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Achieving high data rates in distributed MIMO systems
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Achieving high data rates in distributed MIMO systems
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ACHIEVINGHIGHDATARATESINDISTRIBUTEDMIMOSYSTEMS by HoriaVladBalan ADissertationPresentedtothe FACULTYOFTHEUSCGRADUATESCHOOL UNIVERSITYOFSOUTHERNCALIFORNIA InPartialFulfillmentofthe RequirementsfortheDegree DOCTOROFPHILOSOPHY (COMPUTERENGINEERING) August2013 Copyright 2013 HoriaVladBalan tomyparents ii TableofContents Dedication ii ListofFigures iv ListofTables v Preface vi Chapter1: Introduction 1 1.1 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2 Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Chapter2: TheoreticalConsiderations 8 2.1 AMultiuserMIMOPrimer. . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.2 SynchronizationindistributedMIMOsystems . . . . . . . . . . . . . . 15 2.3 RelatedWork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 Chapter3: Reference-basedSynchronization 24 3.1 AirSync . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 3.2 PerformanceEvaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 3.3 MediumAccessControl . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 Chapter4: AchievingScalabilityandEfficiency 47 4.1 DistributedSynchronization . . . . . . . . . . . . . . . . . . . . . . . . . 48 4.2 SystemDescription . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 4.3 EfficientEstimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 4.4 PerformanceEvaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 Chapter5: TagSpottingattheInterferenceRange 68 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 5.2 RelatedWork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 5.3 IntercarrierInterference . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 5.4 TagSpotting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 5.5 MotivatingtheDesignChoices . . . . . . . . . . . . . . . . . . . . . . . 82 iii iv TABLEOFCONTENTS 5.6 Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 5.7 PerformanceAnalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 5.8 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 5.9 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 Bibliography 104 ListofFigures 1.1 EnterpriseWiFiandDistributedMIMO.Multipleaccesspointscon- nected to a central server through Ethernet (red lines) coordinate theirtransmissionstoseveralclientsbyusingdistributedMIMO. . . . 2 2.1 BIATestbed. WhenusingBlindInterferenceAlignmenteachreceiver switchesbetweentwoantennamodes. . . . . . . . . . . . . . . . . . . . 14 2.2 Pilot phases. The phases of different subcarriers drift at the same speed,suggestingthattheyareonlysubjecttocarrierfrequencyoff- set. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3.1 AirSyncoperation. AsecondaryAP(bottom)synchronizesitsphase to the one of a reference signal (top) by adjusting the phase of its signaltomatchthephaseofthereference. . . . . . . . . . . . . . . . . . 28 3.2 Testbed diagram. The central server is connected to four transmit- ters, themaintransmitterontheleftandthethreesecondarytrans- mittersontheright. Fourreceiversactasclients. . . . . . . . . . . . . . 32 3.3 PhaseSynchronizationAcquisition. Thesecondarytransmitterreceives in-phase and quadrature components (real and imaginary compo- nents)ofthemastersignal(toptwofigures). Itthenobtainsaninitial phase estimate (middle figure) from these samples. The secondary tracks the phase drift of the subcarriers beginning at the 10th sym- bol(secondfrombottomfigure)andusesafiltertopredictitsvalue afewsymbolslater(bottomfigure). . . . . . . . . . . . . . . . . . . . . 33 3.4 ThePrecisionofthePhaseSynchronization. AirSyncachievesphase synchronizationwithinafewdegreesofthesourcesignal. . . . . . . . 34 3.5 The Power Leakage of Zero-Forcing. The leaked power is signifi- cantly smaller than the total transmitted power, transforming each receiver’schannelintoahighSINRchannel.. . . . . . . . . . . . . . . . 35 3.6 Zero-Forcing Scattering Diagram. The scattering diagram for two independentdatastreamstransmittedconcurrentlyusingZFBFdemon- strates that AirSync achieves complete separation of the user chan- nels. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 v vi LISTOFFIGURES 3.7 Tomlinson-Harashima precoding. Tomlinson-Harashima precod- ingbasedonQAM-16constellations. Theachievedspectralefficiency is16bits/second/Hz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.8 BIAScatteringDiagram. BlindInterferenceAlignmentenablesthe multiplexingoffouruserstreamsoverthreetimeslots.. . . . . . . . . . 38 3.9 Experimental Results. The absolute and relative rates of BIA and THPatdifferentSNRvalues,underdifferentmodulations. . . . . . . . 39 3.10 BIAChannelQuality. Thecumulativedistributionfunctionofreceived SNRsundertheBlindInterferenceAlignmentScheme. . . . . . . . . . 42 3.11 PacketDesign. Downlinkdatapacket(left)anduplinkacknowledg- ment(bottomright). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 4.1 CFODrift. Theevolutionofthecarrierfrequencyoffsetbetweentwo WARPboardsasmeasuredoveraonesecondinterval. . . . . . . . . . 52 4.2 Hierarchicalstructure. Thenodesareorganizedinclusterscentered on a set of anchor nodes whose can communicate wirelessly with theiranchorneighborssuchthattogethertheyconstituteaconnected setofnodes.[RBP + ]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 4.3 Superframe. The slot structure includes a synchronization period followedbyadownlinktransmissionperiod.[RBP + ] . . . . . . . . . . 55 4.4 CFOEstimationPeriod. ThebeaconsofdifferentAPsareinterleaved in time. The increased spacing between the constituent sequences allowsforafinerfrequencyestimate. . . . . . . . . . . . . . . . . . . . . 57 4.5 ChannelEstimation. (a)Channelmeasurements(phaseangle)before timing and phase-offset compensation. (b) Channel measurements (phase angle) after bringing the measurements to canonical form. (c) Distance between canonical forms for different pairs of random channels. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 4.6 PlacementDiagramfor4x4Experiments. Thepositionsoftheradios inthe anechoicchamber aremarkedin theabovefigure. Thetrans- mittersaremarkedinblueandthereceiversaremarkedinred. Inthe 2x2 experiments all the nodes were placed in the positions marked ontherightsideofthediagram. . . . . . . . . . . . . . . . . . . . . . . 64 4.7 Residual CFO distribution. The empirical cumulative distribution functionofthefrequencyoffsetsoftheAPthatsendsthebeaconand theAPthanlistenstoit. . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 4.8 Angledriftdistribution. Theempiricalcumulativedistributionfunc- tionoftherelativeanglechangebetweenthepilotsofthetwoAPs. 65 4.9 SINRDistribution. Thecumulativedistributionfunctionofthechan- nelSINRforeachuser. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 4.10 Zero-Forcing Scattering Diagram 2x2. The scattering diagram at the receivers of two independent data streams concurrently trans- mittedfromtwoAPs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 4.11 Zero-Forcing Scattering Diagram 4x4. The scattering diagram at the receivers of four independent data streams concurrently trans- mittedfromfourAPs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 LISTOFFIGURES vii 4.12 RatesofMultiplexedMIMOTransmissionvsPoint-to-PointTrans- mission. The sum rates obtained through multiuser transmission with four multiplexed streams are about 2.65 times higher than the averageratesofpoint-to-pointtransmissions. . . . . . . . . . . . . . . . 67 5.1 Frequencydomainview. ThediscreteandcontinuousFouriertrans- formsofanOFDMframe. . . . . . . . . . . . . . . . . . . . . . . . . . . 75 5.2 Packettransmission. Thesignals(t)(upperpane),atimefrequency representation using 512 frequency bins (middle pane) and a time frequencyrepresentationusing64frequencybins(lowerpane). . . . . 76 5.3 SpectralPlot. Thediscretespectrumofatwo-carriergroup(ampli- tudeandphaserepresentation)anditscontinuouspowerspectrum. 80 5.4 CFO Effects. The spectrum of a received tag in the presence of a frequencyoffset. Upperpane: the512frequencybinsFouriertrans- form of the corresponding detector interval. Middle pane: the 64 frequencybinsrepresentationusedinthedetectiondecision. Lower pane: thestructureofthetransmittedtag. . . . . . . . . . . . . . . . . . 82 5.5 ExperimentalResults. Theprobabilitiesofdetectionandfalsealarm indifferentinterferencescenarios. . . . . . . . . . . . . . . . . . . . . . 89 5.6 Probabilityofmiscalssification. Probabilityoftagmisclassification atdifferentSNRlevels. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 5.7 Detectioncurves. P d andP f fordifferentchoicesofcode,propaga- tionmodelanddetectionthreshold. . . . . . . . . . . . . . . . . . . . . 94 5.8 False Alarms. The probability of typical false alarms as a function ofthenumberofactivecarriers. Thetotalnumberofcarriersusedin tagconstructionis56. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 5.9 Chain-crosstopology. Allcompetingflowsareseparatedbyatmost onetransmissionrange(upper)andwithsomecompetingflowssep- aratedbymorethanthetransmissionrange(lower). . . . . . . . . . . . 100 5.10 Goodput. GoodputresultsforthetopologyinFigure5.9a . . . . . . . 101 ListofTables 2.1 BlindInterferenceAlignmentforthe22scenario . . . . . . . . . . . 15 4.1 Estimatedvariables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 viii Preface Multiple Input Multiple Output (MIMO) transmission increases the spectral efficiency ofwirelesscommunicationbymultiplexingmultiplestreamsofdata,takingadvantage of the spatial diversity characteristic to large wireless networks. The number of multi- plexedstreamsandtheachieveddegreeofspectralreusehavebeensofarlimitedbythe constraintthatallsimultaneoustransmissionshadtooccurfromasinglelocation,over alimitednumberofclosely-placedantennas. Thecurrentthesispresentsatechniqueforrealizingadistributed,coherenttransmis- sionsystemcapableofachievingthefullspatialmultiplexinggain. Thesynchronization amongdifferenttransmittersisrealizedovertheair,replacingthecommonly-usedback- end network capable of clock signal distribution with a much more cost-effective data network. The reduction in deployment cost paves the way for distributed MIMO as a viable technology for enterprise wireless networks and cellular offloading, beyond its current application in single base-station distributed antenna systems. Past advancing the state of the art in wireless system construction, we hope that the techniques pre- sented here will be followed by more advanced implementations, rendering high data ratewirelesscommunicationintoaday-to-daycommodity. Iwouldliketoacknowledgetheassistanceofmythesisadviser,ProfessorKonstanti- nosPsounisandofmycollaborators,ProfessorGiuseppeCaire,RyanRogalinandAnto- niosMichaloliakosduringthedevelopmentofthematerialpresentedinthisthesis. ThisresearchhasbeensupportedbytheMingHsiehInstitute,DocomoInnovations andtheNationalScienceFoundation. LosAngeles,CA May,2013 HoriaVladBalan ix CHAPTER 1 Introduction Theenormoussuccessofadvancedwirelessdevicessuchastabletsandsmartphonesis pushingthedemandforhigherandhigherwirelessdataratesandiscausingsignificant stress to existing networks. While new standards (e.g., 802.11n/ac and 4G) are devel- opedalmosteverycoupleofyears,novelandmoreradicalapproachestothisproblem are yet to be tested. The fundamental bottleneck is that wireless bandwidth is simply upper bounded by physical laws, in contrast to wired bandwidth, where putting new fiber on the ground has been the de-facto solution for decades. Advances in network protocols, modulation and coding schemes have managed steady but relatively mod- estspectralefficiency(bit/s/Hz)improvements. 4G-LTE,forinstance,offerstwotofive times better spectral efficiency than 2.5G-EDGE. Denser spectrum reuse, i.e., placing moreaccesspointspersquaremile,hasthepotentialtosuccessfullymeettheincreasing demand for more wireless bandwidth [cis12]. On the other hand, in contrast to con- ventional cellular systems, a very dense infrastructure deployment cannot be carefully plannedandmanagedforreasonspertainingtoscaleandcost. Therefore,themultiuser interference between different uncoordinated Access Points (APs) represents the main systembottlenecktoachievetrulyhighspectralefficiency. Intheory,theultimateanswertothisproblemisdistributedmultiuserMIMO(also knownas“virtualMIMO”),whereseveral(possiblymulti-antenna)APsareconnected to central server and operate as a large distributed multi-antenna base station. When 1 2 Figure1.1: EnterpriseWiFiandDistributedMIMO.Multipleaccesspointsconnected toacentralserverthroughEthernet(redlines)coordinatetheirtransmissionstoseveral clientsbyusingdistributedMIMO. usingjointdecodingintheuplinkandjointprecodinginthedownlink,alltransmitted signalpowerisuseful,asopposedtoconventionalrandomaccessscenarios(e.g.,carrier- sense)whichwastepowerthroughinterference. Thisapproachisparticularlysuitedto thecaseofanenterprisenetwork(e.g.,aWLANcoveringaconferencecenter,anairport terminal or a university), or to the case of clusters of closely spaced home networks connectedtotheInternetinfrastructurethroughthesamecablebundle. DistributedmultiuserMIMO(MU-MIMO)isregardedtodaymostlyasatheoretical solution because of some serious implementation hurdles, such as providing accurate timingandcarrierphasereferencetoalljointlycoordinatedAPsandtheabilitytoper- formefficientjointprecodingatacentralserverconnectedtotheAPsthroughawired backhauloflimitedcapacity. We consider a typical enterprise network as illustrated in Figure 1.1. Since in such networksthewiredbackhaulisfastenoughtoallowforefficientjointprocessingatthe server(see Section 3.1), themajorobstacletoachievingthefulldistributedMU-MIMO multiplexinggainisrepresentedbythelackofsynchronizationbetweenthejointlypro- cessed APs. The perceived difficulty of this task has led some researchers to believe that it is practically impossible to achieve the full multiplexing gain in the context of distributedMU-MIMO. In this thesis, we present two real-world testbed implementations which achieves the theoretical optimal gain by correcting, in real time, the instantaneous phase offsets CHAPTER1. INTRODUCTION 3 between geographically separated access points. The first one of these is a reference- based system, called AirSync, which synchronizes the access points surrounding a ref- erenceaccesspoint,enablingforthefirsttimemultiplexedtransmissionsfrommultiple access points. The second of these is a system that exploits channel reciprocity, called DistSync,andwhichimplementsanumberofdistributedsynchronizationtechniquesin ordertoenablespatialmultiplexingonamuchlargerscale. In a nutshell, AirSync tracks the instantaneous phase of a pilot signal broadcasted byareferenceAP(themasterAP),andpredictsthephasecorrectionacrosstheduration oftheMU-MIMOprecodedslotinordertode-rotatethecomplexbasebandsignalsam- ples. ThisenablesAPstomaintainphasecoherence,whichisnecessaryforMU-MIMO precoding. NoticethateachAPtransmitstheprecodeddatasignalandreceivesthemas- terAPpilotsignalsimultaneously. Thisisaccomplishedbydedicatingoneantennaper AP to pilot reception, while the others are used for MU-MIMO transmission. We have implementedAirSyncasadigitalcircuitintheFPGAoftheWARPradioplatform[Ric]. We have also implemented Zero-Forcing Beamforming [CS03] and Tomlinson-Harashima Precoding [WFVH04],twopopularMU-MIMOprecodingschemeswidelyinvestigated, fromatheoreticalviewpoint,intheliterature. UsingAirsyncinatestbedconsistingof eight WARP radios, four acting as access points connected to a central server and four actingasclients,wehaveshownthatthetheoreticaloptimalgainofmultiuserMIMOis achievableinpractice. DistSync separates the problems of phase-locking a group of transmitters and of estimatingandusingtheresultingfixedchannelrealization. Itusesadistributedmea- surementschemetodetermineandeliminateallcarrierfrequencyoffsetsbetweenAPs, makingtimephase-lockedforadownlinktimeslotduration,totheaccuracyoftheesti- mates. Subsequently, it efficiently estimates the channel, precodes and transmits the client signals before the coherence time of the channel lapses. DistSync has been simi- larlyimplementedasarealtimedigitalcircuitsupportedbyasoftwarestackandanet- workinfrastructurecapableofcomputingprecodinginformationatacentralserverand returningittothetransmitterswithinthechannelcoherencetime. 4 Multiuser downlink transmission involves taking into account channel state infor- mation and reacting to an unknown amount of interference arising from faulty mea- surementsorimperfectsynchronization. Consequently,weinvestigateprotocoldesigns for the MAC layer in distributed MU-MIMO systems, and the possibility of advancing past the design of the 802.11ac medium access layer [80212],through the use of Incre- mentalRedundancyratelesscodingatthephysicallayer[Sho06][PBS11]. Several extensions and improvements of this basic layout are possible, and are dis- cussed in the thesis. For example, in the case of AirSync, the master pilot signal range can be extended by regenerating and repeating the pilot signal at different frequen- cies. Also, we discuss the possibility of estimating the downlink channel matrix from training signals in the uplink and exploiting the physical channel reciprocity of Time- Division Duplexing (TDD). In particular, this latter issue is discussed in detail in the recent work [SYA + 12] for a large centralized MU-MIMO system where all transmit antennas are clocked together (both timing and carrier frequency) and therefore are perfectly synchronous. Thanks to DistSync, the same approach for calibration can be used in a distributed MU-MIMO system, although in the present implementation we useamoreconventionaldownlinktrainingandfeedbackconfiguration. Asopposedto AirSync, DistSync does not aim to eliminate random phases from the channel matrix, buttoworkwiththecompositechannel. Weexploreindetailtheoverheadsofoursyn- chronization schemes and describe techniques of reducing the amount of information transferred,overtheairandoverthewire,toaminimum. Whilerecentlytherehavebeenanumberofveryinterestingandimportantworksin whichsomeofthegainsofmultiuserMIMOhavebeenshown(seeSection2.3formore details) none of these has managed to achieve both timing and carrier phase synchro- nization between remote transmitters precise enough to implement MU-MIMO with optimalmultiplexinggaininthedistributedtransmittersscenario. Itisalsoworthwhile tonoticethatwhilesingle-userMIMOandsingleAP(centralized)MU-MIMOcanoffer multiplexinggainsforagivenconfigurationoftransmitandreceiveantennas,thesecan befurtherincreasedbyextendingthecooperationtothedistributedcase,providedthat thetransmitters(theAPs)canbesynchronizedwithsufficientaccuracy. Therefore,our CHAPTER1. INTRODUCTION 5 approachcanpotentiallyprovideadditionalmultiplexinggainsontopofanexistingcon- figuration. Afinalpartofthethesisdealswiththeissueofmessagepassinginwirelessnetworks. Message passing is the basic building block of many proposed schemes for apportion- ing the wireless capacity of a network among users and flows of data. We introduce a physical layer primitive that makes many of these techniques practical in real-world deployments and evaluate its impact on two example congestion control and medium access schemes targeted to wireless environments. Message passing complements the synchronization techniques presented in the rest of the thesis and makes distributed MIMOaviablealternativeforadhocdeploymentsaswell[OJTL10,OLT13]. ■ 1.1 Contributions This main contribution of this thesis is providing a clear implementation path for dis- tributedmultiuserMIMOinlarge,distributedwirelessnetworks. Itbridgesthedistance betweenthetheoreticaldevelopmentsofthepastyearsandtheirrealizationinpractical wirelesssystems. Bydoingso,itenablesdistributedmultiuserMIMOtorealizeitsfull potential as a practical, efficient way of increasing spectral reuse in enterprise wireless networks. Asastructureforbuildinguppracticalimplementations,weformalizetheproblem of distributed transmission and outline the challenges to be overcome, i.e. the physi- caleffectspresentwhenusingmultipletransmissionsources. Asolidunderstandingof these effects, their scale and their influence on the received signals is a necessary pre- requisitefordesigningsynchronizationschemesthataddressthem. The dissertation introduces two methods for realizing coherent downlink multi- plexed transmissions: AirSync uses a single access point as a reference source for syn- chronizing a number of neighboring transmitters; DistSync used distributed synchro- nizationinordertophase-lockamoredistributedsetoftransmitters. Eachoneofthese methodsimposesitsownlimitationonthetypeofchannelestimationthatcanbeused andbringswithititsowntimingrequirements. 6 1.2. ORGANIZATION We develop, in each case, complete protocols for the physical layer and investigate the design space of medium access layer protocols. Our system designs are capable of exploiting to the fullest the achieved multiplexing gains. In particular, we show that uplinkchannelestimationisaparticularstrongmatchforDistSync,allowingthesortof timeslot-by-timeslotoperationthatcountersthemanyeffectsofimperfectsynchroniza- tionandallowsforconsiderablylesscentralizationintheoperationofthenetwork. We study how different encoding schemes perform in a distributed MIMO environment, subjecttotheuncertaintiesofimperfectchannelestimationandimperfectsynchroniza- tion and make a strong case for incremental redundancy, rate-achieving schemes as a matchtothisphysicallayer. Each of these systems has been implemented in actual hardware and their perfor- mance has been thoroughly evaluated. The experiments prove that the level of syn- chronization achieved allow them to approach the theoretical optimal gains without sacrificingasensibleamountofbandwidthduetoprotocoloverheads. ■ 1.2 Organization Weconcludethisintroductionbyprovidingabriefoutlineoftherestofthethesis. Chapter 2 introduces distributed MIMO transmission, provides an overview of a number of common precoding schemes, some of which require transmitter-side chan- nelstateinformationandsomeofwhichoperatewithoutknowledgeofthechannel. It continues by establishing a theoretical model of distributed MIMO transmission that takesintoaccountdifferentoscillator-inducedeffectsanditexperimentallyevaluatesits accuracy. It closes by detailing the body of related work relevant to the problem, both theoreticalandexperimental. Chapter3introducesAirSync,asinglereference-basedsynchronizationmethodfor wireless transmitters. This method achieves phase coherence among several transmit- ters located within the range of the reference access point. It starts by presenting the construction of the synchronization scheme and the details of its implementation. It CHAPTER1. INTRODUCTION 7 continuesbyevaluatingitsperformanceinanactualdeployment. Finally,itdescribesa mediumaccesslayercompatiblewithitsoperation. Chapter 4 introduces DistSync, a scalable synchronization scheme aimed at large- scale deployments, beyond the effective range of a single access point. DistSync oper- ates by running a distributed synchronization algorithm which attempts to phase-lock theAPsinthenetworkforthedurationofadownlinktransmissionslot. Theoscillator characteristicsthatinfluencethedesignofthesynchronizationschemearepresentedin detail, along with experimental data that describes the changing oscillator behavior in time. We describe a synchronization scheme capable of compensating frequency drift with a high degree of precision while imposing a low wireless-transmission overhead onthenetwork. Thedownlinktransmissionslotmakesuseoftheshort-termconstancy ofthechannelandusesanefficientestimationalgorithmfollowedbyfastprecodingin ordertodetermineandusethisephemeralchannelinstantiation. Thechaptercontinues bydiscussing theuseofestimatorsinordertoincreasetheprecisionoftiming-specific parameter estimation and to decrease the amount of data sent over the wireless back- haul. Theperformanceofthesynchronizationschemeandtheachieveddegreeofmul- tiplexingarequantifiedthroughanexperimentalimplementation. Chapter5introducestags,wirelessprimitivesaimedtowardsmessagepassing. Tags enablemultipledistributedcontrolschemesinwirelessnetworks. Itdiscussesthecon- structionoftags,characterizestheirperformancetheoreticallyandexperimentallyand presentssampleapplicationsinschedulingandcongestioncontrol. CHAPTER 2 TheoreticalConsiderations ThecurrentchapterintroducesmultiuserMIMOcommunicationanddescribesanum- ber of commonly discussed multiuser precoding schemes. The focus is, on one side, on schemes that require full channel state information at the transmitter (CSIT) and, on the other side, on schemes that forgo channel state information at the expense of realizing a smaller number of degrees of freedom. We establish a theoretical model of a distributed MIMO transmitter that includes all oscillator-induced effects and test its accuracy through a series of microbenchmarks. This exposition constitutes a complete statementofthedistributedMIMOtransmissionproblemforwhichthesynchronization algorithms presented in the following chapters will try to offer compelling solutions. Finally, we present a review of related work, theoretical and experimental, that paved thewaytothecurrentdevelopment. ■ 2.1 AMultiuserMIMOPrimer WeconsidertheOFDMsignalingformat,asinthelastgenerationofWLANsandcellu- lar systems (e.g., IEEE 802.11a/g/n and 4G-LTE[Mol05]). OFDM is a block precoding scheme. OneOFDMsymbolcorrespondstoN frequency-domaininformation-bearing symbols. ByinverseFFT(IFFT),anOFDMsymbolisconvertedintoablockofN