis1.16times(=10,640s/9,200s)longerthantheslottimewithoutanyoverhead,andtheeffectivethroughputistheper-slotthroughputdividedby1.16.Wealsolimitthemaximumnumberoftimesasourcewilltransmitapacketto4,afterwhichthepacketwillbedropped. In Figure4-4 ,weshowthethroughputofthevariousschemes,asafunctionofthenumberofAPs.WeshowtheperformanceofGATORandGATOR-GBRRforseveralvaluesofM,thenumberofmini-slotsusedbytherelays.Foralltheseresults,thenumberofmini-slotsusedbysourcestocontendforthechannelisK=16.ForagivennumberofAPs,themaximumthroughputofgeographictransmissionincreaseswithanincreaseinMuntilM=32.Thereasonisthat,asMincreases,thepotentialrelaysthatareclosertotheAPhavehigherprioritytoforwardthepackettotheAPthanthosepotentialrelaysthatarefarther,andtheprobabilityofcollisionisreduced.However,beyondM=32themaximumthroughputofgeographictransmissionstartsdecreasingsincetheincreasedoverheadexceedsanyadditionalthroughputgain.ForallnumbersofAPsandM,GATORsignicantlyoutperformsdirecttransmission,xedrouting,S-GeRaF,andGATOR-GBRR.ForS-GeRaF,weshowthebestperformancethatwefoundaftervaryingthenumberofforwardingregionsMandRTS/CTSslotsN(see Figure4-5 forsupportingresults). Theresultsin Figure4-6 showthethroughputeffectsofvaryingK,thenumberofsourcecontentionsslots,asthenumberofAPsisalsovaried.ForGATORandGATOR-GBRRthenumberofmini-slotsusedforrelayselection,M,is32.Forthe 69

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Figure4-4. Throughputvs.numberofaccesspointsforvariousnumbersofforwardingregions,M.TheaverageSNRisS0=10dB,andthenumberofcarrier-reservationmini-slotsusedbysourcesisK=16.ForS-GeRaF,thebestcombinationofthenumberofforwardingregions(M=8)andthenumberofRTS/CTSslots(N=10)wasusedsee Figure4-5 valuesofKuntil16,theperformanceofallfourschemesincreases.Thisisreasonable,asincreasingKincreasestheprobabilityofschedulingexactlyonesourcetosendacarriersignalforchannelaccess.However,onceKreaches32,thethroughputofallfourschemesdecreasesbecausetheincreaseinoverheadexceedstheadditionalgainsinthroughputfromincreasingtheprobabilityofschedulingexactlyonesourcetosendacarriersignal. Aspreviouslymentioned,welimitthenumberoftimesapacketcanbetransmitted,asistypicalinmostsystems.Theresultsinthischapterassumethatapacketcanbetransmittedfromasourceamaximumof4times.Animportantissuethenishowthe 70

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Figure4-5. ThroughputofS-GeRaFvs.numberofaccesspointsforvariousnumbersofforwardingregions,M,andRTS/CTSslots,N,forthecollisionavoidanceprotocol.TheaverageSNRisS0=10dB,andthenumberofcarrier-reservationmini-slotsusedbysourcesisK=16. variousprotocolsimpacttheprobabilityofpacketdrop,whichoccurswhenasourcereachesthemaximumnumberoftransmissionsforapacketwithoutitbeingsuccessfullyreceivedattheAP.Toinvestigatethiseffect,welimitedthemaximumdistanceofthesourcesfromtheAPs,andin Figure4-7 weshowtheprobabilityofpacketdropasafunctionofthismaximumdistance.Fortheseresults,thenumberofAPsis4,M=32forGATORandGATOR-GBRR,andM=8andN=10inS-GeRaF.Thebenetsofgeographictransmissionoverdirecttransmissionandxedroutingschemesareparticularlydramatic.Thiscanbeattributedtothefactthatgeographictransmissionisabletoextracthighordersofdiversityfromthechannelstothedestinationandpotentialrelays,whereasdirecttransmissionandxedroutingarelimitedtodiversity 71

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Figure4-6. Throughputvs.numberofaccesspointsforvariousnumbersofcarrier-reservationmini-slotsusedbysources,K.TheaverageSNRisS0=10dB,andthenumberofforwardingregionsisM=32. order1and2,respectively.GATORachievessignicantlybetterperformancethanS-GeRaForGATOR-GBRR.In Figure4-8 ,weshowtheprobabilityofasourcereachingthemaximumnumberoftransmissionsasfunctionofthenumberofAPs.Again,thegeographictransmissionschemesprovidemuchbetterperformancethandirecttransmissionorxedrouting,andGATORoutperformsS-GeRaFandGATOR-GBRR. Theresultsin Figure4-9 showtheeffectsofvaryingtheSNRparameterS0onthroughput,fordifferentnumbersofAPs.TheperformanceofS-GeRaFisnotshown,sinceitisinferiortoGATOR-GBRR.TheresultsshowthatGATORprovidesthebestthroughputoutofalltheschemesforallnumberofAPsandSNRparametersweconsidered.ExceptforsmallnumbersofAPs(1and4)combinedwithS0=20dB, 72

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Figure4-7. Probabilityofpacketdropfromsourcereachingmaximumnumberoftransmissions(Ntx=4)vs.maximumdistancefromaccesspoint.NumberofAPsis4,theaverageSNRisS0=10dB,andthenumberofcarrierreservationmini-slotsusedbysourcesisK=16,thenumberofRTS-CTSslotsusedbyS-GeRaFis10,thenumberofforwardingregionsforS-GeRaFis8,andthenumberofforwardingregionsforGATORandGATOR-GBRRis32. GATORofferssignicantlybetterthroughputthantheotherschemes.ForlargeS0,thegainofthegeographicschemesoverdirecttransmissionandxedroutingdecreases,astheaverageSNRattheAPandrouterbecomesufcientlyhighthatthehigherdiversityofgeographictransmissionofferslessbenet.ThemaximumthroughputofdirecttransmissionincreaseswithanincreaseinS0,butthethroughputissignicantlylessthanthoseofgeographictransmissionandxedroutingschemeevenforS0=20dB. Next,weevaluatetheimpactofthedensityofon-nodesonthethroughputoftheprotocols,theresultsofwhichareshownin Figure4-10 .ForagivennumberofAPs, 73

