Multiuser multi-antenna systems with limited feedback

Institut Euréom

THESIS

In Partial Fulllmentof the Requirements

for the Degree of Dotor of Philosophy

fromEole Nationale Supérieure

des Téléommuniations

Speialization: Communiations and Eletronis

Marios Kountouris

Multiuser Multi-antenna Systems with Limited Feedbak

President J.C.Belore,ENST (Paris,Frane)

Reviewers C.Papadias, AIT(Athens,Greee)

M.Debbah,Supéle (Gif-sur-Yvette,Frane)

Examiners A.I.Pérez-Neira,UPC(Barelona,Spain)

T.Sälzer,FraneTeleomR&D(Paris,Frane)

Thesissupervisor D.Gesbert,EureomInstitute(Sophia-Antipolis,Frane)

January

10 ^th

²⁰⁰⁸

Institut Euréom

THESE

Présentée pour obtenir leGrade de Doteur

de l'Eole Nationale Supérieure

des Téléommuniations

Spéialité: Communiationset Eletronique

Marios Kountouris

Systèmes multi-antennes multi-utilisateurs ave voie de

retour limitée

Président J.C.Belore,ENST (Paris,Frane)

Rapporteurs C.Papadias,AIT(Athènes,Grèe)

M.Debbah,Supéle(Gif-sur-Yvette,Frane)

Examinateurs A.I.Pérez-Neira,UPC(Barelone,Espagne)

T.Sälzer,FraneTeleomR&D(Paris,Frane)

DireteurdeThèse D.Gesbert,EureomInstitute(Sophia-Antipolis,Frane)

January

10 ^th

²⁰⁰⁸

Firstand foremost, I wouldliketo expressmy deepest gratitudeto myadvisorand friend

Prof. David Gesbert for his brilliant supervision and his ontinual guidane and support

throughout the years of my Ph.D. Without his tehnial insight, reativity and on-going

enouragement,thisthesiswouldhaveneverbeenpossible. Ithasbeenarealpleasureand

privilegetohavehad Davidasamentor.

IwouldliketoaknowledgeFraneTeleomR&Dforthenanialsupportofmywork.A

speialandwarmthanktomyindustrialsupervisorDr.ThomasSälzer,forhissupportand

onstrutiveritiismaswellasforprovidingtheproperonditionstopursue myresearh.

I would also like to thankAnne-Gaële Axforhosting mein her group,aswellasall the

teammemberswithwhomIinteratedduringmyseven-monthstayinFraneTeleom'slab

inParis.

IamverygratefultoProf.ConstantinosPapadiasandProf.MérouaneDebbahfortaking

thetimetoreadtherstversionofmydissertationandtoserveasreaders. Iwouldalsolike

tothankProf. JeanClaudeBeloreandProf.Ana Pérez-Neiraforaeptingtobepartof

mythesisommittee. TheinvaluablefeedbakofallthePh.DJurymembersisenormously

appreiated.

IwouldliketoexpressmyappreiationtomyolleaguesandfriendsatEureomInstitute

fortheexellent andtruly enjoyableambiane. Speial thanksgoto Ruben deFraniso,

SaadKiani, Mari Kobayashi, Maxime Guillaud, and Issam Touk. I am also thankfulto

myo-authorsProf.DirkSlokandRubendeFraniso. Partofthisthesiswouldnothave

been possible withouttheir stimulatingdisussions and help. Mywarmest thanksextend

to mydear friends, in Frane, bakin Greee and in manyother ornersof theglobe, for

alltheunforgettablemomentsI sharedwiththem overthepastyears.

Finally,I wantto express mygratitude tomy familyfortheir unonditionallove,sup-

port, and enouragement. I am deeply indebted to Teodora for being aboundless soure

of support, patiene, and inspiration. Thank you for bringing so muh sinere loveand

happinesstomylife.

MariosKountouris

Sophia-Antipolis

January10,2008

Theuseof multiple antennas hasbeen reognizedasakeytehnologyto signiantlyim-

provethespetraleienyofnext-generation,multiuserwirelessommuniationnetworks.

Inmultiusermultiple-input multiple-output (MIMO)networks,thespatial degreesoffree-

domoered bymultiple antennas anbe advantageously exploited to enhane thesystem

apaity,byshedulingmultiple userssimultaneouslybymeansofspatial divisionmultiple

aess (SDMA). A linear inrease in throughput, proportionalto thenumber of transmit

antennas, an be ahieved even by using linear preoding strategies if ombined with ef-

iently designed sheduling protools. However, these promising gains ome under the

oftenunrealistiassumptionoflose-to-perfethannelstateinformationatthetransmitter

(CSIT). Therefore, at the heart of the downlink resoure alloation problem lies that of

feedbakaquisition.

In this thesis, we fous on linear beamforming tehniques relying on low-rate partial

CSIT. Several methods that allow the base station (BS) to live well even with oarse,

limitedhannelknowledgeareidentied. Onerstkeyideaisbasedonsplittingthedesign

betweenthe shedulingand thenal beamdesignstages, thus taking prot from thefat

the number of users to be served at eah sheduling slot is muh smaller than the total

numberof ativeusers. Thistwo-stageapproah isapplied toasenarioin whih random

beamforming(RBF)isexploitedtoidentifygood,spatiallyseparable,usersintherststage.

Intheseond stage,severalrenementstrategies,inludingbeampowerontrolandbeam

seletion,areproposed,oeringvarious feedbakredutionand signiantsumrategains,

eveninsparsenetworksettings(lowtomoderatenumberof users).

In hannels that exhibit some form of orrelation, either in temporal orin spatial do-

main,wepointoutthatsigniantusefulinformationfortheSDMAshedulerlieshiddenin

thehannel struture. We showhowmemory-basedRBF anexploit hannel redundany

in order to ahieve throughput lose to that of optimum unitary beamforming with full

CSITforslowtime-varyinghannels. Inspatiallyorrelatedhannels,long-termstatistial

CSIT,whihanbeeasilyobtainedwithnegligibleper-slotornofeedbakoverhead,reveals

informationaboutthemeanspatialseparabilityofusers. Amaximumlikelihood(ML)han-

nelestimationframeworkisproposed,whiheetivelyombines slowlyvaryingstatistial

CSIT with instantaneous low-rate hannel quality information (CQI).User seletion and

beamforming tehniques suitable for suh settings are also proposed. It is demonstrated

thatinsystemswithreasonablylimitedanglespreadattheBS,feedingbakasinglesalar

CQIparameterperuseris suient to perform SDMA sheduling andbeamforming with

nearoptimumperformane.

Limitedfeedbakstrategiesutilizingvetorquantizationodebooksarealsoinvestigated.

In partiular, the problem of eient, sum-ratemaximizing CQI design is addressedand

several salarfeedbak metris are proposed. These metris are built upon inter-user in-

terferene bounds and an be interpreted as reliable estimates of the reeived signal-to-

interferene-plus-noise ratio(SINR)at thereeiverside. Itis shownthat salarCQIfeed-

bakombinedwithhanneldiretionalinformation(CDI),zero-foringbeamforming,and

greedy user seletion algorithms an ahieve a signiant fration of the apaity of the

full CSIT ase by exploiting multiuser diversity. An eient tehnique that provides the

BStheexibilitytoswithfrommultiuser(SDMA)tosingle-user(TDMA) transmissionis

provided,exhibitinglinearsum-rategrowthat anyrangeof signal-to-noiseratio(SNR).

Further feedbak ompressionan be ahievedif the CSIT informationutilized by the

shedulerisrepresentedbyranking-basedfeedbak. Weshowthatanintegervalueisoften

suientinordertoidentifyuserswithfavorablehannelonditions. Inparallel,itequalizes

the hannel aess probabilityin networks where users' hannels arenot neessarilyiden-

tially distributed andmobile terminalsexperiene unequalaverageSNRs due todierent

distanesfrom theBSandtheorrespondingdierentpathlosses(near-fareets).