time- domainsamples. Thisblockisaugmentedbythecyclicprefix(CP),i.e.,byrepeatingthe 8 CHAPTER2. THEORETICALCONSIDERATIONS 9 LN lastsamplesatthebeginningoftheblock. TheOFDMsymbollengthN andthe CPlengthLaredesignparameters. WithCPlengthL,anyfrequencyselectivechannel with impulse response of lengthℓ L+1 samples is turned into a cyclic convolution channel,suchthat,byapplyinganFFTatthereceiver,itisexactlydecomposedintoaset ofN parallelfrequency-flatdiscrete-timechannelsinthefrequencydomain. TypicalCP length is between 16 to 64 time-domain samples. For example, for a 20 MHz signal, as inIEEE802.11g,thetime-domainsamplingintervalis50ns,sothatatypicalCPlength rangesbetween0.8and3.2s. In a multiuser environment OFDM has also a significant side advantage: as long as the different users’ signals align in time with an offset not larger than Lℓ, where L denotes the CP and ℓ is the maximum length of any channel impulse response in the system, their symbols after OFDM demodulation remain perfectly aligned in time andfrequency. Inotherwords,thetimingmisalignmentproblembetweenusersignals, whichinsingle-carriersystemscreatessignificantcomplicationsforjointprocessingof overlapping signals (e.g., multiuser detection [Ver98], successive interference cancella- tion [TV05], Zig-Zag decoding [GK08]), completely disappears in the case of OFDM, providedthatallusersachievetimingalignmentwithintheCP. Inapoint-to-pointMIMOlinkwithN r receiveandN t transmitantennas,thetime- domain channel is represented by an N r N t matrix of channel impulse responses. ThankstoOFDM,thechannelinthefrequencydomainisdescribedbyasetofchannel matrices of dimensionN r N t , one for each of theN OFDM subcarriers. An intuitive explanation of the MIMO multiplexing gain can be given as follows: in the high-SNR regime,thereceiverobservesN r (noisy)equationswithN t unknowncodedmodulation symbols on each time-frequency dimension, each of which carries log(snr) + O(1) bits,whereO(1)indicatesconstantsthatdependonthechannelmatrixcoefficientsbut areindependentofSNR.Forsufficientlyrichscattering,therankofthechannelmatrixis equaltominfN r ;N t gwithprobability1. Therefore,usingappropriatecodinginorderto eliminatetheeffectofthenoise,uptominfN r ;N t gsymbolsperchanneltime-frequency dimension can be recovered with arbitrarily high probability, thus yielding the high- SNRcapacityscalingC(snr) = minfN r ;N t glogsnr+O(1)bits/s/Hz. 10 2.1. AMULTIUSERMIMOPRIMER Zero-Forcing Beamforming. In contrast to point-to-point MIMO, in a MU-MIMO systemwithoneM-antennassenderandK singleantennareceivers, 1 itisnotgenerally possibletojointlydecodeallthereceivers’observations,sincethereceiversarespatially separatedandarenotgenerallyabletocommunicatewitheachother. Inthiscase,joint precodingfromthetransmitantennasmustbearrangedinordertoinvert,insomesense, the channel matrix and control the multiuser interference. One of the techniques to achievethisislinearZero-ForcingBeamforming(ZFBF). In ZFBF, the transmitter multiplies the outgoing symbols by beamforming vectors such that the receivers see only their intended signals. For instance, let the received signalonagivenOFDMsubcarrieratuserk begivenby y k =h k;1 x 1 +h k;2 x 2 ++h k;Nt x Nt +z k (2.1) whereh k;j isthechannelcoefficientfromtransmitantennaj touserkandz k isadditive white Gaussian noise. Then, the vector of all received signals can be written in matrix formas y =H H x+z (2.2) whereH has dimensionM K. AssumingK M, we wish to find a matrixV such thatH H V is zero for all elements except the main diagonal, that isH H V = 1=2 = diag( p 1 ;:::; p K ). Lettingx =Vu,whereuisthevectorofcoded-modulationsym- bolstobetransmittedtotheclients,wehave y =H H Vu+z = 1=2 u+z; (2.3) sothateachreceiverk seestheinterference-freeGaussianchannely k = p k u k +z k . WhenHhasrankK (whichistruewith probability1forsufficientlyrichpropaga- tionscatteringenvironmentstypicalofWLANsandforK M)acolumn-normalized 1 Weassumesingle-antennareceiversforsimplicityofexposition. Theextensionto1Nr M antenna receiversisimmediate. CHAPTER2. THEORETICALCONSIDERATIONS 11 version of the Moore-Penrose pseudo-inverse generally yields the ZFBF matrix. This takesontheform V =H(H H H) 1 1=2 ; whereischoseninordertoensuresthatthenormofeachcolumnofV isequalto1, thus setting the total transmit power equal to tr(Cov(Vu)) =E[∥u∥ 2 ], i.e., equal to the powerofthedatavectoru. Asfarastheachievablerateisconcerned,sinceZFBFconvertstheMU-MIMOchan- nelintoasetofindependentGaussianchannelsforeachuser,subjecttothesum-power constraintE[∥u∥ 2 ] snr, we have immediately that the maximum sum rate of ZFBF is givenby R zfbf sum (snr) = K ∑ k=1 log(1+ k q k ); (2.4) where q k denotes the power of the k-th data symbol inu. The above expression can be maximized over the power allocationfq k g, subject to the constraint ∑ K k=1 q k snr, resulting in the classical water filling power allocation of parallel Gaussian channels [CT91]. Tomlinson-Harashima Precoding. In Tomlinson-Harashima Precoding (THP), the mappingfromthedatasymbolvectorutothetransmittedsymbolvectorxisnon-linear. Consideragainthechannelmodel(2.2). THPimposesagivenprecodingordering,and itpre-cancelssequentiallytheinterferenceofalreadyprecodedsignals. Withoutlossof generality,considerthenaturalprecodingorderingtobefrom 1toK. LetH =QRbe theQRfactorizationofH,suchthatRisKK uppertriangularwithrealnon-negative diagonalcoefficients,andQisMK tallunitary,suchthatQ H Q =I. THPprecoding is formed by the concatenation of a linear mapping, defined by the unitary matrixQ, withanon-linearmappingthatdoestheinterferencepre-cancellation. Let ^ u = THP(u) denote the non-linear mapping of the data vectoru into an intermediate vector ^ u, that willbedefinedlater. ThelinearmappingcomponentofTHPisthengivenby x =Q^ u; (2.5) 12 2.1. AMULTIUSERMIMOPRIMER whereCov(^ u) = = diag(q 1 ;:::;q K )and,asbefore,q k denotesthepowerallocatedto thek-thdatasymbol. Itfollowsthatthechannelreducesto y = H H x+z = R H Q H Q^ u+z = L^ u+z; (2.6) whereL =R H islowertriangular. Thesignalseenatclientk receiverisgivenby y k = [L] k;k ^ u k + ∑ j<k [L] k;j ^ u j | {z } interference +z k : (2.7) Next, we look at the non-linear mappingu 7! ^ u. The goal is to pre-cancel the term indicated by “interference” in (2.7). Notice that this term depends only on symbols ^ u j withj <k. Therefore,theelements ^ u 1 ;:::;^ u K canbecalculatedsequentially. Asimple pre-subtractionoftheinterferencetermateachstepwouldincreasetheeffectivetransmit powerandwouldresultinasuboptimalversionofthelinearZFBFtreatedbefore. The key idea of THP is to introduce a modulo operation that limits the transmit power of each precoded stream ^ u k . This is defined as follows. Assume that the data symbolsu k arepointsfromaQAMconstellationuniformlyspacedinthesquaredregion ofthecomplexplaneboundedbytheinterval[=2;=2]onboththerealaxisandthe imaginary axis. Then, for a complex number s, let s modulo be given by [s] mod = sQ (s), whereQ (s) is the point (n+jm) with integersn;m closest tos. In short, Q (s)isthequantizationofswithrespecttoasquaregridwithminimumdistance on thecomplexplane,and[s] mod isthequantizationerror. Welet ^ u k = p q k [ u k ∑ j<k [L] k;j ^ u j [L] k;k p q k ] mod : (2.8) Inthisway,thesymbol ^ u k isnecessarilyboundedintothesquaredregionofside p q k , and its variance (assuming a uniform distribution over the squared region, which is approximatelytruewhenweuseaQAMconstellationinscribedinthesquare)isgiven CHAPTER2. THEORETICALCONSIDERATIONS 13 byE[j ^ u k j 2 ] = 2 =6q k . Letting = p 6 we have that the precoded symbols have the desiredpowerq k . Let’s focus now on receiver k and see how the modulo precoding can be undone. Thereceiverscalesthereceivedsymboly k by[L] k;k p q k andappliesagainthesamethe modulo non-linearmapping. Simplealgebrathenshowsthat b y k = [ u k + z k [L] k;k p q k ] mod : (2.9) Itfollowsthattheinterferencetermisperfectlyremoved,butwehaveintroducedadis- tortion in the noise term. Namely, while u k is unchanged by the modulo operation, sincebyconstructionitisapointinsidethesquare,thenoiseterm z k [L] k;k p q k is“folded” bythemodulooperation,i.e., thetailsoftheGaussiannoisedistributionarefoldedon thesquaredregion. Noisefoldingisawell-knowneffectofTHP[FE91]. Asfarastheachievablerateisconcerned,itispossibletoshow(see[BTC06,ESZ05]) thatthisisgivenby R thp sum (snr) = K ∑ k=1 [ log(1+j[L] k;k j 2 q k )log(e=6) ] + ; (2.10) where[] + indicatesthepositivepart. Again,thissumratecanbeoptimizedwithrespect tothepowerallocationfq k g,subjecttothesumpowerconstraint ∑ K k=1 q k snr. Therate penalty term log(e=6) is the shaping loss, due to the fact that THP produces a signal which is uniformly distributed in the square region (therefore, a codeword of n signal componentsisuniformlydistributedinann-dimensionalcomplexhypercube). 2 Blind Interference Alignment. The fundamental idea of BIA is to differentiate the users by inducing special signatures in their channel temporal variations. This is obtainedbyallocatingtoeachuseranantennaswitchingsequence,accordingtowhich theydemodulatethesignalfromoneoftheirantennas. Onlyoneantennaineverygiven slotisused,sothatasingleRFfront-endanddemodulationchainareneeded. 2 ItshouldbenoticedthatthesameshapinglossathighSNRisincurredbyanyotherscheme,including plain CSMA, when practical QAM constellations are used instead of the theoretically optimal Gaussian codingensemble. 14 2.1. AMULTIUSERMIMOPRIMER AP1 AP2 RX1 RX2 Figure 2.1: BIA Testbed. When using Blind Interference Alignment each receiver switchesbetweentwoantennamodes. The scheme that we have implemented sends 2 independent streams per client to two clients, over 3 time slots. Figure 2.1 contains a sketch of the testbed. Receiver 1 usestheswitchingsequenceA,B,A,indicatingthatitusesantennaAinslots1and3and antennaBinslot2ofaprecodingframeformedby3slots. Receiver2usestheswitching sequenceA,A,B,withanalogousmeaning. Denotingbyu [k] i thei-thdatasymbolofuser k, with i = 1;2 and k = 1;2, the BIA scheme transmitsx [1] +x [2] in the first slot,x [1] in the second slot, andx [2] in the third slot, wherex [1] andx [2] are formed out of the symbolstreamsasillustratedinTable2.1. Lettingh kA andh kB denotethe21channel vectorsseenatantennasAandBofuserk,weobservethatthe22matrixwithcolumns [h kA ;h kB ] has rank 2, and that the channels remain constant over the precoding block spanning3slots. After linear interference cancellation at each client, the achievable sum rate with Gaussianrandomcodingensemblesisgivenby[GWJ10]: R sum = K ∑ k=1 E [ logdet ( I+ (K+M1)P M 2 K H H k H k )] M +K1 (2.11) whereforthe22case: H k = [ 1 p 2 h kA ;h kB ] (2.12) CHAPTER2. THEORETICALCONSIDERATIONS 15 Slot t =t 1 t =t 2 t =t 3 [ Tx1Sends Tx2Sends ] x [1] +x [2] = [ u [1] 1 +u [2] 1 u [1] 2 +u [2] 2 ] x [1] = [ u [1] 1 u [1] 2 ] x [2] = [ u [2] 1 u [2] 2 ] User1Antenna A B A User2Antenna A A B User1Receives y 1 (t 1 ) = h H 1A (x [1] +x [2] )+z 1 (t 1 ) y 1 (t 2 ) = h H 1B x [1] +z 1 (t 2 ) y 1 (t 3 ) = h H 1A x [2] +z 1 (t 3 ) User2Receives y 2 (t 1 ) = h H 2A (x [1] +x [2] )+z 2 (t 1 ) y 2 (t 2 ) = h H 2A x [1] +z 2 (t 2 ) y 2 (t 3 ) = h H 2B x [2] +z 2 (t 3 ) User1Decodes e y 1 (1) = y 1 (t 1 )y 1 (t 3 ) = h H 1A x [1] +z 1 (t 1 )z 1 (t 3 ) e y 1 (2) = y 1 (t 2 ) = h H 1B x [1] +z 1 (2) 9 > > > > = > > > > ; ) ^ x [1] = [ h H 1A h H 1B ] 1 [ e y 1 (1) e y 1 (2) ] User2Decodes e y 2 (1) = y 2 (t 1 )y 2 (t 2 ) = h H 2A x [2] +z 2 (t1)z 2 (t2) e y 2 (2) = y 2 (t 3 ) = h H 2B x [2] +z 2 (3) 9 > > > > = > > > > ; ) ^ x [2] = [ h H 2A h H 2B ] 1 [ e y 2 (1) e y 2 (2) ] Table2.1: BlindInterferenceAlignmentforthe22scenario ■ 2.2 SynchronizationindistributedMIMOsystems In a distributed MU-MIMO setting, timing and carrier phase synchronization across thejointlyprecodedAPsareneededinorderforZFBFandTHPprecodingtowork. As discussed above, timing synchronization requires only that all nodes align their slots withinthelengthoftheOFDMCP.Thisisrelativelyeasytoachieve,andithasalready been implemented in software radio testbeds as in [RHK10,TFZ + 10]. Carrier phase synchronization, however, is much more challenging. While a centralized MU-MIMO transmitter has a common clock source for all its RF chains [SYA + 12], in a distributed settingeachAPhasanindividualclock. Therelativetime-varyinginstantaneousphase 16 2.2. SYNCHRONIZATIONINDISTRIBUTEDMIMOSYSTEMS offset between the different transmitters may cause a phase rotation of the transmitter signals across a downlink slot such that, even though at the beginning of the slot we have ideal precoding (e.g., ZFBF or THP), the interference nulling effect is completely destroyedtowardstheendoftheslot. Itisimportanttoremarkherethat, whilesynchronizingareceiverwithatransmit- terforthepurposeofcoherentdetectionisawell-knownproblemforwhichrobustand efficient solutions exist and are currently implemented in any coherent digital receiver [PS07],herewearefacedwithadifferentandsignificantlyharderproblem,whichcon- sists of synchronizing the instantaneous carrier phase of different transmitters. This requires that APs must track an RF carrier reference and compensate for the relative (time-varying)phaserotationwhiletheyaretransmittingthedownlinkslot. Simultane- oustransmissionofthedatasignalandreceptionofthecarrierreferencesignalcannot beimplementedbystandardoff-the-shelfterminals. Instead,wehavedevisedasystem architecturetoaccomplishthisgoal. WhyisdistributedMU-MIMOchallenging? Forsimplicityofexposition,consider adistributedMU-MIMOsystemwithtwoclientsandtwoaccesspoints,eachonewitha singleantennaandusingZFBF(thefollowingconsiderationsapplyimmediatelytomore generalscenarios). Fornomadicusers,asintypicalWLANsetting,thephysicalpropa- gationchannelchangesquiteslowlywithtime,sothatwemayassumethatthechannel impulseresponseislocallytime-invariant. InordertouseZFBF,thechannelmatrixcoef- ficientsateachOFDMsubcarriermustbeestimatedandknowntothetransmittercentral server. Various methods for learning the downlink channel matrix at the transmitter e H(n;t) = 2 4 e j ( 2 NTs 1 n+ϕ 1 (t) ) 0 0 e j ( 2 NTs 2 n+ϕ 2 (t)] ) 3 5 | {z } (n;t) [ H 11 (n) H 12 (n) H 21 (n) H 22 (n) ] 2 4 e j ( 2 NTs 1 n+ 1 (t) ) 0 0 e j ( 2 NTs 2 n+ 2 (t) ) 3 5 | {z } (n;t) (2.13) CHAPTER2. THEORETICALCONSIDERATIONS 17 side have been proposed, including closed-loop feedback schemes (see [CJKR10] and thereferencestherein)oropen-loopschemesthatexploittheuplink/downlinkchannel reciprocityofTDDsystems[JAWV08]. Forsimplicityofexposition,wewillassumehere thatthechannelestimatescorrespondperfectlytotheactualchannel. The central server computes the precoding matrix as seen in Section 2.1, for each subcarriern = 1;:::;N. Let H(n) = 2 6 6 4 H 11 (n) H 12 (n) H 21 (n) H 22 (n) 3 7 7 5 (2.13) denote the 22 downlink channel matrix between the two clients and the two access pointantennasonsubcarriern,andletV(n)denotethecorrespondingprecodingmatrix such thatH H (n)V(n) = 1=2 (n) is diagonal. If the timing and carrier phase reference remain unchanged from the slot over which the channel is estimated and the slot over whichtheprecodedsignalistransmitted,weobtainperfectzero-forcingofthemultiuser interference. Supposenowthatthetimingreferenceandcarrierphasereferencebetweentheesti- mationandtransmissionslotsofthetwoAPsisnotideal. Withperfecttiming,thedown- linkchannelfromAPitoclientj wouldhaveimpulseresponseh ij (). Instead, dueto lackofsynchronization,theimpulseresponseish ij (( i j ))e j(ϕ i (t) j (t)) where i ; j denotethetimingmisalignmentofAPiandclientj,respectively,andϕ i (t); j (t)denote the instantaneous phase differences (with respect to the nominal RF carrier reference) ofAPiandclientj,respectively. Forsimplicity,weassumeherethatthesamplingclock atallnodesispreciseenoughsuchthatwemayassumethatthesamplingfrequencyis thesameanddoesnotchangesignificantlyintimeoverthedurationofaslot. Hence, i and j canbeconsideredasunknownconstants. Furthermore,weassumethattheyare multiplesofthesamplingintervalT s (i.e.,thedurationofthetime-domainsamples)oth- erwisethederivationismorecomplicated,involvingthefoldedspectrumofthechannel 18 2.2. SYNCHRONIZATIONINDISTRIBUTEDMIMOSYSTEMS frequency response, but the end result is equivalent to what derived here. Instead, we modeltheinstantaneousphasesoftheRFcarrieroscillatorsas ϕ i (t) = ϕ i (0)+2∆ i t+w i (t) j (t) = j (0)+2∆ j t+w j (t) (2.14) whereϕ i (0); j (0)areunknownconstants,∆ i = (f c;i f c )(N +L)T s isthenormalized frequencyoffsetofnodeiwithrespecttothenominalcarrierfrequencyf c ,andw i (t)is azero-meanstationaryphasenoiseprocess, whosestatisticsdependsonthehardware implementation. In the above expression, the time index t ticks at the OFDM symbol rate,i.e.,atintervalsofduration(N +L)T s . From the well-known rules of linearity and time-shift of the discrete Fourier trans- form,wearriveattheexpressionfortheeffectivechannelmatrixin(2.13). Thediagonal matrix of phasors(n;t) and(n;t) depend, in general, on both the subcarrier and OFDMsymbolindicesnandt. ThemultiplicationofthenominalchannelmatrixH(n) fromtheright(receiverside, accordingtothechannelmodel(2.2))posesnoproblems, sincethesephaseshiftscanberecoveredindividuallybyeachclientasinstandardcoher- entcommunication[PS07]. Incontrast,thediagonalmatrix(n)multiplyingfromthe left (the transmitter side) poses a significant problem: since the server computes the MIMOprecodingmatrixV(n)basedonitsestimateH(n),itfollowsthatwhenapplied to the effective channel e H(n) in (2.13) the matrix multiplication e H H (n)V(n) is in gen- eral far from diagonal. To stress the importance of this aspect, we would like to make clear that the resulting signal mixing takes place over the actual transmission channel, makingitimpossibleforthereceiverstoeliminateit. Why Synchronization Is Possible. Any discussion on phase synchronization of distributed wireless transmitters must necessarily start with the mechanisms through which phase errors occur. Digital wireless transmissionsystems are constructed using anumberofclocksources,amongwhichthetwomostimportantonesarethesampling clock and the carrier clock. In a typical system, signals are created in a digital form in CHAPTER2. THEORETICALCONSIDERATIONS 19 basebandatasamplingrateontheorderoftensofMHz,thenpassedthroughadigital- to-analogconverter(DAC).Throughtheuseofinterpolatorsandfilters,theDACcreates asmoothanalogwaveformsignalwhichisthenmultipliedbyasinusoidalcarrierpro- ducedbythecarrierclock. TheresultisapassbandsignalatafrequencyofafewGHz whichisthensentovertheantenna. Wireless receivers, in turn, use a chain of signal multiplications and filters to cre- ateabasebandversionofthepassbandsignalreceivedovertheantenna. Somedesigns, suchasthecommonsuperheterodynereceivers,usemultiplehighfrequencyclocksand convertasignalfirsttoanintermediatefrequencybeforebringingitbacktobaseband. Otherdesignssimplyuseacarrierclockoperatingatthesamenominalfrequencyasthe carrierclockofthetransmitterandperformthepassagefrompassbandtobasebandina singlestep. Wewillbefocusingonsuchdesignsintheensuingdiscussion. Afterbase- bandconversion,thesignalissampledandtheresultingdigitalwaveformisdecoded. There are four clocks in the signal path: the transmitter’s sampling clock and RF carrier clock and the receiver’s RF carrier clock and sampling clock. All four clocks manifestphase“drift”(i.e.,alineartime-varyingterm)and“jitter”(i.e.,arandomfluc- tuationterm). Wehaveassumedthatthesamplingclockshavenosignificantdriftand jitter,andtheonlyeffectoftimingmisalignment(withinthelengthofaCP)iscaptured by the constants i and j in (2.13). In contrast, the carrier clocks are affected both by drift and jitter (see (2.14)). 3 Furthermore, the phase noise term w i (t) may have some slowdynamicsthatcanbelinearizedlocally,overthedurationofaslot,andaddupto thelinearphaseterm,suchthattheslopeofthephasedriftisconstantoverasingleslot, butitisnotconstantoverlongertimeintervals,ingeneral. We have verified experimentally the validity of our model, by letting a transmitter send several tone signals, i.e., simple unmodulated sine waves, corresponding to dif- ferent subcarriers of the OFDM modulation, and using a receiver to sample, demodu- lateandextracttheinstantaneousphasetrajectoryofthereceivedtones. Intheabsence 3 In fact sampling clocks and carrier clocks have similar drift and jitter dynamics. However, since the carrier clock is multiplied in order to achieve a 2.4 GHz carrier frequency while the sampling clock fre- quency is in the tens of MHz, the phase effect of the carrier clock drift significantly outweighs the one of thesamplingclockdriftandistheonlyonerelevantoverthedurationofapackettransmission. 20 2.3. RELATEDWORK 5 10 15 20 25 30 35 −180 −120 −60 0 60 120 180 Time (OFDM Symbols) Phase (Degrees) Figure 2.2: Pilot phases. The phases of different subcarriers drift at the same speed, suggestingthattheyareonlysubjecttocarrierfrequencyoffset. of phase offset these signals would exhibit a constant phase when measured over a sequence of several OFDM symbols. Instead, the measured instantaneous phase is time-varying and closely approximate parallel straight lines, as shown in Figure 2.2. The common slope of these straight lines is given by the carrier frequency offset ∆ i between transmitter and receiver. The spacing between the lines is given by constant phaseterms 2 NTs i nfordifferentsubcarrierindexn,anddependsonthetimemisalign- ment i betweentheAPandthenominalslotinitialtime. Thesmallfluctuationsaround thelinearbehavioroftheinstantaneousphaseisduetothephasenoise,whichisquite small for the WARP hardware used in our system, as it can be observed qualitatively fromplotsasinFigure2.2. It follows that by estimating the spacing between the phase trajectories (intercepts with the horizontal axis) and their common slope, we can track and predict across the slot the phase de-rotation coefficients to be applied at each AP in order to “undo” the effect of the matrix(n;t). Notice that the de-rotation factor must be predicted a few OFDM symbols ahead, in order to include the delay of the hardware implementation between when an OFDM symbol is produced by the baseband processor (FPGA) to whenitisactuallytransmitted. ■ 2.3 RelatedWork TheoreticalFoundations. ThepioneeringpapersbyFoschini[FG98]andTelatar[Tel99] have shown that adding multiple antennas both to the transmitter and to the receiver CHAPTER2. THEORETICALCONSIDERATIONS 21 increasesthecapacityofapoint-to-pointcommunicationchannel. Atpracticalmedium- to-highSignaltoNoiseRatios(SNRs),thisgainmanifestsasamultiplicativefactorequal to the rank of the matrix representing the transfer function between the transmit and the receive antennas. For sufficiently rich propagation scattering, with probability 1 this factor is equal to minfN t ;N r g, where N t and N r denote the number of transmit and receive antennas, respectively. The MIMO capacity gain can be interpreted as the implicitabilitytocreateminfN t ;N r g“parallel”non-interferingchannelscorresponding to the channel matrix eigenmodes, and it is referred to in the literature as multiplexing gain,orasthe degrees of freedomofthechannel. Subsequently,CaireandShamai[CS03] have shown that the MIMO broadcast channel, where the transmitter has N t anten- nas and serves K clients with N r antennas each, exhibits an analogous capacity factor increase of minfN t ;KN r g, suggesting that a transmitter with multiple antennas could transmit simultaneously on the same frequency to independent users. Such multiuser communication has two additional requirements. First, precoding of the transmitted data is needed to prevent the different spatial streams from mutually interfering. Sec- ond, the transmitter requires accurate knowledge of the channel matrix (channel state information)inordertorealizethisprecoding. The idea of precoding has spurred a large amount of research, well beyond the scopeofthispaper. DirtyPaperCoding(DPC)[Cos83]withaGaussiancodingensem- ble achieves the capacity of the MIMO broadcast channel [WSS06], but is difficult to implementinpractice. Thewell-knownlinearZero-ForcingBeamforming(ZFBF)[CS03] achieves the same high-SNR capacity factor increase, with some fixed gap from opti- mal that can be reduced when the number of clients is large and the transmitter can dynamically select the clients to be served depending on their channel state informa- tion[YG06,KC06]. Tomlinson-HarashimaPrecodingisanotherwell-studied, butinfre- quently implemented technique, which efficiently approximates DPC at high SNRs [WFVH04]. Anumberofotherprecodingstrategies(e.g.,latticereduction,regularized vectorperturbation)havebeenstudiedandtheinterestedreaderisreferredto[SPSH04] 22 2.3. RELATEDWORK and references therein. For the purposes of this paper ZFBF and THP will be the pri- mary methods of interest because of their conceptual simplicity and good complex- ity/performancetradeoff. PracticalImplementations. Anumberofrecentsystemimplementationshavemadefor- aysintothetopicsofmultiuserMIMOtransmissionanddistributed,slotalignedOFDM transmission. MU-MIMOZFBFasaprecodingschemeinacentralizedsettinghavebeen examined in [AASK10], for a system consisting of a single AP with multiple antennas hosted on the same radio board. A distributed system using a common clock source to drive a large number of radio boards is presented in [SYA + 12]. This system uses conjugate beamforming [Mar10], a completely decentralized precoding scheme. The schemerequiresasignificantlylargernumberofantennasinordertoproviderategains comparable to the ones of centralized precoding schemes [SYA + 12]. The use of inter- ference alignment and cancellation as a precoding technique, which does not require slot synchronization or phase synchronization of the transmitters, has been illustrated in [GPK09]. While this solution achieves some spatial multiplexing, realizing the full spatial multiplexing gain using precoding schemes such as ZFBF requires tight phase synchronizationbetweenthejointlyprecodedtransmitters[LSW05,VV09]. Inordertobeabletoadopttheclassicaldiscrete-timesymbol-synchronouscomplex baseband equivalent channel models used in communication and information theory, thefundamentalunderlyingassumptionisthattransmissionsfromdifferentnodesalign within the cyclic prefix of OFDM (referred to as “slot alignment” in the following). If thisisnotverified,theninter-blockinterferencearisesandthechanneldoesnotdecom- pose any longer into a set of discrete-time parallel channels. Slot alignment was used in SourceSync [RHK10] in conjunction with space-time block coding in order to pro- videadiversitygaininadistributedMIMOdownlinksystem. InFine-GrainedChannel Access [TFZ + 10], a similar technique allows for multiple independent clients to share the frequency band in fine increments, without a need for guard bands, resulting in a flexible OFDMA (OFDM with orthogonal multiple access) uplink implementation. CHAPTER2. THEORETICALCONSIDERATIONS 23 Distributed space-time coding and flexible orthogonal access do not increase the sys- temdegreesoffreedom,sinceatmostasingleinformationsymbolpertime-frequency dimensioncanbetransmitted. 