Multiuser Multi-Antenna Systems with Limited Feedback

HAL Id: pastel-00004259

https://pastel.archives-ouvertes.fr/pastel-00004259

Submitted on 10 Apr 2009

HAL is a multi-disciplinary open access

archive for the deposit and dissemination of

sci-entific research documents, whether they are

pub-lished or not. The documents may come from

teaching and research institutions in France or

abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est

destinée au dépôt et à la diffusion de documents

scientifiques de niveau recherche, publiés ou non,

émanant des établissements d’enseignement et de

recherche français ou étrangers, des laboratoires

publics ou privés.

Feedback

Marios Kountouris

To cite this version:

Marios Kountouris. Multiuser Multi-Antenna Systems with Limited Feedback. domain_other.

Télé-com ParisTech, 2008. English. �pastel-00004259�

Institut Euré om

THESIS

In Partial Fulllmentof the Requirements

for the Degree of Do tor of Philosophy

fromE ole Nationale Supérieure

des Télé ommuni ations

Spe ialization: Communi ations and Ele troni s

Marios Kountouris

Multiuser Multi-antenna Systems with Limited Feedba k

President Jean-ClaudeBelore,ENST(Paris,Fran e)

Reviewers ConstantinosPapadias,AIT (Athens,Gree e)

MérouaneDebbah,Supéle (Gif-sur-Yvette,Fran e)

Examiners AnaIsabelPérez-Neira,UPC (Bar elona,Spain)

ThomasSälzer, Fran eTele omR&D(Paris,Fran e)

Thesisadvisor DavidGesbert,EURECOM Institute(Sophia-Antipolis,Fran e)

January

10

th

Institut Euré om

THESE

Présentée pour obtenir leGrade de Do teur

de l'E ole Nationale Supérieure

des Télé ommuni ations

Spé ialité: Communi ationset Ele tronique

Marios Kountouris

Systèmes multi-antennes multi-utilisateurs

ave voie de retour limitée

Président Jean-ClaudeBelore,ENST (Paris,Fran e)

Rapporteurs ConstantinosPapadias,AIT(Athènes,Grè e)

MérouaneDebbah,Supéle (Gif-sur-Yvette,Fran e)

Examinateurs AnaIsabelPérez-Neira,UPC(Bar elone,Espagne)

ThomasSälzer, Fran eTele omR&D(Paris,Fran e)

First and foremost, I would like to express my deepest gratitude to my advisor and

friend Prof. David Gesbert for his brilliant supervision and his ontinual guidan e and

supportthroughoutmyPh.D years. Without histe hni alinsight, reativityandon-going

en ouragement,thisthesiswouldhaveneverbeenpossible. Ithasbeenarealpleasureand

privilegetohavehad Davidasamentor.

Iwouldliketoa knowledgeFran eTele omR&Dforthenan ialsupportofmywork.

Aspe ial andwarmthanktomyindustrial supervisorDr. ThomasSälzer, forhissupport,

insights,and onstru tive riti ismaswellasforprovidingtheproper onditionstopursue

my resear h. I would also like to thank Anne-Gaële A x for hostingme in hergroup, as

wellasalltheteammemberswithwhomIintera tedduringmyseven-monthstayinFran e

Tele om'slabinParis.

IamverygratefultoProf.ConstantinosPapadiasandProf.MérouaneDebbahfortaking

thetimetoreadtherstversionofmydissertationandtoserveasreaders. Iwouldalsolike

tothankProf. JeanClaudeBeloreandProf.Ana Pérez-Neirafora eptingtobepartof

mythesis ommittee. Theinvaluablefeedba kofallthePh.DJurymembersisenormously

appre iated.

Iwouldliketoexpressmyappre iationtomy olleaguesandfriendsatEure omInstitute

fortheex ellent andtruly enjoyableambian e. Spe ial thanksgoto Ruben deFran is o,

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

my o-authorsProf.DirkSlo kandRubendeFran is o. Partofthisthesiswouldnothave

been possible withouttheir stimulatingdis ussions and help. Mywarmest thanksextend

tomydear friends, in Fran e, ba kin Gree e and in manyother ornersof theglobe, for

alltheunforgettableandmomentsIsharedwiththem overtheyears. Iwouldliketotake

the han e tothank alltheinvaluabletea herswhogotme ex itedaboutengineeringand

mathemati s. IwouldliketosingleoutEmeritusProf.JohnE.Diamessisforbeingsu han

inspiringa ademi rolemodel.

Finally,I wanttoexpress mygratitudeto myparentsand mybrotherfortheir

un on-ditional love, patien e, and boundless en ouragement. I am also deeply indebted to my

grandparentsfortheirsupportandfor ultivatingmy uriosityforthesurroundingworld.

MariosKountouris

Sophia-Antipolis

The use of multiple antennas has beenre ognized as akeyte hnology to signi antly

improve the spe tral e ien y of next-generation, multiuser wireless ommuni ation

net-works. In multiusermultiple-input multiple-output (MIMO) networks, thespatial degrees

of freedom oered by multiple antennas anbe advantageously exploited to enhan e the

system apa ity, by s hedulingmultiple users simultaneouslyby meansof spatial division

multiple a ess (SDMA). A linearin rease in throughput, proportionalto the number of

transmitantennas, an be a hievedeven by using linear pre oding strategies if ombined

withe ientlydesigned s hedulingproto ols. However,these promisinggains omeunder

theoftenunrealisti assumptionof lose-to-perfe t hannelstateinformation atthe

trans-mitter(CSIT).Therefore,attheheartofthedownlinkresour eallo ationproblemliesthat

offeedba ka quisition.

In this thesis, we fo us on linear beamforming te hniques relying on low-rate partial

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

limited hannelknowledgeareidentied. Onerstkeyideaisbasedonsplittingthedesign

betweenthe s hedulingand thenal beamdesignstages, thus taking prot from thefa t

the number of users to be served at ea h s heduling slot is mu h smaller than the total

numberof a tiveusers. Thistwo-stageapproa h isapplied toas enarioin whi h random

beamforming(RBF)isexploitedtoidentifygood,spatiallyseparable,usersintherststage.

Inthese ond stage,severalrenementstrategies,in ludingbeampower ontrolandbeam

sele tion,areproposed,oeringvarious feedba kredu tionand signi antsumrategains,

eveninsparsenetworksettings(lowtomoderatenumberof users).

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

do-main,wepointoutthatsigni antusefulinformationfortheSDMAs hedulerlieshiddenin

the hannel stru ture. We showhowmemory-basedRBF anexploit hannel redundan y

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

CSITforslowtime-varying hannels. Inspatially orrelated hannels,long-termstatisti al

CSIT,whi h anbeeasilyobtainedwithnegligibleper-slotornofeedba koverhead,reveals

informationaboutthemeanspatialseparabilityofusers. Amaximumlikelihood(ML)

han-nelestimationframeworkisproposed,whi hee tively ombines slowlyvaryingstatisti al

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

beamforming te hniques suitable for su h settings are also proposed. It is demonstrated

thatinsystemswithreasonablylimitedanglespreadattheBS,feedingba kasingles alar

CQIparameterperuseris su ient to perform SDMA s heduling andbeamforming with

Limitedfeedba kstrategiesutilizingve torquantization odebooksarealsoinvestigated.

In parti ular, the problem of e ient, sum-ratemaximizing CQI design is addressedand

several s alarfeedba k metri s are proposed. These metri s are built upon inter-user

in-terferen e bounds and an be interpreted as reliable estimates of the re eived

signal-to-interferen e-plus-noise ratio(SINR)at there eiverside. Itis shownthat s alarCQI

feed-ba k ombinedwith hanneldire tionalinformation(CDI),zero-for ingbeamforming,and

greedy user sele tion algorithms an a hieve a signi ant fra tion of the apa ity of the

full CSIT ase by exploiting multiuser diversity. An e ient te hnique that provides the

BStheexibilitytoswit hfrommultiuser(SDMA)tosingle-user(TDMA)transmissionis

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

Further feedba k ompression an be a hievedif the CSIT informationutilized by the

s hedulerisrepresentedbyranking-basedfeedba k. Weshowthatanintegervalueisoften

su ientinordertoidentifyuserswithfavorable hannel onditions. Inparallel,itequalizes

the hannel a ess probabilityin networks where users' hannels arenot ne essarily

iden-ti ally distributed andmobile terminalsexperien e unequalaverageSNRs due todierent