Aknowledgements . . . i

Abstrat . . . iii

ListofFigures . . . ix

ListofTables . . . xiii

Nomenlature . . . xv

1 Introdution 1 1.1 BakgroundandMotivation . . . 1

1.2 FromSingle-userto MultiuserMIMO Communiations. . . 2

1.3 Assumptions . . . 3

1.4 ContributionsandOutlineoftheDissertation . . . 4

2 Multi-antenna Broadast Channels 9 2.1 TheWirelessChannel . . . 9

2.1.1 Pathloss . . . 10

2.1.2 Shadowing . . . 10

2.1.3 Fading. . . 10

2.1.4 ChannelSeletivity. . . 11

2.2 Multiple-Input Multiple-OutputChannels . . . 13

2.3 MultiuserMulti-AntennaSystems . . . 14

2.3.1 Multi-antennaChannelModeling . . . 15

2.4 CapaityofMIMO BroadastChannels . . . 18

2.4.1 CapaitywithperfetCSI atthetransmitter . . . 18

2.4.2 CapaitywithnoCSIat thetransmitter. . . 20

2.5 MultiuserMIMOShemeswithperfetCSIT . . . 21

2.5.1 Non-linearPreoding. . . 21

2.5.2 LinearPreoding . . . 22

2.6 Theardinalroleof ChannelStateInformation . . . 25

2.6.1 ChannelKnowledgeattheTransmitter . . . 25

2.6.2 Capaitysalinglawsin MIMOBCsystems. . . 26

2.6.3 PartialChannelStateInformation . . . 28

2.6.4 StatistialChannelKnowledgeattheTransmitter . . . 28

2.7 ShedulingandMultiuserDiversity . . . 29

2.7.1 AsymptotiSum-rateAnalysiswithOpportunisti Sheduling. . . 30

2.8 Living withpartialCSIT:Limitedfeedbakapproahes . . . 32

2.8.1 Quantization-basedtehniques . . . 32

2.8.2 Dimensionredutionandprojetiontehniques . . . 32

2.9 LinearPreodingandShedulingwith LimitedFeedbak. . . 33

2.9.1 FiniteRateFeedbakModelforCDI . . . 33

2.9.2 Codebook design . . . 34

2.9.3 RandomOpportunistiBeamforming. . . 36

3 Enhaned MultiuserRandomBeamforming 39 3.1 Introdution. . . 39

3.2 Sum-RateAnalysisofRandomBeamforming . . . 41

3.3 CapaitysalinglawsforhighSNR . . . 44

3.4 Two-StageShedulingandLinearPreoding . . . 47

3.5 EnhanedMultiuserRandomBeamforming . . . 48

3.6 EnhanedPreoding withperfetseond-stageCSIT . . . 49

3.7 BeamPowerControlwithBeam GainInformation . . . 49

3.7.1 OptimumBeamPowerAlloationforTwoBeams. . . 50

3.7.2 BeamPowerAlloationformorethantwobeams. . . 52

3.7.3 BeamPowerControlin Spei Regimes(

B ≥ 2

^{) . . . . . . . . . . . . 55}

3.8 BeamPowerControlwithSINRfeedbak . . . 57

3.9 PerformaneEvaluation . . . 58

3.10 Conlusion . . . 62

3.A ProofofLemma 3.1 . . . 64

3.B ProofofLemma 3.2 . . . 64

3.C ProofofLemma 3.3 . . . 65

3.D ProofofCorollary3.2 . . . 65

3.E ProofofTheorem3.1. . . 65

3.F ProofofTheorem3.2. . . 66

3.G ProofofLemma 3.4 . . . 67

3.H ProofofLemma 3.5 . . . 67

3.I ProofofProposition 3.3 . . . 68

4 ExploitingChannel Struture in MIMO Broadast Channels 69 4.1 Introdution. . . 69

4.2 Exploitingredundanyintime-orrelatedhannels . . . 70

4.2.1 UserSeletionintime-orrelatedhannels . . . 70

4.2.2 BeamformingandShedulingexploitingtemporalorrelation . . . 70

4.2.3 Memory-basedOpportunisti Beamforming . . . 71

4.3 Performaneevaluation . . . 74

4.4 ExploitingStatistialCSITinSpatiallyCorrelatedChannels . . . 75

4.4.1 SystemSetting . . . 76

4.4.2 UserSeletionwithMLChannelEstimation. . . 77

4.4.3 MLoarse ChannelEstimationwithCQIFeedbak. . . 78

4.4.4 Interferene-boundedMultiuserEigenbeamformingwithlimitedfeed- bak . . . 83

4.4.5 PerformaneEvaluation . . . 85

4.A ProofofProposition 4.1 . . . 91

5 LimitedFeedbak Broadast Channelsbased on Codebooks 93 5.1 Introdution. . . 93

5.2 Systemmodel . . . 95

5.3 CQIFeedbakDesign . . . 95

5.3.1 Problemformulation . . . 95

5.3.2 BoundsonaveragereeivedSINR . . . 96

5.3.3 Lowerbound oninstantaneousreeivedSINR . . . 98

5.3.4 SDMA/TDMAtransition withlimitedfeedbak. . . 102

5.4 UserSeletionShemes. . . 103

5.4.1 Greedy-SUSalgorithm . . . 103

5.4.2 Greedy-USalgorithm . . . 104

5.5 PerformaneAnalysis . . . 105

5.5.1 Asymptoti(inK)sum-rateanalysis . . . 105

5.5.2 Sum-rateanalysisin theinterferene-limited region. . . 106

5.6 MIMO BroadastChannelswithFiniteSumRateFeedbakConstraint . . . 107

5.6.1 MultiuserDiversity-Multiplexing Tradeoin MIMO BC with Lim- itedFeedbak . . . 107

5.6.2 FiniteSumRateFeedbakModel. . . 108

5.6.3 ProblemFormulation . . . 109

5.6.4 DeoupledFeedbakOptimization . . . 110

5.7 PerformaneEvaluation . . . 111

5.8 Conlusion . . . 117

5.A ProofofTheorem5.1. . . 119

5.B ProofofLemma 5.1 . . . 120

5.C ProofofTheorem5.2. . . 120

5.D ProofofLemma 5.2 . . . 121

5.E ProofofTheorem5.3. . . 122

5.F ProofofTheorem5.4. . . 123

6 Feedbak Redutionusing Ranking-based Feedbak 125 6.1 Introdution. . . 125

6.2 Ranking-basedFeedbakFramework . . . 127

6.2.1 Two-stageapproah . . . 127

6.2.2 Ranking-basedCQIRepresentation. . . 128

6.3 Performaneanalysis . . . 129

6.3.1 Asymptoti optimality of ranking-based feedbak for large window size

W

^{. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129}

6.3.2 Throughputforinteobservationwindowsize

W

^{. . . . . . . . . . . . 130}

6.3.3 Throughputforniteobservationwindowsize

W

^{. . . . . . . . . . . . 131}

6.3.4 Performaneredutionboundfornitewindowsize

W

^{. . . . . . . . . 132}

6.3.5 Windowsizeversusfeedbakredutiontradeo . . . 133

6.4 Ranking-basedCDIModel. . . 133

6.6 PerformaneEvaluation . . . 135

6.7 Conlusion . . . 139

6.A ProofofProposition 6.1 . . . 140

6.B ProofofProposition 6.3 . . . 140

6.C ProofofProposition 6.5 . . . 141

7 SystemAspetsin MultiuserMIMO Systems 143 7.1 Introdution. . . 143

7.2 ChannelStateInformationAquisition . . . 144

7.2.1 CSIat theReeiver . . . 144

7.2.2 CSIat theTransmitter . . . 144

7.3 Codebook-basedPreoding . . . 145

7.4 CQIfeedbakmetrisandLinkAdaptation . . . 147

7.5 OpportunistiSheduling: SystemIssues . . . 147

7.6 Fairness . . . 148

7.6.1 Denitionof Fairnessin Sheduling. . . 148

7.6.2 ProportionalFairSheduler(PFS) . . . 149

7.6.3 MultiuserProportionalFairSheduler(M-PFS). . . 150

8 Conlusions and Perspetives 153

2.1 Multiple-Input MultipleOutputChannelModel. . . 13

2.2 Downlinkof amultiuserMIMO network: A BS/APommuniates simulta-

neouslywithseveralmultiple antennaterminals. . . 15

2.3 Analytial hannelmodelwithloal satterersatmobile station. . . 17

2.4 ShematiofRandomOpportunistiBeamforming. . . 38

3.1 Comparison between simulated and analytial ahievable sum-rate of RBF