4 AirSync has been first published in [BRM + 12] and then in [BRM + 13]. A paral- lel work [RKK12] appearing at the same time used a similar set of ideas to develop a reference-baseddistributedMIMOsystem. Toourknowledge,DistSync,firstpresented here,isthefirstsystemthatextendsdistributedMIMOtransmissiontoanarbitraryscale. 4 Atime-frequencydimensioncorrespondstoonesymbolinthefrequencydomain,spanningoneOFDM subcarrieroveroneOFDMsymbolduration,andspans(approximately)1sHz. CHAPTER 3 Reference-basedSynchronization The current chapter introduces AirSync, a single reference-based synchronization method for wireless transmitters. This method achieves phase coherence among sev- eral transmitters located within the range of the reference access point. We start by presentingtheconstructionofthesynchronizationschemeandthedetailsofitsimple- mentation. Wecontinuebyevaluatingitsperformanceinanactualdeployment. Finally, wedescribeamediumaccesslayercompatiblewithitsoperation. ■ 3.1 AirSync The fact that the common phase drift of all subcarriers can be predicted by observing onlyafewofthempromptsthefollowingapproachtoachievingphasesynchronization between access points: a main access point (master) is chosen to transmit a reference signalconsistingofseveralpilottones 1 placedoutsidethedatatransmissionband,ina reservedportion oftheavailablebandwidth. Aninitialchannelprobingheader, trans- mitted by the master access point, is used by the other transmitters in order to get an initial phase estimate for each carrier. After this initial estimate is obtained, the phase estimateswillbeupdatedusingthephasedriftmeasuredbytrackingthepilotsignals. 1 The use of multiple pilot tones ensures frequency diversity and spreads the pilot signal power over multiplefrequencybins. 24 CHAPTER3. REFERENCE-BASEDSYNCHRONIZATION 25 The estimate is used to calculate the difference between the carrier phase of each sec- ondarytransmitterandthephaseofthemastertransmitter. Thisdifferencedependson the timing offset between the starting points of their frames and the frequency offset between the carrier frequency of the master AP (denoted by f c;1 ) and the carrier fre- quency of each secondary AP (denoted by f c;i , for i > 1). After obtaining the channel estimate, thesecondarytransmittersareabletoundoeffectoftheinstantaneousphase differencebyderotatingthetransmittedfrequency-domainsymbolsbythephasediffer- encetermalongthewholetransmissionslot,thuseliminatingthepresenceofthetime- varyingdiagonalmatrix(n;t)infrontoftheestimatedchannelmatrixandtherefore achievingthedesiredMU-MIMOprecodingalongthewholetransmissionslot. More specifically, at time t = 0, the n-th subcarrier signal generated by the master AP has the phase 2 NTs 1 n + ϕ 1 (0), while the carrier generated by AP i has the phase 2 NTs i n+ϕ i (0). Thephaseoftheinstantaneousphasedifferenceobtainedfromthemas- terpilottonesis,ignoringthephasenoiseterms, 2 NTs ( 1 i )n+ϕ 1 (0)ϕ i (0)+\H i (n), where\H i (n) is the phase of the channel coefficient between the master AP and APi. Ifthisphaseestimateisaddedtothephaseofthegeneratedn-thsubcarrieratAPi,the resultingphasebecomes 2 NTs 1 n+ϕ 1 (0)+\H i (n),thatisthephaseofAPiisthephase ofthemasterAPplusanoffset\H i (n). Tokeepthisoffsetconstantoverthedurationof a transmission slot, the estimate must be adjusted by adding, for allt ranging over the transmissionslot,thelinearrelativephasedriftterm2(∆ 1 ∆ i )t. Inthisway,afterthe phasecompensation,allAPstransmitattheactualfrequencyf c;1 ofthemasterAP. The drift 2(∆ 1 ∆ i )t isestimated based on the out-of-band pilotsusing a sliding windowsmoothingfilteroverfoursamplestocomputeanupdatedvalueofthe“slope” ∆ i ∆ 1 . ThesecondaryAPpredicts, basedonthecurrentestimate,theinstantaneous phase with a few OFDM symbols of look-ahead. The need for look-ahead prediction arises from the fact that the AP must align its phase to the phase of the reference at the moment of the actual transmission, not at the moment that the estimate has been recorded. Thus the look-ahead time of d OFDM symbols corresponds to the synchro- nizationcircuitdelay. Thepredictionisobtainedbysimplelinearextrapolation,bylet- tingthecorrectiontermattimet+dbegivenby2(∆ 1 ∆ i )(t+d),where∆ 1 ∆ i isthe 26 3.1. AIRSYNC estimated slope at time t. The constant offset\H i (n) becomes a part of the downlink channel estimates and poses no further problems with regard to synchronization both whenusingdownlinkanduplinkchannelestimationschemes. In our current implementation, for simplicity, we obtain an individual phase esti- mateoftheform 2 NTs ( 1 i )n+ϕ 1 (0)ϕ i (0)+\H i (n)foreverysubcarrieranduseit independentlyoftheestimatesforothersubcarriersincorrectingthesubcarrierphase. Theformofthephaseestimatesuggeststhatitispossibletoobtainabetterestimateby breakingtheestimationprocessintotwodistinctparts: obtaininganinitial,highquality estimateoftheconstant\H i (n)duringasystemcalibrationstepandthenestimatingjust thetwofactors 1 i andϕ 1 (0)ϕ i (0)insubsequentpackettransmissions. Theconstant estimate in this case is needed since undoing the angle\H i (n) amounts to equalizing the channel between the master AP and the i-th AP. After equalizing the channel, the resultingphasescanbeunwrappedalongthecarrierindexn. Itresultsthat,aftercom- pensatingfortheangle\H i ,thephaseoftheestimateis 2 NTs ( 1 i )n+ϕ 1 (0)ϕ i (0), linear in the carrier index plus a constant term. A linear MMSE fitting can be applied in order to find the two factors mentioned, which are in fact the slope of the line (the carrierphasewithregardtothesubcarrierindex)anditsintercept. SoftwareRadioImplementation. WehaveimplementedAirSyncasadigitalcircuit intheFPGAoftheWARPradioplatform[Ric]. TheWARPradioisamodularsoftware radioplatformcomposedofacentralmotherboardhostinganFPGAandseveraldaugh- terboardscontainingradiofrequency(RF)front-ends. TheentiretimingofeachWARP isderivedfromtwolocalreferenceoscillators,hostedonitsclockboard: a20MHzoscil- lator serving as a source for all sampling signals and a 40 MHz oscillator which feeds thecarrierclockinputsofthetransceiverspresentontheRFfront-ends. Thefrequency accuracyofthecarriergeneratingclockisontheorderof1.5ppm,leadingtoanexpected variance of the CFO of about 4 kHz, for a carrier frequency of 2.4 GHz. The sampling clock has a frequency accuracy on the order of 1ppm. These accuracy values are typ- ical of oscillators used in 802.11 applications and do not preclude the need for phase drift compensation. Within each radio, sharing the local clocks among the RF front- ends assures that all signals sent and received using the different front-ends are phase CHAPTER3. REFERENCE-BASEDSYNCHRONIZATION 27 synchronous. Phasesynchronicityforallsentsignalsorforallreceivedsignalsisacom- mon characteristic of MIMO systems. However, the fact that the design of the WARP ensuresphasesynchronicityamongthesentandreceivedsignals,asopposedtousing separate oscillators for modulation and demodulation, greatly simplifies the synchro- nization task. The system’s data bandwidth is 5 MHz. We place the synchronization tones outside the data bandwidth, at about 7.5 MHz above and below the carrier fre- quency. The slave APs have to track the out of band pilots (i.e., receive these signals) and transmit the data signal at the same time, in an FDD manner. We have dedicated one antennaofeachsecondaryAPtoreceivingandtrackingthereferencesignal,whilethe otherantennasareusedfortransmittingphase-synchronoussignals. Thesystemdesign mustmitigateself-interferencebetweenthetransmitandreceivepaths. In FDD transmission schemes in which the front-ends sample the entire system bandwidth,thedynamicrangesoftheADCandDACcircuitryplaysanimportantlim- itingrole. Asopposedtoacompletefull-duplexsystem,inwhichself-interferencecan- cellation is the main challenge to be solved, in bandwidth sharing systems the main challenge is accommodating both the incoming signal, i.e. the signal from the master AP, and the secondary AP’s data signal within the limited dynamic range of the sec- ondary’s receiver front-end. A second challenge is shaping this data signal in order to prevent any significant power leakage outside the data band, mitigating the need for largeguardbandsbetweenthedataandthepilots. Thedynamicrangeneededcanbecomputedasfollows: assumethatthesecondary AP’s signal and the master AP’s pilots are broadcasted at the same power level. If the secondary’s receiver antenna is times closer to the secondary’s transmitter antenna thantotheoneofthemaster’s,assumingafreespacepropagationmodelinwhichthe powerdecaysas 1 2 ,itresultsthatthedatasignalisreceivedat10log 10 ( 2 )dBabovethe pilotsignals. Forinthe32to128range,thisamountsto30dBto42dB.Forcomparison, theWARP’s14-bitADCsofferadynamicrangeof84dB. 2 2 This requirement could be further relaxed through the use of an analog rejection filter over the data band, before sampling, during the tracking period, thus decreasing the needed dynamic range through receive-sidefiltering. 28 3.1. AIRSYNC 2.4 GHz FFT Phase Smoothing Filter Phase Linear Extrapolation Data Symbol IFFT AP 1 AP i Figure3.1: AirSyncoperation. AsecondaryAP(bottom)synchronizesitsphasetothe oneofareferencesignal(top)byadjustingthephaseofitssignaltomatchthephaseof thereference. Forthesecondproblem,thedesignofWiFi-NC[CRB + 12],offersaclearindicationof whatcanbeachievedinasoftwareradiousingthesamecomponentsastheWARP.To limitthesizeofrequiredguardbandsinabandwidth-sharingsystem,inwhichdifferent APsdividethedatabandintoslicesandcantransmitinduplexoverseparateslices,the authors construct an OFDM transmitterwith a sharp spectralfootprint. By employing digitalfiltersintheFPGA,theyachievea60dBpowerdecaywithguardbandsthattotal 4%ofthedatabandwidth, asprovedbyspectrumanalyzerplots. Theirfilterresponse time is well within the cyclic prefix. This approach allows for decreasing the over-the- channelpowerleakageintothepilotbandthroughsender-sidefiltering. Inoursystem, we achieve a similar effect by using the baseband sender filter present in the transmit signalpathoftheWARP’stransceiver. Ingeneral,self-interferencecanbeavoidedusing anumberofothertechniquessuchasantennaplacement[CJS + 10],digitalcompensation [DDS11], or simply relying on the OFDMA-like property of a symbol aligned system [TFZ + 10]andpreventingthesecondaryAPsfromusingthepilotsubcarriers. Wehaveimplementedacompletesystem-on-chipdesignintheFPGA,takingadvan- tageofthepresenceofhard-codedASICcoressuchasaPowerPCprocessor,amemory controllercapableofsupportingtransfersthroughdirectmemoryaccessoverwidedata busesandagigabitEthernetcontroller. Atopthissystem-on-chiparchitecturewehave ported the NetBSD operating system and created drivers for all the hardware compo- nents hosted on the platform, capable of setting all system and radio board configura- tionparameters. Theoperatingsystemrunslocallybutmountsaremoterootfilesystem CHAPTER3. REFERENCE-BASEDSYNCHRONIZATION 29 through NFS. In the same system-on-chip architecture we integrated a signal process- ing component created in Simulink which provides interfaces for fast direct memory access. Thislattercomponentisresponsibleforallthewaveformprocessingandforthe synthesis of a phase synchronous signal and interfaces directly with the digital ports oftheradiofront-ends. WeinterfacedtheEthernetcontrollerandthesignalprocessing componentusinganoperatingsystemkernelextensionresponsibleforperformingzero- copy,directmemoryaccessdatatransfersbetweenthetwo,withthepurposeofpassing backandforthwaveformdataathighratesbetweenahostmachineandtheWARPplat- form. The large data rates needed (160 Mbps for a 5MHz wireless signal sampled at the 16 bit precision of the WARP DACs for both the real (I) and imaginary (Q) parts of the corresponding baseband signal) required optimizing the packet transfers into and outoftheWARP.Forexample,considerthedirectmemoryaccessringassociatedwith thereceiveendoftheEthernetcontrollerontheboard,whichissharedbetweenpackets destinedtothesignalprocessingcomponentandpacketsdestinedtotheupperlayersof theoperatingsystemstack. Wedonotreleaseandreallocatethememorybuffersoccu- pied by packets destined to the signal processing component. Instead, we use a lazy garbagecollectionalgorithminordertoreclaimthesebufferswhentheyareconsumed in a timely manner or reallocate them at a later point if they are not consumed before thememoryringrunslowonavailablememorybuffers. Therationaleforthisparticular optimizationisthattheoverheadofmanagingthevirtual-memorybasedreallocationof memorybuffersoftensofthousandsofpacketseverysecondwouldbringtheprocessor ofthesoftwareradioplatformtoahalt. AlltransmittingWARPradiosareconnectedtoacentralprocessingserverthrough individualEthernetconnectionsoperatingatgigabitspeeds. Mostofthesignalsynthe- sisforthepackettransmissionisdoneoffline,usingMatlabcode. Weproduceprecoded packets in the form of frequency domain soft symbols. However, the synchronization stepandthesubsequentsignalgenerationislefttotheFPGA.Theserver,afastmachine with32processorcoresand64GBofRAM,encodesthetransmittedpacketsandstreams the resulting waveforms to the radios. Figure 3.1 illustrates the process of creating a phasesynchronoussignalatthesecondaryAP. 30 3.1. AIRSYNC Centralizedjointencoding. Bytransmittingphasesynchronoussignalsfrommul- tiple APs, we have created a virtual single MU-MIMO transmitter, for which standard MU-MIMOprecodingstrategiescanbeused. However,theuseofdistributedAPscom- plicates the design of the transmitter system. In order to eliminate multiuser interfer- ence, the data streams to different clients must be jointly precoded, as we have seen in Section 2.1. For systems with a very large number of jointly processed antennas and targeting mobile cellular communications (e.g., see [SYA + 12]), the centralized compu- tationoftheprecodingmatrix,oftheprecodedbasedbandsignals,anddistributionof thesesignalstoalltheantennaswouldrequirealargedelay,whichisincompatiblewith the short channel coherence time due to user mobility. In contrast, in our enterprise network or residential network scenario, the channel coherence time is much longer (typicalusersarenomadic,andmoveatmostatwalkingspeed). Therefore,computing theprecodingmatrixdoesnotrepresentasignificantproblem,anditisinfactbetterto perform centralized precoding and distribution of the baseband precoded signals. For example, using the conjugate beamforming scheme of [SYA + 12], it is possible to com- putetheprecodedsignalsinadecentralizedway,sinceeachAPineedsjusttocombine theclients’datastreamswiththecomplexconjugatesofitsownestimatedchannelcoef- ficients, i.e., with the elements of the i-th row of the channel matrix. In the notation of Section 2.1, this corresponds to lettingx = cHu, for some power normalizing con- stantc,suchthattheprecodedchannelbecomesy = cH H Hu+z. UnlessM ≫ K,the resultingmatrixH H Hisfarfromdiagonal,andthesystemisinterferencelimited,i.e.,by increasingthetransmitpower,thesystemsumratesaturatestosomeconstantvalue(the system multiplexing gain in this case is 1, corresponding to serving only one client on eachtime-frequencydimension,asinstandardFDMA/TDMA).Hence,whileconjugate beamformingisanattractiveschemeforverylargeM,relativelyhighclientmobilityand limited power (as in a cellular system), it turns out that in the WLAN setting with not solargeM, lowclientmobilityandlargeoperatingSNR(duetocommunicationrange ofatmostafewtensofmeters)thisisnotacompetitivechoice. Asamatteroffact,centralizedZFBForTHPprecodingismuchbetterinoursetting. ItshouldalsobenoticedthatbycentralizedprecodingweneedonlytosendtheIandQ CHAPTER3. REFERENCE-BASEDSYNCHRONIZATION 31 componentsofthefrequency-domainOFDMbaseband(precoded)symbolstotheAPs. Thisrequiresroughly2bW bit/s,forsignalbandwidthW Hzandbquantizationbits perrealsample. Instead,decentralizedprocessingrequirestosendallclientdatastreams toallAPs. AssumeforexamplethatKclientsarereceivingat4bit/s/Hz(corresponding to 20 Mbps over a W = 5 MHz bandwidth). This requires 20K Mbps to be sent to all APs, while in the case of centralized processing, with b = 16 bits of quantization, we need only 325 Mbps. Here, forK > 5, centralized processing is convenient also in terms of the backhaul data rate. For sufficiently large K, centralized processing is eventuallylessdemandingthandecentralizedprocessingintermsofthebackhauldata rates. OurcentralserverhasanindividualgigabitEthernetconnectiontoeachoftheWARP radiosservingasAPs. Wedividethedownlinktimeintoslotsandineachslotschedule for transmission a number of packets destined to various clients, according to an algo- rithmthatwillbepresentedinSection3.3. ForeachAP,theservercomputestheIandQ components of the precoded baseband frequency domain waveform to be transmitted in the next downlink slot. However, it does not perform any phase correction at this point. The only information used in the precoding is the data to be transmitted and the channel state information between APs and clients. The server transmits their cor- respondingwaveformstoallsecondaryAPs,andfinishesbyfeedingthemasterAP,so thatthemasterAPstartstransmittingrightawayandthesecondaryAPcanimmediately synchronizeandfollow. At the moment we obtain CSI using a downlink estimation procedure, similar to the one presented in 802.11ac. In a future refinement of our system, we would like to reduce the overhead of obtaining CSI by using an uplink estimation scheme that takes advantageofchannelreciprocity,therebyreducingconsiderablythelengthofthechan- nelestimationprocedure. Thecurrentimplementationreliesonasinglemasterbroadcastingareferencepilot for all secondary transmitters. A straightforward extension of our system would have 32 3.2. PERFORMANCEEVALUATION Master Secondaries Pilot Data Clients Figure 3.2: Testbed diagram. The central server is connected to four transmitters, the main transmitter on the left and the three secondary transmitters on the right. Four receiversactasclients. some of the secondary access points relaying the pilot signals on different carrier fre- quencies. By using a set of alternating frequencies, in a fashion similar to cellular net- works,thesynchronizationschemecancoverlargertopologies. ■ 3.2 PerformanceEvaluation Our system setup is presented in Figure 3.2. It consists of a primary transmitter, three secondarytransmittersandfourreceivers. ThemainsenderusesasingleRFfront-end configuredintransmitmode,placingan18MHzshapingfilteraroundthetransmitted signal. The secondary senders use an RF front-end in receive mode and a second RF front-endintransmitmode,witha12MHzshapingfilter. Asmentionedpreviously,the pilots used in phase tracking are outside the secondary’s transmission band, therefore the secondary transmitter will not interfere with the pilot signals from the main trans- mitter. Theseriesofexperimentsisintendedtotesttheaccuracyofthesynchronization, the efficiency of channel separation and the extent to which we achieve the theoretical gainsthatmultiuserMIMOpromisesinoursetup. TheSNRvaluesweremeasuredusingthereceivedwaveforms,nottheRSSIindicator oftheWARPtransceiver. Weinitiallymeasuredthenoisefigureofthereceiverandthen, CHAPTER3. REFERENCE-BASEDSYNCHRONIZATION 33 −0.5 0 0.5 Amplitude I Component −0.5 0 0.5 Amplitude Q Component −π 0 π Phase (Rad) Initial Phase Estimate −π 0 π Phase (Rad) Current Phase Drift Predicted Phase Drift 1 5 10 15 20 25 −π 0 π OFDM Symbols Phase (Rad) Master Phase Secondary Phase Figure 3.3: Phase Synchronization Acquisition. The secondary transmitter receives in-phase and quadrature components (real and imaginary components) of the master signal (top two figures). It then obtains an initial phase estimate (middle figure) from thesesamples. Thesecondarytracksthephasedriftofthesubcarriersbeginningatthe 10th symbol (second from bottom figure) and uses a filter to predict its value a few symbolslater(bottomfigure). in subsequent measurements, integrated the received power to obtain the signal plus noisefigure. SynchronizationAccuracy Inthisparticularexperimentwehaveplacedtwotransmittersandtworeceiversatran- dom locations. We placed a third RF front-end on the secondary sender and config- ureditinreceivemode. Thesecondarytransmittersamplesitsownsynthesizedsignal over a wired feedback loop and compares it with the main transmitter’s signal. The synchronizationcircuitmeasuresandrecordsthephasedifferencesbetweenthesetwo signals. Sinceweusetheprimarytransmissionasareference,inthisexperimentwedo notbroadcastthesignalsynthesizedbythesecondarytransmitterinordertoprotectthe primarytransmissionfromunintendedinterference. We have modified the synchronization circuit to produce a signal that is not only phase synchronous with that of the primary transmitter but has the exact same phase whenobservedfromthesecondarytransmitter. Toachievethis,thecircuitestimatesthe 34 3.2. PERFORMANCEEVALUATION phase rotation that is induced between the DAC of the secondary transmitter and the ADC through which the synthesized signal is resampled. It then compensates for this rotationbysubtractingthisvaluefromtheinitialphaseestimate. Itisworthnotingthat this rotation corresponds to the propagation delay through the feedback circuit and is constantfordifferentpackettransmissions,asdeterminedthroughmeasurements. The resultwasasynthesizedsignalthatcloselyfollowsthephaseofthesignalbroadcastby themastertransmitter,asillustratedinFigure3.3. Thefigureillustratestheinitialphase acquisitionprocess,theinitialphaseestimation,thetrackingandestimationofthephase drift,aswellasthesynthesisofthenewsignal. Thephasediscontinuitiesappearingin the main transmitter’s signal are due to the presence of the PN sequence along with a temporarydisturbanceneededinordertotunethefeedbackcircuit. −10 −5 0 5 10 0 0.2 0.4 0.6 0.8 1 Phase Error (Degrees) Percentage of Experiments Figure3.4: ThePrecisionofthePhaseSynchronization. AirSyncachievesphase syn- chronizationwithinafewdegreesofthesourcesignal. Figure 3.4 illustrates the CDF of the synchronization error between the secondary transmitter and the primary transmitter. The error is measured on a frame-to-frame basis using the feedback circuit. In decimal degree values, the standard deviation is 2.37degrees. The95thpercentileofthesynchronizationerrorisatmost4.5degrees. Theradioswereplacedinatypicalofficeenvironment. WehavemeasuredtheSNR value of the synchronization pilots in the signal received by the secondary transmitter to be around 28.5 dB above the noise floor. This is easily achievable between typically placedaccesspoints. CHAPTER3. REFERENCE-BASEDSYNCHRONIZATION 35 Beamforminggain Oursecondexperimentwasdoneusingtwotransmittersandareceiver. UsingAirsync synchronization, the transmitters broadcast their signals over the air in a phase coher- ent fashion. We measured the channel coefficients between the two transmitters and the receiver using standard downlink channel estimation techniques. Based on these measurements, we arranged the amplitudes and the phases of the transmitted signals such that at the receiver the amplitudes of the two signals would be equal, while their phaseswouldaligninabeamformingfashion. Themaximaltheoreticpowergainover transmittingthetwosignalsindependentlyis3.01dB.Wecomparedtheaveragepower oftheindividualtransmissionsfromthetwosenderstotheaveragepowerofthebeam- formedjointtransmission. Ourmeasurementsshowanaveragegainof2.98dB,whichis consistentwiththeprecisionofthesynchronizationdeterminedinthepreviousexper- iment. This result shows that for all practical purposes we are able to achieve the full beamforminggaininourtestbed. Zero-ForcingAccuracy −32 −30 −28 −26 −24 −22 −20 0 0.2 0.4 0.6 0.8 1 Zero Forcing Leaked Power (dB) Percentage of Experiments Figure 3.5: The Power Leakage of Zero-Forcing. The leaked power is significantly smaller than the total transmitted power, transforming each receiver’s channel into a highSINRchannel. The following experiment measures the amount of power which is inadvertently leaked when using Zero-Forcing to non-targeted receivers due to synchronization errors. Again we have placed two transmitters and a receiver at random locations in our testbed. We have estimated the channel coefficients and arranged for two equal amplitude tones from the two transmitters to sum as closely as possible to zero. The 36 3.2. PERFORMANCEEVALUATION residualpoweristheleakedpowerduetoanglemismatching. Figure3.5illustratesthe CDF of this residual power for different measurements. The average power leaked is -24.46dBofthetotaltransmittedpower. ThisestablishesthatZero-Forcingiscapableof almostcompletelyeliminatinginterferenceatnon-targetedreceiverlocations. Zero-ForcingBeamformingDataTransmission Receiver 1 Receiver 2 Figure 3.6: Zero-Forcing Scattering Diagram. The scattering diagram for two inde- pendentdatastreamstransmittedconcurrentlyusingZFBFdemonstratesthatAirSync achievescompleteseparationoftheuserchannels. This experiment transmits data from two transmitters to two receivers using ZFBF. We have used symbols chosen independently from a QAM-16 constellation at similar powerlevels. ThescatteringplotsinFigure3.6illustratethereceivedsignalsatthetwo receivers. From the figure it is clear that we have created two separate channels. The actualratesachievedwilldependonthequalityofthetwochannels. WewouldliketocomparetheperformanceofthemultiuserMIMOsystemtoacur- rent standard. In current enterprise WiFi networks transmissions within a small area occurfromsingleaccesspointstosingleclientsandareseparatedintimeusingTDMA. We use the best achievable point-to-point rate as an upper limit for the rates that the TDMAapproachcanachieveandcomparetheratesachievedbyoursystem. The SINR values at the two receivers are 29 dB and 26 dB respectively. In the sameexperiment,wemeasuredthebestpoint-to-pointlinktohavea32dBSNRvalue. Using Shannon’s formula, these values translate to maximally achievable rates of 9.96 bits/second/Hz(bps/Hz)forthepoint-to-pointchanneland18.27bps/Hzforthecom- pound MIMO channel. Thus, when using ideal codes, we achieve a multiplexing rate gainof1.83,whichisclosetothetheoreticalvalueof2. CHAPTER3. REFERENCE-BASEDSYNCHRONIZATION 37 Figure3.7: Tomlinson-Harashimaprecoding. Tomlinson-Harashimaprecodingbased onQAM-16constellations. Theachievedspectralefficiencyis16bits/second/Hz At all the mentioned SNR levels 802.11g (a point-to-point standard) uses the same 64-QAMmodulation,resultinginarateof6bps/Hz(ignoringtheerrorcorrectingcode overhead, which is identical for all three SNR levels). Thus, we can say that both of thechannelsobtainedthroughzero-forcingsupportWiFioperationatthehighestcom- monlyusedratesandthereforeequivalatetoindependentWiFichannels. Weconclude that, using practical modulations, the experimental multiplexing gain equals the theo- reticalvalueof2. Tomlinson-Harashimaprecoding Thefinalexperimentusesfourtransmittersandfourreceivers. WeemployTomlinson- Harashimaprecoding. TheresultsareillustratedinFigure3.7,whichpresentsthefour distinct wireless channels created for the four users. Thus, we have achieved a multi- plexing factor of 4. As before, the actual rate gains will depend on the quality of the channels. WemeasuredtheSINRvaluesofthefourchannelstobe16.8dB,19.2dB,21.4dBand 20.8dB.ThelowerSINRvaluesarecausedbyincreasedlevelsofpowerleakagedueto the presence of more transmissions to other receivers (see Figure 3.5 for the distribu- tion of leaked power from a single interfering transmission). Again, the Shannon rate formulapredictsachievablechannelratesof5.6bps/Hz,6.4bps/Hz,7.11bps/Hzand 6.91bps/Hz. Thesumrateis26bps/Hz. Asmentionedbefore,thebestpoint-to-point channel in our setup has a quality level of 32 dB, allowing for 9.96 bps/Hz. Therefore therategainisabout2.6whenusingfourdegreesoffreedomandidealcodes. 