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Figure4-8. Probabilityofpacketdropfromsourcereachingmaximumnumberoftransmissions(Ntx=4)vs.numberofaccesspoints.TheaverageSNRisS0=10dB,andthenumberofcarrier-reservationmini-slotsusedbysourcesisK=16,thenumberofRTS-CTSslotsusedbyS-GeRaFis10,thenumberofforwardingregionsforS-GeRaFis8,andthenumberofforwardingregionsforGATORandGATOR-GBRRis32. thethroughputsofGATORandGATOR-GBRRincreasewithanincreaseinovertherangeweinvestigated.ThisisbecausetheGATORschemesareeffectiveatextractingincreasedordersofmultiuserdiversityfromthelargernumberofpotentialrelays. Anareaofconcernforgeographiccommunicationprotocolsiswhethertheadditionalthroughputgainsareachievedbyconsumingadditionalenergy.Comparedtodirecttransmission,thegeographiccommunicationprotocolsutilizeadditionalenergyinrelayingandintherelaycontentionphase.Thus,weconsidertheenergyefciencyofthevariousschemes,measuredbytheenergypersuccessfulpacket,Ep, 74

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Figure4-9. Throughputvs.numberofaccesspointsfordifferentvaluesoftheaverageSNRS0.Thenumberofcarrier-reservationmini-slotsusedbysourcesisK=16,andthenumberofforwardingregionsforGATORandGATOR-GBRRisM=32. whichisdenedastheratioofthetotalenergyconsumptionoverallnodesandAPsinthenetworktothetotalnumberofpacketssuccessfullydeliveredtotheAPs.EpismeasuredinJoules/packet.Thetotalenergyconsumptionisthesumofeachnode'sandAP'senergyconsumptionforpacket,carriersignal,controlmessageandACKtransmissionsduringthesimulationtime.Thenoisepowerisassumedtobe1mWforcalculatingasignalpowerandenergyconsumptionfromSNRparameters.Thepacket-normalizedenergiesofthevariousschemesschemesareshownin Figure4-11 asafunctionofthenumberoftheAPs.ForallnumbersofAPs,GATORachievesthelowestpacket-normalizedenergy.GATORoffersthelargestperformancegainswhenthenumberofAPsissmall.ForlargenumbersofAPs,theprobabilityofsuccessona 75

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Figure4-10. Throughputvs.numberofaccesspointsfordifferentvaluesofthedensityofon-nodes,.TheaverageSNRisS0=10dB,thenumberofcarrier-reservationmini-slotsusedbysourcesisK=16,andthenumberofforwardingregionsforGATORandGATOR-GBRRisM=32. directtransmissionincreasessufcientlythatthebenetsofgeographictransmissiondecrease. 4.6Summary Inthischapter,weconsideredthedesignofageographiccommunicationschemetoachieveopportunisticreceptioninameshnetworkwithblock-fadingchannels.Weintroducedatime-slottedprotocolframework,andconsideredtheproblemofrelayselectioninthatframework.Weshowedthatwecancasttherelayselectionproblemasaconvexoptimizationproblem,thesolutionofwhichresultsindividingspaceintoaseriesofconcentricringscenteredontheAP.Areceiverthatsuccessfullyoverhearsamessagewillcontendtoactasaforwarderforthepacketwithprobability1ina 76

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Figure4-11. Energypersuccessfulpacket,Ep,vs.numberofaccesspoints.TheaverageSNRisS0=10,thenumberofcarrier-reservationmini-slotsforsources'transmissionisK=16,thenumberofRTS-CTSslotsusedbyS-GeRaFis10,thenumberofforwardingregionsforS-GeRaFis8,andthenumberofforwardingregionsforGATORandGATOR-GBRRis32. mini-slotthatcorrespondstotheindexoftheringinwhichthereceiverlies.Theresultingschemeisthegeographictransmissionwithoptimizedrelaying(GATOR)protocol.WecomparedtheperformanceofGATORtodirecttransmission,xedroutingwitharouteroptimallyplacedmidwaybetweenthesourceandAP,aslottedversionofGeRaF,andGATORwithrelayingregionschosenasinGeRaF.Wecomparedtheperformancewithmanydifferentsystemparameters,andevaluatedtheperformanceintermsofdifferentmetrics,suchasthroughput,probabilityofreachingthemaximumnumberofallowedtransmissionsforapacket,andenergyefciency.TheresultsshowthatGATORoffersthebestperformanceofalloftheschemesinallofthescenariosconsidered. 77