with

M = 4

^{antennas andSNR=20dB. . . . . . . . . . . . . . . . . . . . . 42}

3.2 Ahievable sum rate omparison vs. average SNR for RBF with

M = 4

antennas. Both analyti expressions approximate aurately the simulated

performaneathighSNR. . . 43

3.3 Ahievablesumrateomparisonbetweensimulatedandanalytialresultsfor

RBF with

M = 4

^{antennasandSNR =-15dB. . . . . . . . . . . . . . . . . . 43}

3.4 Sum rateversusthenumberof usersforOptimal BeamPowerControlwith

M = 2

^{transmitantennasandSNR =20dB. . . . . . . . . . . . . . . . . . . 59}

3.5 SumrateversusaverageSNRforOptimalBeamPowerControl (strategy3)

with

M = 2

^{transmitantennasand}

K = 10

^{users.. . . . . . . . . . . . . . . . 59}

3.6 Sum rateomparisonof dierentseond-stagepreoders(strategy1)versus

thenumberofusersfor

M = 2

^{and SNR=10dB. . . . . . . . . . . . . . . . 60}

3.7 SumrateversusthenumberofusersforIterativeBeamPowerAlloationand

OptimalPowerControlwith

M = 2

^{transmitantennasandSNR =10dB.. . 60}

3.8 Sum rate versus the number of users for Iterative Beam Power Alloation

with

M = 4

^{transmitantennasandSNR =10dB. . . . . . . . . . . . . . . . 61}

3.9 Sum rate versusthe numberof usersfor On/OBeam PowerControlwith

M = 2

^{transmitantennasandSNR =20dB. . . . . . . . . . . . . . . . . . . 61}

3.10 Sum rateversusaverageSNR for On/OBeamPowerControlwith

M = 4

transmitantennasand

K = 25

^{users.. . . . . . . . . . . . . . . . . . . . . . . 62}

3.11 Sum rate versusthe numberof usersfor On/OBeam PowerControlwith

M = 4

^{transmitantennasandSNR =20dB. . . . . . . . . . . . . . . . . . . 62}

4.1 Sum rate vs. the numberof transmit antennas

M

^{of MOBFwith}

K = 20

usersandvariousDopplerspreads. . . 74

4.2 Sumrateasafuntionofnumberofusers

K

^{ofMOBFfordierentDoppler}

spreads. . . 75

4.3 SumrateperformaneversusanglespreadofproposedMLestimationmethod

for

M = 2

^,and

K = 50

^{users. FullCSITisobtainedfortheseletedusersat}

aseondstep. . . 86

4.4 Sumrateperformaneversusthenumberofusersof MLhannelestimation

method for

M = 2

^{, and}

σ θ = 0.2π

^{. Full CSIT for the seleted users is}

obtainedforpreoderdesign. . . 86

4.5 SumrateperformaneversusanglespreadofproposedMLestimationframe-

workfor

M = 2

^,and

K = 50

^{users. PartialCSITis employedforpreoding}

design. . . 87

4.6 Sum rate as a funtion of the number of users for various user seletion

shemeswith

M = 2

^{,antennaspaing}

d = 0.5λ

^and

σ θ = 0.1π

^{. . . . . . . . . 87}

4.7 Sumrateasafuntionofantennaspaingforvarioususerseletionshemes

with

M = 2

^,

σ θ = 0.1π

^and

K = 50

^{users. . . . . . . . . . . . . . . . . . . . . 88}

4.8 Sumrateasafuntionofanglespreadforvarioususerseletionshemeswith

M = 2

^{,antennaspaing}

d = 0.5λ

^and

K = 50

^{users. . . . . . . . . . . . . . . 88}

4.9 Sumrateasafuntionofthenumberofusersfor

M = 2

^,and

σ θ = 0.1π

^{. . . . . . 89}

4.10 Sumrateas afuntionofanglespread for

M = 2

^{, antennaspaing}

d = 0.4λ

^and

K = 100

^{users. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89}

5.1 FiniteSumRateFeedbakModel. . . 108

5.2 SumrateversustheaverageSNRfor

B D = 4

^bits,

M = 2

^{transmitantennas}

and

K = 30

^{users. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112}

5.3 Sum rate as a funtion of the number of users for

B D = 4

^bits,

M = 2

transmitantennas andSNR=20dB. . . 112

5.4 Sumrateperformaneasafuntion oftheaverageSNR forinreasingvalue

of the number of users,with

B D = 4

^{bits of feedbak per userand}

M = 2

transmitantennas. . . 113

5.5 Sum rate as a funtion of the average SNR for inreasing odebook size,

M = 2

^{transmitantennas,and}

K = 50

^{users. . . . . . . . . . . . . . . . . . . 114}

5.6 Sum rate performane as a funtion of the number of users for inreasing

odebook size,

M = 2

^{transmitantennas,andSNR =10dB. . . . . . . . . . 114}

5.7 SumrateversusthenumberofusersforwithSNR=20dB,

M = 2

^transmit

antennasand 10-bittotalfeedbak bits.

B D = 5

^{bitsareused forodebook}

indexing and (

B Q = 10 − B D

^{bits) forCQI} quantization. FormetriIV, 2 bitsareusedforquantizationofthehannelnormand3bitsforthealignment.115

5.8 Sumratevs. numberofusersfor

M

^{=2andSNR=10dB.. . . . . . . . . . 116}

5.9 Sumratevs. numberofusersfor

M

^{=2andSNR=20dB.. . . . . . . . . . 116}

5.10 Sum rate vs. numberof users in a systemwith optimal

B D /B Q

^balaning

fordierentSNRvalues. . . 117

6.1 Throughputomparisonasafuntionofwindowsize

W

^forsingle-beamRBF with

M = 2

^{antennas,SNR=10dBand}

K

^{=10ativeusers. . . . . . . . . 136}

6.2 Averagerateasafuntion ofthenumberofusersforsingle-beamRBFwith

M

^{=2antennas,SNR =10dBanddierentvaluesofwindowsize}

W

^{. . . . . 137}

6.3 Averagerateasafuntion ofthenumberof usersforsingle-beamRBFwith

M = 2

^{antennas, SNR = 10 dB,}

W

^{=1000 slots, and} ranking-based CQI metriquantizedwithdierentresolutions. . . 137

6.4 Sum rate as a funtion of the number of users for multi-beam RBF with

M = 2

^{antennas,SNR=10dBand}

W

^{=1000slots. . . . . . . . . . . . . . . 138}

6.5 Sumrateasafuntionofusersformulti-beamRBF inaheterogeneousnet-

work in whih users' average SNRs range from -10 dB to 30 dB,

M = 4

antennasand

W = 1000

^{slots. . . . . . . . . . . . . . . . . . . . . . . . . . . . 138}

6.6 Normalizedshedulingprobability vs. userindex formulti-beam RBFwith

M = 4

^{antennas and}

K = 10

^{users. Theusersaresorted fromthelowestto}

thehighestaverageSNR andtheSNRrangeisfrom-10dBto30dB. . . 139

3.1 IterativeBeamPowerControlAlgorithmforSum-RateMaximization . . . . 53

4.1 Memory-basedOpportunistiBeamformingAlgorithm . . . 72

4.2 GreedyUserSeletionwithStatistial CSIT. . . 79

4.3 ResoureAlloationAlgorithmwithStatistialCSIT . . . 84

5.1 GreedySemi-orthogonalUserSeletionwithLimitedFeedbak . . . 118

5.2 GreedyUserSeletionAlgorithmwithLimitedFeedbak . . . 118

Inthissetion, thenotationalonventionofthethesis issummarized. First,weprovidea

listof abbreviations, followedby anoverview ofthe notationof moregeneralnature. We

onludewiththenotationsthat aremorespeiforthisthesis.