38 3.2. PERFORMANCEEVALUATION User 1 Symbol Stream 1 User 1 Symbol Stream 2 User 2 Symbol Stream 1 User 2 Symbol Stream 2 Figure 3.8: BIA Scattering Diagram. Blind Interference Alignment enables the multi- plexingoffouruserstreamsoverthreetimeslots. More practically, we can compare the performance of our system when employing an extended 16-QAM constellation on every channel with the performance of 802.11g using a typical modulation. At 32 dB SNR, 802.11g would use a 64-QAM constella- tionandachieve(ignoringtheerrorcorrectingcodeoverhead)aspectralefficiencyof6 bps/Hz. IntheMIMOcase,wecanachieveasumrateof16bps/Hzusingfour16-QAM constellations,leadingtoamultiplexinggainof2.66underpracticalmodulations,while thetheoreticalvalueis4. Inacommercialimplementation,weexpecttheleakagetobe further reduced and we expect to be able to come closer of a rate gain of 4. In general, nearingthetheoreticalrategainsthroughspatialmultiplexingrequiresprecisechannel stateinformationandtightsynchronization,asevidencedbyourexperiments. BlindInterferenceAlignment Achievablerates. WehaveusedthetestbedtopologyillustratedinFigure2.1through- outourexperiments,placingthereceiversinarbitrarylocationsinaclosedenvironment. In order to compare the performance of THP and BIA to the one of a typical TDMA system,weintroducedathirdtransmissionscheme,inwhichinsteadofmultiuserpre- coding we transmit to one user at a time from the closest access point. In this scheme, transmissionstodifferentusershappeninatime-sharedmanner,justlikein802.11. As opposed to 802.11, we assume that different access points do not collide when doing channelaccess,i.e. theyperformperfectdownlinkscheduling. Weinvestigatethesum rates achievable during downlink transmission. The unit of measure is the number of CHAPTER3. REFERENCE-BASEDSYNCHRONIZATION 39 15 20 25 30 10 15 20 25 30 Receiver Carrier to Noise Ratio (dB) Symbol SINR (dB) THP BIA TDMA (a) Carrier Energy vs. Symbol SINR 15 20 25 10 −8 10 −6 10 −4 10 −2 10 0 Receiver Carrier to Noise Ratio (dB) Bit Error Rate THP BIA TDMA (b)BitErrorRate 15 20 25 30 0 2 4 6 8 Receiver Carrier to Noise Ratio (dB) Sum Rate (bits/s/Hz) THP BIA TDMA (c)Sumrate(16-QAM) 15 20 25 30 0 5 10 15 Receiver Carrier to Noise Ratio (dB) Sum Rate (bits/s/Hz) THP BIA TDMA (d)Sumrate(Gaussiancodes) 15 20 25 30 0 0.5 1 1.5 2 Receiver Carrier to Noise Ratio (dB) Multiplexing Gain Over TDMA THP BIA (e)Multiplexinggain(16-QAM) 15 20 25 30 0 0.5 1 1.5 2 Receiver Carrier to Noise Ratio (dB) Multiplexing Gain Over TDMA THP BIA (f) Multiplexing gain (Gaussian codes) Figure 3.9: Experimental Results. The absolute and relative rates of BIA and THP at differentSNRvalues,underdifferentmodulations. bitspersecondperHertz(bps/Hz)transferredbyeachscheme,wherethecomparison wasdonelookingonlyattheportionofthebandwidthusedfordatatransmission(i.e. we considered only the data carriers and ignored the overhead of null carriers, pilots andcyclicprefix). SincetheOFDMframingforallthreeschemesisidenticalandsimilar totheoneof802.11,weobtainafaircomparisonoftheirthroughputs. Wehavevariedthetransmitters’signalpowersinaproportionalway,tryingtoobtain a typical range of SNRs at the receivers. The receive-side SNR values span the typical highrangeencounteredinWiFisignaltransmission,from15dBto30dB.Thereceived SNRvalues(orcarriertonoiseratios)inourfigureswereestimatedusingnon-precoded and non-synchronized isotropic broadcasts, measuring the raw received power and comparingittothereceivernoise. Thesamelevelsoftotaltransmitpowerwereusedin theprecodedsynchronoustransmissions. We evaluate the SINR (Signal to Noise plus Interference Power Ratio) values of the differentsymbolsstreamsdecodedbythereceivers. DeterminingthesymbolSINRval- uesrequiresmoreeffortinourscenariothaninclassicpoint-to-pointtransmission. Since 40 3.2. PERFORMANCEEVALUATION our system is susceptible to power leakage from one stream to another, we would like tocontinuouslytransmitoverallchannelsinordertoassesstheimpactofinterference. Tothisendwesampledeachsymbolstreamusingsymbolschosenfromarelatively sparseQAM-16constellation. Wemeasuredthevarianceoftheconstellationpointson the receiver side in order to determine the sum of the noise and interference powers. The amplitude of the constellation reflects the received signal power. At the high SNR valuespresentinoursystem,theclustersofconstellationpointsarespacedsufficientlyto allowforanaccuratemappingofthereceivedsymbolstoconstellationpoints. Inorder toassesstheeffectsofinterferenceproducedbystreamsthatfollowotherencodings,we have, in some experiments, fixed a QAM-16 constellation on one symbol stream while employingsymbolschosenaccordingtoaGaussianoruniformdistributionontheother stream. Ourresultshaveshownthatatthelowinterferencelevelsmeasured,noneofthe statisticscollectedshowsconsiderablevariancedependingonthetypeofinterference. Figure 3.9a presents the SINR values for symbols received when using each of the threeprecodingschemes. Figure3.9billustratestheinferredsymbolerrorratesforthe QAM-16 constellation transmitted. It can be easily seen that the THP and BIA curves closelyfollowtheTDMAcurve,withonlyafewdBdifference. Figure 3.9c presents the sum rate achievable by the three different schemes (THP, BIAandplainTDMA)fordifferentlevelsofthetotaltransmitpower,whenemploying a capacity achieving code on top of the transmitted QAM-16 constellation. Figure 3.9e presents the relative gains of THP and BIA over TDMA. It can be easily seen that each schemequicklysaturatesatthemaximumrateof4bits/DoF.SinceTHPandBIAprovide extradegreesoffreedom,theyachievetheirtheoreticalmultiplexinggainoverTDMA. We would like to know how the quality of the resulting symbol streams affects the achievable rates. To this end we have estimated the rates achievable when using capacity-achieving codes instead of the QAM-16 modulation. Figure 3.9d presents the resulting sum rates and Figure 3.9f presents the multiplexing gains. THP achieves an averageincreaseinsumrateof85%. Whilethismayseemshyofthetheoreticalachiev- able multiplexing gain of 2, we must remember that THP allocates power among two CHAPTER3. REFERENCE-BASEDSYNCHRONIZATION 41 degreesoffreedom,whileTDMAallocatesitswholetransmittedpowertoasingletrans- mitter. The second reason for this discrepancy is the shaping loss present in the rate calculationinthecaseofTHP,whichwasindicatedinEquation2.10. TheaveragegainforBIAis22%. Again,thetransmittedpowerisdistributedbetween the two transmitters. Additionally, BIA suffers from noise enhancement, which affects thereceivedsymbols. In the case of a distributed MIMO system, we would expect that phase synchro- nizationerrorcouldleadtorandomrotationsofthereceivedsoftsymbols. Weinvesti- gatedthiseffectbycomparingthevarianceofsoftsymbolscorrespondingtoconstella- tionpointsofdifferentamplitudes. Wewouldexpectthatduetorandomrotations,the varianceoftheouterconstellationpointswouldbehigher. However,ourmeasurements couldnotidentifysuchaneffectforanyofthetransmissionschemes. SinceBIAdoesnotprovidethetransmitterwithchannelstateinformation,toallow ittoguessanappropriatetransmissionrate,itisinterestingtofindoutbyhowmuchthe receivedsymbolqualityisaffectedbysmallvariationsinthepositioningoftheantennas. Suchaneffectisanalogoustofastfading,wheresmallphasechangesaffectthechannel amplitudeatdifferentfrequencies. Wehaveconductedanexperimentinwhichwehave variedthetransmitterantennapositionswithinonewavelengthoftheirinitialposition and measured the channel SINR for the two user symbols. The CDFs of the resulting SINR distributions are shown in Figure 3.10. The high variance of the distribution has profoundimplicationsonthedesignofacodingandmediumaccessschemeforBIA.The higherSNRpresentinoneoftheCDFscanbeeasilyexplainedbythefactthatthetwo symbols are transmitted by antennas placed on different transmitters. The placement oftheusersrelativetothecorrespondingtransmitterdetermineseachsymbol’saverage power. 42 3.3. MEDIUMACCESSCONTROL 10 15 20 25 0 0.2 0.4 0.6 0.8 1 Received SNR (dB) Portion of Measurements Less or Equal User 1 User 2 Figure 3.10: BIA Channel Quality. The cumulative distribution function of received SNRsundertheBlindInterferenceAlignmentScheme. ■ 3.3 MediumAccessControl Given that we have achieved the necessary synchronization accuracy between access pointsandrealizedthefullmultiplexinggain,weturntothelargebodyofworkonopti- malschedulingforcentralizedmultiuserMIMOsystems(seeforexample[KC06,DS05]). Inspiredbythiswork,weproposeaMAClayerthatsignificantlydepartsfromtheclassic networking layered architectural model and adopts a cross-layer “PHY/MAC” design strategy. Highleveldescription Time Division Duplexing. First, we consider the issue of allocating air time and fre- quency spectrum between the uplink and the downlink. We can choose between two natural strategies for separating the uplink from the downlink: time division duplex (TDD) and frequency division duplex (FDD). TDD has the following two advantages. First, with TDD one can exploit channel reciprocity and measure the uplink channel, usingpilotsfromtheuserstoinferthedownlinkchannel. InthecaseofFDD,anexplicit closed-loopchannelestimation(fromthedownlinkpilotssentbytheaccesspoints)and feedback(fromtheclientstotheserver)needstobeimplemented,withaprotocolover- head that increases linearly with the number of jointly precoded access point anten- nas[JAWV11]. Second,TDDisideallysuitedforthetransportofasymmetrictraffic,as CHAPTER3. REFERENCE-BASEDSYNCHRONIZATION 43 Figure 3.11: Packet Design. Downlink data packet (left) and uplink acknowledgment (bottomright). istypicalinanenterpriseWiFiscenario,whereasanFDDsystemprovideslessflexibil- ityformanagingdifferenttrafficpatterns. Specifically,withTDD,thedownlinkchannel estimationprocedureandthedownlinktimereservationproposedinthe802.11acstan- dard[80212]canbeappliedtoourdistributedMIMOsystemaswell. Weshallconsider the scheduling of users in the uplink and downlink periods separately. In the uplink, clientscompeteforbandwidthusingregularCSMA/CA.Thus,intherestofthissection wefocusonthedownlink. Wenoteherethatinorderforoursystemtobebackwardcom- patiblewithlegacy802.11clientsandaccesspoints,protectionmechanismsandmodes ofoperationhavetobeimplemented. Suchmechanismsaredescribedinthe802.11n/ac standards[80212]where,usingRTS/CTS,CTS-to-selfframesandlegacyformatpream- bles,nearbydevicescansensethatthechannelisinuseandavoidcollisions. ProtocolDesign Ourprotocoldesignfocusesonthedownlinkchannel. Figure3.11presentsasimplified schematic of the downlink data packets and corresponding uplink acknowledgments. TheMAClayerprotocolistunedforenablingmultiuserMIMObroadcasts. Thecrucial design constraint is to provide the central server with timely estimates of the channel stateinformationforallclientstowhichitisabouttotransmitorwhichareconsidered forthenextroundoftransmissions. Forthispurpose,wecancollectchannelestimates either at the access points through uplink pilots (based on TDD reciprocity) or at the receiversusingastandarddownlinkestimationprocedureasdescribedin802.11ac. The 44 3.3. MEDIUMACCESSCONTROL centralserverusestheestimatestoselectasetofclientsforthefollowingtransmission slots,accordingtotheschedulingalgorithmsintroducedearlier. The choice between uplink and downlink estimation has an important impact on thedesignofthesynchronizationsystem: Uplinkchannelestimationisa“closedloop" designintroducingaverysmalldelaybetweenthetimeonereceivesthechannelestima- tion,andthetimeonetransmits. Insuchascenario,itisreasonabletoexpectthatonce the CFO is compensated for, the residual CFO will not result in significant phase drift amongthecarriersofthedifferenttransmittersduringachannelmeasurement/packet transmissioncycle. ThissimplifiessynchronizationasonlytheCFO(lineartime-varying phaserotation)needstobetakencareof. 3 Our protocol design follows the lines of 802.11ac [80212]: before a downlink trans- missionperiodtheaccesspointsbroadcastarequestforanumberofclientstoestimate theirchannelsbasedonachannelprobingmessagebroadcastedshortlyafter. Theaccess pointsthentransmitrequestsforfeedbackinsuccessiontoeachtargetedclientandwait forthecorrespondingfeedback. Oncealltheinformationhasbeencollected,thedown- link period can begin. We note that the use of a STBC for control frames can improve theirrobustness,giventhatfromaclientperspectivethephasesoftheaccesspointsare essentiallyrandomduringthisphase. Thedownlinkdatapacketstartswithatransmissionfromthemainsendercontain- ing a pseudo-noise sequence used to achieve frame alignment by the transmitters and for block boundary detection by the receivers. The master access point then transmits the first set of channel estimation pilots which are used by the other access points to determine the initial phases of the subcarrier tones, as described in Section 3.1. After thispoint,allaccesspointstakepartinthedownlinktransmission. 3 To be precise, looking at Equation (2.13) let us distinguish between (t), which is a time-varying frequency-independentphaserotationduetoCFO,and2in=(NTs),whichisatime-invariant,frequency- dependentphaserotationduetotimingmisalignment. Ifuplinkchannelestimationisused,andthechan- nelestimationsubslot(uplink)andthedatatransmissionsubslot(downlink)arecloselyspacedintimesuch thatthetimeaxisreferenceremainsthesameinbothsubslots,thentheeffectofthedelayi onthechannel frequencyresponseisautomaticallyincludedintheuplinkchannelestimation,andthereforethesephase terms are included in the frequency domain channel coefficients for which the precoder is calculated. In thiscase,thereisnoneedforexplicitphasede-rotationoftheseterms. Incontrast,ifthechannelestimation subslotandthedatatransmissionsubslotareseparatedbytoolongofatimeintervalorbyarandom(pos- siblyfractional)numberofsamples,thenwehavetoexplicitlycompensateforthesephaserotationterms. Thisisusuallythecaseindownlinkestimationliketheonewehaveimplemented. CHAPTER3. REFERENCE-BASEDSYNCHRONIZATION 45 Thepacketheaderthatfollowsisbroadcasttoallclients,includingthenon-targeted ones,usingtheAlamoutiencoding[Ala98]. ,asinSourceSync. Duetophasealignment betweentransmitters,theclientsdonotneedtotrackthesecondarysendersinorderto decode this header. The MAC addresses of the hosts targeted in the current transmis- sionandtheMACaddressesoftheclientsthatarerequiredtoprovidetheserverwith channel estimates during the next acknowledgment are the most important pieces of informationcontainedintheheaderfields. Thepositionsoftheaddressesintheheader fieldscreateanimplicitorderingoftheclients,whichwillbeusedintheuplinkperiod. The following part of the header is an allocation map, similar to the one found in the LTE standard, which assigns carriers to small groups of different clients and specifies the constellations used in broadcasting to them. The header is followed by a second setofchannelestimationpilots,transmittedthistimearoundbyallaccesspointsusing ZFBF, which are used by all clients in order to obtain the channel estimates for their individual downlink channels. The clients use the downlink estimates together with thesynchronizationpilottonesinordertogainalockonthesubcarriers. Thedownlink transmissioncontinueswithpayloadtransmission. Incurrent802.11MIMOimplementations,thechannelestimatesareobtainedusing downlink pilots which are in turn quantized by the receivers and communicated back innumericalformtothetransmitter. Thequantizationandcommunicationstepsincur a large overhead. Using the reciprocity property of wireless channels, we can reduce the complexity of the channel estimation process significantly. First, we prefer to per- form uplink channel estimation since uplink estimates can be received simultaneously byallaccesspoints,reducingthenumberofpilottransmissionsneededbyafactorequal to the total number of access point antennas. Second, uplink estimates are sent using analogpilotsignalsinanunquantizedform,leavingthequantizationsteptotheaccess points. This reduces the overhead of the transmission significantly. Third, while the usual estimation pilots are full OFDM symbols, we choose to send pulse-like signals, measurethechannelresponse,andfillthenon-significanttapswithzerosbeforetaking aFouriertransforminordertodeterminethefrequencydomainresponse. Thisensures 46 3.3. MEDIUMACCESSCONTROL thatourpilotsneedtobespacedonlybyanintervalthatcanaccommodatealongchan- nelresponse,i.e. thelengthofacyclicprefix. After the downlink transmission has finished, the clients who have been requested tosendtheirchannelestimatesstartsendingtheseshortestimationpilotsinquicksuc- cession. Wenotethatthereisalargedegreeofsimilaritybetweenthefunctioningofthe downlinkchannelestimationforreceivedecodepurposesandtheuplinkchannelesti- mation step. The timing of the system remains unchanged during the uplink slot and the roles of the transmitters and the receivers are switched. The uplink pilots are fol- lowedbysmartacknowledgmentsforthedatapacketssentusingthetechniquedetailed in[DSGS09a]. We tested each component of the downlink and uplink protocol slots. However, sinceourradiosdonotswitchfromreceivetotransmitinatimelymanner,wecouldnot performcompletereal-timeMACexperiments. Overhead. A note on the overhead of the above MAC is in order. the overhead of our MAC is not more than that of 802.11n. The additional signaling overhead comes fromrequiringafewframestopredicttheinitialphase,andafewframestodictatethe MACaddressesofthenodesfromwhichwewishtorequestchannelstateinformation forthenexttimeslot. Evenwithveryconservativeestimatesthiswillbelessthana20% increaseinheadertimedurationoverthatofatraditional802.11system. Note,however, that we get a bandwidth increase that grows almost linearly in the number of clients. This means that our overhead, normalized such that we consider the total control bits over the total data bits transmitted during a fixed airtime slot, is much less than in a traditional802.11system. CHAPTER 4 AchievingScalabilityandEfficiency The current chapter introduces DistSync, a scalable synchronization scheme aimed at large-scale deployments exceeding the effective range of a single access point. Dist- Sync uses a distributed synchronization algorithm which attempts to phase-lock the network’sAPsforthedurationofadownlinktransmissionslot. AsopposedtoAirSync, DistSync does not attempt to suppress the random phases that different transmitters introduce in the channel model, but tries to estimate and use the effective channel beforeitscoherencetimeends. Thedownlinktransmissionslotmakesuseoftheshort- term constancy of the channel and uses an efficient estimation algorithm followed by fast precoding over a short timeslot duration. The presentation in the current chapter complementsthetheoreticaldescriptiongivenin[RBP + ]andfocusesonsystemdesign problems. The characteristics of oscillator-produced signals that influence the design of the algorithm are presented in detail, along with experimental data that describes the drift of oscillator frequency in time. We describe a synchronization scheme capa- bleofcompensatingfrequencyoffsetwithahighdegreeofprecisionwhileimposinga lowwireless-transmissionoverheadonthenetwork. Weintroduceoptimaltimingand phase estimators that increase estimation precision and decrease the amount of data sent over the wireless backhaul. DistSync has been implemented as a hardware proto- type. The performance of the synchronization scheme and the achieved spatial reuse arequantifiedthroughanexperimentalevaluation. 