7.6 Fairness
7.6.3 Multiuser Proportional F air Sheduler (M-PFS)
PFSwasoriginallyproposedforsystemsthatserveonlyoneuserateahshedulingwindow.
In this setion, we generalize the PFS poliy forany multiuser transmission system. Let
G
be the set of all possible subsets of ardinality|G| = M
of disjoint indies among theompleteset ofuserindies
{ 1, · · · , K }
. LetS t ∈ G
,beonesuhgroupofM
usersseletedfortransmissionatagiventimeslot
t
.Proposition 7.1: The multiuserproportional fair sheduling poliy (M-PFS) is suhthat
the users areseletedas
S t ∗ =
argmax
Proof. In order to show that (7.5) is aproportional fair sheduler, we need to show that
it maximizes the sum of the logarithms of the average throughputs, i.e.
P
k log ¯ R k (t)
.Considertheobjetivefuntion
J = P
k log ¯ R k (t + 1)
. Thenwehave:Thersttermin(7.6)anbeomittedsineit doesnotdepend onthepartiularhoie of
theshedulingset
S
,heneseletingtheusersthatmaximizetheobjetivefuntionresultsinthefollowingoptimizationproblem:
S t ∗ =
argmax
S∈G J =
argmax
S∈G log Y
k ∈S
1 + R k |S (t) (1 − t c ) ¯ R k (t)
(7.7)
whihresultsin(7.5)sinethelogarithmis amonotoniallyinreasingfuntion.
Bydevelopingtheaboveexpressionwehave
S t ∗ =
argmax
S∈G 1 + X
k ∈S
R k |S (t) (1 − t c ) ¯ R k (t) + b
!
where
b
is theby-produts from the multipliation. If we onsider asystemwith parallel hannels, in whih therate provided touserk
doesnotdepend onthe rateof usersj, j ∈ S , j 6 = k
,thenb
an beomittedresultinginthefollowingM-PFSexpressionS t ∗ =
argmax
S∈G
X
k ∈S
R k |S (t) R ¯ k (t)
(7.8)
Weremarkthat(7.5)anbediretlyappliedasthePFSpoliyformultiuserSDMAdownlink
systems,multi-arrier(e.g. OFDMA), andmulti-ellnetworks.
Conlusions and Perspetives
Inthis dissertation,wehavefousedonresourealloationand performaneoptimization
formultiuser multi-antennas systemswith inompleteCSIT. Limitedfeedbaktehniques
that allow the transmitter to live well with partial hannel knowledge and still ahievea
signiantfrationoftheoptimalapaityahievedunderperfetCSIT istheleitmotiv of
thisthesis.
Onerstkeyideaisbasedonsplittingthefeedbakinformationbetweenthesheduling
and the nal beam design (or "user serving") stage, thus taking prot from the fat the
numbersusersto beserved at eah shedulingslot is muh lessthan thenumberof users
simultaneouslyrequestingdatapaketsduringonegivenshedulingwindow. Weintrodued
atwo-stageframeworkthat deouples theshedulingandbeamformingproblems, showing
that user seletion an be performed well using roughhannel estimates, while the stage
of serving the seleted usersis better aomplished with moreaurate feedbak. In one
proposed setting, random beamforming is exploited to identify good, spatially separable,
usersin a rststage. In theseond stage, theinitial random beamsof the seletedusers
arerenedbasedon theavailable feedbakasameansto oerimprovedperformaneand
robustness.Severalrenementstrategies,inludingbeampowerontrolandbeamseletion,
areproposed,oeringvarious feedbak redutionandperformane tradeo. The ommon
featuresoftheaboveshemesistorestorerobustnessofRBFwithrespettosparsenetwork
settings (low to moderate number of ativeusers), at the ost of amoderate omplexity
inrease. The established framework is suitable for resoure alloation in slow varying
multi-antennanetworkswithbest eort,elastitra.
