The ardinal role of Channel State Information

Knowledgeof the hannel stateby the transmitter of aommuniationssystem hasbeen

demonstratedto bebeneialtowirelessommuniations,partiularlyinmultiuserMIMO

systems. The majorimportane of theavailabilityofhannel knowledge hasbeenalready

reognizedin [7℄, bypointingout that lakofperfet CSITresultsin total lossofdegrees

offreedom, in ontrast to what happensin single-userormultiple aess MIMO shemes.

The MIMO BC with no CSIT is degraded no matter whether the reeivers have CSIR

ornot. Hene, when the users havethe same number of antennas, it anbe shown that

superpositionodingisthesameastime-sharing. Therefore,thesumapaityisthesame

asifthereisonlyoneuserinthesystemandnomultiuser diversitygains anbeexpeted.

Thesigniantdiereneonthesumratebehaviorbetweenmultiuserandsingle-userMIMO

revealstheardinalroleofCSITinmultiuserMIMOdownlinksystems,presentedindetail

inthefollowingsetions.

2.6.1 Channel Knowledge at the Transmitter

Inmultiuser MIMO literatureit is often assumedthat the reeiverenjoys lose-to-perfet

hannel knowledge, whereasthe transmitter hasdierentlevelsof CSIT, ranging from no

CSITatalltofullCSIT.Theassumptionthatthereeiverhasauratehannelinformation

isoftenreasonableespeiallyin thedownlink,wherepilotsymbol-basedhannelestimation

ismoreeientsinetheterminalsanshareaommonpilothannel. Channelaquisition

at the transmitter relies on hannel measurements at a reeiver, sine the transmitter is

informedbythereeiveron thehannel statein animpliitorexpliitway. Themethods

available to gatherCSI at thetransmitter mainly relyonhannel reiproityorfeedbak.

Insystemsforwhih hannel reiproity annotbeexploited,the needfor CSIT feedbak

plaes a signiant burden on uplink apaity. The feedbak load is further exaerbated

inhigh-mobilitysystems(suhas3GPP-LTE,WiMAX,et.) wherethehannelonditions

hangerapidly and in widebandsystems, wheremorefeedbaktrainingisrequireddue to

2.6.2 Capaity saling laws in MIMO BC systems

ThedominantroleofCSITin multiusermulti-antennasystemsanbeidentiedby

study-ing theasymptotiapaitygrowthunder dierentassumptionson CSIT.Speially, the

fundamentalroleplayedbythemultipleantennasinexpandingthehannelapaityisbest

apprehendedbyexamininghowthesumratesaleswiththetransmitpowerandthenumber

ofativeusers.

Full CSI atthe Transmitter

High Power Regime: Thesalinglawofthesum-rateapaityofMIMO BC forxed

N k = N

M

^,^and

K

^and^large

P

^is^given^by^[44,^46℄

P lim →∞

C ^{DP C}

log P = min(M, max(N, K))

^(2.42)

The above result implies that at high SNR,the apaity exhibits linear growth with the

numberoftransmitantennas. Furthermore,thenumberofreeiveantennas peruserplays

verylittlerolein theapaityofMIMObroadasthannelsomparedto

M

^(provided^that

K > M

^).

Large

K

^Regime: ^The ^saling ^law ôf ^the ^sum-rate âpaity ôf ^MIMO ^BC ^for ^xed

N k = N

M

^,^and

P

^and^large

K

^is^given^by^[44℄

K lim →∞

C ^{DP C}

log log KN = M

^(2.43)

The result in (2.43) indiates that, with full CSIT, the system an enjoy a multiplexing

gainof

M

^,^obtained^by^the^BS^seleting^and^sending^data^to

M

ârefully^seletedûsersôut

K

^(multiuserdiversity). Sine eah userexhibits

N

independentfadingoeients, the totalnumberofdegreesoffreedomformultiuserdiversityis

KN

^,^thus^giving^the^extra^gain

log log KN

In ontrast, if the BS seletsand transmitsonly to the userwith maximumrate, the

apaityoftime-sharing,

C ^{T S}

^,^is^given^by^[44℄

K lim →∞

C ^{T S}

min(M, N ) log log K = 1

^(2.44)

Fromtheaboveresults,itisevidentwhytheapaitysalinglawsprovidetheneessary

justiationforthegreatappealofmultiuserMIMOsystems. Thespatialmultiplexinggain

M

^,^whihîs^the^pre-log^fatorôf^the^sum^rate,împliesâ^linear⁽ⁱⁿ^the^numberôf^transmit

antennas)inreasein apaityforno additionalpower. Theorrespondinggainis realized

by simultaneouslytransmittingindependent data streams in the same frequeny band to

spatially separableusers.