47 48 4.1. DISTRIBUTEDSYNCHRONIZATION ■ 4.1 DistributedSynchronization ConsideragaintheEquation2.13: e H(n;t) =(n;t)H(n;t)(n;t) where (n;t) = diag(e j ( 2 NTs 1 n+ϕ 1 (t) ) ;e j ( 2 NTs 2 n+ϕ 2 (t) ) ;:::;e j ( 2 NTs M n+ϕ M (t) ) ) and (n;t) = diag(e j ( 2 NTs 1 n+ 1 (t) ) ;e j ( 2 NTs 2 n+ 2 (t) ) ;:::;e j ( 2 NTs K n+ K (t) ) ). TheequationdescribestheeffectivechannelmatrixofasystemwithKclientsandM accesspoints. Keepingwiththenotationofthepreviouschapter,theimpulseresponse of the downlink channel from AP i to client j is h ij ( ( i j ))e j(ϕ i (t) j (t)) where i ; j denote the timing misalignment of APi and clientj, respectively, andϕ i (t); j (t) denotetheirrespectiveinstantaneousphasedifferences(whencomparedtothenominal RFcarrierreference). The previous chapter described a system that diagonalizes the transmitter side matrix(n;t) by using a single access point as a phase and timing reference for the otheraccess points. Thesecondaryaccesspointsmimicthephaseofthereferenceand thetransmitter-sidematrixbecomesconstantintime. Whilethissystemallowsseveral accesspointstotransmitcoherently,theneedforareferenceimpactsitsscalability. The effective deployment range is the beacon transmission range of a single access point, which can be increased by adding relays and their corresponding signaling overhead, butremainsneverthelesslimited. Thisapproachdoesnotmanagetosolvetheessential problemofsingle-referencedistributedMIMOsynchronization,namelythatduetothe limitedrangeofwirelessbeacons,synchronizingfromasinglepointovertheairisnot themosteffectivewaytoattainphasecoherenceandissubjecttoerroraccumulationas therangeoverwhichthereferenceisrepeatedisincreased. A simple observation simplifies significantly the synchronization problem: for any one client, the signals that it receives, i.e. the beamformed packet transmitted to this particular user, is broadcasted from a limited number of access point within its own wireless range. Similarly, the packets that might affect its reception, for example the CHAPTER4. ACHIEVINGSCALABILITYANDEFFICIENCY 49 packets concurrently transmitted to other users simultaneously, which are broadcasted such that their signals null at this client, are sent from its wireless proximity. It results that the SINR figure at the user and the characteristics of the signal propagated to it areaffectedonlybetheprecisionofthesynchronization,infrequency,timeandphase, between the access points within its range. The global synchronization requirement is thus replaced by a local synchronization requirement, and the network has to fulfill a morerelaxedprecisionconstraint. Inthecurrentchapterwereplacethecentralizedarchitecturepresentedintheprevi- ouschapterwithadecentralizedsynchronizationmethodwhichmeasuresthedifferent frequencyandtimeoffsetsbetweenpairsofneighboringaccesspointsandthengathers, overthewirednetworkconnectingthem,thisinformationtoacentralserverandcom- putes for each of them the necessary adjustments. Due to the locality of the wireless transmissions,frequencyandtimingoffsetsbetweenAPsneedonlybemeasuredwhen theAPsarewithintherangeofthesameclient. Thatis,themeasurementproblemcan bedecomposedintosubproblemsovermultiple,possiblyoverlapping,neighborhoods. Ideally,wewouldliketodecentralizethefinalcomputationalstepaswell. However,as longasthewirelessneighborhoodsofthesimultaneouslyactiveuserscreateaconnected cover of the access points, the synchronization problem cannot be partitioned easily andoptimallyintoindependentsubproblems,duetotheinterdependencybetweenthe adjustmentscomputedforAPsbelongingtomultipleneighborhoods. Sometimessucha connectedcoverdoesnotexistandeachgroupofindependentuserscanbeapproached asaseparateproblemandtheaccesspointscanbeclusteredintoindependentcompo- nents. Inthegeneralcase,thesystemwillhavetodealwithasynchronizationproblem involving all access points in the network. In case the size of the problem makes the computationintractable,aquicksolutionwouldbetoassignclientstoanumberofsets ofconcurrentlyservedclientswhereeachsetcanbeseparatedinsmallenoughcompo- nents. Inthecaseofsynchronization,thetotaldelayisgiventheoverheadofmeasurements, thetimenecessaryforcollectingdatathroughoutthewirednetwork,thecomputational hardness of the adjustment computation and returning the results to the APs. In the 50 4.2. SYSTEMDESCRIPTION caseofprecoding,thedelayconsistsofcollectingchannelstateinformation,precoding andreturningtheprecodertotheAPs. Thecomplexityoftheproblemmustbelimited, suchthattheaforementioneddelaysareunderthemaximumtolerabletimeforsolving theproblem,muchlessthanthechannelcoherencetimeforprecodingandlessthanthe timeittakesforoscillatorstosignificantlychangetheirfrequencyoffsetsduetothermal effectsinthecaseoftimeandfrequencysynchronization. Thesizeoftheinstancestobe solvedinfluencesalltheabovedelayfactors. Thecentralelementofournewapproachisadifferentwayofdealingwiththeeffec- tive channel matrix. Instead of modifying the transmitter side matrix(n;t), we seek, through the use of precise timing and frequency offset estimation and compensation, to maintain it constant throughout a slot comprised of a channel estimation time and severaldownlinkpackettransmissions. Weprecodeusingtheeffectivechannelmatrix asaninputtotheprecodingalgorithmandacceptthecomplicationthattheprecoding algorithmmustberunwithinaslotduration,whenevertheeffectivechannelmatrixhas significantly changed 1 . While this approach introduces a hard real-time constraint on our precoding calculation, it allows the system to continue functioning based on over- the-air synchronization while removing any barriers caused by the wireless coverage area of the reference access point. The possibility of using the effective channel matrix in precoding was discussed in [BRM + 13], while the theoretical considerations behind thisapproachhavebeendiscussedin[RBP + ]. ■ 4.2 SystemDescription Thenovelsynchronizationtechniquespresentedhereareaffectedmainlybythebehav- iorofthefrequencydriftofAPoscillators. Weexpandherethediscussionofthehard- ware characteristics of our system and insist on the details that impact frequency esti- mation. Followingthat,forcompletenesspurposes,wedescribethesystemarchitecture introducedin[RBP + ]. Whilethispresentationwillfocusongivingahigh-levelprotocol 1 Thequantitativemeaningofthisstatementwillbediscussedlaterinthischapter. CHAPTER4. ACHIEVINGSCALABILITYANDEFFICIENCY 51 overview,thefollowingsectionswillpresentinmoredetailthepilotsandtheestimation procedureusedatdifferentstepsintheprotocols’operation. Hardware Our system is based on the WARP hardware platform [Ric]. WARP radios provide an FPGA capable of hosting digital logic for real-time waveform processing, a number of RFfront-endscapableoftransmittingandreceivinginthe2.4GHzfrequencybandand aclockboardhostingoscillatorsusedforcreatingthesamplingclockofthedigitalbase- bandcircuitryaswellasthecarrierclockusedinpassingsignalsfrompassbandtobase- band and in reverse. The oscillators have frequency stability on the order of 2.5 ppm (parts-per-million), which create carrier frequency offsets of up to 4 kHz between the different transmitters. Moreover, the oscillator frequencies are not fixed but are influ- enced by thermal variations and drift in a random fashion. Figure 4.1 illustrates the evolution of the carrier frequency offset present between two transmitters over a one secondinterval. Itcanbereadilyobservedfromthisfigurethatthethermaleffectscon- tinuouslyaffectthetwooscillatorsandthatthedrifttheyinducecanchangetheirrelative frequency offset by a few tens of Hertz every second. The stability of these oscillators is by no means uncommon in low-cost WiFi equipment. Most routers, access points andclientdevicesareconstructedusingTCXOs(thermal-controlledcrystaloscillators) whose frequency precision is typically in the ppm range. A different class of oscilla- tors, OCXOs(oven-controlledcrystaloscillators)offersfrequencystabilityintheparts- per-billion range, leading to CFOs of only a few Hertz. Such accurate oscillators are heavy and expensive, with prices currently ranging in the hundreds of dollars. While suchhigh-endcomponentsareanappropriatechoiceinthedesignofcellularbasesta- tions, their use in WiFi routers, access points or femtocells is quite prohibitive. How- ever,allowingcarrierfrequencyoffsetsontheorderofKiloHertzbetweentransmitters wouldcompletelycanceltheirabilitytobeamformcoherentlyoveratimedurationcom- parabletoapackettransmissiontime,i.e. theirrelativephaseswoulddriftsignificantly 52 4.2. SYSTEMDESCRIPTION over such a short period. We choose therefore to eliminate the carrier frequency off- setspresentbetweentransmittersbycarefullyestimatingthemandcompensatingthem duringtransmission. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 3740 3745 3750 3755 3760 3765 3770 Frequency (Hz) Time(s) Figure4.1: CFODrift. TheevolutionofthecarrierfrequencyoffsetbetweentwoWARP boardsasmeasuredoveraonesecondinterval. In designing a wireless system, it is possible to use a single oscillator for creating bothsamplingandcarrierclocks,whichhastheadvantageoflinkinginanunambigu- ous way the carrier frequency offset (CFO) and the sampling frequency offset (SFO) of its radio transmitter. In fact, with this optimization, measurements of the former can beusedtoexactlycomputethelater. Ingeneral,CFOestimationisasimplerprocedure thanestimatingtheSFO,duetothefactthatthecarrierfrequencyismuchhigherthan thesamplingfrequency. PhasechangesinducedbytheCFOaremuchmorerapidand can be estimated over shorter time intervals and with greater accuracy than the corre- spondingphasechangesinducedbySFO.Itresultsthat,underthissetup,thepresence of a separate sampling frequency offset estimator is not needed and the system’s com- plexitycanbegreatlyreduced. Thedifferentradiosfulfillingtheroleofaccesspointsareconnectedthroughaswitch followedbyasinglegigabitEthernetconnectiontoacentralserver. Theserverhasthe role of collecting channel data sent by the access points, computing precoding coeffi- cients and transmitting them back to the access points in a very short time interval, typically well under a millisecond. The software in charge of collecting the channel dataandcomputingtheprecodingcoefficientswasimplementedasasimpleuserspace UDPserverwhichmakesuseofATLAS[WPD01],LaPACK[ABD + 90]andBLAS[WP05] CHAPTER4. ACHIEVINGSCALABILITYANDEFFICIENCY 53 librariesforperformingitslinearalgebraoperations. Theonlyoptimizationdoneonthe server-sideforreducingtheresponsetimewassettingthenetworkcard’sinterruptcoa- lescingparameterstovaluesthatassuredthatanetworkinterruptwasgeneratedassoon astheexpectednumberofcoefficientpacketsarrivedattheserverandthatthenetwork cardwouldtransmitanyoutboundpacketswithoutanydelay. Architecture The architecture of our system is hierarchical but decentralized. There are three main tasksthatweaimtoachievethroughover-the-airsynchronization: establishingarough symbol alignment between transmitters, capable of supporting OFDMA (OFDM with Multiple Access) operation; eliminating, to the extent of achievable accuracy, carrier frequency errors between neighboring access points; lastly, using the resulting near- constantdownlinkchannelsfordownlinkdatatransmission. Weaimtoachieveallthese goalsinacompletelydistributedmanner,withouttheneedforacentralwirelessrefer- encepointaspresentinMegaMIMO[RKK12]orAirSync[BRM + 13]. Figure4.2: Hierarchicalstructure. Thenodesareorganizedinclusterscenteredonaset of anchor nodes whose can communicate wirelessly with their anchor neighbors such thattogethertheyconstituteaconnectedsetofnodes.[RBP + ] Hostsareorganizedinatwo-levelhierarchycomprisingasetofanchornodesanda setofregularnode. Anchornodesareplacedfurtherapartbutarecapableofwirelessly communicating with each other (see Figure 4.2). Time alignment and frequency offset are measured and compensated first between the anchor nodes and then between all 54 4.3. EFFICIENTESTIMATION nodespresentinthesystem. Therateatwhichthesynchronizationalgorithmmustbe run is about ten times per second. This number was obtained by quantifying the drift rateofthefrequencyoffsetsinducedbytheoscillatorsandlimitingthemaximumdrift allowedbeforecomputingafreshestimatetoavalueofatmost10Hz. Whentheaccess pointsaresymbolalignedandtheirrelativefrequencyoffsetsarewithinafewHertzof eachother,theirdownlinkchannelscanbeassumedtobeconstantformillisecond-scale durations,sinceanyresidualphasedriftsareunlikelytocausephasechangeslargerthan afewdecimaldegreesandcausesignificantrateimpairments. As previously mentioned, we take advantage of the static nature of the channel at thisshorttimescaleandtrytoestimateitanduseitforprecodingandtransmittingdata before any significant change occurs. This approach is different from the one followed by MegaMIMO [RKK12] and AirSync [BRM + 13], which were distributing a reference wirelesssignalinordertoeliminateanytransmitter-inducedwirelesschannelchanges andkeepthetransmitter-sidephasematrixconstantforindefinitetimedurations. Oursystemusescentralizedprecoding. Allchannelcoefficientscollectedatthedif- ferent access points are sent over a wired backbone to a single server. The server com- putestheprecodingcoefficientsusingtheZero-Forcingtechnique[CS03]. ■ 4.3 EfficientEstimation Aspreviouslymentioned,hostsmustperformperiodicestimationoftheirrelativetim- ing offsets and carrier frequency offsets, since these quantities vary in time according tothethermaldriftoftheiroscillators. Wechoosetointerleaveestimationperiodswith data transmission periods in a TDD manner, as illustrated in Figure 4.3. For the level ofprecisionrequired bycoherentbeamformedtransmission, theestimationprocedure mustberepeatedseveraltimespersecond. Moreover,everypairofneighboringaccess pointsmustproduceestimatesofthetwoquantitiesmentioned. In our design, each access point transmits beacons that are used by its neighbors fordeterminingtheirrelativefrequencyoffsets. Ideally,allbeaconsshouldbereceived CHAPTER4. ACHIEVINGSCALABILITYANDEFFICIENCY 55 withoutinterferencebythesender’sneighborsduringtheestimationprocess. Schedul- ingthetransmissionofbeaconswithoutreceiver-sideinterferenceinordertocoverevery linkinaminimalnumberofslotsisawell-knownprobleminadhocnetworks. Oursys- temhastheadvantageofawiredcontrolplanewhichallowsforsolvingthisallocation probleminacentralizedmanner. Exactandapproximatesolutionstothisproblemare well-known. synch slot data 1 data 2 data 3 synch slot request to send pilots uplink pilots downlink multiuser precoded data pilot1 pilot2 pilot3 pilot1 pilot2 pilot3 frame Figure4.3: Superframe. Theslotstructureincludesasynchronizationperiodfollowed byadownlinktransmissionperiod.[RBP + ] TherequiredprecisionforeachoftheestimatesmentionedisrecordedinTable4.3. The table also includes the rate of change of each parameter in the case of the oscilla- tors used in our wireless platform. These rates of change have been established either experimentally(inthecaseofthethermalinducedCFOdrift)orbyanalyzingtheclock characteristicspresentedinthedatasheet. Interpreting the values in the table motivates the design decisions behind the syn- chronization procedure. The first thing to notice is that for the high SNR regime cor- responding to wireless links between neighboring access points in WiFi deployments (forexample,above20dB),achievingtherequiredCFOestimationprecisionrequiresa pilotoverheadmuchlargerthanachievingthetimingestimationprecision[RBP + ]when usingstandardestimationtechniques(e.g. PN-basedtimingoffsetestimation[TEF99a] and sine-based CFO estimation [Tre85,Kay89]). Moreover, the drift in the case of the CFOisessentiallyarandomprocesswhichmustbecontinuouslymeasuredantracked, possibly using a Kalman filter. By contrast, the drift in the case of the timing offset is frequency-offset induced and occurring at a constant rate. The evolution of the timing offset can be readily predicted from the CFO value. For example, for our oscillators, 56 4.3. EFFICIENTESTIMATION Parameter RequiredPrecision RateofChange CFO 10Hz 100Hz/sec SFO 5Hz .5Hz/sec Timingoffset 200ns 1500nsec/sec Table4.1: Estimatedvariables. which have 1.5 ppm frequency stability, the expected drift within a second is 1.5 sec. Thiscorrespondstoacarrierfrequencyoffsetofabout4kHz. However,lookingatTable 4.3,thecarrierfrequencyoffsetcanbeestimatedwitha100Hzprecision,thereforethe timingdriftoverthesamesecondintervalcanalsobeestimatedwitha40nsecpreci- sion. ThereforeanaccurateCFOestimatorgreatlyreducesthenumberofmeasurements needed for timing offset estimation. It results from the above considerations that fre- quencyoffsetestimationisthemainproblemtobesolvedandincursthegreatestpilot overhead. Wehavedecidedtoadaptastandardfrequencyestimationtechniqueusedbymany OFDM-compatible transmission schemes, namely the Schmidl-Cox estimation proce- dure [SC97]. Standard Schmidl-Cox estimation uses the cross-correlation between two identical pilot sequences spaced one symbol duration apart in order to determine the phase change over the symbol duration. We introduce a simple modification that improves the accuracy of the estimator without increasing the pilot overhead. By increasing the spacing between the two sequences, the sensitivity of the phase change estimate to channel noise is severely reduced. The risk that we incur by increasing the spacingisthatthephasemightrollbackwithoutthesystembeingabletodetectit,pro- ducing a significantly lower frequency offset estimate than the correct value. In fact, thespacingofthesequencesdeterminesthemaximumfrequencyrangethattheestima- torcancover. Thesystemdesignermusteitherbeabletoguaranteethattheoscillators will not produce frequency offsets larger than this range or use a second, less accurate frequency estimator that works over shorter periods, for example over the period of a single sequence, in order to place the accurate estimate in the right frequency bin. We havechosenthelateroptioninourdesign. CHAPTER4. ACHIEVINGSCALABILITYANDEFFICIENCY 57 Figure 4.4 illustrates a CFO estimation period. The beacons transmitted by differ- ent APs are interleaved in order to take advantage of the spacing of the two sequences comprisingthem. Generally,thesequencelengthcorrespondstoafewOFDMsymbols, which is smaller by an order of magnitude than a typical data packet duration. If the chromatic number of the interference graph is sufficiently low, the whole estimation procedure can be executed during a single packet transmission time, i.e. in less than a millisecond. Figure4.4: CFOEstimationPeriod. ThebeaconsofdifferentAPsareinterleavedintime. The increased spacing between the constituent sequences allows for a finer frequency estimate. Oncealltherelativecarrierfrequencyoffsetsmeasurementsareavailable,thecentral controllersolvesaconstrainedleastsquaresoptimizationprobleminordertocombine themintoauniformview. Thisprocedureisoptimalundertheassumptionthatcarrier frequency offset measurements are linear, which for small oscillator imprecision is a reasonableassumption. For a more detailed description of the synchronization slot and a model of the oscillator-inducedeffectsonthetransmittedsignals,wedirectthereaderto[RBP + ]. Afterestimatingthetimingandthefrequencyoffsets,theycanbecompensatedfor eachslotseparately,Hostsmaintainconstanttheirrelativetimingoffsetsduringtheslot, allowing for small timing drifts. However, over a slot duration these drifts are signifi- cantlysmallerthanthedurationofacyclicprefixand,afterthetransmittersaligntheir symboltransmission,alsoOFDMAoperationispossible. ToachieveMIMOoperation, whichalsorequiresphasecoherence,CFO-effectshavetobealsocompensated. Remem- berthatthevalueofthefrequencyoffsetdependsonthesubcarrierfrequency,sinceitis actuallytheresultofatimecompression/dilationduetodifferentsamplingspeeds. For 58 4.3. EFFICIENTESTIMATION eachsubcarrier,forsmallfrequencyoffsetvalues,wecancompensatetheCFObyinduc- ingphasechangesinthetransmittedsoftsymbols,i.e. rotatingthemtocompensatethe CFO-inducedrotations 2 . Inoursystem,receiversalsocompensatetheirfrequencyoff- sets, however in a general deployment this is not a requirement and this optimization can be sacrificed in order to preserve compatibility with legacy devices. The effect of maintaining constant the timing offsets and compensating for the frequency offsets is thattheeffectivechannelmatrixinEquation2.13ispreservedconstantfortheduration ofadownlinkslot. In each slot, the effective matrix will still include a set of random transmitter-side phasesandreceived-sidephases. Thereforethematrixchangesfromslottoslotdepend- ingnotonlyonthechangesinthechannel(whichoccurattherateofthechannelcoher- ence time) but also on the two diagonal matrices that describe the mentioned phases. The effective channel can be estimated in each slot using downlink channel estimation involving downlink pilot transmission followed by feedback from the clients, uplink channel estimation involving beacons transmitted form the clients to the network-side transmittersoraphaseestimationprocedureamongthetransmitterssimilartothesyn- chronizationprocedureusedforestimatingcarrierfrequencyoffsets. Whilethetestbed implementationuseddownlinkchannelestimates,thesystemdesigniscompatiblewith uplinkchannelestimationaswell. Wehaveconsidereduplinkchannelestimationsince it measures the effective channel matrix, i.e. it combines the antenna-to-antenna chan- nel matrix estimation with estimating the two diagonal matrices. The advantage over downlinkchannelmeasurementsisthatwhiledownlinkchannelestimationinvolvesa feedback step in which the measurement are reported over the air in quantized form, withahighoverhead,uplinkestimationonlytransmitsthepilotsinanalogform. When 2 Thisapproachdoesnoteffectivelychangethefrequencyofthetransmittedsubcarriers,butforasmall ratioofCFO/subcarrierbandwidthitdoesnotproducesignificantinter-carrierinterference(ICI).Alterna- tivesincludechoosingtheCFOofthenullsubcarrierasacommonCFOvalueandusingasinesynthesizer to change the frequency of the transmitted signal by this amount while still applying the pre-IFFT phase rotations to compensate for the CFO differences between subcarriers or renouncing the IFFT completely and generating each subcarrier signal separately using a frequency synthesizer. The later approaches are suitable for LTE-compatible networks where the subcarrier separation is much smaller than in WiFi net- worksandICIeffectsaremoreofaconcern. Infact, inLTEnetworkstheclients, whichuselow-precision oscillatorspronetogeneratingfrequencyoffsetsleadingtosignificantICI,correcttheirsignalsbasedona base-stationbroadcastedfrequencyreferencebeforetransmission. CHAPTER4. ACHIEVINGSCALABILITYANDEFFICIENCY 59 using the slot structure presented in Section 3.3, the overhead is only one OFDM sym- bol/client. The basic assumption involved in realizing a system based on uplink estimation is that of reciprocity between the downlink and the uplink transmission channels (see [SYA + 12]fordetails). Specifically,thedownlinkchannelcoefficientsanduplinkchannel coefficientsforeachsubcarriershouldbeidenticaluptoacomplexscalingvaluewhich isconstantacrossmeasurements. When dealing with channel changes, we would like to know to which extent the changes are determined by actual antenna-to-antenna channel changes (the matrix H(n;t) or by electronics induced phase changes (the matrices m (n;t) and m (n;t)). For this purpose, we estimate the timing offsets and random phase factors from the measured channel and compensate them in order to gain more information about the actualchannel. It turns out that estimating the channel offset over the different subcarriers is anal- ogous to a well-known problem in communication theory, namely estimating the fre- quencyofanoisysinusoid. AthighSNR,solutionstothisproblemhavebeenprovided by[Tre85,Kay89]. Thefollowingexpositionadaptstheirtreatmentoftheproblemtothis situation,mentioningalongthewayafewkeydifferences. Considertheendtoendchannelbetweentransmittermandreceiverk: e H km (n;t) =e j ( 2 NTs (m k )n+(ϕm(t) k (t)) ) H km (n;t) (4.1) Itfollowsthat \ e H km (n;t) = ( 2 NT s ( m k )n+(ϕ m (t) k (t)) ) +\H km (n;t) (4.2) Assuming that the n-th subcarrier is measured at time t with a pilot received with power P and assuming a receiver noise power N, under the high SNR approximation [Tre85],theSNRfigureforthemeasuredangleis 2P N . Linearregressionoffersusawayofestimatingtheparameters m k andϕ m (t) k (t). AssumethattheanglesinEquation4.2havebeenunwrappedalongthenvariable. 60 4.3. EFFICIENTESTIMATION In the following we will have to ignore the presence of the\H km (n;t) factor, which is nonlinear. ThestandardestimatorsforthetwoparametersinthecaseofN c subcarriers numbered0;1; ;N c 1placedsymmetricallyaroundthecenterfrequencyare[Tre85]: \ m k = 12 N c (N 2 c 1) Nc1 ∑ c=0 c\ e H km (c;t) 6 N c (N c +1) Nc1 ∑ c=0 \ e H km (c;t) (4.3) and \ k (t)ϕ m (t) = 1 N c Nc1 ∑ c=0 \ e H km (c;t) (4.4) Equivalently, Kay [Kay89] proposes the following form which at high SNR is also equivalenttothemaximumlikelihoodestimator: \ m k = Nc2 ∑ c=0 w c \ e H km (c;t) e H km (c+1;t) (4.5) with w c = 3 2 N c N 2 c 1 8 < : 1 [ c ( N 2 1 ) N 2 ] 2 9 = ; (4.6) whichavoidstheneedforphaseunwrapping. The variances of the estimated values can be easily computed [Tre85,Kay89] and meettheCramer-Raoboundforthisproblem[Tre92,RB74]: Var( \ m k ) = 1 (N c 1) 2 P N (4.7) while Var( \ ϕ m (t) k (t)) = 1 N c 1 2P N (4.8) Returning to the factor\H km (n;t), we can see that it induces the following biases intotheestimates: CHAPTER4. ACHIEVINGSCALABILITYANDEFFICIENCY 61 Bias( \ m k ) = 12 N c (N 2 c 1) Nc1 ∑ c=0 c\H km (c;t) 6 N c (N c +1) Nc1 ∑ c=0 \H km (c;t) (4.9) and Bias( \ ϕ m (t) k (t)) = 1 N c Nc1 ∑ c=0 \H km (c;t) (4.10) Thesebiasesmaketheestimateschannel-dependentandpreventusfromusingthe timingandphaseestimateinordertolocallycorrectfortherandomphasesofthetrans- mitters. However, if we know that the channel H km (n;t) are constant in time, we can readilyseethatthebiaseswillbeconstantandthetransmitterscancomputeexactlytheir timingandphaseoffsets. Itresultsthat,withafixedchannel,thetransmitterscanusea setofpreviouslycomputeddownlinkcoefficientsandjustcompensatetheirownphase changes, which are now known. With a constant channel to the user, the transmitters canthusavoidrepeatingtheprecodingprocedure. While the clients to the users cannot be assumed to stay constant, the channels between the access points themselves are constant to a large degree, so a set of inter- access point estimations can be used to determine the relative phase changes and cor- rect for them. If the changes are measured relative to a single other access point, we are back to the reference-based synchronization scenario. If the changes are measured betweenallpairsofaccesspoints,thetransmitterswillneedtocentralizetheirmeasure- ments,similarlytotheprocedureappliedinthecaseoffrequencyestimatesinorderto computethenecessaryadjustments. Assuming we have a set of channel measurements taken at different times we can usetheaboveestimatestobringthemtoacanonicalform: C( e H km (n;t)) =e j ( 2 NTs ((m k )( \ m k ))n+(ϕm(t) k (t))( \ ϕm(t) k (t))) ) e H km (n;t) (4.11) 62 4.3. EFFICIENTESTIMATION 0 20 40 60 0 50 100 −π −π/2 0 π/2 π Carrier Channel Phase (a) 0 20 40 60 0 50 100 −π −π/2 0 π/2 π Carrier Channel Phase (b) 10 20 30 40 5 10 15 20 25 30 35 40 Channel A Channel B 5 10 15 20 25 30 35 (c) Figure4.5: ChannelEstimation. (a)Channelmeasurements(phaseangle)beforetiming andphase-offsetcompensation. (b)Channelmeasurements(phaseangle)afterbringing themeasurementstocanonicalform. (c)Distancebetweencanonicalformsfordifferent pairsofrandomchannels. In order to evaluate the precision of our canonical form, we generated a set of ran- dom channel instantiations according to a 10-tap channel model with coefficients gen- eratedaccordingtoaRayleigh-distributionwithamplitudedecreasingexponentiallyin thetapcountandwithrandomphases. Figure4.5aillustrates,forasinglechannel,the measured phases for each subcarrier under a set of random timing and phase offsets, wherethetimingoffsetsareuniformlyrandomfromCP=5toCP=5whereCP isthe lengthofthecyclicprefixandthephaseoffsetsareuniformlyrandomover[0;2). The samechannelmeasurementsincanonicalformarerepresentedinFigure4.5b. Itcanbe seen that the compensation applied almost completely removes the timing and offset effects. Encouraged by these results, we wanted to see whether the canonical form of the channel could be an indicator of whether the channel has significantly changed. For pairs of different random channels, with random timing offsets we have used the l 2 metricinordertoquantifythedistancebetweenthephasevectors. Theresultsareillus- trated in Figure 4.5b, where for each pair of channels the likelihood has been obtained byaveragingoveralargenumberoftimingoffsets. Whileforthesamechannelthedis- tanceremainslow,foralargenumberofpairsofdifferentchannelsthedistancedoesnot increasetomuchlargervalues,suggestingthatthismethodcannotbeusedtoprecisely distinguishbetweendifferentantenna-to-antennachannelmeasurements. CHAPTER4. ACHIEVINGSCALABILITYANDEFFICIENCY 63 ■ 4.4 PerformanceEvaluation OurtransmissionsystemiscomprisedoftwoWARPradiosconfiguredasaccesspoints, connectedtothesameserverandanothertwoWARPradiosconfiguredasclients. One of the two access points broadcasts synchronization beacons used by the other three hostsincorrectingthefrequencyofincomingandoutgoingsignals. 