Furthermore,wehavestudied theproblem ofuserseletionandpreodingwithpartial
CSITinmorerealistihannelsenarios. Weshowedthatusefulinformationthatlieshidden
intheseond-orderstatistisofthehannel-eitherinthetemporalorinthespatialdomain
- anbe exploited by the SDMA sheduler. In time-orrelated hannels, the redundany
(memory),whih appearsduetothehannelstruture,isexploitedinordertosuessively
reneovertimetherandombeamsofRBF. Aframework,oinedasmemory-based
oppor-tunisti beamforming, hasbeenestablished, whih allowsto llthe apaity gap between
a purely opportunisti RBF and a hannel-aware preoding and sheduling sheme with
full CSIT.Ourapproahissuitableforlowmobility(indoor)settings(i.e. limitedDoppler
spread), while is shown to approah the apaity of optimal unitary preoding with full
CSIT forhannelswithlargeoherenetime.
Inspatially-orrelatedMIMOhannels,long-termstatistial hannelknowledgean
re-veal information aboutthe mean spatial separability of users, whih is instrumental to a
properbeamformingdesign. Themeritofombiningstatistial andinstantaneoushannel
informationhasbeenhighlightedthroughseveralapproahes. Amaximum-likelihood(ML)
hannelestimationframeworkisestablished,whiheetivelyombinesslowlyvarying
sta-tistial CSIT, assumed available at thetransmitter, with instantaneouslow-rateCSIT. In
partiular,weonsideredbothhannelnormandeetivehannelgain(beamgain
informa-tion)assalarCQIfeedbak. Eientalgorithmsweredevelopedforomputingtheoarse
ML estimates, whih enable the SDMA sheduler to identify users with large gains and
separablespatial signatures. A greedyuserseletionshemeand alow-omplexity,SDMA
eigenbeamformingtehniquebasedonmultiuserinterfereneboundswerealsoproposedand
evaluated. It wasdemonstrated that, in systems with reasonablylimited angle spreadat
thetransmitter, suhas wide-areaellularnetworkswithelevatedbase stations,itis
su-ienttofeedbakasinglesalarbutproperlydesignedCQIparameterandombineitwith
long-termstatistial CSITinorderto ahievenear-optimalthroughputperformane.
Limited feedbak strategies utilizing quantization odebooks were also investigated in
the thesis. Inpartiular, theproblem ofeient,sum-ratemaximizingCQI metridesign
is addressed. Weidentied severalsalarfeedbakmetristhatinorporate informationon
thehannel gain,thehanneldiretion,andthequantizationerror,andanbeinterpreted
asreliableestimatesofthereeivedSINR.Forthat,boundsontheinstantaneousinter-user
interferenewhenZFBFisemployedwerederived. AlthoughtheexatSINRisinpriniple
not available to the individual users, the use of interferenebounds and approximate
ex-pressionsresultsinsimpliationsthatgiveusersthepossibilityofestimatingaprioritheir
individual reeived SINR. It was demonstrated that salar CQI feedbak ombined with
CDIandeientuserseletionandZFBFanahieveasigniantfrationoftheapaity
ofthefullCSITasebymeansofmultiuserdiversity. However,amajorlimitationofSDMA
systems relyingon quantized CSIT is that they beome interferene dominated and their
multiplexinggainisreduedathighSNRunderxedfeedbakloadrate. Motivatedbythe
fat thatSDMAdoesnotalwaysoutperformTDMAwhenthetransmitterrelieson
inom-plete CSIT, we showed the importane of dynami SDMA/TDMA transition algorithms.
Properlydesignedshedulingmetrisallowingasoft,adaptiveswithingfrom multiuserto
single-usertransmissionmodeareshownto beapromisingmeanstoirumventthis
prob-lem, guaranteeing a linear sum-rategrowth at any SNR range. Moreover, we onsidered
a pratially relevant system in whih eah user has a sum feedbak rate onstraint. A
tradeo betweenmultiuserdiversityandspatialmultiplexinghasbeenidentied, sinethe
available feedbakbits ought to be sharedbetweenCDIand CQIinformation. The
prob-lemofoptimizingthefeedbakbit splithasbeenstudied, revealinganinterestinginterplay
betweenthenumberofativeusers,theaverageSNR andthefeedbakload.