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CHAPTER5MULTI-HOPGEOGRAPHICTRANSMISSIONWITHOPTIMIZEDRELAYING(GATOR)FORTHEUPLINKINMESHNETWORKS 5.1IntroductionofMulti-hopGeographicTransmission InChapter 4 ,GATORisproposedtoachieveopportunisticreceptionanddeliverpacketstodestinationAPsinmeshnetworks,inwhichthedestinationcanbereachedinatmosttwohopswithhighprobability.Theproblemofrelayselectionisconsideredasanoptimizationproblemandoptimalforwardingresolutionprotocolisprovided.GATORisshowntoofferslargeperformancegainsoverdirecttransmission,xedrouting,andaslottedversionofGeRaF,especiallytheaverageSNRarelow.However,inapracticalmeshnetwork,sourcesmayoftenbetoofartoreachthedestinationdirectlyorwiththehelpofasinglerelay.Forsuchnetworks,wewishtoapplyageographicapproachlikeGATOR,butitisnotclearhowtoextendGATORtoallowmultiplehopsfromthesourcetodestination. Inthischapter,weconsiderthedesignofgeographictransmissionprotocolsbasedonGATORfortheuplinkofameshnetworkwithtime-varyingfadingchannelsinwhichAPsaresparseandthedimensionofthenetworkissolargethatthepacketmayhavetobeforwardedinmultiplehopsbetweenthenodeanddestinationAP.Weintroducetwomulti-hopGATORprotocolsthatusethesameslottedrelayselectionapproachasinGATOR.However,inmulti-hopGATOR,arelaythathassuccessfullyreceivedapacketwillthenactjustasifitwerethesourceforthepacket.Whenthepacketistransmittedbyarelayandnotreceivedatthedestination,anotherrelaythatisclosertothedestinationmaybeselectedtobethenext-hopforwardingagent.Thetwovariantsofmulti-hopGATORdifferonlyinhowtherelayingregionsaredeterminedateachtransmission.Foreachprotocol,therelayingregionswillbeconcentriccirclescenteredonthelinefromthesourcetodestinationAP.Wecallthedistancefromthesourcetothecenteroftherelayingregionsthedesigndistance.Inmulti-hopGATORwithfulldesigndistance(mhGATOR-FDD),thedesigndistanceisthefulldistancefromthe 78

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sourcetodestination;thatis,therelayingregionsarecenteredaroundthedestinationandhencearegivenby( 4 ).Therelayingregionsdeterminedinthiswaymayresultinasmallprobabilityofsuccessfullydeliveringthepackettoarelaybecausetheseregionsmaximizetheprobabilityofsuccessfullydeliveringapackettoarelay,havingthatrelaybetheonlyrelayinitsrelayingregiontosendacarriersignaltoindicatethatitwillrelaythepacket,andhavingthatrelaysuccessfullytransmitthepackettothedestinationinthenextslot.Thislastconditionisnolongerrequiredundermulti-hopGATORandresultsinrelayingregionthatmaybefarfromthetransmittingnode.Thus,weproposetolimitthedesigndistancetoavaluethatmaybesmallerthanthesourcetodestinationdistance.Wecallthisapproachmulti-hopGATORwithintermediatedesigndistance(mhGATOR-IDD).Bychoosingthedesigndistance,wecanbalancebetweentheprobabilityofsuccessfullydeliveringthepackettoarelayingandtheprogresstowardthedestinationwhenthepacketisreceivedatarelay.Wecomparetheperformancetomulti-hoprouting,2-hopGATOR,anddirecttransmission. 5.2NetworkModel Weconsiderawirelessmeshorsensornetwork,withxedAPsplacedonaregulargridinasquareareaofdimensionDkm,asdescribedin section4.2 .Thefulldetailsofthesystemmodelaregivenin section4.2 ,butwereviewsomekeydetailshere.TheAPsaresurroundedbynodesthatwishtotransmitinformationontheuplinktotheAPs.WeassumethatthenodesknowtheirownlocationsandthoseoftheAPsandalwayssendinformationtothenearestAP. Timeisassumedtobeslotted,withnodesturningonandofffromslottoslottoconserveenergy.TheAPsarealwayson.Inagivenslot,thedistributionofthenodesthatareon(hereaftercalledon-nodes)followsahomogeneousPoissonpointprocesswithdensityperkm2.Theprocessisassumedtobei.i.d.fromslottoslot.Whenanodeison,itwillgenerateapacketwithprobabilityps.Suchanodewillbecalledasourceandwillremainonuntilthepacketissuccessfullydeliveredtoanext-hop 79

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AMulti-hopGeographicTransmissionwithOptimizedRelaying(GATOR). BDirecttransmission. CMulti-hoprouting. Figure5-1. Structureofonetimeslotfortheprotocolsinthischapter. relaynodeortheAP.Ifanon-nodedoesnothaveapackettosend,itwilllistentotransmissionsfromthesourceorarelay.Ifitsuccessfullyreceivesapacketfromthesourceorarelay,itmayremainoninthenexttimeslottocontendforforwardingthepackettoanext-hoprelayortheAP.Otherwise,itmayturnoffinthenextslot. Furtherassumethatthelinkforeachtransmitter-receiverpairisafrequencynon-selective,slowRayleighfadingGaussianchannel.Thefadingeventsforallthelinksareindependentspatiallyandfromslottoslot.Thepath-lossexponentis2.Pleasereferto section4.2 fortheotherdetailsofthepropagationmodelandpacketsuccesscondition. 5.3Multi-hopGeographicTransmissionwithOptimizedRelaying(GATOR) Multi-hopgeographictransmissionschemesaredesignedformeshnetworksinwhichapacketcanberelayedmultipletimesifitisnotreceiveddirectlybytheAP.Itneedstobedeterminedwhichnodesshouldcompeteasrelaysineachhopandhowtheyshouldcompetetoavoidcollisionifaxednumberofslotswithineachframeareavailableforcontention.Weassumethatnodesknowtheirlocationandwhethertheyhavereceivedthepacketcorrectly,buttheydonotknowthechannelfadinggaintotheAP.Thus,weproposeamulti-hopgeographicstrategyinwhichpotentialrelaysusetheirlocationinformationandthoseofatransmitterandtheAPindeterminingwhetherandhowtocontendforthechannel.InChapter 4 ,theoptimalforwardingresolutionprotocol 80