3 The experiments have been conducted in an anechoic chamber and the hosts have beenplacedasshowninFigure4.6atvariouspositions. Thetwobluehostsontheright side serve as access points while the two red hosts placed near them serve as users. As mentioned, one of the access points transmits reference beacons used by the other hosts for obtaining timing and frequency offset estimates. The access points use the timing estimates not only to align their OFDM symbols, but also to identify and count theminparallelfashion,makingitpossibletostartpackettransmissionsfromdifferent access points on the same symbol. In our experiment, each packet transmission takes place according to the following sequence of operations: first the downlink channel is estimated and the coefficients are collected at the server. The implementation uses 64 subcarriersand,foreachsubcarrier,theIandQcomponentsofthechannelcoefficients are each sampled with 16 bit precision. It results that for every link in the system, the channelcoefficientsaddupto256bytes. Eachusercollectsasetofchannelestimatesfor eachAP,thatiseachusermustmeasurethechannelcoefficientsfortwolinks,resulting inatotalof512bytesofdatatransferredbyeachusertotheserver. Theserver, inturn computes the precoding coefficients and returns them to every access point in a mes- sageequalinsizetotheonereceivedfromanuser,thatis512bytes. Onceallprecoding coefficients have been broadcasted, which the access point can observe by sniffing the packetsbroadcastedoverthewirednetwork,theaccesspointsstarttransmittingcoher- ently,startingonthesamesymbol. 3 Due to the small scale of our setup, we have not implemented the entire synchronization protocol usingleastsquaresestimation. Accordingtothespecificationofthefullimplementation,bothaccesspoints shouldbebroadcastingbeacons,givingasecondsourceofbeaconstobeusedinthefrequencyoffsetesti- mation process. However, we believe that in this case the estimation results obtained with two beacon sourceswouldcloselymatchtheonesobtainedwithasinglesource. 64 4.4. PERFORMANCEEVALUATION 1m Figure4.6: PlacementDiagramfor4x4Experiments. Thepositionsoftheradiosinthe anechoicchamberaremarkedintheabovefigure. Thetransmittersaremarkedinblue and the receivers are marked in red. In the 2x2 experiments all the nodes were placed inthepositionsmarkedontherightsideofthediagram. The users record the received data and attempt to decode it. If the channel coef- ficients have been determined correctly and the carrier frequency offsets are properly compensated, the transmitters should be able to accuratelyzeroforce the signals trans- mittedtotheusers,allbuteliminatinganyinterferencebetweenthesignalsdestinedto differentusers. Whileourimplementationincludesidletimes,inapracticaldeploymentthepassing of coefficients to and from the server and the downlink data transmissions could be pipelined and done in parallel. Due to the intricacies of running multiple consecutive experimentsontheWARPs,wehavenotimplementedthisoptimization. Synchronization Thefirstsetofexperimentsisconcernedwiththeaccuracyofourfrequencyoffsetesti- mation. Weusedsimplesinesignals,broadcastfromanaccesspointtoanuser,inorder to get an upper bound on the frequency offset between the two. Figure 4.7 shows the distributionofthemeasuredfrequencyoffsetsbothwhenthetransmissionsourcewas thesameaccesspointbroadcastingsynchronizationbeaconsandwhenthetransmission sourcewastheotheraccesspoint. CHAPTER4. ACHIEVINGSCALABILITYANDEFFICIENCY 65 −20 −10 0 10 20 30 0 0.2 0.4 0.6 0.8 1 CFO (Hz) Empirical CDF AP transmitting beacon AP listening to beacon Figure4.7: ResidualCFOdistribution. Theempiricalcumulativedistributionfunction ofthefrequencyoffsetsoftheAPthatsendsthebeaconandtheAPthanlistenstoit. WenextwantedtoquantifytheeffectsoftheremainderCFObetweenthetwoaccess points on the phase coherence of the access points, namely measure the difference between their relative phase at the time of channel estimation and their relative phase atthetimeofdatatransmission,whichoccursuptoonemillisecondlater. Forthispur- pose,webroadcastedpilotsfromthetwoaccesspointsbothduringthechannelestima- tionperiodand,withoutmakinguseofanyprecodingcoefficients,duringthedownlink datatransmissionperiod. Wemeasuredthechangeinrelativeanglebetweenthepilots fromthetwoAPs. Figure4.8showsthedistributionofourresults. −30 −20 −10 0 10 20 30 0 0.2 0.4 0.6 0.8 1 Relative Angle Change Empirical CDF Figure4.8: Angledriftdistribution. Theempiricalcumulativedistributionfunctionof therelativeanglechangebetweenthepilotsofthetwoAPs. Finally,wehaveusedthemeasuredpilotsinordertoZero-Forceourdatatransmis- sions. We measured the channel SINR corresponding to each user channel in order to determinetheaccuracyofoursignalseparation. Theresultingdistribution,forthetwo usersisplottedinFigure4.9. Theresultsareconsistentwiththeangledifferencesmea- suredinthepreviousexperiment. 66 4.4. PERFORMANCEEVALUATION 0 5 10 15 20 25 30 0 0.2 0.4 0.6 0.8 1 SINR (dB) Empirical CDF Receiver 1 Receiver 2 Figure 4.9: SINR Distribution. The cumulative distribution function of the channel SINRforeachuser. ThehighSINRfiguresallowforsendingrelativelycleanQAM-modulatedsignalsto thetwousers,asillustratedinFigure4.10. Receiver 1 Receiver 2 Figure 4.10: Zero-Forcing Scattering Diagram 2x2. The scattering diagram at the receiversoftwoindependentdatastreamsconcurrentlytransmittedfromtwoAPs. Inasimilarexperimentwithfouraccesspointshavingeachareceivernearbywehave measuredthescatteringdiagramsfoundinfigure4.11. Wehavevariedthetransmitted powerinordertoassesstherategainsoverpoint-to-pointtransmission. Figure 4.11: Zero-Forcing Scattering Diagram 4x4. The scattering diagram at the receiversoffourindependentdatastreamsconcurrentlytransmittedfromfourAPs. Thecomparativemediumratesareillustratedinfigure4.12. Theaveragerategainin sumrateisabout2.65,closelymimickingthebehaviorofthereference-baseddistributed MIMO system. We can conclude that the modifications that enable scaling up the size ofthedeploymentdonotaffecttheachievedperformance. CHAPTER4. ACHIEVINGSCALABILITYANDEFFICIENCY 67 −29 −26 −23 −20 −17 −14 −11 −8 −5 −2 1 4 7 10 0 5 10 15 20 25 30 35 Transmit Power (dBm) Sum Rate (bps/Hz) Figure 4.12: Rates of Multiplexed MIMO Transmission vs Point-to-Point Transmis- sion. The sum rates obtained through multiuser transmission with four multiplexed streams are about 2.65 times higher than the average rates of point-to-point transmis- sions. Thereference-basedsystemandthecurrentsystemaresimilarinthewayinwhich theyperformchannelestimationandprecoding. Anopenquestionishowthesefactors affect the achievable performance and whether they leave space for further improve- mentsineachofthetwosystemsconsidered. CHAPTER 5 TagSpottingattheInterferenceRange The current chapter introduces tags, wireless primitives aimed at message passing in adhoc networks. We discuss the construction of tags, conduct a theoretical analysis of their performance, present their overhead, evaluate them experimentally under differ- ent interference conditions. Through two sample applications in scheduling and con- gestion control we showcase the way in which tags enable a large number of capacity- sharingschemesbasedoninformationsharing. Asopposedtoregularmessagepassing methods, we show that tags can reach beyond the data transmission range to the edge oftheinterferencerangeofthetransmitter. ■ 5.1 Introduction Many of the challenges encountered in the design of wireless networks with multi- ple transmission and reception points stem from the quirks of wireless signal prop- agation. Using currently prevailing transmission techniques, wireless signals cannot befocusedexclusivelytowardstheirintendedrecipient,makingwirelessaninherently shared medium. Wireless transmissions are local in their coverage, and, in general, no sender or receiver will have access to complete channel state information. Because of these characteristics, a wireless network is commonly modeled as a set of links among 68 CHAPTER5. TAGSPOTTINGATTHEINTERFERENCERANGE 69 which interference may occur depending on the particular choice of senders transmit- ting at the same time. The effects of wireless interference are far reaching, affecting all network layers, from physical layer and medium access to flow control and user satis- faction. Theyextendbeyondthespaceofasinglehostorasinglelink,asflowsthatdo not share any hosts or links in their paths might in fact find themselves competing for resources. Itsdirectconsequenceisunfairnessleadingtoflowstarvationandunderuti- lizationofavailableresources. Astudyoftheexactmechanismsthroughwhichinterfer- enceleadstounfairnessrevealsproblemsatmultiplenetworklayers. Themostgeneral statements of these problems frequently preclude finding a decentralized and optimal solution. However, interference is a local disruption, and therefore leaves hope that a local,ifimperfect,solutionmaybefound. Distributed algorithms often make use of local exchanges of information. This cre- atesaneedforacommunicationbackplanecapableofconnectingeachhosttothesetof hostsaffectedbyitstransmissions. Thisrequirementismorecumbersomethanitmight seematfirstsight,forsuccessfuldatatransmissionatcommondataratesrequiresrather large signal to noise ratios. The capacity of links is however affected even by interfer- ers reaching them at far lower signal levels. Connecting the recipients of interference with transmitters requires thus a communication backplane capable of operating over channelsofferinglowsignal-to-noiseratios. This,inturn,impliesthatconstructingsuch a communication backplane will require designing a physical layer different from the standardphysicallayersusedforhighratedatatransmissions. Furtherdifferencesarise fromthefactthat,inawirelessenvironmentdesignedtosupportprimarilydatatrans- missions over short links operating at strong signal levels, long range communication is at best opportunistic. Backplane communication receivers are therefore required to beabletodiscriminateactualbackplanetransmissionsfromhighlevelsofbackground chatter. Moreover,inordertoofferasignificantimprovementwithoutfurtheraggravat- ing the interference problem, communications along the backplane should not create newinterferenceconstraints. In this paper we propose a signaling scheme enabling the creation of a communi- cation backplane which meets all the above requirements. Our scheme induces a low 70 5.1. INTRODUCTION per-packetoverhead,isresilienttohighlevelsofnoiseandinterference,andminimizes thedisruptionofdatatransmissionsduetotheinterferencethatitinduces. Our first contribution is the design of tags, members of a set of signals designed to be easily detectable and recognizable in the presence of high levels of noise and inter- ference, in the absence of time and phase synchronization and with only approximate frequency synchronization. Their increase in range over regular data transmissions is obtained in part through added redundancy. Tag signals are modulated using multi- tonemodulationoveratimedurationthatislargerthanthedurationofaregulardata- transmitting tone. A tag is a distinct superposition of several tones whose frequencies arechosenaccordingtothecodewordsofabinaryalgebraiccode. Onthereceiverside, tagsarerecognizedusingareceiverbasedonspectralanalysis. Whataboutinterferencecausedbytagsondatapayload? OFDM,theprevalentmod- ulation for data transmission in today’s wireless networks, used in this study as well, exhibits flat time and frequency power densities. We will prove that interference dis- ruptionscausedbytagsarecomparabletotheonescausedbydatatransmissions. Oursecondcontributionisananalysisoftheperformanceoftagsatdifferentnoise andinterferencelevelsandwhenmakingdifferentdesignchoices. Startingfromdetec- tion theory principles, we derive, under a sufficiently general propagation model, the detection likelihood/false alarm likelihood curves at different SNR levels. We are par- ticularly interested in evaluating the trade-off between transmitting more information (i.e. more bits per tag) and the corresponding increase in the likelihood of false alarm ormisclassification. Ourfindingsarelateroncomparedtoexperimentalresults. Our third contribution is the implementation and testing of Tag Spotting through experimentsperformedusingasoftwareradioplatforminatestbedcomprisingsenders, receivers and interferers. This series of experiments makes use of a tag family capable of conveying about one byte of information. The results of our evaluation support the conclusionthatcommunicationthroughtagsiseffectiveatSNR 1 valuesaslowas0dB 1 ThroughoutthispresentationweunderstandthenoisepartoftheSNRfiguretoalsoincludeinterfer- encepower,unlessspecificallynotedotherwise. CHAPTER5. TAGSPOTTINGATTHEINTERFERENCERANGE 71 andisrobusttotheeffectsofinterference. Inaddition,throughaseriesofchannelsim- ulations,weestablishthepossibilityofconstructingtagscapableofconveyingmorebits ofinformationandwesurveytheeffectsofdesigndecisionsonthesystemperformance. Our fourth contribution is the use of Tag Spotting in two applications, showcasing theperformanceimprovementsbroughtbytheexistenceofacontrolplaneabletoreach all nodes within the interference range. Specifically, we use tags to efficiently imple- mentastateoftheartcongestioncontrolschemeformulti-hopnetworkswhichrequires neighboring nodes, i.e, nodes that interfere with each other, to exchange control infor- mationinanefforttofairlysharetheavailablebandwidth. Wealsousetagsinorderto designandtestasimpleMAC-layersignalingmechanismmeanttopreventthestarva- tionofTCPflowsinmulti-hopwirelessnetworks. This chapter is organized as follows: In Section 5.2 we give an overview of related workandindicatesomecongestioncontrolandschedulingmechanismsthatwouldben- efitfromtheuseoftags. Section5.3introducesmultitonemodulationalongwithasim- plemodelforestimatingthespectralfootprintofmultitonesignalsanddiscussestech- niques for limiting inter-carrier interference. Armed with the conclusions of Section 5.3, weproceedinSection5.4todescribeindetailthestructureoftagsandconstructa tag detector capable of distinguishing tags from interference. Section 5.5 discusses in detailtherationalebehindeachdesigndecisionpresentintagconstruction. Section5.6 experimentally evaluates, using a software radio platform, the communication range of tags as well as the rate of false detections. It is shown experimentally that tags can be reliably identified at SNR values as low as 0 dB while the likelihood of false detec- tions can be sufficiently limited. The same section evaluates the impact of noise, tag transmissions, and data transmissions, on each other. Section 5.7 presents an analysis grounded on detection theory principles of the effects of different choices available in theprocessofdesigningthemodulationoftagsand,moreimportantly,ofthetrade-off betweenthedatarateoftags(i.e. thenumberofbitstransmitted)andthelikelihoodof falsealarms. Twoexamplesofusingtagstofacilitatetheimplementationandimprove theperformanceofcongestioncontrolandschedulingarepresentedinSections5.8and 5.8. Finally,Section5.9concludesthepaper. 72 5.2. RELATEDWORK ■ 5.2 RelatedWork 1. CommunicationandDetectionTheory. TagSpottingiscloselyrelatedtoaclassic researchtopicincommunicationtheory,namelyinformationtransmissionatlow signal-to-noiseratios. Themotivationofthisresearchhasvariedfromsecuringthe transmitteddatasuchasinthecaseofspread-spectrumcommunication[SOSL94] toprotectionagainst interferencein the case of the widelyused CDMA standard [Vit95]andtoachievinglong-rangetransmission[RBMR63]. Tagsemployamulticarrierspread-spectrummodulation. Theyareclearlyrelated toMC-CDMA[YLF93],howevertheyuseanon-coherentmodulationanddonot useorthogonalcodewords. LikemultitoneFSK[LM02],tagsuseacombinationof tonesinordertotransmitinformation. ThedesignofthetagdetectorpresentedinSection5.4isbasedonthedetectionthe- ory of multipulse signals with constant amplitudes and unknown phases. While theclassicaldetectorforsuchasituationiswell-studiedandunderstood(see,for example [MW95,Tre92]), it requires a precise estimate of the background noise level in order to set appropriate detection thresholds. Interference from compet- ing packet transmissions will confront tags with different levels of background noise,makingapreciseandtimelyestimateimpossible. Ourdetectorisindepen- dentofthelevelofbackgroundnoise,requiringonlyabaseSINRasprerequisite fortheaccuracyofthedetection. Intheappendixweapplyatheoreticalanalysis similartotheoneoftheclassicaldetectorinorderderivethedetection/falsealarm trade-offcurvesofourowndetector. 2. PhysicalLayerExtensions. Inthewirelessnetworkingworld,carriersense[BM09] can be seen as an example of a message passing mechanism operating beyond thedatatransmissionrange. Closelyrelatedistheuseofdualbusytones[HD02] in order to signal channel occupancy. A recently proposed physical layer exten- sion,CSMAwithcollisionnotificationCSMA/CN[SRCN10],aimsatreducingthe impactofcollisionsthroughanearlyterminationsignalsentbythereceiverofthe CHAPTER5. TAGSPOTTINGATTHEINTERFERENCERANGE 73 collidingpacket. Thetransmitter-baseddetectorusesself-interferencecancellation techniquesinordertoimprovetheSNRofthereciprocalchannelanddetectsthe termination signal using correlation, in a manner similar to [TEF99b]. However, as the authors of both these papers find out, a correlation based receiver cannot function without prior channel and frequency offset estimation, which prevents theiruseforbroadcastsoverarbitrarychannels,asinthecaseoftags. Carrier sense, dual busy tones and collision notifications are binary signaling mechanisms,notsuitedfortransmittingnumericinformation,asrequiredbymes- sagepassingprotocols. Anotherrecentphysicallayerextension[WTL + 10]aimsat realizingaside-channeloverspread-spectrumbasedprotocolsthroughperturba- tions of certain chips comprising a transmitted symbol. These perturbations are in turn compensated for by the normal error correcting codes employed in data transmission,thusallowinginmostcasesforthepayloadtobedecodedcorrectly, and they are also detected by a special pattern analyzer, allowing for the trans- mission of side information. While the motivation and design constraints of this worksaresimilartoours,thedesignchoicesmadeinthecreationoftagsarevery different. Most importantly, tags do not require the data transmission scheme to bespread-spectrumbased. Thetechnologyofsoftwaredefinedradios[Ett,GHMS09]hasactedasanenabler forsomeoftherecentadvancesinmultiuserwirelessnetworkresearch. Itallowed, for example, the experimentation of techniques such as zigzag decoding [GK08], interferencecancellation[HAW08]ordynamicbandwidthadaptation[CMM + 08]. Perhaps the most similar technique to the one presented in this paper is the one of smart broadcast acknowledgments, introduced in [DSGS09b], in which mul- titone modulation is used for the purpose of simultaneously conveying positive acknowledgmentsfrommultiplereceivers. Otherrecentadvancesthatalsomake use of software radios for evaluation purposes include multi-user beamforming [AASK10], fine grained channel access in which bandwidth allocation based on an increased number of carriers is coupled with frame synchronization used in 74 5.2. RELATEDWORK creatinganeffectiveuplinkOFDMimplementation[TFZ + 10]andframesynchro- nizationusedinobtainingdiversitygains[RHK10]. 3. Congestion Control and Scheduling. Prior works on congestion control for multi-hop wireless networks differ in the way in which congestion is reported to the source. One class of schemes sends implicit or imprecise feedback by dropping or marking packets [XGQS03,RJJ + 08] in the tradition of TCP conges- tion control [Jac88], or by regulating transmissions based on queue differen- tials [WJHR09] along the lines of back-pressure ideas [TE92]. Another class of schemes[RJJ + 08,TJZS07]explicitlycomputesavailablechannelcapacityandthen sends precise rate feedback, in the spirit of wired network congestion control mechanismssuchasXCP[KHR02]andRCP[DKZSM05]. In an effort to tackle the complexity of creating optimal schedulers, recent work on medium access for multihop networks has proposed distributed algorithms capableofapproximatingtheoptimalsolution[Sto05][LS04][JPPQ03][KMPS05] [JLS09]. A common theme here is the use of local, neighborhood-centered infor- mationinachievingaglobalsolution. Ourworkispartlymotivatedbytherecent developmentofanumberofcongestioncontrolandschedulingschemesformulti- hopwirelessnetworksthatarebasedonthelocalsharingofinformation,suchas, for example, [RJJ + 08] and [Chi05].. Local information is at the heart of several other wireless multi-hop problems: neighbor discovery [VTGK09], reliable rout- ing [YKT03], capacity estimation [XGQS03] and signaling congestion and starva- tion. Themechanismproposedinthispaperoffersanefficientwaytoimplement theneighborhood-widesharingofcontrolinformationintheschemesmentioned. Whiletheseschemesappendcontrolplaneinformationtodatapacketsandrelyon packetoverhearing,ithasbeenrecognizedthatthisinformationneedstoreachall nodeswithinthecarriersenserangeofanodeofinterest. Theinformationsharing mechanism proposed in this paper eases the implementation of many of these ideasandimprovestheirperformance(seeSection5.8),ascontrolinformationwill reachnodesoutsidethedatatransmissionbutwithinthecarriersenserange. CHAPTER5. TAGSPOTTINGATTHEINTERFERENCERANGE 75 ■ 5.3 IntercarrierInterference An OFDM encoder uses an inverse discrete Fourier transform in order to encode a sequenceofsymbolsintoasetoftonesoverafinitetimeinterval, fromhereonnamed either a frame or an OFDM symbol. Consider the sequencex of lengthN = 2 k whose elementsarechosenfromasignalconstellation,arrivingforencodingatanIFFT(inverse fastFouriertransform)framegenerator. Theresultingsignalwillbegeneratedaccording totheformula: X(t) = ∑ 8k2f0;N1g x k e ik2t : Passing to the continuous Fourier transform exposes a windowing effect and pro- videsuswithaninsightintothespectralfootprintofthegeneratedsignal. Thediscrete spectrum of an OFDM frame is illustrated in the upper half of Figure 5.1 and corre- spondstotheoriginalencodedsymbolsequencex. Sincethesummedexponentialsare boundedintime,theircontinuoustransformsaresincfunctionsandthespectrumofthe encodedsignalisthesumofthesesincfunctions,asdepictedinthelowerhalfofFigure 5.1. Theorthogonalityofdifferentsignalsispreserved: thepeakofeachsincfunctionis alignedwiththezerosofallothersincfunctions. 1 2 3 4 5 6 7 8 Amplitude 1 2 3 4 5 6 7 8 Amplitude Frequency Figure5.1: Frequencydomainview. ThediscreteandcontinuousFouriertransformsof anOFDMframe. Let’s focus on non-coherent communication, i.e. we assume that the phase of each receivedsignalisindependentlyrandom,andtrytoderiveaconcentrationresultforthe powerleakedoutsidetheintendedtransmissionbandwidth. InSection5.4wewilluse this result in order to motivate that the modulation of tag signals exhibits a fast spec- tral decay and limited inter-carrier interference. The reasoning behind our approach 76 5.3. INTERCARRIERINTERFERENCE Amplitude 2449.5 2450 2450.5 Frequency (MHz) Time 2449.5 2450 2450.5 Frequency (MHz) Figure5.2: Packettransmission. Thesignals(t) (upperpane), a timefrequencyrepre- sentationusing512frequencybins(middlepane)andatimefrequencyrepresentation using64frequencybins(lowerpane). is encompassed in Equations (5.1) and (5.2) below, which describe the effects of self- interference on OFDM signals and give the speed of their spectral decay. In the pres- enceofasmallfrequencyoffset,theinterferencesignaladdedbyacarrierwithunitary amplitudetoacarrierplacedk positionsawayis l(k;) = ∫ [0;1] e 2i(k+)t dt = sin() (k+) e i ; andinpowerterms, p(k;) = sinc 2 ((k+)) 1 (k+) 2 : (5.1) It can be easily verified that the magnitude of the interference among two carriers doesnotdependontheabsolutedifferenceofcarrierfrequenciesbutonlyonthenumber ofcarrierpositionsseparatingthem. CHAPTER5. TAGSPOTTINGATTHEINTERFERENCERANGE 77 Considernowacarrieratcarrierpositionzeroandaninfiniteblockofcarriersstart- ing at carrier position k. The average power leaked by this block of carriers into the zero-positionedcarriercanbeboundedaccordingtoEquation(5.1)tobe: p b (k) = 1 ∑ c=k 1 c 2 = 2 6 k1 ∑ c=1 1 c 2 ; (5.2) whereweassumethatsymbolsondifferentcarriersareindependent. TheseriesinEqua- tion(5.2)israpidlyconverging. Basedontheobservationsaboveweconcludethatreplacingasinglecarrierthrough a block of random-phase, lower-bandwidth carriers that occupies the same part of the frequencybandwillsharpenthespectrumofamultitonesignalandaccelerateitsspec- traldecay. Moreover,theinsertionofarelativelysmallnumberofnull-carrierswillsig- nificantlyreduceinterferencebetweentwoneighboringactiveregionsofthespectrum. Creating the replacement carrier block calls for an increase in the number of carriers, andacorrespondingincreaseinthetimelengthoftheOFDMframe,asdescribedfully inSection5.4. ■ 5.4 TagSpotting 1. High Level Design Overview. Tag Spotting uses a set of signals (tags) that are easily detectable in low SNR conditions. The design of tags is determined by a numberofconstraints. Firstly,duetotheirshorttimespan,thepresenceofmulti- pleindistinguishablesourcesandthepresenceofvaryinglevelsofinterference,the tag detector cannot perform accurate channel estimation, or achieve time, phase andfinefrequencysynchronization. Secondly,inordertoprotectcompetingdata transmissions from further levels of interference, tags must abide by a maximal spectralpowerconstraint,whichpreventstheuseofapeakytransmissionscheme such as multiple frequency shift keying (MFSK). Finally, a tag detector must per- formidenticallyinthepresenceofaddedinterference,aslongastheSINRremains unchanged. 