Abbreviations and Aronyms

The abbreviations and aronyms used throughout the thesis are summarized here. The

meaningofanaronymisusuallyindiatedone,whenitrstoursinthetext.

3GPP ThirdGenerationPartnershipProjet

AMC AdaptiveModulationandCoding

AoA AngleofArrival

AoD AngleofDeparture

AP AessPoint

AWGN AdditiveWhiteGaussian Noise

BC BroadastChannel

BD BlokDiagonalization

BER BitErrorRate

BF Beamforming

BGI BeamGainInformation

bps bitsperseond

BS BaseStation

CCI ChannelCovarianeInformation

CDMA CodeDivision MultipleAess

CDF CumulativeDistributionFuntion

CDI ChannelDiretion Information

CMI ChannelMeanInformation

CQI ChannelQualityInformation

CSI ChannelState Information

CSIR ChannelStateInformation atReeiver

CSIT ChannelStateInformation atTransmitter

DMT DiversityMultiplexingTradeo

DPC DirtyPaperCoding

EVD EigenvalueDeomposition

FDD FrequenyDivision Duplex

GEV GeneralizedEigenvalue

HSDPA High-SpeedDownlinkPaketAess

i.i.d. independentandidentiallydistributed

i.ni.d. independentandnon-identiallydistributed

KKT Karush-Kuhn-Tukeroptimalityonditions

l.d. LimitDistribution

LOS Line-of-Sight

MAC MultipleAessChannel

MIMO Multiple-Input Multiple-Output

MISO Multiple-Input Single-Output

ML MaximumLikelihood

MMSE MinimumMean-SquareError

NLOS NonLine-of-Sight

OFDM OrthogonalFrequenyDivisionMultiplexing

OFDMA OrthogonalFrequenyDivisionMultipleAess

PDF ProbabilityDensityFuntion

PFS ProportionalFairSheduling

QoS QualityofServie

RBF Random(opportunisti)Beamforming

RHS RightHandSide

rms rootmeansquare

RVQ RandomVetorQuantization

SDMA Spae DivisionMultipleAess

SINR Signal-to-Interferene-plus-NoiseRatio

SISO Single-InputSingle-Output

SNR Signal-to-NoiseRatio

s.t. Subjetto

STC Spae-TimeCode

SVD SingularValueDeomposition

TDD TimeDivision Duplex

TDMA TimeDivision MultipleAess

THP Tomlinson-HarashimaPreoding

UCA UniformCirular Array

ULA UniformLinearArray

UMTS UniversalMobile TeleommuniationsSystem

VQ VetorQuantization

WLAN WirelessLoalAreaNetwork

WMAN WirelessMetropolitanAreaNetwork

ZF ZeroForing

WloG WithoutlossofGenerality

Notations

Thenotationsusedinthisdissertationarelistedinthissetion. Weuseboldfaeupper(e.g.

X

^{)andlowerase(e.g.}

x

^{)lettersformatriesandolumnvetors,}respetively. Plainletters

areused forsalarsand upperase alligraphiletters (e.g.

S

^{)denote sets. Nonotational}

distintionisused forarandomvariable andits realization. Othernotationalonventions

aresummarizedasfollows:

C

,

R

Thesetsofomplexandrealnumbers,respetively.

| x |

^{Theabsolutevalueofasalar.}

∠x

^{Thephaseofaomplexsalar(inradians).}

k x k

^TheEulidean(

ℓ ²

^)normofvetor

x k X k F

^{TheFrobeniusnormofmatrix}

X

⌈ x ⌉

^{Theeilingoperator,i.e. thesmallestintegernotlessthanx.}

∠( x , y )

^{Theanglebetweentwovetors}

x

^and

y

^.

|X |

^{The ardinality of theset}

X

^{, i.e. the numberof elementsin the nite}

set

X

^.

E {·}

^{Theexpetation operator.}

CN ( x , X )

^{The irularly symmetri omplex Gaussian} distribution with mean

x

andovarianematrix

X

^.

( · ) ^∗

^{Theomplexonjugateoperator.}

( · ) ^T

^{Thetransposeoperator.}

( · ) ^H

^{Theomplexonjugate}(Hermitian)transposeoperator.

X ^†

^TheMoore-Penrosepseudoinverseofmatrix

X

^.

X ^{− 1}

^{Theinverseofmatrix}

X

^.

I

^{Theidentitymatrix.}

Tr

( X )

^{Thetraeof matrix}

X

^{,i.e. thesumofthediagonalelements.}

vec(X)

^{Thevetorobtainedbystakingtheolumnsof}

X

^.

⊗

^{TheKronekermatrixprodut.}

O( · )

^{The big-Onotation, i.e.}

f (x) = O(g(x))

^as

x → ∞

ⁱ

∃ x 0 , c > 0

^suh

that

| f (x) | ≤ c | g(x) |

^for

x > x 0

^.

exp( · )

^Theexponentialfuntion.

log( · )

^{Thenaturallogarithm.}

log ₂ ( · )

^{Thebase 2logarithm.}

Thesis Spei Notations

Wesummarizeherethesymbolsandnotationsthat areommonly usedin thisthesis. We

havetriedto keeponsistentnotationsthroughout thedoument,but somesymbolshave

dierentdenitionsdepending onwhentheyourin thetext.

M

^{Numberoftransmitantennas}

N k

^{Numberofreeiveantennasat user}

k

^.

K

^{Numberof ativeterminals,i.e. theset of users}simultaneouslyasking

forservieduring onegivenshedulingwindow.

h _k

^{Thehannelfrombasestationto user}

k

^{(frequenyat).}

h ¯ _k

^{Thehannelofuser}

k

^{normalizedbyitsamplitude,i.e.}

h ¯ _k = h _k / k h _k k

^.

W

^{Thepreodingmatrix.}

w _k

^Thebeamformingvetorofuser

k

^.

Q

^An isotropiallydistributed unitarymatrix.

q

^An orthonormalvetor(beam),i.e. olumn of

Q

^.

n k

^{TheAWGNnoisevetorofuser}

k

^.

R ^k

^{Theahievablerateofuser}

k

^.

P

^{Themaximumtransmitpower.}

S

^{Thesetof seleted(sheduled) users.}

B

^{Thenumberofativebeams.}

γ k

^{TheCQIfeedbakofuser}

k

^.

ζ k

^{Thesheduling(deision)metriforuser}

k

^.

Introdution

1.1 Bakground and Motivation

The last deade the wireless industry has been onfronted with a galloping demand for

higherdata rates and enhanedquality of servie(QoS). The appliations oered to us-

tomers nowadays are no longer limited to voie transmission, but new types of servies,

suh as streaming multimedia, internet browsing, le transfer and video telephony, eah

withdierentQoSrequirements,areprovided. Thesuessstory ofellulartelephonyhas

openedthewaytothedevelopmentofvarioustypesof wirelesssystems,suhasloaland

metropolitanareanetworks(LAN,MAN),ad-hoandsensornetworks,short-rangewireless

protools, et. Thevariety ofwireless protools ombinedwith theinreasing demand for

dataservieshaveamendedthewireless servievisiontoananywhere-anytimebasis.