No CSI at the Transmitter

IntheabseneofCSIT,usermultiplexingisgenerallynotpossible,astheBSdoesnotknow

HighPower Regime: Thesaling lawofthe sum-rateapaityofMIMO BC forxed

N k = N

M

^,^and

K

^,^satises

P lim →∞

C ^{DP C}

log P = min(M, N )

^(2.45)

whih impliesthat at high SNR theapaity isessentiallythe sameasthat ofa

point-to-pointMIMOsystem. Inotherwords,TDMAisoptimalin thisregime.

Large

K

^Regime: ^The ^saling ^law ôf ^the ^sum-rate âpaity ôf ^MIMO ^BC ^for ^xed

N k = N

M

^,^and

P

^and^large

K

^is

K lim →∞

C ^{DP C}

log log KN = 0

^(2.46)

Inontrastto (2.43),there is nomultiusergainsinethetransmitter hasnoknowledge of

theusershannelsin ordertoexploitthem.

NotethattheaboveresultsholdundertheassumptionofperfetCSIR.Theimpatoflak

ofCSI at bothends of theMIMO network and in theasymptotially high SNR regime is

studiedin [25,47℄,where itis shownthat boththemultiuserdownlinkand thesingleuser

apaitysaledouble logarithmiallywiththeSNR.

Information theoretidesign guidelines

TheaboveapaitygrowthresultshighlightseveralfundamentalaspetsofmultiuserMIMO

systems,whihomeinmuhontrastwiththeonventionalsingle-userMIMOsetting. The

designguidelinesthat anbeextratedaresummarizedasfollows:

•

^Capaity^saling^laws^advoate^for^serving^multiple^userssimultaneouslyinanSDMA fashion, with asuitably hosenpreoding sheme at the transmitter. Although the

multiplexing gain is limited by thenumber of transmit antennas, the numberof

si-multaneouslyservedusersisinpriniplearbitrary. Howmanyandwhihusersshould

eetively beservedwithnon-zeropowerat anygiveninstantoftimeisthe problem

addressedbytheresourealloationstrategy.

•

^Unlikeⁱⁿ ^thepoint-to-pointMIMO setting,thespatial multiplexingofdierentdata streamsan bedonewhileusersareequipped withsingle-antennareeivers,thus

en-abling the apaity gains of MIMO while maintaining low ost for user terminals.

Having multiple antennas at theterminalanthus beviewedasoptional equipment

allowingextradiversitygainforertainusersorgivingtheexibilitytoward

interfer-eneanelingandmultiplexingofseveraldatastreamstosuhusers(reduingthough

thenumberofotherusersservedsimultaneously).

•

^Themultiplexinggainof

M

ⁱⁿ^the^downlinkômesât^theônditionôf^lose^to^perfet

CSIT. IntheabseneofCSIT, usermultiplexing isgenerallynotpossible,astheBS

justdoesnotknowinwhih`diretion'toformspatialbeams. Thus,theompletelak

ofCSI knowledgeredues themultiplexing gainto one. Thisis akeydierene with

point-to-pointMIMO,inwhihtheasymptotiapaityisnotsensitivetoCSIT,and

exeption lies in senarioswith terminal devies having enoughantennas to remove

o-streaminterfereneatthereeiver(

N k ≥ M

^). ^In^the^latter^ase,^the^BS^may^deide

toeithermultiplexseveralstreamstoasingleuserorspreadthestreamsovermultiple

users, ahieving an equivalent multiplexing gain in bothases. This is onditioned

howeverontheindividualuserhannelstobefullrank.

2.6.3 Partial Channel State Information

The oftenunrealistiassumption oflose toperfet CSIT, aswell asthe onsiderablegap

betweentheahievablesumrateoffullCSITomparedtothenoCSITase,havemotivated

researh workon shemesemployingpartial CSIT. PartialCSIT orlimitedfeedbak refers

to anypossibleform of inompleteinformationonthehannel. Thisterm inludes,butis

notlimitedto,salarCQIfeedbak(e.g. estimateofreeivedSINR),quantizedCSIT

(quan-tization ofhannel vetor),hanneldiretion information, statistialCSIT, et. Multiuser

MIMO shemesrelyingonpartialCSITlieat theheartofthis dissertation.