78 5.4. TAGSPOTTING Toaddresstheseconstraints,weemployedanoncoherentcommunicationscheme thatspreadsatag’senergyoverthefrequencydomain. Thenumberofcarrierswas increasedinordertosharpenthesignal’sspectralfootprintandeasespectralanal- ysisthroughdiscreteFouriertransformevenintheabsenceofcompletefrequency synchronization. The symbol sequences encoded over the different carriers were chosenaccordingtoanalgebraiccode,thusaddingextraredundancy. The current section presents the details of tag construction. The following sec- tionwillpresentthereasoningbehindthedesigndecisionsmadethroughoutthe construction. 2. MultitoneStructure. Figure 5.2 presents a packet transmission in time domain representationaswellasintwodifferenttime-frequencyrepresentations. Thetwo time-frequency representations, pictured in the lower two panes, are realized by performingthespectralanalysisofsuccessiveblocksof512samples(middlepane) or 64 samples (lower pane). As we will see, these lengths are natural choices for describing the structures of tags and packet payloads respectively. In the same representations,eachverticalcolumncorrespondstoananalyzedblock,whilethe horizontal line pattern present in each such column illustrates the block’s power spectral decomposition. In order to make the representation more meaningful, wehavestrippedtagsanddataframesoftheircyclicprefixesandwealignedthe boundariesoftheanalysisperiodswiththeboundariesoftagsanddataframes. Tagsareencodedusing512OFDMcarrierswhilepacketinformationmakesuseof 64widerdatacarriers. Therefore,intimedomain,atagspansaperiodequivalent toeightregulardataframes,whileinfrequencydomaineach“wide”datacarrier correspondstoeight“thin”tagcarriers. Thetransmissionbeginswithatag,whose spectrumcanbeobservedinthethirdcolumnofthemiddlepane,andcontinues with data frames containing synchronization data followed by the packet’s pay- load. Tobothtagsanddataframesweappendacyclicprefixwhichincreasestheir respectivelengthsby 1 4 -th. CHAPTER5. TAGSPOTTINGATTHEINTERFERENCERANGE 79 Thespectrumofatagisconstructed,atabasiclevel,bytransmittingasymbolfrom a 0-1 (on/off) constellation in the frequency space corresponding to each of the wide carriers. Wide carriers are in turn grouped into groups of two neighboring carriers, and in each group only one of the two carriers will be active. This last constraintrendersthemodulationinsideeachcarriergrouptobeaformofbinary frequency shift keying. For tag construction purposes, eight of the wide carriers havebeendesignatednullcarriers,whiletheremaining56carriersgiveriseto28 two-carrier groups. Every tag can thus be naturally mapped to a 28-bit string in whicheachbitmarksthechoiceofstateinoneofthegroups. ThestructureofataginfrequencydomainisdepictedinthelowerpaneofFigure 5.4,whileatwo-carriergroupisdepictedinFigure5.3. On the receiver side, the tag detector operates in the presence of small, tolerable but unknown frequency offsets, which may cause power spillage from the active widecarrierstotheinactivecarriers. AsillustratedinFigure5.3,wechosetosend the entire signal power allotted to an active wide carrier using the central four of the eight thin carriers corresponding to this particular wide carrier. We also chosetoencodethetonessentonthesethincarriersusingdifferentrandomphases. LookingatEquation (5.2)itcanbereadilyseenthattheabovechoicesreducethe amount of power leaked onto inactive wide carriers. A straightforward compu- tation assuming a frequency offset distributed uniformly between zero and two thincarrierwidthsrevealsthattheexpectedpowerleakedis,inexpectation,about 2.3%ofthetotalpower. Figure5.4furtherillustratesthisaspectbypresentingthe spectrumofareceivedtaginthepresenceofafrequencyoffsetequalto10%ofa regularcarrierwidth. Bycomparingthedistributionofthereceivedsignalpower inthefrequencybinscorrespondingtowidecarriers(middlepane)withthestruc- ture of thetransmittedtag(lowerpane), itcanbeseenthatthereceivedpoweris concentratedinthosebinswhichcorrespondtoactivewidecarriers. Asanote,the useofrandomphasesinsignalconstructionhasonefurtheradvantage: itallows samplingtagsfromalargersignalsetinordertolimittheirpeaktoaveragepower ratio. 80 5.4. TAGSPOTTING 3. Encoding. As it is common in communication system design, modulation is supplementedbyacodinglayer. Thepurposeofthislayeristocreateasubsetof maximallydifferentiablesignals,andtoreducethenumberofhypothesestested. The tag signal construction detailed above produces 2 28 different basic tags, too manyforefficientdetectionandinsufficientlydistinguishablefromeachother. A furtherrestrictionmakesuseofa(28;60;13) 2 nonlinearcodeproposedbySloane andSeidel[SS70]. Outofthebasictagsonlythosehavingbinaryrepresentations correspondingtothe60codewordsofthiscodearepreserved. Wediscusstheuse ofothercodesinSection5.6. 0 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Amplitude -π π 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Phase 0 1 2 Power (mW) Frequency Figure5.3: SpectralPlot. Thediscretespectrumofatwo-carriergroup(amplitudeand phaserepresentation)anditscontinuouspowerspectrum. Regular data frames dissipate the transmitted power over 48 carriers while tags make use of only 28 carriers. Since the average power spectral densities of used carriers in tags and data transmissions are equal, it results that the transmitted power in the case of tags is lower than the transmitted power in the case of data, asitcanbeobservedinFigure5.2. 4. Constructing a Tag Detector. LetT = ft 1 ;t 2 ;:::;t 60 g denote the set of all tags and C i be the set of all data carriers activated when transmitting tag t i . Let r f denotethepowerofthereceivedsignalinthefrequencybincorrespondingtothe 2 Thenotationforcodesusedhereisintheform (N;M;D)whereN isthebinarycodewordlength,M denotesthenumberofdistinctcodewordsandDdenotestheminimalHammingdistancebetweenanytwo codewords. CHAPTER5. TAGSPOTTINGATTHEINTERFERENCERANGE 81 f-thcarrier. Ourdetectordoesnotassumethechannelphaseresponsetobeuni- formandcanthereforebeusedinawidebandscenario. Wecomputethefollowing quantitywhichwewillnamefromnowontagstrength: ∑ f2C i r 2 f ∑ 8f r 2 f : (5.3) Tag strength is compared against a fixed threshold and in case the threshold is exceededapossibletagobservationisrecorded. 3 Detection intervals have the same length as a tag from which the cyclic prefix has been removed and are spaced one tag cyclic prefix length apart. It results thatsuccessiveanalyzedintervalshavesignificantoverlap. Everytransmittedtag willcompletelycoveratleastonedetectioninterval. Thedetectorprocessesevery intervalbyfirstcomputingtheFouriertransformofthecontainedsignalandthen computing,basedontheresultingspectrum,thestrengthofeachtagaccordingto Equation(5.3). Inorderforatagrecognitioneventtoberecorded,thecorrespond- ingtagstrengthmust,firstly,exceedthethresholdvalueand,secondly,bemaximal amongalltagstrengths(foralltags)derivedfromdetectionintervalsthatoverlap thecurrentinterval. Afurtherdetectionmetriceffectiveinfilteringoff-bandinter- ference is computed for each detection interval by weighting the power levels in different carriers through the carrier’s position in the frequency band, summing the resulting values and afterward dividing the result through the total interval power. As long as the resulting “center of mass” is placed in the central quarter of the frequency band, the tag observations are considered valid, otherwise they willbeattributedtooff-bandinterference. 3 Thisequationissimilartotheoneofthelow-SNRmultipulsedetectorwithnsamplesforasignalwith unknownphase(t)varyingateachpulse:s(t) =Acos(2ft+(t)),atagivenSNRvalue = A 2N . Denote byHS thehypothesisthatsignalshasbeensentandbyHnthehypothesisthatnosignalhasbeensent. That detector is based on the equation log p(rjH S ) p(rjHn) ∑ N i=1 r(ti) 2 > ′N where ′ is a constant (see [MW95, p. 293]); in our case, the correction factor ∑ 8f r 2 f can be seen as an approximation of A 2 4 +N = ( + 1)N, meant to remove the linear dependence of the threshold on the noise powerN, allowing thus for added noise-likeinterference. 82 5.5. MOTIVATINGTHEDESIGNCHOICES -40 -30 -20 -10 0 2449.5 2450 2450.5 Power (dB) Frequency (MHz) -30 -20 -10 0 10 2449.5 2450 2450.5 Power (dB) Frequency (MHz) Figure5.4: CFOEffects. Thespectrumofareceivedtaginthepresenceofafrequency offset. Upper pane: the 512 frequency bins Fourier transform of the corresponding detectorinterval. Middlepane: the64frequencybinsrepresentationusedinthedetec- tiondecision. Lowerpane: thestructureofthetransmittedtag. In order to reduce the number of intervals analyzed and the likelihood of false alarms,asimplecarriersenseschemeisemployed. Thereceivermaintainsarun- ning estimate of channel noise and processes only those intervals for which the SNRexceeds1dB. 5. Overhead. Addingatagtoapacketincursatransmissiontimeoverhead. Assume for now that only data packets are tagged and that a typical data packet has a payloadofabout1500bytes. EncodedusingtheparameterspresentedinSection 5.6, the payload will span 125 data frames, to which six synchronization frames are appended. A tag spans the equivalent of eight data frames and therefore its overhead is about 6.1% in terms of the normal packet duration. In some control schemessomeofthedatamessageswillnotrequiretagstobepiggybacked,allow- ingforalesseroverhead. ■ 5.5 MotivatingtheDesignChoices Theprevioussectionhaspresentedinconsiderabledetailthestructureoftags. Whilethe abovedescriptionis complete, thedecisions takenin the construction of tags maywell seemarbitrary. Thepurposeofthecurrentsectionistomotivateeverydesigndecision takenintagconstruction. CHAPTER5. TAGSPOTTINGATTHEINTERFERENCERANGE 83 MultitoneStructure The design space of tag signals is frequency space. At the lowest level, tags use the sameformofmodulationinfrequencyspace,usingorthogonalsignalsoverafinitetime interval,thatisusedinregulardatatransmission. 1. OFDM. In an opportunistic reception system that searches for the short occur- rences of tags, the price of exact frequency synchronization and of exact channel estimation should be avoided. Tags are therefore transmitted and received with- out performing channel estimation or frequency synchronization. This raises a challengeinsolvinginter-carrierinterference. Remember that the choice of OFDM for data transmission is linked to the prop- agation behavior of wireless signals. Since sine signals are the eigenfunctions of thewirelesschannel,theuseoforthogonalsinesalongwithanappropriatecyclic prefix is meant to prevent any channel-caused interference among the different transmittedsymbols. Thelimitedtimespanofthetransmissionintervalprecludes theuseofactualsinesoranyothersignalswithnarrowsupportinthefrequency space. Asit wasdiscussedinSection 5.3, theactualsignalsusedinthetransmis- sions have a slowly-decaying spectral footprint. In OFDM data transmission, the inter-carrierinterferencewhichtheslowspectraldecayentailsisavoidedthrough exactfrequencysynchronization, usingthefactthatinfrequencyspacethezeros of the base sine-like signals align with the peaks of all other signals in the base set. In contrast, for tags, the packing of noncoherent carriers into larger building blocksreducestheamountofpowerleakedamongthefrequencybinscorrespond- ingtothickcarriers. Thisreductioninleakedpowerallowsthesystemtofunction as intended even when the receiver is not frequency-locked onto the transmitter. Thelackoffrequencysynchronizationtogetherwiththelackofanestimateofthe channel phase response at different frequencies also leads to uncertainty regard- ingthephaseofthetransmittedsignal. Theuseofanoncoherentencodingallows ustoovercomethelackofknowledgeofthechannelphaseresponsewithoutfur- thercomplications. Itcouldbearguedthatthesechannelcharacteristicsshouldbe 84 5.5. MOTIVATINGTHEDESIGNCHOICES measuredinadvance. However,ourreceptionsareatbestopportunistic,andthe channel could be any one of a multitude of fast changing channels between any pair of hosts. Certainly, obtaining an exact estimate of the channel response and of the frequency offset, at the low SNR levels for which our system is designed, wouldgreatlycomplicatethetagtransmissionproblem. 2. Fading. Another characteristic of wireless channel transmission, frequency- selective fading, provides the rationale for the use of groups of two carriers as a encoding unit: since neighboring data carriers are likely to experience similar fadingandsinceanyofthecodewordsmakesuseofeitheroneortheotherofthe twocarriersinatwo-carriergroupinordertoencodeabitvalue,fadingoveratwo- carriergroupwillnotinduceabiastowardsanyofthehypothesesthataparticular codewordhasbeentransmitted. Thereceivedpowerandthelikelihoodofdetec- tionmaywelldecreaseduetofading. However,whenconsideringagivenoverall signaltonoiseratio,i.e. computedoverallthecarriers,thedetectionprobabilities over fading and non-fading channels are quite similar, as shown in Section 5.7, while the false alarm probabilities are the same. We can conclude that this par- ticular design decision manages to overcome most of the difficulties that fading introducesintagdetection. ConstructingaTagDetector 1. It is worth mentioning here a significant difference betweenthe main purpose of atagreceiverandthepurposeofacommunicationsystemreceiver. Whileacom- municationsystemreceiverismeanttoaccuratelydistinguishbetweenanumber ofhypothesescorrespondingtosignaltransmissionsundertheassumptionthatan actualtransmissionhasoccurred,thetagreceiverlistensforthemostparttonoise andbackgroundchatter. Themaintaskofatagreceiveristhereforetodetect,with sufficientconfidence, atagtransmissionwhenoneoccursand,ifpossible,tocor- rectlyidentifythetransmittedtag. Tagdetectionisthereforeadetectionproblem more than a communication problem and the design of the detector reflects this fact. Theprobabilitiesoffalsealarmallowedinthecaseoftagsarewellunderthe CHAPTER5. TAGSPOTTINGATTHEINTERFERENCERANGE 85 typicalprobabilitiesofmisclassificationallowedinacommunicationsystem,since theoccurrenceoftagtransmissionsareassumedaprioritoberatherrareevents. Falsealarmsweighinmoreheavilywhencomparedtothetotalnumberofdetected tags. Due to the fact that tag detection is essentially a detection theory problem, we choose the detection metric (probability of false alarm versus the probability of detection) to be the main measure of tags performance. The secondary metric considered will be the probability of misclassification of a transmitted tag. The experimentalsectionwillrevealthatthisprobabilityisnegligibleduetothehigh threshold required for a positive tag detection, even when using a rather large numberofcodewords. 2. DetectingPatterns. Ingeneral,tagobservationsoccurovershortintervalsoftime andchannelconditionschangetoofrequentlyforthereceivertoobtainandupdate anaccuratenoiseandinterferencepowerestimate. Theonlyassumptionmadein thefollowingisthatthespectralenvelopeofthenoiseandinterferencesignalsis flat,anassumptionthatcanbejustifiedinthecaseofdatanetworksusingOFDM- basedencoding. Wedesignthereforeourmodulationschemeandourreceiverto use as a detection indication not the sheer amount of power received but rather theconcentrationofthereceivedpowerintopre-determinedfrequencybins. The receiver detects a transmission event whenever the concentration of the received power(theratioofthepowerreceivedinthedesignedfrequencybinstotheover- all received power) exceeds a certain threshold. Therefore, the receiver searches not just for the presence of a signal but for a certain spectral shape. The fact that apowerratiomeasurementisusedasadetectionmetricguaranteesanuniversal receiver in a wider sense: the probability of detection for a threshold value cho- senasthereceiverparameterwillonlyincreasewithincreasingSINR.Astandard detector is denoted as universal when a similar guarantee exists in terms of the SNR. 86 5.5. MOTIVATINGTHEDESIGNCHOICES 3. Tags and FSK. The attentive reader might have noticed that a simpler encoding scheme might have provided a similar detection/false alarm performance trade- off without the use of an algebraic code. Frequency shift keying simply concen- trates the available power into the frequency space corresponding to one of the available carriers, thus offering similar received power characteristics. However, FSK has a large power spectral density, due to the fact that all the transmitted power is effectively concentrated in one point of the frequency spectrum, which makes it undesirable in a network environment, where we would like to guaran- teeacertainflatenvelopeforthefrequencyspectrumofourtransmission,witha fast decay outside the data band. Our choice of modulation limits the transmit- tedpoweratanygivenfrequency,resultingthusinaflatspectrum,similartothe one corresponding to OFDM data transmissions. The experiments in Section 5.6 verifythatthetypicalinterferenceeffectsoftagsoncompetingdatatransmissions arenotworsethantheinterferenceeffectscausedbynormalpacketdatatransmis- sionssentatasimilaroverallpowerlevel,whichwouldnotbethecaseiftagswere modulatedusingFSK. 4. Choosing the number of active carriers. In Section 5.4 it was mentioned that tagsareaspecificformofmultiplefrequencyshiftkeying(MFSK),amodulation whichmakesuseofmultiplenoncoherentcarrierstransmittedsimultaneouslyas asinglesymbol. AkeyparameterofMFSKisthenumberoftransmittedcarriers. Having chosen the MFSK modulation and the power ratio detector as the basic building blocks of our system, we must find next a value of this parameter that offers reasonable detection performance while also allowing for the construction of a large set of tags. As a definition of performance, we seek to minimize the probability offalsealarmswhilepreserving acertainprobability ofdetection. In Section 5.7 this measure of detection performance is evaluated, as a function of the number of carriers transmitted, in the case of a detector that is searching for a single tag. It is revealed that, for a detector operating at a target SNR of 0 dB, the optimal allocation of power uses a bit less than half of the available carriers. Therefore, the decision to use exactly half of the carriers in the modulation does CHAPTER5. TAGSPOTTINGATTHEINTERFERENCERANGE 87 notimpactthedetector’sperformance,whilethesamedecisioneasestheuseofan algebraiccode. Encoding 1. Families of Codewords. The decision to use exactly half of the carriers in the construction of tags is motivated by the details of constructing a tag family. In particular,welookattherelationshipbetweentagsandthebinarycodesusedin their construction, namely codes over the same number of bits as the number of thick carriers. The simple binomial expansion indicates that the binary strings whose weight is half this number of bits are most numerous. We expect that for small Hamming distances the codes of this particular fixed weight would have more membersthancodesconstructedusinganysetofbinarystringsofadiffer- entfixedweight. Ourconstruction,whichconvertscodewordfamiliesconstructed over a number of bits equaling half the number of thick carriers into families of codewords of fixed weight over twice that length, is almost optimal, as it can be checkedusingtablesofoptimalknowncodesoffixedweight. Moreover,thiscon- structionallowsfortheuseofwell-knownalgebraiccodesintagconstructionand thereforeleavesopenthepossibilityofdevelopingfastalgorithmsforidentifying themostlikelycodewordinthecaseoflargecodewordfamilies,inamannersimi- lartotheidentification,incommunicationsystems,ofthemostlikelytransmitted codewordbasedonreceiversoftsymbolvalues. 2. Construction Procedure. Based on this description of the intricacies of tag con- structionwearenowabletogiveageneralprocedureforconstructingasetoftags that meet a desired set of performance criteria. Firstly, a codeword family that guarantees a low enough probability of misclassification at the target SNR while offeringasufficientnumberofdifferentcodewordsmustbeselected. Theproba- bility of misclassification is computed in this step using Monte Carlo simulation, aspresentedinSection5.7. Secondly,againusingMonteCarlosimulation,aspre- sented in Section 5.6, the tag designer must determine the probabilities of false alarmforthechosentagfamily. Theprobabilityofdetectioncanbemorereadily 88 5.6. EVALUATION computedsinceitdoesnotdependonthechoiceofcodewordfamilybutonlyon thenumberofcarriersthatacodeworduses. Thisprocessmustbeiterateduntila suitable trade-off between the number of codewords available, the probability of detectionandtheprobabilityoffalsealarmisachieved. Whensatisfactoryresults cannotbeachieved,thetagdesignermayincreasethetimelengthoftagthrough the use of a larger FFT window and a correspondingly increased number of thin carriers,addingmoreredundancytothesignals. ■ 5.6 Evaluation ExperimentalSetup 1. (a)SystemParametersTheexperimentswereconductedusingtwoUSRPboards [Ett], one transmitter and one receiver, in an indoor environment without line of sight and with multiple concrete walls between the sender and the receiver. The GNU Radio software suite was used for signal transmission and recording. The carrierfrequencychosenwas2.45GHzandthebandwidthofthesystemwasset to 1 MHz. In order to obtain a linear channel suitable for OFDM transmission withoutdistortioneffectsintroducedbythetransmittermixerandthereceiver,the signal has been oversampled by a factor of four on both transmitter and receiver sides. The data transmission part of the system uses the Schmidl and Cox algorithm [SC97]forpacketdetectionandinitialCFOestimationandtheTufvesson[TEF99b] algorithm for block boundary detection. Channel gain is measured using the preamble, while phase response is tracked using four pilot carriers and a linear phaseinterpolator. Thesymbolconstellationusedwas16-QAM.Packetpayload was encoded using a rate 1=2 punctured Trellis code. The resulting link speed is 2.4Mbps. CHAPTER5. TAGSPOTTINGATTHEINTERFERENCERANGE 89 10 -5 10 -4 10 -3 10 -2 10 -1 10 0 0 5 10 15 20 25 SER 0.60 0.70 0.80 0.90 1.00 0 5 10 15 20 25 Tag Strength 0.00 0.25 0.50 0.75 1.00 0 5 10 15 20 25 P d SNR (dB) (a) Experimental results in the presence of channelnoise. 10 -4 10 -3 10 -2 10 -1 10 0 0 2 4 6 8 10 12 14 16 18 SER data interf. noise 0.60 0.70 0.80 0.90 1.00 0 2 4 6 8 10 12 14 16 18 Tag Strength 0.00 0.25 0.50 0.75 1.00 0 2 4 6 8 10 12 14 16 18 P d SINR (dB) (b) Experimental results in the presence of data-likeinterference. 10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 12 14 16 18 20 22 24 26 SER SINR (dB) tags interf. noise (c) Experimental results in the presence of tag-likeinterference. 10 -3 10 -2 10 -1 10 0 10 1 0.5 0.52 0.54 0.56 0.58 0.6 0.62 Time (s) Threshold (28,60,13) (28, 2 28 ,1) (d)Averagetimebetweenfalsealarmsatdif- ferentthresholds. Figure5.5: ExperimentalResults. Theprobabilitiesofdetectionandfalsealarmindif- ferentinterferencescenarios. While the design of an efficient OFDM transmission and reception system is not thefocusofthispresentation,havingaviablesystemwasapreconditionforshow- ingthatanyinterferenceeffectsproducedbyoursetofheadertagsarecomparable tointerferenceeffectscausedbydatatransmissionsandbyenvironmentalnoise. 2. (b)ExperimentDescription. Weperformedthreeseriesofexperimentsintended toevaluatetheimpactofdecreasingthesignaltonoiseratioontheeffectivenessof tag spotting, the impact of rising interference power on tag spotting and the dis- ruption caused to data transmission by interference in the form of tags. In order todeterminethelikelihoodoffalsealarms,wehaveconductedafurtherseriesof experiments using half minute-long recorded signal sequences containing ambi- entradionoisepertainingtostandard802.11b/gtransmissionsinanofficebuild- ing occupied by numerous wireless networks in order to measure the detector’s robustnesstodifferentkindsofradiointerference. Wehavealsoevaluatedthrough simulationsthelikelihoodofmisclassifications. 