Theintrodutionofnewdataserviesisoneoftheunderlyingreasonsforthetransition

fromiruit-swithedsystemstopaket-swithednetworks. Networksaommodatingdelay-

tolerant, best-eort tra havenowevolved, oeringexibility to the resourealloation

unit to shedule transmissions in slots where the ommuniation link exhibits favorable

hannelonditions. Thisgivesriseto theso-alledmultiuserdiversity gain [1℄,whih aims

at abetter utilization ofthe spetruminside eahellat the expenseof userfairnessand

delay.

In addition to multiuser diversity, another key tehnology that eiently utilizes the

sarebandwidthresoureismulti-antennaommuniations. Multiple-InputMultiple-Output

(MIMO)tehniqueshavegenerated agreatdeal ofinterestdue to theirpotentialforhigh

spetraleieny,inreaseddiversity,andinterferenesuppressionapabilities. Asaresult,

the use of multiple antennas is envisioned in most of next-generation wireless protools,

inluding3GPPLongTermEvolution(LTE)[2℄,HighSpeedDownlinkPaketAess(HS-

DPA),IEEE802.16e(WiMAX)[3℄,andIEEE802.11n[4℄.

1.2 From Single-user to Multiuser MIMO Communia-

tions

The high throughput and diversity gains promised by point-to-point (single-user) MIMO

ommuniations are essentially ahieved via the use of diversity gain-oriented tehniques

(e.g. spae-time oding [5℄) ombined with rate maximization-oriented tehniques (e.g.

spatial stream multiplexing). Insuh atraditionalsingle-userviewof MIMO systems,the

extra spatial degreesof freedom brought bythe useof multiple antennas are exploited to

expandthe dimensionsavailable forsignalproessinganddetetion,thusatingmainly as

aphysiallayerperformanebooster. Inthisapproah,thelinklayerprotoolsformultiple

aess indiretlyreap theperformane benetsof MIMO antennas in theform of greater

per-user rates,ormorereliablehannelquality, despitenotrequiringfull awarenessof the

MIMO apability.

Reently,therehasbeenavividinterestintheroleofmultipleantennasinmultiusernet-

worksettings,andespeiallyinbroadastandmultipleaesssenarios.Themultipleaess

hannel(MAC),alsoreferredtoastheuplink,appliestosettingswheremanytransmitters

sendsignalstoonereeiverinthesamefrequenyband. Thebroadasthannel(BC),also

referredtoasdownlink,modelsanetworkinwhihabasestation(BS)ommuniates(sends

data)tomanyuserssharingthesamemedium. Investigationofthemorehallengingbroad-

asthannelliesattheoreofthisthesis. InmultiuserMIMOnetworks,thespatialdegrees

of freedom oered by multiple antennas an be advantageously exploited to enhane the

system apaity, by sheduling multiple users simultaneously by meansof Spae Division

MultipleAess(SDMA).Suhamultipleaessprotoolrequiresmoreomplexsheduling

strategies and transeivermethodologies, but does notinvolve any bandwidth expansion.

In spatial multiple aess, the resulting multiuser interferene is handled by the multiple

antennas,whihinadditiontoprovidingper-linkdiversityalsogivethedegreesof freedom

neessarytoseparateusersin thespatialdomain.

Reentinformationtheoretiadvanesrevealthattheapaity-ahievingtransmitstrat-

egyfortheMIMO broadasthannelistheso-alleddirtypaper oding (DPC)[68℄. How-

ever,this optimumtransmit strategy, whih involvesatheoretialpre-interferene anel-

lation tehniqueombined with an impliit usershedulingand power loadingalgorithm,

is highly omplex toimplement andsensitiveto hannelestimation errors. The apaity-

ahieving tehnique in MIMO broadast hannels revealed the fundamental role played

by the spatial dimension on multiple aess and sheduling, replaing the simplisti view

of MIMO as a pure physial layer tehnology. This gave rise to the development of the

so-alledross-layerapproahes, whihaimat thejointdesignofthephysiallayer'smod-

ulation/odingandlink layer'sresourealloationandshedulingprotools.

MultiuserMIMO tehniquesand theirperformane havebegunto beintenselyinvesti-

gatedbeauseofseveralkeyadvantagesoversingle-userMIMOommuniations. Inparti-

ular, multiuser MIMO shemes allowfor alinear inreasein apaity, proportional to the

number oftransmit antennas, thanksto their spatial multiplexing apabilities. Theyalso

appear more robust with respet to most of propagation limitations plaguing single-user

MIMOommuniations,suhashannelranklossorline-of-sight. Furthermore,thespatial

multi-antennaterminals, thereby allowing the development of small and heap terminals

whileintelligeneandostiskeptontheinfrastrutureside.

As everythinggood in life, nothing omes for free. All these promising results unfor-

tunatelyome at theritialassumption ofgoodhannelstateinformation at transmitter

(CSIT).MultiuserMIMOsystems,unlikethepoint-to-pointase,benetsubstantiallyfrom

CSIT, thelak ofwhih maysigniantlyredue thesystem throughput. This isbeause

withoutCSIT,theBSdoesnotknowinwhihdiretiontosendthebeams. IfaBSwith

M

transmitantennasommuniatingwith

K

single-antennareeivershasperfethannelstate information(CSI),amultiplexinggainof

min(M, K)

^{anbeahieved. Althoughtheapprox-}

imationoflosetoperfetCSIatthereeiver(CSIR)isoftenreasonable,thisassumptionis

oftenunrealistiatthetransmitterside. IftheBShasimperfethannelknowledge,thefull

multiplexinggainmayberedued,andinsettingswithompleteabseneofCSIknowledge,

themultiplexinggainollapsesto one. CSITaquisition seemstobethemost substantial

ost to pay in order to properly servethe spatially multiplexed users and boost the sys-

temapaityofmultiuserMIMOsystems. Insystemswherehannelreiproityannotbe

exploited oris proneto errors,the needfor CSIT feedbak plaes asigniantburden on

uplink apaity, exaerbatedin wideband ommuniations (e.g. OFDM) or high mobility

systems(suh as3GPP-LTE, WiMAX,et.).

Inthis dissertation, we fouson themulti-antennadownlinkhannel and aimat iden-

tifyingwhat kindofpartialCSIT, alsoreferredtoaslimitedfeedbak,anbeonveyedto

theBSinordertoahieveapaitylosetothatofthefullCSITase. Motivatedbyreent

keyndings, whih showthat linearpreoding strategieswith partial CSITanahievea

signiant fration of the full CSIT apaity if ombinedwith eient sheduling proto-

ols [912℄, we fous on low-omplexity, linear beamforming tehniques. We try to shed

somelight on theproblem of partial CSIT design by proposing several low-rate feedbak

strategiesthatallowtheBStoopewellwithlimitedhannelknowledgeandahievenear-

optimalsumrate. Aswewill see in thefollowinghapters,the roleof multiuser diversity

andopportunisti shedulingisinstrumental in ourapproahes. Ourthesisis that thanks

to the multiuser diversity gain, it is generally suient to feed bakone ortwo properly

designed salarfeedbak parametersin order to perform beamforming and user seletion

thatahievesthroughputrelativelylosetotheoptimumone.

1.3 Assumptions

Inaneortto provide alearand oniseframework to this work,wemakethefollowing

standardassumptions:

•

^{Singleellnetwork.}

Asingleellisonsideredandtheinter-ellinterfereneistreatedasnoise.

•

^{Perfethannel state}informationatthe reeiver.

Usersan estimateperfetlytheirhannels,sothat fullhannel stateinformationat

the reeiver(CSIR) is always assumed. CSIR is often obtained from pilot symbols

andblindhannelestimationtehniques,espeiallyindownlinkhannels,wherepilot-

pilothannel. Thisassumptionmaybequestionedinhigh-mobilitysettingsandresults

insigniantoverheadinwideband systems.

•

^{Narrowbandhannels}

Flat-fadinghannels are onsidered,i.e. thesignalbandwidthis muh lessthan the

reiproal of the propagation time of the wavefront aross the antennaarray. Our

proposedmethodsanbeeasilyappliedonapersubarrierbasisinwidebandOFDM

systems.