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ispresentedwiththeoptimalrelayregionfor2-hoptransmission.WeemploytheoptimalforwardingresolutionprotocolofGATORtoextendformulti-hoptransmission. Inmulti-hopGATOR,timeisdividedintoconsecutiveframesofequaldurationandstructure.Thestructureforoneframeisshownin Fig.5-1A .Therearetwosetsofmini-slotsatthebeginningofeachframethatareusedtocontendforthechannel.TherstMmini-slotsareusedbypotentialrelays,whosuccessfullyreceivedapacket,tocontendtoforwardapacketthatwasnotreceivedattheAPinthepreviousframe.TheremainingKmini-slotsareforsourcesthathaveapackettosendtocontendforthechannel.Wedescribetheuseofthesemini-slotsfromasource'sperspectiverst.Relayingisgivenpriority,soasourcewillrstsensethechannelduringtheMmini-slotsbeforecontendingforthechannelintheremainingKmini-slots.IfasourcedoesnotsenseanysignalsintherstMslots,thenthesourcewillselectauniformrandomnumberbetween1andK.Ifsourcesselectsi,thenitwillsensethechannelforcarriersignalsinmini-slots1toi)]TJ /F4 11.955 Tf 12.41 0 Td[(1.Ifacarriersignalisdetectedinthosemini-slots,thenthesourcewillnottransmititspacketinthecurrentframeandwillcompeteforthechannelagaininthenextframe.Ifnocarrierisdetectedinthesemini-slots,thesourcewillsendacarrierinmini-slotitoindicatethatithasacquiredthechannelandwilltransmititspacketintheDataPacketslot.Theremainingslotsintheframearefordatatransmissionandacknowledgments.ApacketmaybedirectlyreceivedbythedestinationAP,inwhichcasetheAPsendsanAP-ACK(AACK).IftheAACKisreceived,thesourcecandeletethesuccessfulpacketfromitsbuffer. IftheAACKisnotreceived,thesourcewillsensethechannelintheMmini-slotsinthenextframe.IfnosignalisdetectedintheMmini-slots,thenthesourcewillassumethatneitherthesourcenoranypotentialrelayreceivedthepacket,anditwillcontendforthechannelagain.IfasignalisdetectedintheMmini-slots,thenthesourcewilllistentothedatapackettoseeifitspacketisbeingrelayed.IftheAPreceivesapacketfromarelay,itwillsendanAACK.IftheAACKisreceived,boththesourceandtherelay 81

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candeletethesuccessfulpacketfromitsbuffer.IftheAACKisnotreceived,therelaywillsendaRelay-ACK(RACK)backtothesourcetoinformthattherelaywilltakeoverresponsibilityfordeliveringthepackettothedestinationAP.IftheRACKisreceived,thesourcecandeletethepacketfromitsbuffer. Again,inthenextframe,thecurrentrelaywillsensethechannelintheMmini-slots.IfnosignalisdetectedintheMmini-slots,thentherelaywillassumeanynext-hoppotentialrelaydidn'treceivethepacketanditwillcontendforthechannelwithsources.IfasignalisdetectedintheMmini-slots,thentherelaywilllistentothedatapackettoseeifitspacketisbeingrelayedbyanext-hoprelay.Thus,hopafterhopthepacketwillreachthedestinationAP.NotethatweassumethattherateofinformationintheACKsignalsissubstantiallylowerthanthatofthedatapacket.Hencewiththeuseofpowerfulchannelcoding,theACKsignalscanbesuccessfullyreceivedbythesourceortherelayevenwhendirectdatapackettransmissionfromthesourceortherelaytotheAPfails. 5.3.1Multi-hopGATORwithFullDesignDistance(mhGATOR-FDD) ConsidertheproblemofdeterminingwhichofthepotentialrelaysshouldcontendtorelayapacketandhowthosepotentialrelaysshouldusetheMmini-slotstocontendtoforwardapacketinmhGATOR-FDD.Toavoidcollision,exactlyoneofthepotentialrelaysshouldrelayittotheAP.ArelayclosetotheAPwillhaveahighprobabilityofsuccessfultransmissiontotheAPbuthasasmallprobabilityofcorrectlyreceivingthepacket.Therelayselectionschemeshouldbalancebetweenthesefactors.InChapter 4 ,theoptimalforwardingresolutionprotocolalongwithoptimalrelayregionispresented.TherelayregioncontainsMpriorityregions,andtheithpriorityregionisacircularringcenteredonthedestinationwithradiiRi)]TJ /F6 7.97 Tf 6.59 0 Td[(1andRi.InmhGATOR-FDD,sincetherelayingregionsarealwayscenteredaroundthedestinationAP,theradii,R1,R2,...,RMareselectedbasedonthefulldistancefromthetransmittertodestinationAPtomaximizetheprobabilitythatexactlyoneon-nodeforwardstotheAPandsucceedsindoingso. 82

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A1sthoptransmission. B2ndhoptransmission. Figure5-2. Depictionofmulti-hopGATORwithFullDesignDistance(mhGATOR-FDD). Anon-nodethatsuccessfullyreceivesapacketusesthelocationsofthetransmitterandAPtodetermineinwhichringthenodelies.Theon-nodesintheinnerringshavehigherprioritytoforwardthepacketfromthesourcethanon-nodesinouterrings.Thispriorityisassertedbytransmittingacarriersignalinthepropermini-slot:on-nodesintheringwithouterradiusRiusemini-sloti,whereon-nodesoutsideRMwillnotforwardthepacket.Thering-basedforwardingresolutionprotocolabovealsominimizestheaveragenumberoftimeslotsneededforapackettotraversefromthesourcetotheAPingeographictransmission. TheexampleofmhGATOR-FDDisillustratedin Figure5-2 .Intheithtimeframe,asourcethatacquiredthechanneltransmitapacket.ThedirecttransmissiontoanAPfails,butmultipleon-nodesinrelayingregions.successfullyreceivedthepacketfromthesource,wheretherelayingregionisdeterminedbasedonthedistancefromthe 83