Finally,alow-raterepresentationofCSIT feedbakparameters,referredtoas
ranking-information. Eah useralulates and reportsto theBS theinteger-valued rankingof its
instantaneousCSIT amongasetof storedpastCSITmeasurements. This alternative
rep-resentationenablestheshedulerto identify usersthat are instantaneouslyon thehighest
peak(quantile)withrespettotheirownhanneldistribution,independentlyofthe
distribu-tionofotherusers. Interestingly,innon-symmetrinetworks,withi.ni.d. hannelstatistis
amongusers,theproposedranking-basedfeedbakallowstorestoretemporalfairnesssine
itequalizestheprobabilitythat auserwillbeseleted,independentlyofitsaverageSNR.
FutureResearh
Theresultsof this dissertation shed somelight onhowto ahieveasigniantfration
ofthemulti-antennabroadastapaityaspromisedbyinformation-theoreriresults,even
whenthetransmitter relies onlimitedandinompletehannelknowledge. Inparallel,the
thesisbroughtup severalinterestingopenissuesand topis forfurther researh, asbriey
disussedinwhatfollows.
OurworkinChapters3to5haveidentiedlinearpreodingombinedwitheientuser
seletionandlimitedasapromisingtehniquetoahievethesumrateofMIMObroadast
hannels. Nevertheless,theresultsrelyonseveralsimplifying assumptionsonthebehavior
of the feedbak hannel. Sine the uplink hannel is not instantaneous and error-free in
pratie,anaturalextensiontotheseresultsanbestudyingtheeet offeedbakhannel
noise, delays and CSIT estimation on the system performane. This investigation is of
primary importane in high mobility networks with large Doppler spread hannels where
delays are more prominent. Clearly, the feedbak delay would aet the validity of the
feedbakandwouldausetheshedulertomistakenlyhooseusersthatdonothavethemost
favorablehannelonditions. One simplemethod would beto bako the reported CQI;
howeverunderstanding theamountof bak o and theeet of estimation errorvariane
onthethroughputarehallengingopenproblems.
Inallourwork,exeptinChapter6,westudynetworksettingswithi.i.d. hannelfading
statistis. It is of partiular interest to assess the real throughput gain of the proposed
methods in hannels with shadowing and path loss, in whih the users exhibit unequal
averageSNRs. Suh senarioswouldertainly impatthemultiuserdiversitygains aswell
asthesystem overallsum-rate and fairnessperformane. Additionally, if we onsider the
impatofrealistitra modelsand systemloads,theavailabledegreesoffreedomat the
disposal ofthe sheduler anbe severely redued. It mightbe of interestto identify how
many eetive ative users are available for seletion by the sheduler at eah time and
howtotakeadvantageofthedierentdegreesoffreedomtosatisfytheQoSonstraintsfor
dierent types of tra. Fairness issues, whih have notbeen taken into aount in our
work here presented, need to be inorporated, in order to providehigh throughput while
satisfyingertainQoSonstraints.
Extensionsof theproblem of resourealloationfor multiuser multi-antennadownlink
hannelswithlimitedfeedbaktowidebandsystemsandmultiellsettingsarealsoproblems
oftimelyrelevanethatrequirefurtherresearh.
Finally,wehaveinvestigatedtehniquesmathed toaquantized(digital) hannel
feed-bak where eah user sends bak a suitably enoded and modulated quantization index.
Nevertheless, reentndingshavestarted onsidering analogfeedbak shemes. Although
workmaygiverisetohybriddigital/analogfeedbakapproahes. Forinstane,thefeedbak
linkdesignanbemodeledasaWyner-Zivodingproblem,wherethetransmitterombines
thedigital,quantizedCSITinformationthatombineswithanalogsideinformation.
Inordertoonlude,wemightsaythatthetheoretiallimitsofmultiusermulti-antenna
systems are relatively well understood nowadays. However, the gap between the urrent
pratialshemesandthetheoretiallimitsisstillsigniant,makingtheoptimaldesignof
limitedfeedbakmultiuserMIMO transmissionanopenandexitingproblem.
[1℄ R. Knopp and P. Humblet, Information apaity and power ontrol in single ell
multiuserommuniations, inPro.IEEEInt.Conf.onComm.(ICC),Seattle,June
1995.
[2℄ 3GPP,LongTermEvolution,EvolvedUniversalTerrestrialRadioAess(E-UTRA);
Physiallayer;Generaldesription, TS 36.201 v1.0.0,Marh2007.