A knowledgements . . . i

Abstra t . . . iii

ListofFigures . . . ix

ListofTables . . . xiii

Nomen lature . . . xv

Résumé . . . 1

1 Introdu tion 3 1.1 Ba kgroundandMotivation . . . 3

1.2 FromSingle-userto MultiuserMIMO Communi ations. . . 4

1.3 Assumptions . . . 5

1.4 ContributionsandOutlineoftheDissertation . . . 6

2 Multi-antenna Broad ast Channels 11 2.1 TheWirelessChannel . . . 11

2.1.1 Pathloss . . . 12

2.1.2 Shadowing . . . 12

2.1.3 Fading. . . 12

2.1.4 ChannelSele tivity. . . 13

2.2 Multiple-Input Multiple-OutputChannels . . . 15

2.3 MultiuserMulti-AntennaSystems . . . 16

2.3.1 Multi-antennaChannelModeling . . . 17

2.4 Capa ityofMIMO Broad astChannels . . . 20

2.4.1 Capa itywithperfe tCSI atthetransmitter . . . 20

2.4.2 Capa itywithnoCSIat thetransmitter. . . 22

2.5 MultiuserMIMOS hemeswithperfe tCSIT . . . 23

2.5.1 Non-linearPre oding. . . 23

2.5.2 LinearPre oding . . . 24

2.6 The ardinalroleof ChannelStateInformation . . . 27

2.6.1 ChannelKnowledgeattheTransmitter . . . 27

2.6.2 Capa itys alinglawsin MIMOBCsystems. . . 28

2.6.3 PartialChannelStateInformation . . . 30

2.6.4 Statisti alChannelKnowledgeattheTransmitter . . . 30

2.7 S hedulingandMultiuserDiversity . . . 31

2.7.1 Asymptoti Sum-rateAnalysiswithOpportunisti S heduling. . . 32

2.8.1 Quantization-basedte hniques . . . 34

2.8.2 Dimensionredu tionandproje tionte hniques . . . 34

2.9 LinearPre odingandS hedulingwith LimitedFeedba k. . . 35

2.9.1 FiniteRateFeedba kModelforCDI . . . 35

2.9.2 Codebook design . . . 36

2.9.3 RandomOpportunisti Beamforming. . . 38

3 Enhan ed MultiuserRandomBeamforming 41 3.1 Introdu tion. . . 41

3.2 Sum-RateAnalysisofRandomBeamforming . . . 43

3.3 Capa itys alinglawsforhighSNR . . . 46

3.4 Two-StageS hedulingandLinearPre oding . . . 49

3.5 Enhan edMultiuserRandomBeamforming . . . 50

3.6 Enhan edPre oding withperfe tse ond-stageCSIT . . . 51

3.7 BeamPowerControlwithBeam GainInformation . . . 51

3.7.1 OptimumBeamPowerAllo ationforTwoBeams. . . 52

3.7.2 BeamPowerAllo ationformorethantwobeams. . . 54

3.7.3 BeamPowerControlin Spe i Regimes(

B ≥ 2

) . . . 57

3.8 BeamPowerControlwithSINRfeedba k . . . 59

3.9 Performan eEvaluation . . . 60

3.10 Con lusion . . . 64

3.A ProofofLemma 3.1 . . . 66

3.B ProofofLemma 3.2 . . . 66

3.C ProofofLemma 3.3 . . . 67

3.D ProofofCorollary3.2 . . . 67

3.E ProofofTheorem3.1. . . 67

3.F ProofofTheorem3.2. . . 68

3.G ProofofLemma 3.4 . . . 69

3.H ProofofLemma 3.5 . . . 69

3.I ProofofProposition 3.3 . . . 70

4 ExploitingChannel Stru ture in MIMO Broad ast Channels 71 4.1 Introdu tion. . . 71

4.2 Exploitingredundan yintime- orrelated hannels . . . 72

4.2.1 UserSele tionintime- orrelated hannels . . . 72

4.2.2 BeamformingandS hedulingexploitingtemporal orrelation . . . 72

4.2.3 Memory-basedOpportunisti Beamforming . . . 73

4.3 Performan eevaluation . . . 76

4.4 ExploitingStatisti alCSITinSpatiallyCorrelatedChannels . . . 77

4.4.1 SystemSetting . . . 78

4.4.2 UserSele tionwithMLChannelEstimation. . . 79

4.4.3 ML oarse ChannelEstimationwithCQIFeedba k. . . 80

4.4.4 Interferen e-boundedMultiuserEigenbeamformingwithlimited feed-ba k . . . 85

4.5 Con lusions . . . 92

4.A ProofofProposition 4.1 . . . 93

5 LimitedFeedba k Broad ast Channelsbased on Codebooks 95 5.1 Introdu tion. . . 95

5.2 Systemmodel . . . 97

5.3 CQIFeedba kDesign . . . 97

5.3.1 Problemformulation . . . 97

5.3.2 Boundsonaveragere eivedSINR . . . 98

5.3.3 Lowerbound oninstantaneousre eivedSINR . . . 100

5.3.4 SDMA/TDMAtransition withlimitedfeedba k. . . 104

5.4 UserSele tionS hemes. . . 105

5.4.1 Greedy-SUSalgorithm . . . 105

5.4.2 Greedy-USalgorithm . . . 106

5.5 Performan eAnalysis . . . 107

5.5.1 Asymptoti (inK)sum-rateanalysis . . . 107

5.5.2 Sum-rateanalysisin theinterferen e-limited region. . . 108

5.6 MIMO Broad astChannelswithFiniteSumRateFeedba kConstraint . . . 109

5.6.1 MultiuserDiversity-Multiplexing Tradeoin MIMO BC with Lim-itedFeedba k . . . 109

5.6.2 FiniteSumRateFeedba kModel. . . 110

5.6.3 ProblemFormulation . . . 111

5.6.4 De oupledFeedba kOptimization . . . 112

5.7 Performan eEvaluation . . . 113

5.8 Con lusion . . . 119

5.A ProofofTheorem5.1. . . 121

5.B ProofofLemma 5.1 . . . 122

5.C ProofofTheorem5.2. . . 122

5.D ProofofLemma 5.2 . . . 123

5.E ProofofTheorem5.3. . . 124

5.F ProofofTheorem5.4. . . 125

6 Feedba k Redu tionusing Ranking-based Feedba k 127 6.1 Introdu tion. . . 127

6.2 Ranking-basedFeedba kFramework . . . 129

6.2.1 Two-stageapproa h . . . 129

6.2.2 Ranking-basedCQIRepresentation. . . 130

6.3 Performan eanalysis . . . 131

6.3.1 Asymptoti optimality of ranking-based feedba k for large window size

W

. . . 131

6.3.2 Throughputforinteobservationwindowsize

W

. . . 132

6.3.3 Throughputforniteobservationwindowsize

W

. . . 133

6.3.4 Performan eredu tionboundfornitewindowsize

W

. . . 134

6.5 S hedulingwithHeterogeneousUsers. . . 136

6.6 Performan eEvaluation . . . 137

6.7 Con lusion . . . 141

6.A ProofofProposition 6.1 . . . 142

6.B ProofofProposition 6.3 . . . 142

6.C ProofofProposition 6.5 . . . 143

7 SystemAspe tsin MultiuserMIMO Systems 145 7.1 Introdu tion. . . 145

7.2 ChannelStateInformationA quisition . . . 146

7.2.1 CSIat theRe eiver . . . 146

7.2.2 CSIat theTransmitter . . . 146

7.3 Codebook-basedPre oding . . . 147

7.4 CQIfeedba kmetri sandLinkAdaptation . . . 149

7.5 Opportunisti S heduling: SystemIssues . . . 149

7.6 Fairness . . . 150

7.6.1 Denitionof Fairnessin S heduling. . . 150

7.6.2 ProportionalFairS heduler(PFS) . . . 151

7.6.3 MultiuserProportionalFairS heduler(M-PFS). . . 152

8 Con lusions and Perspe tives 155

2.1 Multiple-Input MultipleOutputChannelModel. . . 15

2.2 Downlinkof amultiuserMIMO network: A BS/AP ommuni ates

simulta-neouslywithseveralmultiple antennaterminals. . . 17

2.3 Analyti al hannelmodelwithlo al s atterersatmobile station. . . 19

2.4 S hemati ofRandomOpportunisti Beamforming. . . 40

3.1 Comparison between simulated and analyti al a hievable sum-rate of RBF

with

M = 4

antennas andSNR=20dB. . . 44

3.2 A hievable sum rate omparison vs. average SNR for RBF with

M = 4

antennas. Both analyti expressions approximate a urately the simulated

performan eathighSNR. . . 45

3.3 A hievablesumrate omparisonbetweensimulatedandanalyti alresultsfor

RBF with

M = 4

antennasandSNR =-15dB. . . 45

3.4 Sum rateversusthenumberof usersforOptimal BeamPowerControlwith

M = 2

transmitantennasandSNR =20dB. . . 61

3.5 SumrateversusaverageSNRforOptimalBeamPowerControl (strategy3)

with

M = 2

transmitantennasand

K = 10

users.. . . 61

3.6 Sum rate omparisonof dierentse ond-stagepre oders(strategy1)versus

thenumberofusersfor

M = 2

and SNR=10dB. . . 62 3.7 SumrateversusthenumberofusersforIterativeBeamPowerAllo ationand