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sourcetotheAP.AfteranAACKisnotreceivedfromtheAP,theon-nodescontendforforwardingthepacketintheMmini-slotsinthei+1thframe.TherelaynodeR1whoacquiredthechannelforwardsthepackettotheAP.AssumethatneithertheAPnoranyon-nodeintherelayingregionreceivethepacket.Here,therelayingregionsisobtainedbasedonthedistancefromtherelayR1totheAP.AfteranAACKisnotreceived,therelayR1sendsaRACKbacktothesourcetoinformthatitwilltakeoverresponsibilityfordeliveringthepacket.IftheRACKisreceived,thesourcedeletesthepacketfromitsbuffer.Inthei+2thframe,therelayR1sensesthechannelintheMmini-slots.Therelaydetectsnosignalandtherelaycontendforthechannelwithothersources. Ineachhop,thismulti-hopprotocolofGATORenablestheclosestsuccessfulreceivertoadestinationAPtomoveapackettowardtheAPandsotoachieveaminimumresidualdistancetransmissiontotheAP.Thus,thepacketisabletoreachthedestinationAPbytheleastnumberofhopbyachievingmultiuserdiversity. 5.3.2Multi-hopGATORwithIntermediateDesignDistance(mhGATOR-IDD) Weconsidermulti-hopprotocolofGATORwithintermediatedesigndistanceinwhichtherelayfornexthopischosenamongpotentialrelaysinMrelayingregionscenteredonahoppoint.ThehoppointisdhopdistanceawayfromtransmitteronthelinejoiningthetransmitterandadestinationAP.Theshorterdhopis,themorepotentialrelaysfornexthopexits.Thatincreasetheprobabilityofsuccessfultransmissiontonext-hoppotentialrelays.ThelongerdhopenablesarelayclosetoadestinationAPandthatwillhaveahightprobabilityofsuccessfultransmissiontotheAP.Thedhopisselectedtobalancethesefactors.Forselectionofdhop,weconsidertheexpectedsumofforwardprogressperhopwhichistheproductofthenumberofpotentialrelaysperhopandtheexpectedforwardprogressperhop.Theexpectedforwardprogressperhop,isdenedasthedistancetraveledbythetransmissionalongthethedirectionofthedestination,tonodesthatsuccessfullyreceived,projectedontoalinejoiningthetransmitterandthedestination[ 7 ].Theoptimalvalueofdhopthatmaximizestheexpectedsumofforward 84

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A1sthoptransmission. B2ndhoptransmission. Figure5-3. Depictionofmulti-hopGATORwithIntermediateDesignDistance(mhGATOR-IDD). progressperhopcanbeobtainedbydhop=argmaxdE"NXi=0Pi#, wherePiistheforwardprogressofithpotentialrelayandNisthenumberofpotentialrelaysinrelayregions.IftheremainingdistancefromatransmittertotheAPissmallerthanthedesignhopdistance,therelayingregionsarecenteredaroundthedestinationAP.Theframestructureisshownin Fig.5-1A ,whichisthesameasformhGATOR-FDD.TheentireprotocolissameasmhGATOR-FDDexceptthenext-hoppotentialrelaysasdescribedabove. Theexampleofmulti-hopgeographiccommunicationschemewithintermediatedesigndistanceisillustratedin Figure5-3 .Intheithtimeframe,asourcethatacquiredthechanneltransmitapacket.ThedirecttransmissiontoanAPfails,butmultipleon-nodesinrelayingregionssuccessfullyreceivedthepacketfromthesource.The 85

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Figure5-4. Depictionofmulti-hoproutingschemewithintermediatedesigndistance. relayingregionischosenbasedonthehopdistance,distancebetweenthesourceandthehopcenterpoint.AfteranAACKisnotreceivedfromtheAP,theon-nodescontendforforwardingthepacketintheMmini-slotsinthei+1thframe.TherelaynodeR1whoacquiredthechannelforwardsthepackettotheAP.AssumethattheAPdoesn'treceivethepacketbutmultipleon-nodesinthenextrelayingregionreceivethepacket.Here,therelayingregionsisobtainedbasedonthedistancefromtherelayR1tothenexthopcenterpoint.AfteranAACKisnotreceived,therelayR1sendsaRACKbacktothesourcetoinformthatitwilltakeoverresponsibilityfordeliveringthepacket.IftheRACKisreceived,thesourcedeletesthepacketfromitsbuffer.Inthei+2thframe,therelayR1sensesthechannelintheMmini-slots.Therelaydetectscarriersignalsandthustherelaydoesn'tcontendforthechannelintheframe.AssumethatrelayR2acquiresthechannelforforwarding.TherelayR2willforwardthepacketandwilltakeoverresponsibilityfordeliveringthepacketinthefollowingframe. 5.4SimulationResults Inthissection,weevaluatetheperformancesofmulti-hopprotocolsofGATORinameshnetwork,asshownin Figure4-1 .Wecomparetheperformancetotwoconventionalcommunicationschemes.Therstconventionalschemesisdirecttransmissionandtheframestructuresisshownin Fig.5-1B .Indirecttransmission,sourcescontendforthechannelasdescribedin subsection5.3.1 ,andthesourcetransmitstothenearestAPwithnorelayingallowed.Packetsareretransmittedifthetransmissionfails.Thesecondconventionalschemeisxedrouting.In2-hoprouting,anon-node(router)isplacedmidwaybetweenthesourceandthecorrespondingAP,asdescribedinChapter 4 .Inmulti-hoprouting,routersareplacedeverydhopdistancefrom 86

