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.We

em-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 are

iden-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-basedshedulingandbeamformingsenariothatbuildsonRBFis

onsid-ered. Weintrodueatwo-stageframeworkthatdeouplestheshedulingandbeamforming

designproblems in twophases. Several renementstrategies, inluding beam power

on-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,"EnhanedMultiuserRandom Beamform-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.^Kountouris^and^D.^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,^and^M.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.^Kountouris^and ^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:

•

^PCT^WO2007057568,"Informationenodingforabakwardhannel,"(assigned)

•

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

•

"Feedbakommuniationfrom aterminalto atransmitter toredue inter-beam in-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

modelisintroduedandknownapaityresultsforthebroadasthannelarepresented

un-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,whihformthebuildingblokofthe

dis-sertation.Thelimitedfeedbakmodelthatweadoptandinvestigateinsubsequenthapters

ispresentedindetailanditslimitationsareidentied.

2.1 The Wireless Channel

Thewireless radiohannel isapartiularlyhallengingmediumforreliablehigh-rate

om-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

^between^the^reeiver^and^the

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

îs^the^path^lossêxponentând

β

îsâ^saling^fator^thatâounts^forântenna

har-ateristis and average hannel attenuation. The pathlossexponentvaries normallyfrom

2to6,dependingonthepropagationenvironment. Fortheaseof fullspeularreetions

from groundis4,whileforbuildingsandindoorenvironmentsitantakevaluesfrom4to

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

âre^the^meanând^standard^deviationôf^theshadowing'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. ^The^envelope^of^the^reeived^signal^will

thereforebeRayleighdistributed withPDFgivenby

p(x) = 2x Ω e ⁻ ^x

2 Ω x > 0

^(2.3)

where

Ω = E { x ² }

^is^the^average^reeived^power.

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

îs ^the âverage ^reeived ^powerând

m = _E{ _x 2 ^Ω − ² Ω ² }

^. ^The

m

^fator ^determines ^the

severityof fading, i.e. for

m = ∞

^there ^is^no ^fading. ^F^or

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

^is^the^mobile^speed^and

λ c

^is^the^arrierwavelength.

Howfastthehanneldeorrelateswithtimeisspeiedbythetemporalautoorrelation

funtion. The Doppler power spetrum

ρ d (f d )

îs ^dened âs ^the ^Fôurier^transform ôf ^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

îs^the^k-thôrder^Bessel^funtionôf^the^rst^kindând

τ

^is^the^sampling ^interval.

Ameasureofthetimeseletivityisthehanneloherenetime

T c

^,^dened^as^the^interval

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

^(typially^theârrival^timeôf ^the^LOS ômponent)ând^the^minimum

pathdelay

τ min

îsâlled^delay^spread. ^Delay^spreadâuses^frequeny^seletive^fadingâs^the

hannelatslikeatapped-linelter. Therangeoffrequeniesoverwhihthehannelanbe

onsidered`at'denestheoherenebandwidth

B c

ând^dependsôn^the^form ôf^the^power

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

non-seletiveifthesignalbandwidth

B

îs^signiantly^smallômpared^to^the^hannelôherene

time, i.e.

B << B c = 1/τ max

^. În^the ^subsequent ^hapters,ônly ât ^fading ^hannelsâre

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

^,^whih^is^the^maximum^distane^between

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

^is^the^maximum^angleseparation,i.e. therangein whihthepowerazimuth spetrumisnonzero.

Dans le document Multiuser multi-antenna systems with limited feedback (Page 26-35)

Contributions and Outline of the Dissertation

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•

•

•

•

d

L = βd − ǫ

ǫ

β

p(x) = 1 xσ √

2π e (log 2σ x−µ)2 2 x > 0

µ

σ

π

p(x) = 2x Ω e − x

2

Ω x > 0

Ω = E { x 2 }

K

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

Ω e − K − (K+1)x

2

Ω I 0 2x

r K(K + 1) Ω

!

x > 0

Ω = E { x 2 }

I 0 (x)

I 0 (x) = 1 2π

Z 2π 0

e − x cos θ dθ

p(x; m) = 2m m x 2m − 1

Γ(m)Ω e − mx Ω 2 x > 0

Ω

m = E{ x 2 Ω − 2 Ω 2 }

m

m = ∞

m = 1

m = (K+1) 2 /(2K+1)

K

f m = v λ c

v

λ c

ρ d (f d )

ρ d (f d ) =

( 1

πf m √

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

0

ρ d (τ) = J 0 (2πf m τ)

J k

τ

T c

T c ∼ 1 f m

τ max

τ min

B c

B

B << B c = 1/τ max

d c

d c ≤ λ c

2 sin(∆θ max /2)

∆θ max

L = βd ⁻ ^ǫ

2π e ^(log ^2σ ^x−µ)2 ² x > 0

p(x) = 2x Ω e ⁻ ^x

Ω = E { x ² }

Ω e ⁻ ^K ⁻ ^(K+1)x

Ω = E { x ² }

e ⁻ ^x ^cos ^θ dθ

p(x; m) = 2m ^m x ^2m ⁻ ¹

Γ(m)Ω e ⁻ ^mx ^Ω ² x > 0

m = _E{ _x 2 ^Ω − ² Ω ² }

m = (K+1) ² /(2K+1)

( ₁

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