OptimalPowerControlwith

M = 2

transmitantennasandSNR =10dB.. . 62 3.8 Sum rate versus the number of users for Iterative Beam Power Allo ation

with

M = 4

transmitantennasandSNR =10dB. . . 63

3.9 Sum rate versusthe numberof usersfor On/OBeam PowerControlwith

M = 2

transmitantennasandSNR =20dB. . . 63

3.10 Sum rateversusaverageSNR for On/OBeamPowerControlwith

M = 4

transmitantennasand

K = 25

users.. . . 64 3.11 Sum rate versusthe numberof usersfor On/OBeam PowerControlwith

M = 4

transmitantennasandSNR =20dB. . . 64

4.1 Sum rate vs. the numberof transmit antennas

M

of MOBFwith

K = 20

usersandvariousDopplerspreads. . . 76

4.2 Sumrateasafun tionofnumberofusers

K

ofMOBFfordierentDoppler spreads. . . 77

4.3 Sumrateperforman eversusanglespreadofproposedMLestimationmethod

for

M = 2

and

K = 50

users. FullCSITisobtainedforthesele tedusersat

ase ondstep. . . 88

4.4 Sumrateperforman eversusthenumberofusersof ML hannelestimation

methodfor

M = 2

and

σ

θ

= 0.2π

. FullCSITforthesele tedusersisobtained forpre oderdesign.. . . 88

4.5 Sumrateperforman eversusanglespreadofproposedMLestimation

frame-workfor

M = 2

,and

K = 50

users. PartialCSITis employedforpre oding

design. . . 89

4.6 Sum rate as a fun tion of the number of users for various user sele tion

s hemeswith

M = 2

,antennaspa ing

d = 0.5λ

and

σ

θ

= 0.1π

. . . 89 4.7 Sumrateasafun tionofantennaspa ingforvarioususersele tions hemes

with

M = 2

,

σ

θ

= 0.1π

and

K = 50

users. . . 90

4.8 Sumrateasafun tionofanglespreadforvarioususersele tions hemeswith

M = 2

,antennaspa ing

d = 0.5λ

and

K = 50

users. . . 90

4.9 Sumrateasafun tionofthenumberofusersfor

M = 2

,and

σ

θ

= 0.1π

. . . 91 4.10 Sumrateasafun tionofangle spreadfor

M = 2

, antennaspa ing

d = 0.4λ

and

K = 100

users. . . 91

5.1 FiniteSumRateFeedba kModel. . . 110

5.2 SumrateversustheaverageSNRfor

B

D

= 4

bits,

M = 2

transmitantennas

and

K = 30

users. . . 114

5.3 Sum rate as a fun tion of the number of users for

B

D

= 4

bits,

M = 2

transmitantennas andSNR=20dB. . . 114

5.4 Sumrateperforman easafun tion oftheaverageSNR forin reasingvalue

of the number of users,with

B

D

= 4

bits of feedba k per userand

M = 2

transmitantennas. . . 115

5.5 Sum rate as a fun tion of the average SNR for in reasing odebook size,

M = 2

transmitantennas,and

K = 50

users. . . 116

5.6 Sum rate performan e as a fun tion of the number of users for in reasing

odebook size,

M = 2

transmitantennas,andSNR =10dB. . . 116 5.7 SumrateversusthenumberofusersforwithSNR=20dB,

M = 2

transmit

antennasand 10-bittotalfeedba k bits.

B

D

= 5

bitsareused for odebook indexing and (

B

Q

= 10

− B

D

bits) forCQI quantization. Formetri IV, 2 bitsareusedforquantizationofthe hannelnormand3bitsforthealignment.117

5.8 Sumratevs. numberofusersfor

M

=2andSNR=10dB.. . . 118 5.9 Sumratevs. numberofusersfor

M

=2andSNR=20dB.. . . 118 5.10 Sum rate vs. numberof users in a systemwith optimal

B

D

/B

Q

balan ing

fordierentSNRvalues. . . 119

6.1 Throughput omparisonasafun tionofwindowsize

W

forsingle-beamRBF

with

M = 2

antennas,SNR=10dBand

K

=10a tiveusers. . . 138

6.2 Averagerateasafun tion ofthenumberofusersforsingle-beamRBFwith

M

=2antennas,SNR =10dBanddierentvaluesofwindowsize

W

. . . 139

6.3 Averagerateasafun tion ofthenumberof usersforsingle-beamRBFwith

M = 2

antennas, SNR = 10 dB,

W

=1000 slots, and ranking-based CQI

metri quantizedwithdierentresolutions. . . 139

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

M = 2

antennas,SNR=10dBand

W

=1000slots. . . 140

6.5 Sumrateasafun tionofusersformulti-beamRBF inaheterogeneous

net-work in whi h users' average SNRs range from -10 dB to 30 dB,

M = 4

antennasand

W = 1000

slots. . . 140 6.6 Normalizeds hedulingprobability vs. userindex formulti-beam RBFwith

M = 4

antennas and

K = 10

users. Theusersaresorted fromthelowestto

3.1 IterativeBeamPowerControlAlgorithmforSum-RateMaximization . . . . 55

4.1 Memory-basedOpportunisti BeamformingAlgorithm . . . 74

4.2 GreedyUserSele tionwithStatisti al CSIT. . . 81

4.3 Resour eAllo ationAlgorithmwithStatisti alCSIT . . . 87

5.1 GreedySemi-orthogonalUserSele tionwithLimitedFeedba k . . . 120

Inthisse tion, thenotational onventionofthethesis issummarized. First,weprovidea

listof abbreviations, followedby anoverview ofthe notationof moregeneralnature. We

on ludewiththenotationsthat aremorespe i forthisthesis.

Abbreviations and A ronyms

The abbreviations and a ronyms used throughout the thesis are summarized here. The

meaningofana ronymisusuallyindi atedon e,whenitrsto ursinthetext.

3GPP ThirdGenerationPartnershipProje t

AMC AdaptiveModulationandCoding

AoA AngleofArrival

AoD AngleofDeparture

AP A essPoint

AWGN AdditiveWhiteGaussian Noise

BC Broad astChannel

BD Blo kDiagonalization

BER BitErrorRate

BF Beamforming

BGI BeamGainInformation

bps bitsperse ond

BS BaseStation

CCI ChannelCovarian eInformation

CDMA CodeDivision MultipleA ess

CDF CumulativeDistributionFun tion

CDI ChannelDire tion Information

CMI ChannelMeanInformation

CQI ChannelQualityInformation

CSI ChannelState Information

CSIR ChannelStateInformation atRe eiver

CSIT ChannelStateInformation atTransmitter

DMT DiversityMultiplexingTradeo

DPC DirtyPaperCoding

EVD EigenvalueDe omposition

GEV GeneralizedEigenvalue

HSDPA High-SpeedDownlinkPa ketA ess

i.i.d. independentandidenti allydistributed

i.ni.d. independentandnon-identi allydistributed

KKT Karush-Kuhn-Tu keroptimality onditions

l.d. LimitDistribution

LOS Line-of-Sight

MAC MultipleA essChannel

MIMO Multiple-Input Multiple-Output

MISO Multiple-Input Single-Output

ML MaximumLikelihood

MMSE MinimumMean-SquareError

NLOS NonLine-of-Sight

OFDM OrthogonalFrequen yDivisionMultiplexing

OFDMA OrthogonalFrequen yDivisionMultipleA ess

PDF ProbabilityDensityFun tion

PFS ProportionalFairS heduling

QoS QualityofServi e

RBF Random(opportunisti )Beamforming

RHS RightHandSide

rms rootmeansquare

RVQ RandomVe torQuantization

SDMA Spa e DivisionMultipleA ess

SINR Signal-to-Interferen e-plus-NoiseRatio

SISO Single-InputSingle-Output

SNR Signal-to-NoiseRatio

s.t. Subje tto

STC Spa e-TimeCode

SVD SingularValueDe omposition

TDD TimeDivision Duplex

TDMA TimeDivision MultipleA ess

THP Tomlinson-HarashimaPre oding

UCA UniformCir ular Array

ULA UniformLinearArray

UMTS UniversalMobile Tele ommuni ationsSystem

VQ Ve torQuantization

WLAN WirelessLo alAreaNetwork

WMAN WirelessMetropolitanAreaNetwork

ZF ZeroFor ing

Notations

Thenotationsusedinthisdissertationarelistedinthisse tion. Weuseboldfa eupper(e.g.