•

^{Ideal link}adaptation.

Ideallinkadaptationprotoolsareassumedandtheontinuous-rate,ontinuous-power

Shannonapaityformulaisalulatedasuserthroughputmeasure. Thisisareason-

ableassumptionsineurrentpowerfulodingshemesanperformlosetoShannon

limit. Furthermore,theSNR-gapifpratialodingandmodulationshemesareused

doesnotaetthesum-ratesalingof theproposedtehniques.

•

^{Innitebaklogged users.}

An innite baklog of pakets in eah queue is assumed, thus the base station has

alwaysdata to transmitto theseleted(sheduled) users. Sine theresourealloa-

tionpoliiesare studied from athroughputmaximizationpoint ofview, queuestate

informationandtraarrivalproesseshavebeennegleted.

1.4 Contributions and Outline of the Dissertation

Foreword: This dissertation stems from an ANRT CIFRE (Convention Industrielle de

FormationparlaReherhe/IndustrialAgreementforTrainingthroughResearh)agreement

betweenTeleomParisTeh/EURECOM,Sophia-Antipolis, andtheRadioAessNetworks

(RESA)groupatFraneTeleomResearhandDevelopment,Paris. Theondutedresearh

workwas fullyfundedbyFraneTeleomResearh andDevelopment (OrangeLabs).

Themain fous ofthe thesisis user seletionand linear preoding in multiuser multi-

antennasystemswithlimitedfeedbak. Weprovidebelowanoutlineofthedissertationand

desribetheontributionsmadeineahhapter.

Chapter 2-Multi-antennaBroadast Channels

Inthis hapter,wereviewreentfundamental ndingsin MIMO broadasthannels. The

general multi-antenna system model is introdued and apaity results for the broadast

hannelarepresentedunderdierentassumptionsonthequality/amountofCSIT.Weem-

phasizeontheardinalimportaneofCSITandtheroleofmultiuserdiversityforahieving

losetooptimumapaity. Capaitysalinglawsforopportunistishedulingunder dier-

ent hannel statistial distributions are provided. The apaity growth for networks with

path loss and fading is a ontribution of this hapter. Finally, we present in detail lin-

earpreodingstrategiesombinedwithshedulingusing limitedfeedbak,whihforms the

building blokofthedissertation. Theadvantages anddrawbaksof thissetting areiden-

tied, motivatingourworkand thesolutionsproposed inthesubsequenthapters. Partof

•

^D.Gesbert,M.Kountouris,R.W.Heath,Jr.,C.-B.Chae,andT.Sälzer,"FromSingle Userto MultiuserCommuniations: Shiftingthe MIMO Paradigm,"in IEEE Signal

ProessingMagazine,Speial IssueonSignalProessingforMultiterminalCommun.

Systems,vol.24,no.5,pp. 36-46,Sept. 2007.

Chapter 3- Enhaned MultiuserRandomBeamforming

Theontributionsofthishapteraretwo-fold: Intherstpart,weprovideanunpublished

exatsum-rateanalysis of onventionalrandom beamforming (RBF)[9℄. Capaitysaling

lawsfortheinterferene-limitedregion(highSNR)arederivedusingextremevaluetheory,

showingtheardinalimportaneofmultiuserdiversityinthisregime. Intheseondpart,a

limitedfeedbak-basedshedulingandbeamformingsenariothatbuildsonRBFisonsid-

ered. Weintrodueatwo-stageframeworkthatdeouplestheshedulingandbeamforming

designproblems in twophases. Several renementstrategies, inluding beam poweron-

trolandbeamseletion,areproposed,oeringvariousfeedbakredutionandperformane

tradeos. TheommonfeatureoftheseshemesistorestorerobustnessofRBFwithrespet

tosparsenetworksettings(lowtomoderatenumberofativeusers),attheostofmoderate

omplexityinrease.

Theworkin thishapterhasbeenpublished in:

•

^{M. Kountouris and D. Gesbert,} "Robust multi-user opportunisti beamforming for sparse networks," in Pro. 6th IEEE Workshop on Signal Proessing Advanes in

WirelessCommuniations(SPAWC2005),pp. 975-979,NewYork,USA,June5-8,

2005(invitedpaper).

andwillappearin:

•

^M.Kountouris,D.Gesbert,andT.Sälzer,"EnhanedMultiuserRandomBeamform- ing: Dealingwiththenotsolargenumberofusersase,"IEEEJournalonSel. Areas

inCommuniations(JSAC),SpeialIssueonLimitedFeedbakWirelessComm. Net-

works,Ot. 2008.

Chapter 4- ExploitingChannel Struture in MIMO Broadast Channels

Inthis hapter,we onsidermultiuser MIMO hannels orrelatedin either time orspatial

domain,and provideseveraltehniquesthat inreasethesystemthroughputbyexploiting

thehannel struture. Intime orrelatedhannels, anopportunisti beamforming sheme

exploitinghannelmemoryisproposed. Thisshemeisshowntolltheapaitygap with

optimum unitary preoding with full CSIT for slow time-varying hannels. In spatially

orrelated hannels, a maximum likelihood (ML) oarse hannel estimation framework is

established,whih eetivelyombines slowlyvaryingstatistial CSIT -assumedavailable

atthetransmitter -with instantaneouslow-ratefeedbak. A greedyuserseletion sheme

andalow-omplexitySDMA eigenbeamformingtehniquebasedonmultiuser interferene

bounds are also proposed and evaluated. It is demonstrated that, in wide-area ellular

networks,salarCSITfeedbakissuienttoahievenear-optimalthroughputperformane

ifitisproperlyombinedwithlong-termstatistialknowledge.

Theworkin thishapter hasbeenpublished in:

•

^{M.KountourisandD.Gesert,}"Memory-basedopportunistimulti-userbeamforming,"

in Pro. of IEEEInternationalSymposium onInformation Theory (ISIT2005), pp.

•

^M. Kountouris, D. Gesbert, and L. Pittman, "Transmit Correlation-aided Oppor- tunistiBeamformingandSheduling,"in Pro. of14thEuropeanSignalProessing

Conferene(EUSIPCO),Florene,Italy,September4- 8,2006(invitedpaper).

•

^{D.Gesbert,L.Pittman,andM.}Kountouris,"TransmitCorrelation-aidedSheduling inMultiuserMIMONetworks,"inPro. IEEEInternationalConfereneonAoustis,

Speeh, andSignalProessing(ICASSP2006),Vol.4,pp. 249-252,Toulouse,Frane,

May14-19,2006.

•

^M. Kountouris, R. de Franiso, D. Gesbert, D.T.M. Slok, and T. Sälzer, "Low omplexityshedulingandbeamformingformultiuserMIMO systems,"in Pro. 7th

IEEEWorkshoponSignalProessingAdvanesinWirelessCommuniations(SPAWC

2006),Cannes,Frane,July2-5,2006.

Chapter 5-LimitedFeedbak Broadast Channelsbased on Codebooks

Thishapterdealswithlimitedfeedbakstrategiesutilizingvetorquantizationodebooks.

In partiular, the problem of eient, sum-rate maximizing hannel quality information

(CQI) feedbak design is addressed. We proposed several salar feedbak metris that

inorporate information on the hannel gain,the hannel diretion, and the quantization

error. Thesemetrisarebuiltuponboundsontheinstantaneousinter-userinterferene,and

anbeinterpreted asreliableestimatesofthe reeived SINR.It is shown thatsalar CQI

feedbakombined withhanneldiretional information (CDI) andeientuser seletion

algorithmanahieveasigniantfrationoftheapaityofthefullCSITasebyexploiting

multiuser diversity. An adaptive sheme transiting from SDMA to TDMA transmission

modeisproposedandisshowntoahievelinearsum-rategrowthatanySNRrange.

Theworkin thishapterhasbeenpublished in:

•

^M.Kountouris,R. deFraniso, D. Gesbert, D.T.M.Slok, andT.Sälzer, "Eient metrisforshedulingin MIMObroadasthannels withlimitedfeedbak,"in Pro.