90 5.6. EVALUATION 3. (c)Metrics TagStrength is the quantity defined in Equation (5.3), the primary metric for deciding whether a tag observation will be recorded. It is a measure of the ratioofpowercontainedinthefrequencybinsallottedtoagiventagandthe totalreceivedpower. Inorderforatagobservationtoberecordedoneofthe necessary conditions is that the tag strength must exceed a threshold value . Inallexperimentspresented = 0:62wasused. Thischoiceofthreshold accomplishestwogoals: itishighenoughtocorrespondtoalowrateoffalse alarms,asverifiedthroughtheexperimentalresultspresentedinthecurrent section(seeFigure5.5d)anditislowenoughtoallowdetectionatthetarget SNRvalues. Usingthenaïveassumptionthatnoise(andinterference)power contributeequallytothepowerlevelsdetectedinthedifferentfrequencybins, theSNRvaluethatcorrespondstothisthresholdcanbederivedtobeabout 0.4dB. SymbolErrorRate(SER) is measured for the payload of all correctly identified packets,thatis,packetsforwhichthepacketdetection,blockboundarystart estimationandCFOestimationsucceed. Itistheprimarymetricforestimat- ing the effects of various noise and interference levels on data transmission. This metric was considered more fundamental than the bit error rate(BER), whichisheavilydependentonthetypeofcodingemployed,asystemdesign parameterthatvarieslargelyincurrentdesigns. ProbabilityofDetection(P d ) is defined as the probability that a header tag will becorrectlydetectedandidentifiedatdifferentSNRandSINRlevels. Itisthe primarymetricforthesuccessoftagspotting. ProbabilityofFalseAlarm(P f ) is defined as the likelihood that, in any given detectioninterval,noiseandinterferencewillcauseaspurioustagdetection andidentificationintheabsenceofatagtransmission. ProbabilityofMisclassification(P m ) isthelikelihoodofincorrecttagidentifica- tioninthepresenceofatagtransmission. CHAPTER5. TAGSPOTTINGATTHEINTERFERENCERANGE 91 4. (d)PracticalConsiderations. The tag detector presented in Section 5.4 is unable tocompensateforfrequencyvariationsbetweenthesenderandthereceiver. The structureoftagsandthedetectionmethoddescribedmakesitpossibletotolerate frequency offsets of up to two thin carriers, or about 4 kHz, without perceivable performanceimpacts. WehavefoundthattheclockjittersoftheUSRPradiosare wellwithinthislimit,howeverdifferentradioshaveinitialfrequencyoffsetsofup to200kHz,necessitatingasupplementarycalibrationstepbeforeeachexperiment. WeassumetheeffectsofDopplerspreadtobeminimal,i.e. anear-staticscenario. In a practical scenario the clock components could be replaced with more accu- rately designed/packed counterparts, and therefore we conclude that construct- ingself-sufficienttagdetectorsispossible. ExperimentalResults 1. (a) Impact of Noise. The first series of experiments tries to quantify the range effectiveness of tag spotting in the presence of different levels of noise, in an interference-freeenvironment. The transmitter was configured to send sequences of 100 packets with random headertags. Onthereceiversidethetransmittedsequencewasdecodedandthe sequence of detected tags was compared to the original transmitted sequence, in order to obtain an estimate of the detection probabilityP d . The decoded symbol payload of received packets was compared with the known symbol payload on the transmitter side in order to estimate the SER . The transmission’s SNR was estimated for each detected packet using a low-pass filter-based average power estimator. The power level of the transmitter was varied between levels spaced 3 dBapart,resultingindifferentchannelSNRvalues. Figure 5.5a illustrates the results obtained. The upper pane shows the Symbol Error Rate (SER) for the payload as a function of the Signal to Noise ratio (SNR). The curve is typical for a receiver employing 16-QAM modulation, however the receiver appears to exhibit an error floor at the higher SNR values measured. At 92 5.6. EVALUATION SNR values of 20-25 dB, the system can sustain data transmission, when using a typical error-correcting code. This curve serves as a reference for the next exper- iments,inwhichnoise-baseddisruptionswillbereplacedwithdata-likeinterfer- enceandtag-likeinterference. The middle pane shows the Tag Strength as a function of the SNR. The curve decreases steadily as the SNR decreases, reaching the threshold value around 0dB. Finally,thelowerpaneshowstheprobabilityofdetectionasafunctionoftheSNR. Itcanbeseenthattheprobabilityofdetectionisclosetooneovertheentirerange considered. 0 0.2 0.4 0.6 0.8 1 -15 -12 -9 -6 -3 0 3 P M SNR (dB) (28, 60, 13) (28, 2 8 , 7) (28, 2 18 , 5) (28, 2 23 , 3) (28, 2 28 , 1) Figure 5.6: Probabilityofmiscalssification. Probability of tag misclassification at dif- ferentSNRlevels. 2. (b) Impact of Interference. Figure 5.5b present the results of the same experi- ment in the presence of a second source transmittingan uninterruptedstream of payload-likedata. AsbeforetheupperpaneplotstheSymbolErrorRate,themid- dlepanetheTagStrength,andthelowerpanetheprobabilityofdetection,allasa functionoftheSNR.TheSERhasaslightlydifferentbehaviorinthiscase,dueto thepresenceofadifferenttypeofinterference,ascanbeseenwhencomparingthe SERcurveinthepresenceofdatainterferencewiththeSERcurveinthepresence of just noise. The other quantities of interest, tag strength and the probability of detectionP d remainessentiallyunchanged. Theprobabilityofdetectionclimbsa steepcurveandquicklysettlesclosetoone. Weconcludethatthetagdetectoracts almostidenticallyinthepresenceofpurenoiseornoisecombinedwithtemporary interference. CHAPTER5. TAGSPOTTINGATTHEINTERFERENCERANGE 93 3. (c)ImpactofTagInterferenceonData. Figure5.5cpresentstheeffectoftagson data transmissions. The SER curve is very close to the SER curve of Figure 5.5a, demonstrating that interference from tags does not increase the error likelihood beyondtheerrorlikelihoodinthepresenceofcomparablelevelsofnoise. 4. (d)LikelihoodofFalseAlarm. Figure5.5dpresentsthedependenceoftheaverage time in-between false alarms on the threshold , when analyzing recordings of ambientWiFitraffic. Carriersensehasbeendisabledinthisexperimentandevery inputdetectionintervalisanalyzed. Theseresultssupportourchoiceofdetection threshold,sincefalsealarmsoccuratarateoflessthanonceevery20seconds. 5. (e) Likelihood of Misclassification. Figure 5.6 presents the dependence of the probability of misclassification on the receive SNR when tags are constructed using either the code mentioned in Section 5.4, a few extended BCH codes with smaller minimal distance or an unencoded modulation. No lower tag strength thresholdwasemployed. Thisplotrevealsthat,foralltheseschemes,misclassifi- cationdoesnotoccuratthetargetedsignallevels. Moredetailsonthesignificance ofthisresultwillbegiveninthenextsection. 6. (f) Choice of algebraic code. The choice of algebraic code affects two quantities of interest, P m and P f . It has already been noted that, for a large class of codes, the probability of misclassification is negligible at the targeted signal levels. On theotherhand,theprobabilityoffalsealarmwillincreaseasthenumberofcode- wordsincreases,asillustratedinFigure5.5d,duetothepresenceofsupplemental hypotheses. Itresultsthatthereisatrade-offbetweenthenumberofbitsofinfor- mationavailablepertagandthedesiredrateoffalsealarms. TagRange The possible use of tags in wireless multi-hop networks prompts us to calculate the increase in range, expressed in distance terms, that transmission through tags brings overregulardatatransmission. Itiswell-knownthatpowerdecayexponentsarehighly dependent on the environment. Measurements of signal propagation in the 2.4 GHz 94 5.7. PERFORMANCEANALYSIS 10 -1 10 0 10 -8 10 -7 10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 10 0 P d P f -5 db -3.5 db -2 db -0.5 db (a)one-tag(widebandmodel) 10 -1 10 0 10 -8 10 -7 10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 10 0 P d P f -5 db -3.5 db -2 db -0.5 db (b) the (28;13;60) code (wide- bandmodel). 10 -1 10 0 10 -8 10 -7 10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 10 0 P d P f -5 db -3.5 db -2 db -0.5 db 1 db (c) the (28;1;2 28 ) code (wide- bandmodel). 10 -1 10 0 10 -8 10 -7 10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 10 0 P d P f -5 db -3.5 db -2 db -0.5 db (d)one-tag(narrowbandmodel) 10 -1 10 0 10 -8 10 -7 10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 10 0 P d P f -5 db -3.5 db -2 db -0.5 db (e) the (28;13;60) code (narrow- bandmodel). 10 -1 10 0 10 -8 10 -7 10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 10 0 P d P f -5 db -3.5 db -2 db -0.5 db 1 db (f) the (28;1;2 28 ) code (narrow- bandmodel). Figure5.7: Detectioncurves. P d andP f fordifferentchoicesofcode,propagationmodel anddetectionthreshold. band described in [PO08] reveal a dependence of received power on distance of the formp/ 1 r d wheretheexponentdvariesfrom3forlineofsightpropagationtoabout6 fornon-lineofsightpropagation. Regulardatatransmissionsusingthe16-QAMmod- ulation present in our system necessitate a SNR value of about 20 dB while tags are detectable at a SNR value of 0 dB. It results that the ratio of the range of tag commu- nication to the range of the data transmissions can be, depending on the power decay coefficient,anywherebetween2.15and4.65. Thecarriersensethresholdisusuallysetabout10-20dBabovethenoiselevel[BM09] [VRW05],whichsubstantiatesourclaimthatTagSpottingcancommunicateinformation beyondthecarriersenserange. CHAPTER5. TAGSPOTTINGATTHEINTERFERENCERANGE 95 ■ 5.7 PerformanceAnalysis Section5.4hasdescribedthedesignoftagsandintroducedanuniversaldetector 4 that doesnotrequireanestimateofthecombinedpowerofnoiseandbackgroundinterfer- ence. However,theclassictheoreticalresultsonthedetectionandfalsealarmprobabil- itydistributionsarenotreadilyapplicabletoourmorecomplicatedtagdetector. Inthe following we will analyze, using rather conservative fading models, the performance achievable by a few particular tag families. At first we will consider the performance achievablewhensearchingforasingletagsignal,afterwhichwewillgeneralizetolarger familiesoftags. Theanalysiswillmakeuseoftwofadingmodels,anarrowbandfading modelandawidebandfadingmodelwhichassumesRayleighpropagation. Duetothe limitedtimespanoftags,thesetwomodelsdescribeshort-termfadingeffectsonly. Single Tag. Let us consider a tag t. In what follows, we will denote by c the number oftwo-carriergroupsusedinthetag’sconstruction. Assumethat,foreachthincarrier, thereceivernoisehaspowernanditsdistributioncanbemodeledbyacomplexGaus- sian random variableN(0;n). We further assume that for the active thin carriers the average signal power in the frequency band corresponding to any carrier is p. Under the assumption of narrowband transmission and without including the receiver noise contribution,thereceivedsignalobtainedafterdemodulatingoneofthecarrierscanbe modeled as a circularly uniform complex variable of constant amplitude p p, while in the case of wideband transmission the signal is modeled by a complex Gaussian ran- domvariableN(0;p). Assumethateachthickcarrieriscomposedofthincarriers,out ofwhich areactive. Inthecaseofthesystempresentedintheprevioussection = 8 and = 4. LetP t denotethesetofthincarriersactivatedwhentagtistransmitted,Q t representthethincarriersthat,whiletheyarenotactivated,belongtoactivethickcarri- ersandR t thethincarriersthatbelongtounactivatedthickcarriers. Inaccordancetothe definitiongivenwhenintroducingthetagdetector,wedenotethroughC t =P t [Q t the set of all thin carriers belonging to activated thick carriers, regardless of whether they 4 adetectorforwhich,foranychosenprobabilityoferrorP f ,thecorrespondingprobabilityofdetection P d canonlyincreasewhentheSINRisincreased. Auniversaldetectorisparticularlysuitedtoourpurposes, giventheunpredictablenatureofinterferencepower. 96 5.7. PERFORMANCEANALYSIS are active or not. Letr f be the complex values obtained after computing a fast Fourier transformoftherealandcomplexcomponentsofasampledtagsignal,i.e. thereceived signalvaluescorrespondingtothevariousthincarriers. Letjjjjdenotethel 2 norm. UndertheassumptionofindependentRayleighfading,itresultsthatforeachactive thin carrier the amplitude of the received signal is distributed according to a complex Gaussian random variableN(0;p+n). Choosing a threshold value for the quantity definedinEquation5.3,wecanwritetheprobabilityofdetectionas: P d =P ( ∑ f2Ct jjr f jj 2 ∑ f= 2Ct jjr f jj 2 > 1 ) (5.4) or P d =P ( ∑ f2Pt jjr f jj 2 + ∑ f2Qt jjr f jj 2 ∑ f2Rt jjr f jj 2 > 1 ) (5.5) It results from the previous paragraph and due to the independence of the circu- lar random variables considered that the sums in the above equations can be written using the Chi-Square distribution with d components, denoted through 2 d . Namely 1 p+n ∑ f2Pt jjr f jj 2 2 2c , 1 n ∑ f2Qt jjr f jj 2 2 2()c and 1 n ∑ f2Rt jjr f jj 2 2 2c . Inthecaseofnarrowbandfading,theamplitudeofthereceivedsignalforeachactive carrier is constant. Therefore the first of these sums can be written using the noncen- tral Chi-Square distribution with parameter = 2c p n . We write 1 n ∑ f2Pt jjr f jj 2 2 2c ( 2c p n ) . Theprobabilityoffalsealarminthecaseofasingletag(andasingletestedhypoth- esis)canbeobtainedbysettingp = 0intheaboveformulas. Therefore,writingtheratio of the two Chi-Squared random variables using a random variable f that follows the Fisher-SnedcorF-distribution[JSN95],f F(2c;2c), P f (t) =P ( f > 1 ) (5.6) CHAPTER5. TAGSPOTTINGATTHEINTERFERENCERANGE 97 Figures5.7aand5.7dpresentthedetector’sbehavioratdifferentSNRvaluesinthe caseofwidebandandnarrowbandsignals,respectively. 5 Choosing the number of active carriers. Consider in the following a problem men- tionedinSection5.5,namelytheoptimalnumberofthickcarriersq thatshouldbeacti- vated during a tag transmission in order to maximize the performance of the detector. LetN denotethetotalnumberofthickcarriers. Inordertoobtainclosed-formresults, we use a simplified model of tags in which we set = , that is active thick carriers will use all thin subcarriers for transmission. Let f ′ be a random variable generated using the corresponding Fisher-Snedcor distribution, f ′ F(2q;2(N q)). Under thisassumptionwecansimplifytheformulasfortheprobabilityofdetectionandfalse alarminthewidebandcaseto: P ′ d (t) =P ( ( 1+ p n ) f ′ > 1 ) andP ′ f (t) =P ( f ′ > 1 ) It results that the probability distribution of the receiver response corresponding to detections is just a scaled version of the probability distribution corresponding to false alarms. We introduce a new performance measure in order to characterize the performancechangeduetothechoiceofq. Let 0 bethevalueof forwhichP ′ d = 1 2 ,at aSNRvalueof0dB.Figure5.8plotsthebehaviorofP ′ f ,foradetectorwithathreshold 0 ,fordifferentvaluesofq,whenN = 56. Thequantityplottedrepresentsthevalueof thetailoftheprobabilityoffalsealarminthetypicaldetectionregion. Families of Tags. The next point in our analysis will be considering the situation in whichthedetectorsearchesformultiplehypotheses. Assumethereforethatthetagtis a member of a family of tags T, as described in Section 5.4. It can be readily observed that both in the narrowbandand wideband cases the probabilities of detection remain unchanged. Theprobabilityoffalsealarmcanberewrittenas: P f (T) =P ( max t2T ( ∑ f2Ct jjr f jj 2 ∑ f= 2Ct jjr f jj 2 ) > 1 ) wherejjr f jj 2 2 2 . 5 TheSNRfiguresarecomputedusingthepowerandnoisefiguresforathickcarrier,thatisSNR = p n . 98 5.7. PERFORMANCEANALYSIS 10 -14 10 -12 10 -10 10 -8 10 -6 10 -4 10 -2 10 0 0 10 20 30 40 50 60 P ’ f Active Carriers Figure 5.8: False Alarms. The probability of typical false alarms as a function of the numberofactivecarriers. Thetotalnumberofcarriersusedintagconstructionis56. Figures5.7band5.7epresentthedetector’sbehavior,evaluatedthroughMonteCarlo simulation,atdifferentSNRsinthecaseofwidebandandnarrowbandsignals,respec- tively for the (28;13;60) code mentioned in Section 5.4. In particular, Figure 5.7e com- paresthetheoreticalpredictionswiththeexperimentalresultspresentedinSection5.6. Thegreencrossatthetopofthefigurepresentstheexperimentallymeasureddetection probabilityfortagsinthepresenceofbackgroundnoiseonly,atanSNRvalueof1dB, asshownininFigure5.5a,whiletheredcrosspresentsthetheoreticalvalueatthesame SNR. The experimental data and the theoretical curve, which indicates a probability of detection nearing one, are in agreement. Figures 5.7c and 5.7f illustrate the same detectioncurvesinthecaseofthesimple(28;1;2 28 )code. Thepowerlevelsonthecarriersarebeingsummedupinthehypothesesindifferent ways. Since the variables that are summed up are chosen from the same set, the prob- ability that the maximum present in the function will cross any chosen threshold ′ is significantly lower than what the sum bound on the individual probabilities of errors associatedwiththedifferentcodewordswouldpredict. The simpler quantity max t2T ∑ f2Ct jjr f jj 2 can be bounded using an initial sym- metrization step [LT06] and deriving, using generic chaining [Tal96], a Dudley-like inequality [Dud67] on the probability that the maximum exceeds any given threshold. The resulting bound limits the increase of the necessary threshold, for any fixed prob- ability of false alarm, to a quantity of the form O(log(N)) where N is the number of codewordsused. Forreasonsofspacewehavenotincludedthederivationofthebound. For the code construction using the two-carrier groups presented in Section 5.4, a simple upper bound on the probability of false alarm can be derived by considering CHAPTER5. TAGSPOTTINGATTHEINTERFERENCERANGE 99 thecaseofthesimplest(28;1;2 28 )code,whichhasthelargestprobabilityoffalsealarm of all possible codes since it includes all possible codewords . Consider a set of pairs ofChi-Squaredistributedrandomvariables(x i;1 ;x i;2 )andletx M i andx m i representthe maximum and minimum, respectively, in each pair. The probability of false alarm can bethuswritten,fortheaforementionedcode,as: P f (T) =P (∑ 8i x M i ∑ 8i x m i > 1 ) Theformulaabovehasbeenusedinordertoderivethedetectioncurvesforthecode mentioned,whicharepresentedinFigures5.7cand5.7f. ■ 5.8 Applications In this section we present the use of Tag Spotting in two applications aimed towards obtaining a fair resource allocation in multi-hop wireless networks. We would like to emphasizethatattainingafairdistributionofresourceswhenusingawirelessmedium is,inouropinion,aneighborhood-centricproblem. Weexplorethestructure,thegran- ularity and the rate of information that hosts within a neighborhood should exchange inordertosolvethefairnessproblem CongestionControl In a wireless setting, congestion is not always primarily experienced by the flow that causesitandaneighborhood-widesignalingmechanismbecomesnecessary. Withthisinmind,weextendWCP[RJJ + 08],arecentAIMD-basedschemefromthe congestioncontrolliterature,byusingTagSpottingforcommunicatingcongestionnoti- fications,andweassesstheachievedperformanceofboththeoriginalWCPprotocoland its extended derivative through simulations. In the original WCP, there are two types ofinformationbroadcastedbyeachnodeindataandackpackets: acongestionbitthat indicates congestion events to its neighbors and the maximum of the round trip times (RTTs)offlowstraversingit,ametricusedinachievingamax-minfairallocation. This maximumRTTisthenusedtopacetherateincreasesoftheAIMDcontrollerswhichset 100 5.8. APPLICATIONS 1 2 3 4 5 6 7 8 11 9 10 1 2 3 4 5 6 7 8 11 9 10 a) b) (a) (b) Figure 5.9: Chain-cross topology. All competing flows are separated by at most one transmissionrange(upper)andwithsomecompetingflowsseparatedbymorethanthe transmissionrange(lower). the rates of the flows traversing the neighborhood. Both loss rates and delays experi- encedbycompetingflowspassingthroughacongestedneighborhoodmayvarywidely, significantlymorethaninwirednetworks. Thiscausesthesenders’AIMDcontrollersto increase their rates at significantly different paces following a congestion event, unless a common loop duration is used. For more details on WCP, the interested reader is referredto[RJJ + 08]. We have simulated the performance of WCP using the Qualnet network simula- tor [Sca]. We have extended Qualnet’s physical layer simulation in order to also han- dlethelikelihoodoftagdetectionusingthedetectionprobabilitiesmeasuredinSection 5.6. Thecontentoftagsiscomposedofonecongestionbitandafieldthatencodes,ona logarithmic scale with base 3 p 2, the value, in milliseconds, the longest RTTof all flows traversing the tag emitter. We call the tag-based implementation of WCP, WCP-Tags. For the original WCP we have used a broadcasting mechanism that shares the same information as WCP-Tags, however the limit SNR for broadcast detection has been set atthesamevalueatwhichsuccessfulpayloaddatadecodingoccurs, sincetheoriginal WCPbroadcastsareinsertedintothepayloadofdatapackets. Allhostsusetheregular 802.11MACforad-hocnetworkswithdefaultsimulatorvalues,withtheonlymodifica- tionthat thenumberofallowedMAClayerretransmissionshasbeendoubledfromits defaultvalueinordertodecreasetherateofpacketdropsandincreasethelikelihoodof tagreception. CHAPTER5. TAGSPOTTINGATTHEINTERFERENCERANGE 101 0 200 400 600 800 1000 TCP WCP WCP-Tags max-min Goodput (kbps) 1->2 1->7 6->7 8->9 10->11 (a)forthetopologyinFigure5.9a. 0 200 400 600 800 1000 TCP WCP WCP-Tags max-min Goodput (kbps) 1->2 1->7 6->7 8->9 10->11 (b)forthetopologyinFigure5.9b. 50 100 0 200 400 600 800 1000 802.11 802.11-Tags max-min Goodput (kbps) 1->2 1->7 6->7 8->9 10->11 (c)underthemodifiedscheduling policy for the topology in Figure 5.9b. Figure5.10: Goodput. GoodputresultsforthetopologyinFigure5.9a Figure5.9aillustratesatextbookconfigurationforevaluatingcongestioncontrolpro- tocolsinwirelessenvironments. Thetwoshortflowsontheoutsideofthecentralchain ofnodesarewithinthetransmissionrangeofnode2,andwecanthereforeexpectthat thetwovariantsofWCPwillhavesimilarperformance. Figure5.10aillustratestherates obtained by TCP, original WCP (“WCP”) and the tag-based implementation of WCP (“WCP-Tags”). Itcanbereadilyobservedthat,whileTCPleadstostarvationofthecen- tralflow,bothWCPandWCP-Tagsmanageafairerrateallocation. Discussing the results of these experiments requires taking into account, above all, thefairnessachievedandsecondlythethroughput. Itiswellknownthatsupportinga long flow in a wireless multi-hop network is possible only at rates significantly lower thanthemaximallinkspeed[LBDC + 01]. Anyincreaseintherateofthelongflowinthe figure will involve a drastic reduction in the rates of the other, shorter flows. To make this point more precise, we compute using brute force simulations and the theoretical framework in [JP09] the max-min rate allocation for these flows and compare it to the other allocations. It is evident that both the original WCP and WCP-Tags yield rates whichareclosetothemax-minoptimalrateallocation. Figure5.9billustratesavariationoftheprevioustopologyinwhichtheoriginalWCP cannoteffectivelysignalcongestionbetweentheinvolvedhosts,duetothefactthatsome hostsarewithintheinterferencerangebutoutsidethedatatransmissionrangeofeach other. Inparticular,undertheoriginalWCPnode2cannotinformnodes8and10thatit iscongestedandthelongflowisalmoststarved,similarlytowhathappensunderTCP. Incontrast,WCP-Tagsdoesnotstarvethelongflowasnodes8and10reducetheirrates oncetheyreceivenotificationsthroughtagsthatnode2iscongested. Therateallocations 102 5.8. APPLICATIONS achievedbythethreeprotocolsaswellasthemax-minrateallocationforthistopology are illustrated in Figure 5.10b. As before, WCP-Tags yields rates which are close to the max-minoptimalallocation. Scheduling Alargeclassofschedulingalgorithmsforwirelessmulti-hopnetworksarecenteredon ideas such as queue equalization using backpressure [Sto05], broadcasting local con- gestionindications[XGQS03]orcreatingacomputationallytractableapproximationof an optimal schedule [LS04] [JPPQ03]. Some of the benefits of schemes that use local communication will be illustrated in the current section through the evaluation of a rather simple scheduling scheme, designed as an extension to the ad-hoc mode of the the802.11 MAC.The simplemechanism presentedhere targetssome ofthe unfairness effectsintroducedbythe802.11MACwhichmayleadtoflowstarvation. ConsideragainthetopologyillustratedinFigure5.9b. TheresultsofSection5.8have already shown that using a standard 802.11 MAC in conjunction with TCP drives the longest flow in this topology into starvation. Our solution preserves TCP as the trans- port protocol but seeks to relieve such severely disadvantaged flows by enhancing the scheduling algorithm. The key to achieving this goal is an exchange of tags conveying ameaningfulmeasureofstarvation, namelytheaveragedelayofthepacketscurrently enqueuedfortransmission. The hosts observe all detected tags and decide that a host in their neighborhood is starvedformediumaccesswhenevertheyreceiveatagconveyinganaveragequeueing timewhichisatleast32timeslargerthantheirownaveragequeueingtime. Inthiscase thetagreceiverwillenterasilenceperiodof15milliseconds,allowingthestarvedhostto gainaccesstothechannelandtransmititspackets. Thesenumbersarenotparticularly optimized since our focus is to showcase the benefits of using tags in scheduling with a very simple addition to 802.11, rather than to provide a fully optimized and tested solution. All other medium access activity proceeds according to the normal 802.11 specification. Wecallthisscheme802.11-Tags. TheonlyotherMAC-layermodification CHAPTER5. TAGSPOTTINGATTHEINTERFERENCERANGE 103 appliedtobothvanilla802.11and802.11-TagsconsistsindoublingthenumberofMAC- layerretriesperformedincaseofcollision,justasintheprevioussection. InterpretingtheresultsinFigure5.10crequireslookingbeyondtheperformanceof individual links. In order for the long flow to achieve a transmission rate on the order of tens of kilobytes, all other flows must lower their rates far below the hundreds of kilobytes available on individual links. As shown in the previous section, a fair distri- butionofratesisassociatedwithadrasticdecreaseofoverallthroughput. Asexpected, thissimpleMAClayermodificationcannotachieveamax-minfairdistributionofrates whenusedinconjunctionwithastandardAIMDratecontrollerlikeTCPatthetransport layer. As the results in Figure 5.10c show, the improved scheduler alleviates flow starva- tion. Theshortestofthetwostarvedflowsinthefigurereachesaratesimilartotheones oftheotherthreeshortflows. Thelongflowinthefigureincreasesitsachievedratefrom alevelthatcannotpreventconnectiontimeoutsandinterruptionstoasustainedrateof about15kbps. ■ 5.9 Conclusion This paper has proposed a mechanism forsharing control information in wireless net- works, able to function in low SNR conditions and without introducing new interfer- ence constraints. It evaluated its performance through a theoretical analysis as well as experiments realized using software radios. It was found that the communication schemepresentediseffectiveatSNRvaluesaslowas0dB,effectivelycoveringthecar- rier sense range of a wireless host. Two algorithm implementations that make use of this scheme have been evaluated through simulations, confirming its applicability in protocoldesign. 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Achieving high data rates in distributed MIMO systems
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