X

)andlower ase(e.g.

x

)lettersformatri esand olumnve tors,respe tively. Plainletters areused fors alarsand upper ase alligraphi letters (e.g.

S

)denote sets. Nonotational distin tionisused forarandomvariable andits realization. Othernotational onventions

aresummarizedasfollows:

C

,

R

Thesetsof omplexandrealnumbers,respe tively.

|x|

Theabsolutevalueofas alar.

∠x

Thephaseofa omplexs alar(inradians).

kxk

TheEu lidean(

ℓ

2

)normofve tor

x

kXk

F

TheFrobeniusnormofmatrix

X

⌈x⌉

The eilingoperator,i.e. thesmallestintegernotlessthanx.

∠(x, y)

Theanglebetweentwove tors

x

and

y

.

|X |

The ardinality of theset

X

, i.e. the numberof elementsin the nite set

X

.

E

_{·}

Theexpe tation operator.

CN (x, X)

The ir ularly symmetri omplex Gaussian distribution with mean

x

and ovarian ematrix

X

.

(

·)

∗

The omplex onjugateoperator.

(

_·)

T

Thetransposeoperator.

(

·)

H

The omplex onjugate(Hermitian)transposeoperator.

X

†

TheMoore-Penrosepseudoinverseofmatrix

X

.

X

−1

Theinverseofmatrix

X

.

I

Theidentitymatrix.

Tr

(X)

Thetra eof matrix

X

,i.e. thesumofthediagonalelements.

vec(X)

Theve torobtainedbysta kingthe olumnsof

X

.

⊗

TheKrone kermatrixprodu t.

O(

_·)

The big-Onotation, i.e.

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

as

x

→ ∞

i

∃x

0

, c > 0

su h

that

|f(x)| ≤ c |g(x)|

for

x > x

0

.

exp(

_·)

Theexponentialfun tion.

log(

·)

Thenaturallogarithm.

log

2

(

·)

Thebase 2logarithm.

Thesis Spe i Notations

Wesummarizeherethesymbolsandnotationsthat are ommonly usedin thisthesis. We

havetriedto keep onsistentnotationsthroughout thedo ument,but somesymbolshave

dierentdenitionsdepending onwhentheyo urin thetext.

M

Numberoftransmitantennas

N

k

Numberofre eiveantennasat user

k

.

K

Numberof a tiveterminals,i.e. theset of userssimultaneouslyasking forservi eduring onegivens hedulingwindow.

¯

h

k

The hannelofuser

k

normalizedbyitsamplitude,i.e.

h

¯

k

= h

k

/

kh

k

k

.

W

Thepre odingmatrix.

w

k

Thebeamformingve torofuser

k

.

Q

An isotropi allydistributed unitarymatrix.

q

An orthonormalve tor(beam),i.e. olumn of

Q

.

n

k

TheAWGNnoiseve torofuser

k

.

R

k

Thea hievablerateofuser

k

.

P

Themaximumtransmitpower.

S

Thesetof sele ted(s heduled) users.

B

Thenumberofa tivebeams.

γ

k

TheCQIfeedba kofuser

k

.

Résumé

L'utilisationdesantennesmultiples aété re onnue ommeune te hnologie- léquipeut

onsidérablementaméliorerl'e a itéspe traledesfutursréseauxde ommuni ation

multi-utilisateurssansl. Danslessystèmesàentréesmultiplessortiesmultiples(MIMO)

multi-utilisateurs, les degrés de liberté spatiaux oerts par les antennes multiples peuvent être

avantageusement exploités an d'augmenter la apa ité du système. Cela est fait en

or-donnançantplusieursutilisateurssimultanémentparuneméthoded'a èsmultiple ave

ré-partitionspatiale(SDMA). Uneaugmentationlinéairededébit,proportionnelleaunombre

d'antennesdetransmission,peutêtreréaliséemêmeenutilisantdesstratégiesdupré odage

linéairesiellessont ombinéesave desproto olesd'ordonnan emente a es. Cependant,

esgainsprometteursrelèventdel'hypothèsesouventirréalistequ'uneinformationdu anal

parfaiteàl'émetteur (CSIT)estdisponibleàlastationdebase(SB).

Dans ettethèse, on onsidèredeste hniquesdeformationlinéairedefais eaux

(beam-forming)et d'ordonnan ementbaséessurdesCSIT partiellesàbasdébit. Plusieurs

méth-odes qui permettent à la SB de bien vivremême ave une onnaissan edu anal limitée

sontidentiées.

Onproposede dédoublerla on eptionentre l'ordonnan ementet les étapesnales de

formationdefais eaux, andebéné ierdufaitquelenombred'utilisateursàservirdans

haque réneaud'ordonnan ementestbeau oupplusbasquelenombretotald'utilisateurs

a tifsdansla ellule. Cetteappro heàdeuxétapesestappliquéedansun ontextede

forma-tiondefais eauxaléatoires(RBF)an d'identierdesutilisateursspatialementséparables

durantlapremièreétape. Dans ladeuxièmeétape,plusieursstratégiesd'amélioration

su - essive, y ompris le ontrle de puissan e de fais eau et la séle tion de fais eaux, sont

proposées,enorantunerédu tionimportante dufeedba kainsiquedesgainssigni atifs

endébitsomme,mêmedansdesréseauxave unnombred'utilisateursfaibleàmodéré.

Dansdes anauxMIMO temporellementouspatialement orrélés,onidentiequel'

in-formationextrêmementutilepourl'ordonnan eurSDMAsetrouve a héedanslastru ture

du anal. Onmontre ommentleRBF peutexploiterlaredondan edu anal et atteindre

undébit pro he de elui dubeamforming unitaire optimal ave CSIT omplète pour des

anauxquivarientlentementave letemps.

Dansdes anauxspatialement orrélés,laCSITstatistique àlongterme,qui peut être

fa ilement obtenue ave un taux de rétroa tion négligeable, révèle des informations sur

la séparabilité spatiale moyenne des utilisateurs. Une te hnique d'estimation du anal à

maximumdevraisemblan e(MV)estproposée,qui ombinee a ementlaCSITstatistique

à long terme ave l'information de qualité de anal (CQI) instantanée à bas débit. Des

te hniques de séle tion d'utilisateurset de beamforming sont également proposées. Ilest

démontré que dans des systèmes ave étalement angulaire à l'émetteur raisonnablement

faible,mêmeunseulparamètres alairedeCQIparutilisateurest susantpoura omplir

d'ordonnan ementetbeamformingave une performan epro hedel'optimale.

Desstratégiesdefeedba klimitéenutilisantdes odebooksdequanti ationsont

égale-mentétudiées. En parti ulier,leproblèmedela on eptiondeCQIestadresséetplusieurs

métriquess alairesderétroa tionsontproposés. Cesmétriquessontbaséssurdesbornesde

que es métriques s alairesdeCQI, ombinésave l'information sur la dire tion du anal

(CDI),forçageàzéroetdesalgorithmesdeséle tiond'utilisateur'greedy',peuventatteindre

une partie signi ative dela apa itéoptimale enexploitant legainde ladiversité

multi-utilisateur. Unete hniquee a equioreàlaSBlaexibiliténé essaireandepasserde

latransmissionmulti-utilisateuràlatransmissionmon-utilisateurestaussiproposée. Cette

méthode présente une roissan e linéaire du débit-somme à fort rapport signal-sur-bruit

(RSB) (régionlimitéeparl'interféren e).

Letauxdelavoiederétroa tionpeutêtredeplusdiminué enreprésentantlefeedba k

par une métrique basée sur le rang (ranking-based feedba k). On montre qu'une valeur

entièreest souventsusante pouridentierlesutilisateursave les onditionsdu analles

plus favorables. En parallèle, ette représentation de la rétroa tion égalise la probabilité

d'a èsdanslesréseauxoùles anauxdesutilisateursnesontpasné essairement

identique-mentdistribuéset lesterminauxmobilesontdesRSBsmoyensinégauxdueauxdiérentes

Introdu tion

1.1 Ba kground and Motivation

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

higherdata rates and enhan edquality of servi e(QoS). The appli ations oered to

us-tomers nowadays are no longer limited to voi e transmission, but new types of servi es,

su h as streaming multimedia, internet browsing, le transfer and video telephony, ea h

withdierentQoSrequirements,areprovided. Thesu essstory of ellulartelephonyhas

openedthewaytothedevelopmentofvarioustypesof wirelesssystems,su haslo aland

metropolitanareanetworks(LAN,MAN),ad-ho andsensornetworks,short-rangewireless

proto ols, et . Thevariety ofwireless proto ols ombinedwith thein reasing demand for

dataservi eshaveamendedthewireless servi evisiontoananywhere-anytimebasis.