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thesourcetothecorrespondingAP,asshownin Figure5-4 .IftheremainingdistancefromatransmittertoanAPissmallerthandhop,thetransmittersendsapackettotheAPdirectly.Theoptimalvalueofdhopthatmaximizetheexpectedprogressperhopcanbeobtainedbydhop=argmaxddP(d), whereP(d)=P(Z>d2 Sr)istheprobabilitythatatransmissionfromasourcetoarouteratthedistancedawayfromthesourceissuccessful,andSristherate-normalizedSNRasin section5.2 .Sincetheroutersareoptimallyplaced,thisgivesthebestpossibleperformanceforrouting.Theframestructuresisshownin Fig.5-1C .FirstistheRequest-for-Relay(RR)mini-slot,whichisusedbyaroutertoassertthatitisforwardingapacketduringtheframe.IfnocarrierisdetectedintheRRmini-slot,sourcescontendforthechannelasin subsection5.3.1 .AsourcethathasacquiredthechannelwilltransmititspacketintheDataPacketslot.IftheAPcorrectlyreceivesthepacketfromasource,itsendsanacknowledgmentframeintheAACKmini-slot.IfthecurrentrouterdoesnotheartheAACKsignalbuthassuccessfullyreceivedthepacket,itwillsendaRACK.Thenthecurrentrouterwilltakeoverresponsibilityfordeliveringthepacket.IfeithertheAACKortheRACKisreceived,thesourcecandeletethepacketfromitsbuffer.Inthenextframe,ifthecurrentrouterhasthepacket,itwillsendacarriersignalintheRRmini-slotandtransmititspacketintheDataPacketslot.Again,iftheAPcorrectlyreceivedthepacket,itsendsanAACK.Ifthenext-hoprouterdoesnotheartheAACKsignalbuthassuccessfullyreceivedthepacket,itwillsendaRACKbacktothecurrentrouterandtakeoverresponsibilityfordeliveringthepacket.Ifthecurrentroutercouldn'theareithertheAACKortheRACK,therouterwillassumethatneithertheAPnorthenext-hoprouterreceivedthepacket,anditwillcontendforthechannelinthenextframe.Forperformancecomparison,wealsoconsidertheperformanceof2-hopGATOR,asdescribedinChapter 4 87

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Foralloftheresultspresented,thereisoneAP,theinformationrateisr=1bits/s/Hz,thenodedensityis=10nodes=km2,theaverageSNRis10dB,thenumberofcarrier-reservationmini-slotsusedbysourcesisK=16,andthenumberofforwardingregionsisM=32forGATOR.Wealsolimitthemaximumnumberoftimesasourcewilltransmitapacketto8,afterwhichthepacketwillbediscarded.Toavoidtheedgeeffectcausedbyhavinganitesimulationeld,weallowtheboundariestowraparound,suchthatthetopandbottomedgesbecomeadjacent,asdotheleftandrightedgesofthegridin Figure4-1 .Foreachprotocol,weconsiderthebestperformanceoverallofferedloadsbyndingthevalueofpsthatmaximizesthethroughput,wherethethroughputisdenedastheaveragetotalnumberofpacketssuccessfullydeliveredtotheAPspertimeslot.Sincethedifferentprotocolsrequiredifferentnumbersofmini-slots(protocoloverhead),weplotnormalizedthroughputsrelativetothedirecttransmissionschemewithnocontentionslots(i.e.,justData+ACK),asdescribedin section4.5 In Figure5-5 ,weshowthethroughputofGATOR,asafunctionofdimensionDofthenetworkandforvarioushopdistance,dhopformulti-hopGATOR.Forsmallvaluesofthedimension(4and8),multi-hopGATORwithsmallvalueofhopdistance(dhop=4)offersbetterthroughputthantheothermulti-hopGATOR.Thisisbecause,eveninthesmalldimensionnetwork,somesourcesstillmaybefartoreachanAPandthepacketsmaybeabletobeforwardedmoreefcientlyinmultiplehops.However,multi-hopGATORusingoptimalhopdistance,dhop=7achievesthebestperformance,providedthedimensionissufcientlylarge.Asthedimensionincreases,multi-hopGATORwithdhopachievesthesignicantgainovermhGATOR-FDDand2-hopGATOR.InmhGATOR-IDD,apacketneedstobedeliveredtonext-hoppotentialrelayscenteredatthevirtualpointjustdhopdistanceawayfromatransmitter.However,inbothmhGATOR-FDDand2-hopGATOR,apacketneedstobedeliveredtopotentialrelaysaroundadestinationAP.Asthedimensionincreases,increasestheprobability 88

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Figure5-5. ThroughputofGATORvs.dimensionofnetworkwithparameterdhop.S0=10dB,K=16,M=32,andNtx=8 ofthedistancefromasourcetotheAPincreasing.Thus,ifthedimensionissufcientlylargeandasourceislongdistanceawayfromtheAP,thepotentialrelaysofthesourcemostlylieonouterrelaysregions.ThatcausesalowerprobabilityofthepotentialrelayssuccessfultransmissiontotheAPacrossthelongdistanceaswellasahigherprobabilityofcollisionbytherelaystransmittingcarriersignalsinthesamemini-slot. Theresultsin Figure5-6 showthethroughputofroutingandforvariousdhopformulti-hoprouting,asthedimensionisalsovaried.Multi-hoproutingwithdhop=1providebetterthroughputthantheothermulti-hopand2-hoproutinguntilthedimensionisequalto8.Thisisbecause,iftheremainingdistanceofatransmittertoanAPissmallerthandhop,thetransmittersendsapackettotheAPdirectlywithoutanyhelpofarouter.Beyondthedimensionisequalto8,multi-hoprougingwiththeoptimalhopdistance(dhop=2.24)providesthebestthroughputoutofalltheothermulti-hopand2-hoproutingschemes. 89

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Figure5-6. Throughputofroutingvs.dimensionofnetworkwithparameterdhop.S0=10dB,K=16,andNtx=8 Figure5-7. Throughputvs.dimensionofnetworkwhenS0=10dB,K=16,andNtx=8.ForGATOR,M=32 90