IEEEInternationalConfereneonAoustis,Speeh,andSignalProessing(ICASSP

2007),Honolulu,USA,April15-20, 2007.

•

^M.Kountouris,R.deFraniso,D.Gesbert,D.T.M.Slok,andT.Sälzer,"Multiuser diversity-multiplexingtradeoinMIMObroadasthannelswithlimitedfeedbak,"

inPro. of40thAsilomarConfereneonSignals,Systems&Computers,PaiGrove,

CA,USA,Ot. 29-Nov. 1,2006(invitedpaper).

andaeptedto:

•

^M.Kountouris,R.deFraniso,D.Gesbert,D.T.M.Slok,andT.Sälzer,"Exploiting MultiuserDiversityin MIMOBroadastChannelswithLimitedFeedbak,"aepted

toIEEETrans. onSignalProessing,August2007(underrevision).

Chapter 6-Feedbak Redution using Ranking-basedFeedbak

In this hapter, a low-rate representation of CSIT feedbak parameters, referred to as

ranking-based feedbak, is identiedas ameansto further ompress thereported hannel

feedbak. This representation enables the sheduler to identify users that are instanta-

neouslyonthehighestpeakwithrespettotheirownhanneldistributions,independently

restoredin heterogeneousnetworks withi.ni.d. hannel statistisamong users. Thework

inthishapterhasbeenpublishedin:

•

^M.Kountouris,T.Sälzer,andD.Gesbert,"ShedulingforMultiuserMIMODownlink Channels with Ranking-based Feedbak," EURASIP Journalon Advanes in Signal

Proessing,SpeialIssueonMIMOTransmissionwithLimitedFeedbak,Marh2008.

Chapter 7- SystemAspets in MultiuserMIMO Systems

Thishapterfousesonseveralsystemissuesanddesignhallengesthatariseinreal-world

wireless systems. We disuss the main pratial and implementation hallenges that one

mayfaewhendeployingtehniquesasthoseproposedinChapters3-6. Emphasisisputon

fairnessissuesand theproportionalfairsheduling(PFS)rule isgeneralizedformultiuser

systemsettings,inludingOFDM,SDMA,multiellnetworks,et. Partoftheseresultshas

beenpublishedin:

•

^{M.Kountourisand D. Gesbert,} "Memory-based opportunisti multi-user beamform- ing,"in Pro. ofIEEEInternationalSymposiumonInformationTheory(ISIT2005),

pp. 1426-1430,Adelaide,Australia,September4-9,2005.

Patents

Inadditionto theabovepubliations,ourresearhwork resultedin thefollowingpatents:

•

^PCTWO2007057568,"Informationenodingforabakwardhannel,"(assigned)

•

^{FR 2893474,} "Method of information enoding for abakwardhannel of a SDMA system,userterminalandbasestationofsuhasystem," (assigned).

•

"Feedbakommuniationfrom aterminalto atransmitter toredue inter-beamin- terferene,"(led,Jan. 2008).

Multi-antenna Broadast

Channels

In this hapter, we review multiuser MIMO ommuniations fousing on the more hal-

lengingdownlink,theso-alledbroadasthannel(BC).Thegeneralmulti-antennasystem

modelisintroduedandknownapaityresultsforthebroadasthannelarepresentedun-

derdierentassumptionsregardingtheamountofCSIT.Informationtheoretiresultsshed

lightontheardinalimportaneofCSITandsheduling,aswellasontheroleofmultiuser

diversityforahievingtheoptimumsystemapaity. Capaitysalinglawsforopportunisti

sheduling under dierent hannel models are investigated. Several approahes inluding

non-linearand linearhannel-awarepreodingare reviewed, disussingdesign hoiesand

performane tradeos. Emphasis is given on low-omplexity, linear preoding strategies

ombinedwithshedulingusinglimitedfeedbak,whihformthebuildingblokofthedis-

sertation.Thelimitedfeedbakmodelthatweadoptandinvestigateinsubsequenthapters

ispresentedindetailanditslimitationsareidentied.

2.1 The Wireless Channel

Thewireless radiohannel isapartiularlyhallengingmediumforreliablehigh-rateom-

muniations. Apartfrombeingsubjettonoise,interfereneandseveralotherimpairments,

thewireless medium is aboveall amultipath time-varying hannel. A signaltransmitted

overaradio hannel issubjetto thephysial lawsof eletromagnetiwavetheory, whih

ditatethat multiplepaths ourasaresultofreetion onlargesurfaes(e.g. buildings,

walls, and ground), diration on edges, and sattering on various objets. Therefore, a

reeived signal is a superposition of multiple signalsarriving from dierent diretions at

dierent time instanes and with dierent phases and power. These paths may ombine

onstrutively or destrutively, reating a multi-tap hannel impulse response, with eah

tap havingrandom phase and time-varying amplitude. We rst review the physial phe-

nomena that attenuate the signalpower. Foramoredetailed presentation,the interested

readerisreferredto [13℄.

2.1.1 Path loss

Pathlossisarange-dependenteetandisduetothedistane

d

^{betweenthereeiverandthe}

transmitter. Inidealfreespae,thereeivedsignalpowerisdesribedbytheFriisequation

and follows aninverse square lawpowerloss. Several deterministiand empirial models

have been developed for various ellular environments (miroells, maroells, pioells,

et.), suh as Okumura-Hata, Walsh-Ikegami, and their COST-231 extensions, plane-

earthandlutter fatormodel[13℄. Ageneripathlossmodelisgivenby

L = βd ^{− ǫ}

^(2.1)

where

ǫ

^{isthepathlossexponentand}

β

^{isasalingfatorthataountsforantennahar-}

ateristis and average hannel attenuation. The pathlossexponentvaries normallyfrom

2to6,dependingonthepropagationenvironment. Fortheaseof fullspeularreetions

from groundis4,whileforbuildingsandindoorenvironmentsitantakevaluesfrom4to

6.

2.1.2 Shadowing

Shadowing, also known as marosopi or long-term fading, results from large obstales

blokingthemain signalpathbetweenthe transmitterandreeiver,and isdetermined by

theloalmeanofafastfadingsignal. Therandomshadowingeets,whihareinuened

by antennaheights, operatingfrequenyand thefeaturesof thepropagationenvironment,

maybemodeled aslog-normaldistributedwithprobabilitydensityfuntion (PDF):

p(x) = 1 xσ √

2π e ^{(log 2σ x−µ)2 2} x > 0

^(2.2)

where

µ

^and

σ

^{arethemeanandstandarddeviationofthe}shadowing'slogarithm.

2.1.3 Fading

Fading,oftenreferredtoasmirosopiorsmall-salefading, resultsfrom theonstrutive

ordestrutivesuperpositionofmultipathsanddesribestherapidsignalutuationsofthe

amplitudes,phases,ormultipathdelays. Thestatistialtimevaryingnatureofthereeived

envelopeisommonlydesribedbythefollowingthree fadingdistributions:

Rayleighfading

Rayleighfading is areasonable model when there is nodominantpropagation path (non

line-of-sight, NLOS) betweenthe transmitter andthe reeiverandis used to desribe the

amplitude ofasignalwhen there is alargenumberof independentsattered omponents.