Thepratial,thoughsuboptimal,approahesdesribedinSetion2.5.1areshowntobe

highly sensitiveto hannel estimationerrors,thus diulttobeimplementedwithpartial

CSIT. The low-omplexity alternative of downlink beamforming and sheduling, despite

being less sensitive to CSIT imperfetions, requires full CSI as a means to minimize the

multiuserinterferene[12℄. Fortunately,worklike[9℄demonstratesthattheoptimalapaity

salingofMIMOBC(i.e.

M log log K

⁾^assuming

K

single-antennausers,anbeahievedfor

K → ∞

^even^though^thetransmitterreliesonsalarCQI.Severalshemesbasedonpartial CSITareshowntoahievelosetoDPCsum-rateperformaneinsomeasymptotiregimes.

However,themajorityoftheseapproahesbeomeinevitablyinterferenedominatedathigh

SNR sine theerrorintrodued(and theinreasein inter-user interferene) dueto partial

CSIT saleswithSNR.Hene,inthelargepowerregime,suhshemesexhibitasumrate

eilingbehaviorandfailto ahievefull multiplexinggain.

Itwouldhavebeenawedtoonludethatpartial CSITleadsneessarilytoaollapse

ofmultiplexing gain. Thismultiplexinggainlossanbemitigatedbyusingavariable-yet

nite -ratefeedbak hannel. In[10℄,Jindal showedthat thefeedbakloadperusermust

inrease approximatelylinearlywith thenumberof transmitantennas aswell aswith the

transmitpower(indB)in ordertoahievethefullmultiplexinggain. Inthisthesis,wetry

toshedsomelightontheseissues,byproposingseveralrobustlinearbeamformingshemes

with limitedfeedbak. Theinterferene dominatedbehaviorofsuh shemesis studied in

detailandseveralofourproposalsprovidemeanstoirumventthesum-rateeilingeet.

2.6.4 Statistial Channel Knowledge at the Transmitter

AnotherkindofpartialhannelstateknowledgethatanbeobtainedattheBSwithlittleor

nofeedbakoverheadisthestatistial CSIT.As seond-orderhannel statistisvarymuh

slowerin time ompared to the hannel realization itself, expliit statistial CSIT anbe

onveyedperiodiallyto theBS resultingin littleuplink overhead. Impliit knowledge on

thehannelstatistisanbeobtainedwithoutanyadditionalfeedbakbyaveraginguplink

measurements(statistialreiproity).

•

^Channel ^Mean Information (CMI), whih refers to the ase where the mean of the hannel distribution is available while the ovariane matrix is unknown and often

assumedaswhite.

•

^Channel ^Covariane Information (CCI), whih refersto the asewhere themean is assumed zero (as it is assumed to vary rapidly) and the information regarding the

relativegeometry of the propagation paths is available through anon-white spatial

ovarianematrix.

Channelknowledgeaquisition using ovariane feedbakan be applied to bothtime

di-visionduplex(TDD) and frequenydivision duplex(FDD) systems. Inontrast to

deter-ministireiproityinTDD systems,thehannel statistisoftheuplinkand thedownlink

remainrelatedinFDDandthedierenebetweenthefrequenybandsanbeoveromeby

usingfrequenyalibrationmatrix. Long-termstatistial hannelknowledgeisassumedin

Chapter4, whereweshow howstatistial CSIT anbe ombinedwith instantaneous

low-rate CQI feedbak to inrease system throughput by seleting spatially ompatible users

withlargehannelsgains.

Dans le document Multiuser multi-antenna systems with limited feedback (Page 47-51)

The ardinal role of Channel State Information

N k = N

M

K

P

P lim →∞

C DP C

log P = min(M, max(N, K))

M

K > M

K

N k = N

M

P

K

K lim →∞

C DP C

log log KN = M

M

M

K

N

KN

log log KN

C T S

K lim →∞

C T S

min(M, N ) log log K = 1

M

N k = N

M

K

P lim →∞

C DP C

log P = min(M, N )

K

N k = N

M

P

K

K lim →∞

C DP C

log log KN = 0

•

•

•

M

N k ≥ M

M log log K

K

K → ∞

•

•

C ^{DP C}

C ^{DP C}

C ^{T S}

C ^{T S}

C ^{DP C}

C ^{DP C}