Theintrodu tionofnewdataservi esisoneoftheunderlyingreasonsforthetransition

from ir uit-swit hedsystemstopa ket-swit hednetworks. Networksa ommodating

delay-tolerant, best-eort tra havenowevolved, oeringexibility to the resour eallo ation

unit to s hedule transmissions in slots where the ommuni ation link exhibits favorable

hannel onditions. Thisgivesriseto theso- alledmultiuserdiversity gain [1℄,whi h aims

at abetter utilization ofthe spe truminside ea h ellat the expenseof userfairnessand

delay.

In addition to multiuser diversity, another key te hnology that e iently utilizes the

s ar e bandwidth resour e is multi-antenna ommuni ations. Multiple-Input,

Multiple-Output(MIMO)te hniqueshavegeneratedagreatdealofinterestduetotheirpotentialfor

highspe trale ien y, in reaseddiversity,and interferen esuppression apabilities. Asa

result,theuseofmultipleantennas isenvisionedinmostofnext-generationwireless

proto- ols,in luding3GPP LongTermEvolution(LTE)[2℄,HighSpeedDownlinkPa ketA ess

1.2 From Single-user to Multiuser MIMO Comm

uni a-tions

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

ommuni ations are essentially a hieved via the use of diversity gain-oriented te hniques

(e.g. spa e-time oding [5℄) ombined with rate maximization-oriented te hniques (e.g.

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

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

expandthe dimensionsavailable forsignalpro essinganddete tion,thusa tingmainly as

aphysi allayerperforman ebooster. Inthisapproa h,thelinklayerproto olsformultiple

a ess indire tlyreap theperforman e benetsof MIMO antennas in theform of greater

per-user rates,ormorereliable hannelquality, despitenotrequiringfull awarenessof the

MIMO apability.

Re ently,therehasbeenavividinterestintheroleofmultipleantennasinmultiuser

net-worksettings,andespe iallyinbroad astandmultiplea esss enarios.Themultiplea ess

hannel(MAC),alsoreferredtoastheuplink,appliestosettingswheremanytransmitters

sendsignalstoonere eiverinthesamefrequen yband. Thebroad ast hannel(BC),also

referredtoasdownlink,modelsanetworkinwhi habasestation(BS) ommuni ates(sends

data)tomanyuserssharingthesamemedium. Investigationofthemore hallenging

broad- ast hannelliesatthe oreofthisthesis. InmultiuserMIMOnetworks,thespatialdegrees

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

system apa ity, by s heduling multiple users simultaneously by meansof Spa e Division

MultipleA ess(SDMA).Su hamultiplea essproto olrequiresmore omplexs heduling

strategies and trans eivermethodologies, but does notinvolve any bandwidth expansion.

In spatial multiple a ess, the resulting multiuser interferen e is handled by the multiple

antennas,whi hinadditiontoprovidingper-linkdiversityalsogivethedegreesof freedom

ne essarytoseparateusersin thespatialdomain.

Re entinformationtheoreti advan esrevealthatthe apa ity-a hievingtransmit

strat-egyfortheMIMO broad ast hannelistheso- alleddirtypaper oding (DPC)[68℄.

How-ever,this optimumtransmit strategy, whi h involvesatheoreti alpre-interferen e

an el-lation te hnique ombined with an impli it users hedulingand power loadingalgorithm,

is highly omplex toimplement andsensitiveto hannelestimation errors. The

apa ity-a hieving te hnique in MIMO broad ast hannels revealed the fundamental role played

by the spatial dimension on multiple a ess and s heduling, repla ing the simplisti view

of MIMO as a pure physi al layer te hnology. This gave rise to the development of the

so- alled ross-layerapproa hes, whi haimat thejointdesignofthephysi allayer's

mod-ulation/ odingandlink layer'sresour eallo ationands hedulingproto ols.

MultiuserMIMO te hniquesand theirperforman e havebegunto beintensely

investi-gatedbe auseofseveralkeyadvantagesoversingle-userMIMO ommuni ations. In

parti -ular, multiuser MIMO s hemes allowfor alinear in reasein apa ity, proportional to the

number oftransmit antennas, thanksto their spatial multiplexing apabilities. Theyalso

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

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

whileintelligen eand ostiskeptontheinfrastru tureside.

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

unfor-tunately ome at the riti alassumption ofgood hannelstateinformation at transmitter

(CSIT).MultiuserMIMOsystems,unlikethepoint-to-point ase,benetsubstantiallyfrom

CSIT, thela k ofwhi h maysigni antlyredu e thesystem throughput. This isbe ause

withoutCSIT,theBSdoesnotknowinwhi hdire tiontosendthebeams. IfaBSwith

M

transmitantennas ommuni atingwith

K

single-antennare eivershasperfe t hannelstate information(CSI),amultiplexinggainof

min(M, K)

anbea hieved. Althoughthe approx-imationof losetoperfe tCSIatthere eiver(CSIR)isoftenreasonable,thisassumptionis

oftenunrealisti atthetransmitterside. IftheBShasimperfe t hannelknowledge,thefull

multiplexinggainmayberedu ed,andinsettingswith ompleteabsen eofCSIknowledge,

themultiplexinggain ollapsesto one. CSITa quisition seemstobethemost substantial

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

sys-tem apa ityofmultiuserMIMOsystems. Insystemswhere hannelre ipro ity annotbe

exploited oris proneto errors,the needfor CSIT feedba k pla es asigni antburden on

uplink apa ity, exa erbatedin wideband ommuni ations (e.g. OFDM) or high mobility

systems(su h as3GPP-LTE, WiMAX,et .).

Inthis dissertation, we fo uson themulti-antennadownlink hannel and aimat

iden-tifyingwhat kindofpartialCSIT, alsoreferredtoaslimitedfeedba k, anbe onveyedto

theBSinordertoa hieve apa ity losetothatofthefullCSIT ase. Motivatedbyre ent

keyndings, whi h showthat linearpre oding strategieswith partial CSIT ana hievea

signi ant fra tion of the full CSIT apa ity if ombinedwith e ient s heduling

proto- ols [912℄, we fo us on low- omplexity, linear beamforming te hniques. We try to shed

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

strategiesthatallowtheBSto opewellwithlimited hannelknowledgeanda hieve

near-optimalsumrate. Aswewill see in thefollowing hapters,the roleof multiuser diversity

andopportunisti s hedulingisinstrumental in ourapproa hes. Ourthesisis that thanks

to the multiuser diversity gain, it is generally su ient to feed ba kone ortwo properly

designed s alarfeedba k parametersin order to perform beamforming and user sele tion

thata hievesthroughputrelatively losetotheoptimumone.

1.3 Assumptions

Inaneortto provide a learand on iseframework to this work,wemakethefollowing

standardassumptions:

•

Single ellnetwork.

Asingle ellis onsideredandtheinter- ellinterferen eistreatedasnoise.

•

Perfe t hannel stateinformationatthe re eiver.

Users an estimateperfe tlytheir hannels,sothat full hannel stateinformationat

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

pilot-pilot hannel. Thisassumptionmaybequestionedinhigh-mobilitysettingsandresults

insigni antoverheadinwideband systems.

•

Narrowband hannels

Flat-fading hannels are onsidered,i.e. thesignalbandwidthis mu h lessthan the

re ipro al of the propagation time of the wavefront a ross the antennaarray. Our

proposedmethods anbeeasilyappliedonapersub arrierbasisinwidebandOFDM

systems.

•

Ideal linkadaptation.

Ideallinkadaptationproto olsareassumedandthe ontinuous-rate, ontinuous-power

Shannon apa ityformulais al ulatedasuserthroughputmeasure. Thisisa

reason-ableassumptionsin e urrentpowerful odings hemes anperform losetoShannon

limit. Furthermore,theSNR-gapifpra ti al odingandmodulations hemesareused

doesnotae tthesum-rates alingof theproposedte hniques.

•

Inniteba klogged users.

An innite ba klog of pa kets in ea h queue is assumed, thus the base station has

alwaysdata to transmitto thesele ted(s heduled) users. Sin e theresour e

allo a-tionpoli iesare studied from athroughputmaximizationpoint ofview, queuestate

informationandtra arrivalpro esseshavebeennegle ted.