Applying the entral limit theorem, the hannel impulse response an be onsidered asa

omplex-valued Gaussian proessirrespetiveof thedistribution of the individual ompo-

phaseevenlydistributedbetween0and2

π

^{radians. Theenvelopeofthereeivedsignalwill}

thereforebeRayleighdistributed withPDFgivenby

p(x) = 2x Ω e ^{− x}

2

Ω x > 0

^(2.3)

where

Ω = E { x ² }

^{istheaveragereeivedpower.}

Rieanfading

Ifadiret,possiblyaline-of-sight(LOS),pathexists,theassumptionofazero-meanfading

proess does no longer hold and the distribution of the signal amplitude is modeled as

Riean. The Riean distribution is often dened in terms of the Riean fator

K

^whih

denotestheratio ofthepowerin the meanomponentofthehannel(diret path)to the

powerin thesatteredpaths. TheRieanPDFisgivenby

p(x) = 2x(K + 1)

Ω e ^{− K − (K+1)x}

2

Ω I 0 2x

r K(K + 1) Ω

!

x > 0

^(2.4)

where

Ω = E { x ² }

^and

I 0 (x)

^{is the zero-order modied Bessel funtion of the rst kind}

denedas

I 0 (x) = 1 2π

Z 2π 0

e ^{− x cos θ} dθ

^(2.5)

Nakagami fading

Ageneralfading distributionthat ts wellwith empirialmeasureddata is theNakagami

distributiongivenby

p(x; m) = 2m ^m x ^{2m − 1}

Γ(m)Ω e ^{− mx Ω 2} x > 0

^(2.6)

where

Ω

^{is the average reeived powerand}

m = _{E{ x} 2 ^Ω − ² Ω ² }

^{. The}

m

^{fator determines the}

severityof fading, i.e. for

m = ∞

^{there isno fading. For}

m = 1

^the distribution in (2.6) reduestoRayleighfading,whilefor

m = (K+1) ² /(2K+1)

^thedistributionisapproximately Rieanfadingwithfator

K

^.

2.1.4 Channel Seletivity

Multipathpropagationresultsinthespreadingofthesignalindierentdimensionsaeting

signiantlythereeivedsignal. These dimensionsaretime(Dopplerspread),spae(angle

spread)andfrequeny(delayspread).

Dopplerspread and timeseletive fading

Themotionof thetransmitter,thereeiverorthesatterersresultsin timeseletivity, i.e.

a single tone spreads in frequeny over a nite spetral bandwidth. The variations due

to Doppler shiftsare spei to eah path anddepend on their angle with respet to the

movingdiretion ofthetransmitter/reeiver. DierentDopplershiftsleadto theso-alled

Dopplerspread, whih is themaximumfrequenyspread amongall Dopplershifts, and is

givenby

f m = v λ c

(2.7)

where

v

^{isthemobilespeedand}

λ c

^isthearrierwavelength.

Howfastthehanneldeorrelateswithtimeisspeiedbythetemporalautoorrelation

funtion. The Doppler power spetrum

ρ d (f d )

^{is dened as the Fouriertransform of the}

temporalautoorrelationfuntion ofthehannelresponseto aontinuouswave

ρ d (f d ) =

( ₁

πf m √

1 − (f d /f m ) ² ∀ f d ∈ [ − f m , f m ]

0

^elsewhere

(2.8)

ThemostommonlyusedmodelfortheautoorrelationfuntionistheClarke-Jakes'model,

whihassumesuniformlydistributedsatterersonairlearoundtheantenna

ρ d (τ) = J 0 (2πf m τ)

^(2.9)

where

J k

^{isthek-thorderBesselfuntionoftherstkindand}

τ

^{isthesampling interval.}

Ameasureofthetimeseletivityisthehanneloherenetime

T c

^{,denedastheinterval}

over whih the hannel remains stronglyorrelated. The shorter the oherene time, the

fasterthehannelhangesovertime. Theoherenetimeisastatistialmeasureandsatises

T c ∼ 1 f m

(2.10)

AsweshowinChapter4,theshedulerantakeadvantageofthetimeseletivityandbenet

fromtheresultinghannelredundany(timediversity),asameanstofurtherompressthe

hannelfeedbakorsuessivelyrenetheshedulingdeisions.

Delay spread and frequeny seletivefading

Delayspreadis aused whenseveral delayedand saled versions of thetransmitted signal

arriveatdierenttimeinstantsatthereeiver. Thetimedierenebetweenthemaximum

multipath delay

τ max

^{(typiallythearrivaltimeof theLOS omponent)andtheminimum}

pathdelay

τ min

^{isalleddelayspread. Delayspreadausesfrequenyseletivefadingasthe}

hannelatslikeatapped-linelter. Therangeoffrequeniesoverwhihthehannelanbe

onsidered`at'denestheoherenebandwidth

B c

^{anddependsontheform ofthepower}

delay spetrum (rms delay spread). A hannel is haraterized as at orfrequeny non-

seletiveifthesignalbandwidth

B

^{issigniantlysmallomparedtothehanneloherene}

time, i.e.

B << B c = 1/τ max

^{. Inthe subsequent hapters,only at fading hannelsare}

onsidered.

Angle spread and spae-seletivefading

Angle spreadat thereeiver/transmitterrefersto thespreadin angles ofarrival(AoAs) /

angles of departure (AoDs) of the multipath omponent at the reeive/transmit antenna

array,respetively. Thedierentdiretions ofarrivalleadtospatialseletivitythat implies

that signalamplitudedependsonthespatialloationoftheantennaarray. Spaeseletive

fadingisharaterizedbytheoherenedistane

d c

^{,whihisthemaximumdistanebetween}

two antenna elementsfor whih the fading remains strongly orrelated. An upperbound

fortheoherenedistaneisgivenby

d c ≤ λ c

2 sin(∆θ max /2)

^(2.11)

where

∆θ max

^{isthemaximumangle}separation,i.e. therangein whihthepowerazimuth spetrumisnonzero.

2.2 Multiple-Input Multiple-Output Channels

Multiple-InputMultiple-Output(MIMO)hannelsariseinmanydierentsenariossuhas

multi-antennawirelesssystemsorwirelinesystems(e.g. DSL),andanberepresentedinan

elegant,ompat,anduniedwaybyahannelmatrix.Thebasidisrete-time,narrowband

signalmodel forapoint-to-pointMIMOhannel with

M

^transmitand

N

^{reeiveantennas}

isgivenby

y = Hx + n

^(2.12)

where

x ∈ C ^{M × 1}

isthetransmittedsymbol,

H ∈ C ^{N × M}

isthehannelmatrix,

y ∈ C ^{N × 1}

is thereeivedsignal,and

n ∈ C ^{N × 1}

isthenoisevetor. Weassumezero-meanirularlysym- metriomplexGaussian noisewith ovarianematrix

R n

^{1. Foronveniene, a whitened}

hannel

H ˜ = R ⁻ n ^1/2 H

^{isoften usedsuh that thewhitenoise}

w = R ⁻ n ^1/2 n

^hasaunitary

ovarianematrix, i.e.

E { ww ^H } = I

^{. Due tothenoise}normalization, thetransmitpower onstraint

P = T r( E { xx ^H } )

^takesontheinterpretationoftheaveragesignal-to-noiseratio (SNR)perreeiveantennaunderunityhannelgain. Knowledgeofthehannelgainmatrix

H

^atthe transmitterand reeiveris referredto ashannel stateinformation atthe trans-

mitter (CSIT)andhannel stateinformationatthe reeiver (CSIR),respetively.

x ₁

x ₂

x _M

y ₁

y ₂

y _N h 11

h 21

h N1

h 12

h 22

h N2

h 1M h 2M

h NM

Figure2.1: Multiple-InputMultipleOutput ChannelModel.

Intheaseofafrequeny-atMIMO system,thehannelhasonlyonetapand anbe

representedasadisrete-timehannelmatrix

H[n] =













h 11 [n] h 12 [n] . . . h 1M [n]

h 21 [n] h 22 [n] . . . h 2M [n]

.

.

.

.

.

. .

.

. .

.

.

h N 1 [n] h N2 [n] . . . h N M [n]













(2.13)

1

Aomplexrandomvetor

x

^{isirularlysymmetriifits}distributionisthesamewiththedistribution of

e ^jθ x

^,

∀θ ∈ [0, 2π]

^{. For}

θ = π

^wehave

E{x} = 0

^{and for}

θ = π/2

^,

x

^{isa proper random vetor,i.e.}

E{ xx ^H } = 0

^.