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Figure5-8. Energypersuccessfulpacket,Epvs.dimensionofnetworkwhenS0=10dB,K=16,andNtx=8.ForGATOR,M=32 Figure5-7 showsthethroughputofthevariousschemes,asafunctionofthedimension.Formulti-hopGATORandrouting,weshowthebestperformancethatwefoundovervariousdhop,asin Figure5-5 and Figure5-6 ,whicharefordhop=7forGATORandfordhop=2.24forrouting.Forthedimensiongreaterandequalto8,eachmulti-hopschemeprovidesthebetterthroughputthanitscorresponding2-hopschemeanddirecttransmission.Multi-hopGATORsignicantlyoutperformsalltheotherschemes.Thisisbecausemulti-hopGATORcanextracthighordersofdiversityfromthechannelstotheAPandpotentialrelays,whereasdirecttransmissionandroutingarelimitedtodiversityorder1and2,respectively.However,forthedimensionequalto4,directtransmissionprovidesthebestthroughputoutofalltheschemessincetheaverageSNRatthedestinationAPbecomessufcientlyhightohaveahighprobabilityofsuccessonadirecttransmissionwhilesimultaneouslyhavingloweroverheadcomparedtotheotherschemes. 91

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Figure5-9. Averagenumberofhoppersuccessfulpacketvs.dimensionofnetworkwhenS0=10dB,K=16,andNtx=8.ForGATOR,M=32 Next,weevaluatetheenergyefciencyofthevariousschemes,measuredbytheenergypersuccessfulpacket,Ep,whichisdenedastheratioofthetotalenergyconsumptionoverallnodesandAPsinthenetworktothetotalnumberofpacketsuccessfullydeliveredtotheAPs.EpismeasuredinJoules/packet.Thetotalenergyconsumptionisthesumofeachnode'sandAP'senergyconsumptionforpacket,carriersignal,andACKtransmissionsduringthesimulationtime.Theenergypersuccessfulpacketofthevariousschemesareshownin Figure5-8 asafunctionofthedimension.Forlargevaluesofthedimension,bothmulti-hopschemesofferlowerenergypersuccessfulpacketthan2-hopschemesanddirecttransmission,andparticularlymulti-hopGATORachievesthelowestenergypersuccessfulpacket.Whenthedimensionissmall,theprobabilityofsuccessonadirecttransmissionincreasessufcientlythattheadditionaloverheadusedinGATORandroutingschemeslimitstheenergyefciency. 92

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Theresultsin Figure5-9 showtheaveragenumberofhoppersuccessfulpacketforthemulti-hopschemesthatweconsidered.TheaveragenumberofhoppersuccessfulpacketistheratioofthetotalnumberofhopsspenttodeliverpacketstodestinationAPsfromsourcestothetotalnumberofpacketssuccessfullydeliveredtotheAPs.Multi-hopGATORwithdhoprequiresmoreaveragenumberofhoptosuccessfullydeliverapacketthanmhGATOR-FDD,whichisexpected,since,formhGATOR-FDD,theforwardprogressisnotlimitedbythexeddhop.Somewhatsurprisingly,multi-hoproutingschemerequirestheleastaveragenumberofhoppersuccessfulpacketforallvalueofthedimension.Weobservethat,astheroutingschemeislimitedtodiversityorder2,theprobabilityofapacketbeingsuccessfullydeliveredtoanAPthroughmorethancertainnumberofhopisverylow,andthepacketisdiscardedbyreachingmaximumallowednumberoftransmission,especiallywhenthedimensionislarge. 5.5Summary Inthischapter,westudiedtheuseofmulti-hopGeographicTransmissionwithOptimizedRelaying(GATOR)toimprovethroughputandenergyefciencyfortheuplinktransmissioninmeshnetworksinwhichAPsarespareandthedimensionofthenetworkislargethatthepacketmayneedtobedeliveredinmultiplehopsbetweenthesourceandtheAP.Weintroducedtwotime-slottedmulti-hopGATORprotocols,multi-hopGATORwithfulldesigndistance(mhGATOR-FDD)andmulti-hopGATORwithintermediatedesigndistance(mhGATOR-IDD),andcomparedtheperformanceofmulti-hopGATORwiththatof2-hopGATOR,multi-hoprouting,anddirecttransmission.Theresultsshowthatthemulti-hopGATORwithoptimalxedhopdistanceofferslargeperformancegainsover2-hopGATOR,multi-hoprouting,ordirecttransmission,especiallywhenthedimensionofthenetworkislargeandandAPsaresparse. 93

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CHAPTER6CONCLUSIONS Inthisdissertation,theefcientuseof2-SPCinanetwork-codedsystemhasbeenpresentedtoimprovetheefciencyofreliablemulticastingbytakingadvantageofdiversityinfadingchannels.Theproposedapproachescanbeeasilyappliedforthedownlinktransmissioninthewirelessnetworks.Theperformanceofreliablemulticastingusingnetworkcodingiscomparedwithandwithout2-SPCintwoscenarios.Intherst,thetransmissionratesforallofthemessageswereequal,xedvaluesthatwereindependentofthechannelSNR.Forthisscenario,itisshownthat2-SPCmayprovidesignicantgains.Inthesecondscenario,Thecommunicationparametersareoptimizedtomaximizethemulticastingthroughput.Inthissecondscenario,2-SPCshowedlittleperformanceimprovementovernetworkcodingwithoutSPC.TheresultsindicatethatSPCmaybeusefultoimprovetheperformanceofnetworkcodingforreliablemulticastifthechannelconditionsarenotknownexactly.Also,SPCmaybeusefulifitisusedtoincludemessagesotherthanthosefromthemulticastingstream. Next,theuseofsimulcastingbyemploying2-SPChasbeenconsideredtotransmitmulticastandunicastinformationonaRayleighfadingchannelwithaverageSNRdeterminedbyatwo-stateMarkovchain.Theeffectoffeedback(withorwithoutdelays)ontheabilitytoimprovethethroughputofcombinedmulticastingandunicastingisconsidered,wherethefeedbackisusedtooptimizethesimulcastingsignalconstellation.Knowledgeofthechannelstatesallowssimulcastingtotakeadvantageofdifferencesinchannelconditionsbetweenthereceivers.Thethroughputofsimulcasting2-SPCiscomparedwithtime-sharingbetweennetworkcodingandunicasting,wherelinearnetworkcodingisusedtotransmitthemulticastdataefcientlyovertheunreliablefadingchannel.Theresultsshowthatwhenthesourcehasareliableestimateofthechannelstate,simulcastingcansignicantlyoutperformtimesharingbetweenmulticastingandunicasting.Ifthefeedbackisdelayed,theperformanceincreaseover 94