1.4 Contributions and Outline of the Dissertation

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

FormationparlaRe her he/IndustrialAgreementforTrainingthroughResear h)agreement

betweenTele omParisTe h/EURECOM,Sophia-Antipolis, andtheRadioA essNetworks

(RESA)groupatFran eTele omResear handDevelopment,Paris. The ondu tedresear h

workwas fullyfundedbyFran eTele omResear h andDevelopment (OrangeLabs).

Themain fo us ofthe thesisis user sele tionand linear pre oding in multiuser

multi-antennasystemswithlimitedfeedba k. Weprovidebelowanoutlineofthedissertationand

des ribethe ontributionsmadeinea h hapter.

Chapter 2-Multi-antennaBroad ast Channels

Inthis hapter,wereviewre entfundamental ndingsin MIMO broad ast hannels. The

general multi-antenna system model is introdu ed and apa ity results for the broad ast

hannelarepresentedunderdierentassumptionsonthequality/amountofCSIT.We

em-phasizeonthe ardinalimportan eofCSITandtheroleofmultiuserdiversityfora hieving

losetooptimum apa ity. Capa itys alinglawsforopportunisti s hedulingunder

dier-ent hannel statisti al distributions are provided. The apa ity growth for networks with

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

lin-earpre odingstrategies ombinedwiths hedulingusing limitedfeedba k,whi hforms the

building blo kofthedissertation. Theadvantages anddrawba ksof thissetting are

•

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

Pro essingMagazine,Spe ial IssueonSignalPro essingforMultiterminalCommun.

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

Chapter 3- Enhan ed MultiuserRandomBeamforming

The ontributionsofthis hapteraretwo-fold: Intherstpart,weprovideanunpublished

exa tsum-rateanalysis of onventionalrandom beamforming (RBF)[9℄. Capa itys aling

lawsfortheinterferen e-limitedregion(highSNR)arederivedusingextremevaluetheory,

showingthe ardinalimportan eofmultiuserdiversityinthisregime. Inthese ondpart,a

limitedfeedba k-baseds hedulingandbeamformings enariothatbuildsonRBFis

onsid-ered. Weintrodu eatwo-stageframeworkthatde ouplesthes hedulingandbeamforming

designproblems in twophases. Several renementstrategies, in luding beam power

on-trolandbeamsele tion,areproposed,oeringvariousfeedba kredu tionandperforman e

tradeos. The ommonfeatureoftheses hemesistorestorerobustnessofRBFwithrespe t

tosparsenetworksettings(lowtomoderatenumberofa tiveusers),atthe ostofmoderate

omplexityin rease.

Theworkin this hapterhasbeenpublished in:

•

M. Kountouris and D. Gesbert, "Robust multi-user opportunisti beamforming for sparse networks," in Pro . 6th IEEE Workshop on Signal Pro essing Advan es in

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

2005(invitedpaper).

andwillappearin:

•

M.Kountouris,D.Gesbert,andT.Sälzer,"Enhan edMultiuserRandom Beamform-ing: Dealingwiththenotsolargenumberofusers ase,"IEEEJournalonSel. Areas

inCommuni ations(JSAC),Spe ialIssueonLimitedFeedba kWirelessComm.

Net-works,O t. 2008.

Chapter 4- ExploitingChannel Stru ture in MIMO Broad ast Channels

Inthis hapter,we onsidermultiuser MIMO hannels orrelatedin either time orspatial

domain,and provideseveralte hniquesthat in reasethesystemthroughputbyexploiting

the hannel stru ture. Intime orrelated hannels, anopportunisti beamforming s heme

exploiting hannelmemoryisproposed. Thiss hemeisshowntollthe apa itygap with

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

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

established,whi h ee tively ombines slowlyvaryingstatisti al CSIT -assumedavailable

atthetransmitter -with instantaneouslow-ratefeedba k. A greedyusersele tion s heme

andalow- omplexitySDMA eigenbeamformingte hniquebasedonmultiuser interferen e

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

networks,s alarCSITfeedba kissu ienttoa hievenear-optimalthroughputperforman e

ifitisproperly ombinedwithlong-termstatisti alknowledge.

Theworkin this hapter hasbeenpublished in:

•

M.KountourisandD.Gesert,"Memory-basedopportunisti multi-userbeamforming," in Pro . of IEEEInternationalSymposium onInformation Theory (ISIT2005), pp.

•

M. Kountouris, D. Gesbert, and L. Pittman, "Transmit Correlation-aided Oppor-tunisti BeamformingandS heduling,"in Pro . of14thEuropeanSignalPro essing

Conferen e(EUSIPCO),Floren e,Italy,September4- 8,2006(invitedpaper).

•

D.Gesbert,L.Pittman,andM.Kountouris,"TransmitCorrelation-aidedS heduling inMultiuserMIMONetworks,"inPro . IEEEInternationalConferen eonA ousti s,

Spee h, andSignalPro essing(ICASSP2006),Vol.4,pp. 249-252,Toulouse,Fran e,

May14-19,2006.

•

M. Kountouris, R. de Fran is o, D. Gesbert, D.T.M. Slo k, and T. Sälzer, "Low omplexitys hedulingandbeamformingformultiuserMIMO systems,"in Pro . 7th

IEEEWorkshoponSignalPro essingAdvan esinWirelessCommuni ations(SPAWC

2006),Cannes,Fran e,July2-5,2006.

Chapter 5-LimitedFeedba k Broad ast Channelsbased on Codebooks

This hapterdealswithlimitedfeedba kstrategiesutilizingve torquantization odebooks.

In parti ular, the problem of e ient, sum-rate maximizing hannel quality information

(CQI) feedba k design is addressed. We proposed several s alar feedba k metri s that

in orporate information on the hannel gain,the hannel dire tion, and the quantization

error. Thesemetri sarebuiltuponboundsontheinstantaneousinter-userinterferen e,and

anbeinterpreted asreliableestimatesofthe re eived SINR.It is shown thats alar CQI

feedba k ombined with hanneldire tional information (CDI) ande ientuser sele tion

algorithm ana hieveasigni antfra tionofthe apa ityofthefullCSIT asebyexploiting

multiuser diversity. An adaptive s heme transiting from SDMA to TDMA transmission

modeisproposedandisshowntoa hievelinearsum-rategrowthatanySNRrange.

Theworkin this hapterhasbeenpublished in:

•

M.Kountouris,R. deFran is o, D. Gesbert, D.T.M.Slo k, andT.Sälzer, "E ient metri sfors hedulingin MIMObroad ast hannels withlimitedfeedba k,"in Pro .

IEEEInternationalConferen eonA ousti s,Spee h,andSignalPro essing(ICASSP

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

•

M.Kountouris,R.deFran is o,D.Gesbert,D.T.M.Slo k,andT.Sälzer,"Multiuser diversity-multiplexingtradeoinMIMObroad ast hannelswithlimitedfeedba k,"

inPro . of40thAsilomarConferen eonSignals,Systems&Computers,Pa i Grove,

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

anda eptedto:

•

M.Kountouris,R.deFran is o,D.Gesbert,D.T.M.Slo k,andT.Sälzer,"Exploiting MultiuserDiversityin MIMOBroad astChannelswithLimitedFeedba k,"a epted

toIEEETrans. onSignalPro essing,August2007(underrevision).

Chapter 6-Feedba k Redu tion using Ranking-basedFeedba k

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

ranking-based feedba k, is identiedas ameansto further ompress thereported hannel

feedba k. This representation enables the s heduler to identify users that are

restoredin heterogeneousnetworks withi.ni.d. hannel statisti samong users. Thework

inthis hapterhasbeenpublishedin:

•

M.Kountouris,T.Sälzer,andD.Gesbert,"S hedulingforMultiuserMIMODownlink Channels with Ranking-based Feedba k," EURASIP Journalon Advan es in Signal

Pro essing,Spe ialIssueonMIMOTransmissionwithLimitedFeedba k,Mar h2008.

Chapter 7- SystemAspe ts in MultiuserMIMO Systems

This hapterfo usesonseveralsystemissuesanddesign hallengesthatariseinreal-world

wireless systems. We dis uss the main pra ti al and implementation hallenges that one

mayfa ewhendeployingte hniquesasthoseproposedinChapters3-6. Emphasisisputon

fairnessissuesand theproportionalfairs heduling(PFS)rule isgeneralizedformultiuser

systemsettings,in ludingOFDM,SDMA,multi ellnetworks,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 theabovepubli ations,ourresear hwork resultedin thefollowingpatents:

•

PCTWO2007057568,"Informationen odingforaba kward hannel,"(assigned)

•

FR 2893474, "Method of information en oding for aba kward hannel of a SDMA

system,userterminalandbasestationofsu hasystem," (assigned).

•

"Feedba k ommuni ationfrom aterminalto atransmitter toredu e inter-beam in-terferen e,"(led,Jan. 2008).

Multi-antenna Broad ast

Channels

In this hapter, we review multiuser MIMO ommuni ations fo using on the more

hal-lengingdownlink,theso- alledbroad ast hannel(BC).Thegeneralmulti-antennasystem

modelisintrodu edandknown apa ityresultsforthebroad ast hannelarepresented

un-derdierentassumptionsregardingtheamountofCSIT.Informationtheoreti resultsshed

lightonthe ardinalimportan eofCSITands heduling,aswellasontheroleofmultiuser

diversityfora hievingtheoptimumsystem apa ity. Capa itys alinglawsforopportunisti

s heduling under dierent hannel models are investigated. Several approa hes in luding

non-linearand linear hannel-awarepre odingare reviewed, dis ussingdesign hoi esand

performan e tradeos. Emphasis is given on low- omplexity, linear pre oding strategies

ombinedwiths hedulingusinglimitedfeedba k,whi hformthebuildingblo kofthe

dis-sertation.Thelimitedfeedba kmodelthatweadoptandinvestigateinsubsequent hapters

ispresentedindetailanditslimitationsareidentied.

2.1 The Wireless Channel

Thewireless radio hannel isaparti ularly hallengingmediumforreliablehigh-rate

om-muni ations. Apartfrombeingsubje ttonoise,interferen eandseveralotherimpairments,

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

overaradio hannel issubje tto thephysi al lawsof ele tromagneti wavetheory, whi h

di tatethat multiplepaths o urasaresultofree tion onlargesurfa es(e.g. buildings,

walls, and ground), dira tion on edges, and s attering on various obje ts. Therefore, a

re eived signal is a superposition of multiple signalsarriving from dierent dire tions at

dierent time instan es and with dierent phases and power. These paths may ombine

tap havingrandom phase and time-varying amplitude. We rst review the physi al

phe-nomena that attenuate the signalpower. Foramoredetailed presentation,the interested

readerisreferredto [13℄.

2.1.1 Path loss

Pathlossisarange-dependentee tandisduetothedistan e

d

betweenthere eiverandthe transmitter. Inidealfreespa e,there eivedsignalpowerisdes ribedbytheFriisequation

and follows aninverse square lawpowerloss. Several deterministi and empiri al models

have been developed for various ellular environments (mi ro ells, ma ro ells, pi o ells,

et .), su h as Okumura-Hata, Wals h-Ikegami, and their COST-231 extensions,

plane-earthand lutter fa tormodel[13℄. Ageneri pathlossmodelisgivenby

L = βd

−ǫ

(2.1)

where

ǫ

isthepathlossexponentand

β

isas alingfa torthata ountsforantenna har-a teristi s and average hannel attenuation. The pathlossexponentvaries normallyfrom

2to6,dependingonthepropagationenvironment. Forthe aseof fullspe ularree tions

from groundis4,whileforbuildingsandindoorenvironmentsit antakevaluesfrom4to

6.

2.1.2 Shadowing

Shadowing, also known as ma ros opi or long-term fading, results from large obsta les

blo kingthemain signalpathbetweenthe transmitterandre eiver,and isdetermined by

thelo almeanofafastfadingsignal. Therandomshadowingee ts,whi hareinuen ed

by antennaheights, operatingfrequen yand thefeaturesof thepropagationenvironment,

maybemodeled aslog-normaldistributedwithprobabilitydensityfun tion (PDF):

p(x) =

1

xσ

√

2π

e

(log x−µ)2

2σ2

x > 0

(2.2)

where

µ

and

σ

arethemeanandstandarddeviationoftheshadowing'slogarithm.

2.1.3 Fading

Fading,oftenreferredtoasmi ros opi orsmall-s alefading, resultsfrom the onstru tive

ordestru tivesuperpositionofmultipathsanddes ribestherapidsignalu tuationsofthe

amplitudes,phases,ormultipathdelays. Thestatisti altimevaryingnatureofthere eived

envelopeis ommonlydes ribedbythefollowingthree fadingdistributions:

Rayleighfading

Rayleighfading is areasonable model when there is nodominantpropagation path (non

line-of-sight, NLOS) betweenthe transmitter andthe re eiverandis used to des ribe the

amplitude ofasignalwhen there is alargenumberof independents attered omponents.

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

ompo-phaseevenlydistributedbetween0and2

π

radians. Theenvelopeofthere eivedsignalwill thereforebeRayleighdistributed withPDFgivenby

p(x) =

2x

Ω

e

−

x2

Ω

x > 0

(2.3) where

Ω = E

{x

2

}

istheaveragere eivedpower. Ri eanfading

Ifadire t,possiblyaline-of-sight(LOS),pathexists,theassumptionofazero-meanfading

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

Ri ean. The Ri ean distribution is often dened in terms of the Ri ean fa tor

K

whi h denotestheratio ofthepowerin the mean omponentofthe hannel(dire t path)to the

powerin thes atteredpaths. TheRi eanPDFisgivenby

p(x) =

2x(K + 1)

Ω

e

−K−

(K+1)x2

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 fun tion 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 empiri almeasureddata is theNakagami

distributiongivenby

p(x; m) =

2m

m

_x

2m−1

Γ(m)Ω

e

−

mx2

Ω

x > 0

(2.6)

where

Ω

is the average re eived powerand

m =

Ω

2

E{x

2

_−Ω

2

_}

. The

m

fa tor determines the severityof fading, i.e. for

m =

∞

there isno fading. For

m = 1

the distribution in (2.6) redu estoRayleighfading,whilefor

m = (K+1)

2

_/(2K+1)

thedistributionisapproximately

Ri eanfadingwithfa tor

K

.

2.1.4 Channel Sele tivity

Multipathpropagationresultsinthespreadingofthesignalindierentdimensionsae ting

signi antlythere eivedsignal. These dimensionsaretime(Dopplerspread),spa e(angle

spread)andfrequen y(delayspread).

Dopplerspread and timesele tive fading

Themotionof thetransmitter,there eiverorthes atterersresultsin timesele tivity, i.e.

a single tone spreads in frequen y over a nite spe tral bandwidth. The variations due

to Doppler shiftsare spe i to ea h path anddepend on their angle with respe t to the

movingdire tion ofthetransmitter/re eiver. DierentDopplershiftsleadto theso- alled

Dopplerspread, whi h is themaximumfrequen yspread amongall Dopplershifts, and is

givenby

f

m

=

v

λ

c

where

v

isthemobilespeedand

λ

c

isthe arrierwavelength.

Howfastthe hannelde orrelateswithtimeisspe iedbythetemporalauto orrelation

fun tion. The Doppler power spe trum

ρ

d

(f

d

)

is dened as the Fouriertransform of the temporalauto orrelationfun tion ofthe hannelresponseto a ontinuouswave

ρ

d

(f

d

) =

(

₁

πf

m

√

1−(f

d

/f

m

)

2

∀f

d

∈ [−f

m

, f

m

]

0

elsewhere (2.8)

Themost ommonlyusedmodelfortheauto orrelationfun tionistheClarke-Jakes'model,

whi hassumesuniformlydistributeds atterersona ir learoundtheantenna

ρ

d

(τ ) = J

0

(2πf

m

τ )

(2.9)

where

J

k

isthek-thorderBesselfun tionoftherstkindand

τ

isthesampling interval. Ameasureofthetimesele tivityisthe hannel oheren etime

T

c

,denedastheinterval over whi h the hannel remains strongly orrelated. The shorter the oheren e time, the

fasterthe hannel hangesovertime. The oheren etimeisastatisti almeasureandsatises

T

c

∼

1

f

m

(2.10)

AsweshowinChapter4,thes heduler antakeadvantageofthetimesele tivityandbenet

fromtheresulting hannelredundan y(timediversity),asameanstofurther ompressthe

hannelfeedba korsu essivelyrenethes hedulingde isions.

Delay spread and frequen y sele tivefading

Delayspreadis aused whenseveral delayedand s aled versions of thetransmitted signal

arriveatdierenttimeinstantsatthere eiver. Thetimedieren ebetweenthemaximum

multipath delay

τ

max

(typi allythearrivaltimeof theLOS omponent)andtheminimum pathdelay

τ

min

is alleddelayspread. Delayspread ausesfrequen ysele tivefadingasthe hannela tslikeatapped-linelter. Therangeoffrequen iesoverwhi hthe hannel anbe

onsidered`at'denesthe oheren ebandwidth

B

c

anddependsontheform ofthepower delay spe trum (rms delay spread). A hannel is hara terized as at orfrequen y

non-sele tiveifthesignalbandwidth

B

issigni antlysmall omparedtothe hannel oheren e time, i.e.