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axedtransmissionschememaybegreatlyreduced(dependingonthestatetransitionprobabilities).Thus,simulcastingshowsthegreatestpotentialforchannelsthatchangerelativelyslowlyincomparisontotherateoffeedback. Fortheuplinktransmissionofwirelessmeshnetworks,thedesignofageographictransmissionschemehasbeenstudiedtoachieveopportunisticreceptionoverbock-fadingchannels.Atime-slottedprotocolframeworkisintroducedandtheproblemofrelayselectionintheframeworkisconsidered.Itisshownthattherelayselectionproblemcanbecastasanoptimizationproblem,thesolutionofwhichturnsouttobethatradionodeswithinaringtransmitwithprobability1inamini-slotcorrespondingtotheirring.Theradiioftheringscanbefoundofinenumerically.Theresultingschemeisthegeographictransmissionwithoptimizedrelaying(GATOR)protocol.TheperformanceofGATORwasevaluatedintermsofseveralmetrics,suchasthroughput,probabilityofreachingthemaximumnumberofallowedtransmissionsforapacket,andenergyefciency,andcomparedtheperformancetoconventionaltransmissionschemesandothergeographictransmissionschemes.ItisobservedthatGATORoffersthebestperformanceofalloftheschemesinallofthescenariosconsidered. Finally,GATORisgeneralizedtoascenarioinwhichtheradionodesmaybetoofartoreachtheaccesspoints(APs)intwohops.Thisapproachiscalledmulti-hopGATOR.Multi-hopGATORbasedonaxeddesigndistanceisproposedtobalancetheforwardprogressandnumberofpossiblepotentialrelaysineachhop.Theresultsshowthatmulti-hopGATORprovidesbetterperformancethanconventionalorothergeographictransmissiontechniques. 95

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REFERENCES [1] R.Ahlswede,N.Cai,S.-Y.Li,andR.Yeung,Networkinformationow,IEEETrans.Inform.Theory,vol.46,no.4,pp.1204,Jul2000. [2] R.YeungandN.Cai,NetworkCodingTheory.NowPublishersInc,2006. [3] M.Ghaderi,D.Towsley,andJ.Kurose,Networkcodingperformanceforreliablemulticast,inProc.2007IEEEMilitaryCommun.Conf.,Orlando,FL,Oct.2007,pp.1. [4] ,Reliabilitygainofnetworkcodinginlossywirelessnetworks,inProc.2008IEEEINFOCOM,June2008,pp.2171. [5] B.Choi,S.Boppana,andJ.M.Shea,Superpositioncodingandlinearnetworkcodingforreliablemulticastingoverfadingchannels,inProc.IEEEMilitaryCom-mun.Conf.,SanDiego,CA,Nov.2008,pp.1. [6] P.GuptaandP.R.Kumar,Thecapacityofwirelessnetworks,IEEETrans.Inform.Theory,vol.46,pp.388,Mar.2000. [7] L.KleinrockandJ.Silvester,Optimumtransmissionradiiforpacketradionetworksorwhysixisamagicnumber,inProc.NationalTelecom.Conf.,Birmingham,AL,Dec.1978,pp.4.3.1.3.5. [8] M.R.Souryal,B.R.Vojcic,andR.L.Pickholtz,Informationefciencyofmultihoppacketradionetworkswithchannel-adaptiverouting,IEEEJ.Select.AreasCommun.,vol.23,no.1,pp.40,Jan.2005. [9] D.S.Lun,M.Medard,R.Koetter,andM.Effros,Oncodingforreliablecommunicationoverpacketnetworks,Arxivpreprintcs.IT/0510070,2005. [10] S.Chachulski,M.Jennings,S.Katti,andD.Katabi,Tradingstructureforrandomnessinwirelessopportunisticrouting,inACMSIGCOMM'07,Kyoto,Japan,Aug.2007,pp.169. [11] S.Katti,H.Rahul,W.Hu,D.Katabi,M.Medard,andJ.Crowcroft,XORsintheair:practicalwirelessnetworkcoding,inACMSIGCOMM'06,Pisa,Italy,Sep.2006,pp.243. [12] R.Koetter,Networkcodingbibliography, https://hermes.lnt.e-technik.tu-muenchen.de/DokuWiki/doku.php?id=network coding:bibliography for network coding .[Online].Available: http://tesla.csl.uiuc.edu/koetter/NWC/Bibliography.html [13] S.Deb,M.Effros,T.Ho,D.R.Karger,R.Koetter,D.S.Lun,M.Medard,andN.Ratnakar,Networkcodingforwirelessapplications:Abrieftutorial,Proc.Intl.WorkshoponWirelessAd-hocNetworks,May2005. 96

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BIOGRAPHICALSKETCH ByonghyokChoi(S'05)receivedtheB.S.inelectronicsengineeringandtheM.S.inelectroniccommunicationengineeringfromHanyangUniversity,RepublicofKoreain1997and1999,respectively.HereceivedhisPh.D.fromtheUniversityofFloridainthespringof2011.Hiscurrentresearchinterestslieintheareaofcommunicationtheoryappliedtocross-layerapproachestoimprovethroughputperformanceoverfadingchannelsinad-hocandsensornetworks. 100