B << B

c

= 1/τ

max

. Inthe subsequent hapters,only at fading hannelsare onsidered.

Angle spread and spa e-sele tivefading

Angle spreadat there eiver/transmitterrefersto thespreadin angles ofarrival(AoAs) /

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

array,respe tively. Thedierentdire tions ofarrivalleadtospatialsele tivitythat implies

that signalamplitudedependsonthespatiallo ationoftheantennaarray. Spa esele tive

fadingis hara terizedbythe oheren edistan e

d

c

,whi histhemaximumdistan ebetween two antenna elementsfor whi h the fading remains strongly orrelated. An upperbound

forthe oheren edistan eisgivenby

d

c

≤

λ

c

2 sin(∆θ

max

/2)

where

∆θ

max

isthemaximumangleseparation,i.e. therangein whi hthepowerazimuth spe trumisnonzero.

2.2 Multiple-Input Multiple-Output Channels

Multiple-InputMultiple-Output(MIMO) hannelsariseinmanydierents enariossu has

multi-antennawirelesssystemsorwirelinesystems(e.g. DSL),and anberepresentedinan

elegant, ompa t,anduniedwaybya hannelmatrix.Thebasi dis rete-time,narrowband

signalmodel forapoint-to-pointMIMO hannel with

M

transmitand

N

re eiveantennas isgivenby

y

= Hx + n

(2.12)

where

x

∈ C

M×1

isthetransmittedsymbol,

H

∈ C

N ×M

isthe hannelmatrix,

y

∈ C

N ×1

is

there eivedsignal,and

n

∈ C

N ×1

isthenoiseve tor. Weassumezero-mean ir ularly

sym-metri omplexGaussian noisewith ovarian ematrix

R

n

1

. For onvenien e, a whitened

hannel

˜

H

= R

−1/2

n

H

isoften usedsu h that thewhitenoise

w

= R

−1/2

n

n

hasaunitary ovarian ematrix, i.e.

E

{ww

H

} = I

. Due tothenoisenormalization, thetransmitpower

onstraint

P = T r(E

{xx

H

})

takesontheinterpretationoftheaveragesignal-to-noiseratio (SNR)perre eiveantennaunderunity hannelgain. Knowledgeofthe hannelgainmatrix

H

atthe transmitterand re eiveris referredto as hannel stateinformation atthe trans-mitter (CSIT)and hannel stateinformationatthe re eiver (CSIR),respe tively.

x

₁

x

₂

x

_M

y

₁

y

₂

y

_N

h11

h21

hN1

h

12

h

22

h

N2

h

1M

h

2M

h

NM

Figure2.1: Multiple-InputMultipleOutput ChannelModel.

Inthe aseofafrequen y-atMIMO system,the hannelhasonlyonetapand anbe

representedasadis rete-time hannelmatrix

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

N 2

[n] . . . h

N M

[n]













(2.13) 1

A omplexrandomve tor

x

is ir ularlysymmetri ifitsdistributionisthesamewiththedistribution of

e

jθ

_x

,

∀θ ∈ [0, 2π]

. For

θ = π

wehave

E{x} = 0

and for

θ = π/2

,

x

isa proper random ve tor,i.e.

E{xx

H

_{} = 0}

inwhi h

h

ij

[n]

isthespatio-temporalsignature( hannelgain)indu edbythe

j

-thtransmit antenna a ross the

i

-th re eive antenna and

n

is the dis rete-time index. Ea h hannel elementmayhavedierentamplitudeandphaseduetospatialsele tivity.

Whenthebandwidth-delayspreadprodu tofthe hannelislargerthan0.1,the hannel

isgenerally hara terizedasfrequen y-sele tive,anditsre eivedsignalisgivenby

y[n] =

L

X

l=0

H[l]x[n

_{− l] + n[n]}

(2.14)

where

L

isthe hannelorder.Tosimplifythenotationinthesubsequentpartsofthethesis, wedropthetimeindex

n

assumingthe hannelatagiventimeinstant.

When

M = 1

, the MIMO hannel redu es to a single-input multiple-output (SIMO)

hannel, and when

N = 1

, the MIMO hannel redu es to a multiple-input single-output (MISO) hannel. Whenboth

M = N = 1

,theMIMO hannelsimpliesto asimples alar orsingle-inputsingle-output(SISO) hannel.

2.3 Multiuser Multi-Antenna Systems

A multiuser hannel is generally any hannel that must be shared among multiple users.

Therearetwotypesofmultiuser hannels: theuplinkandthedownlink hannel. Anuplink

hannel, also referred to as multiple a ess hannel (MAC)or reverse hannel, has many

transmitterssendingsignalstoonere eiverinthesamefrequen yband. Adownlink hannel,

alsoreferredtoasbroad ast hannelorforward hannel,hasonetransmittersendingsignals

tomanyre eivers.Inthisse tion,wepresentbothmultiusermulti-antenna hannels(uplink

and downlink), however the dissertation fo uses solely on the hallenges asso iated with

the downlink hannel. Ina multi-user setting, we onsider ommuni ationbetween aBS

equipped with

M

antennas and

K

a tiveterminals, where ea h a tive user

k

is equipped with

N

k

antennas. Among allterminals, the set of a tiveusersis roughly dened by the set of userssimultaneouslydownloadingoruploading pa kets during onegiven s heduling

window. Thelengthofthe s hedulingwindow anbearbitrarybut should notex eed the

maximumlaten y expe ted by the servi e (likelyas small asa few tens of ms to several

hundredms). Byallmeansthea tiveusersoveronegivenwindowwillbeasmallsubsetof

the onne tedusers,themselvesforming asmallsubsetofthesubs ribers.

Intheuplink,there eivedsignalatthetransmitter anbewritten as

y

=

K

X

k=1

H

T

_k

x

k

+ n

(2.15) where

x

k

∈ C

N

k

×1

is the

k

-th usersignalve tor, possibly en ompassingpower- ontrolled, linearly ombined, onstellation symbols.

H

k

∈ C

N

k

×M

representsthe hannel matrixand

n

_{∼ CN (0, σ}

2

I)

is the omplex ir ularlysymmetri additivewhiteGaussian noiseve tor

(AWGN) at the transmitter. The transpose operator is simply used by onvention for

onsisten ewiththedownlinknotationanddoesnotpresume are ipro al link.

Inthedownlink,illustratedin Fig.2.2,the re eivedsignal

y

k

∈ C

N

k

×1

of the

k

-th user anbemathemati allydes ribedas

where

H

k

∈ C

N

k

×M

represents the downlink hannel response and

n

k

∈ C

N

k

×1

is the

omplex ir ularlysymmetri AWGNatre eiver

k

with

n

k

∼ CN (0, σ

2

k

I)

. Thetransmitted signal

x

isafun tionofthemultipleusers'informationdata,anexampleofwhi htakesthe superpositionform

x

=

X

k

x

k

(2.17) where

x

k

∈ C

M×1

isthetransmittedve torsignal arrying,possiblynon-linearlyen oded,

message for user

k

, with ovarian e

Σ

k

= E

{x

k

x

H

k

}

. The power allo ated to user

k

is thereforegivenby

P

k

=

Tr

(Σ

k

)

. Twopower onstraintsare ommonlyused:

•

individual power onstaint, also referredto asper antenna power onstraint, where

P

min

k

≤ P

k

≤ P

k

max

,

∀k

and

P

k

≥ 0

.

•

sum power onstraint,wherethepowerallo ationneedstomaintain

P

k

P

k

≤ P

.

NK

user 1

user k

user K

N1

Nk

base station (M antennas)

K users (user k has Nk antennas)

Figure2.2: Downlinkof amultiuser MIMO network: A BS/AP ommuni ates

simultane-ouslywithseveralmultipleantennaterminals.

In broad ast hannels the available transmit power is divided among the dierent users,

whereas in the uplink ea h user has an individual power onstraint asso iated with its

transmittedsignal. Inthisthesis,unlessotherwisestated,weassumeashort-termaverage

sumpower onstraint,whi h impliesthat the transmitterhas to usethe power

P

at ea h hanneluse.

2.3.1 Multi-antenna Channel Modeling

ThemodelingofMIMO hannelsisamulti-steppro edureofessentialimportan einsystem

analysis, deployment and network planning sin e it enables performan e predi tion and

omparison of dierent system ongurations in various propagation environments. The

various hannel models one an nd in the literature an be lassied in two ategories:

propagation-basedmodels andanalyti almodels.

Therst ategoryaimsatreprodu ingthephysi alwavepropagationin adeterministi

orsto hasti way. Indeterministi models,the hannelmatrixisgenerallygeneratedbased