[3℄ IEEE, Air interfaeforxedandmobilebroadbandwirelessaess systems
amend-ment 2: Physial and medium aess ontrol layersfor ombined xed and mobile
operationinliensedbands, IEEEStd 802.16e-2005, Febr.2006.
[4℄ NGMN: `Next Generation Mobile Networks Beyond HSPA and EVDO - A white
paper',V3.0, Available athttp://www.ngmn-ooperation.om, Deember2006.
[5℄ J.-C.Belore,G.Rekaya,andE.Viterbo, TheGoldenode: a
2 × 2
full-ratespae-time ode with non-vanishing determinants, IEEE Trans. Inform. Theory, vol. 51,
no.4,pp.14321436,Apr.2005.
[6℄ M.H.M.Costa, Writingondirtypaper, IEEE Trans.Inform. Theory,vol.29,no.
3,pp.439441,May1983.
[7℄ G. Caireand S. Shamai (Shitz), On theahievablethroughput of amulti-antenna
Gaussianbroadasthannel, IEEE Trans.Inform. Theory, vol.49, no.7,pp.1691
1706,July2003.
[8℄ H. Weingarten, Y. Steinberg, and S. Shamai (Shitz), The apaity region of the
Gaussian multiple-input multiple-output broadast hannel, IEEE Trans. Inform.
Theory,vol.52,no.9,pp.39363964,Sept. 2006.
[9℄ M.SharifandB.Hassibi, OntheapaityofMIMObroadasthannelwithpartial
side information, IEEE Trans. Inform. Theory, vol. 51, no. 2, pp. 506522, Febr.
2005.
[10℄ N.Jindal,MIMObroadasthannelswithniteratefeedbak, IEEETrans.Inform.
Theory,vol.52,no.11,pp.50455059,Nov.2006.
[11℄ G.Dimi¢andN.D.Sidiropoulos, Ondownlinkbeamformingwithgreedyuser
sele-tion: Performaneanalysisandasimplenewalgorithm, IEEETrans.Sig.Proessing,
vol.53,no.10,pp.38573868,Ot.2005.
[12℄ T.YooandA. Goldsmith, Ontheoptimalityofmultiantennabroadastsheduling
usingzero-foringbeamforming, IEEEJour.onSel.AreasinCommun.(JSAC),vol.
24,no.3,pp.528541,Mar.2006.
[13℄ T.S.Rappaport, WirelessCommuniations,2nded., PrentieHall,NJ,2002.
[14℄ T. Cover, Broadast hannels, IEEE Trans. Inform. Theory, vol. 18, no. 1, pp.
214,Jan.1972.
[15℄ A.El Gamal, Theapaityofalass ofbroadasthannels, IEEE Trans. Inform.
Theory,vol.25,no.2,pp.166169,Mar.1979.
[16℄ W. Yu and J. Cio, The sum apaity of a Gaussian vetor broadast hannel,
IEEETrans.Inform. Theory, vol.50,no.9,pp.18751892,Sept.2004.
[17℄ S.Vishwanath,N.Jindal,andA.Goldsmith, Duality,ahievableratesandsum-rate
apaityofGaussian MIMO broadasthannels, IEEETrans. Inform. Theory, vol.
49,no.10,pp.26582668,Ot.2003.
[18℄ P.ViswanathandD.N.Tse,SumapaityofthevetorGaussianhanneland
uplink-downlinkduality, IEEE Trans. Inform. Theory, vol.49,no.8,pp.19121921,Aug.
2003.
[19℄ N. Jindal, S. Vishwanath, and A. Goldsmith, On theduality of Gaussian multiple
aess and broadast hannels, IEEE Trans. Inform. Theory, vol. 50, no. 5, pp.
768783,May2004.
[20℄ S.P.BoydandL.Vandenberghe, Convex Optimization, CambridgeUniversityPress,
Cambridge,2004.
[21℄ W.YuandT.Lan, MinimaxdualityofGaussianvetorbroadasthannels, inPro.
IEEEInt.Symp. Info.Th.(ISIT),Chiago,IL,USA,June2004.
[22℄ W. Yu and W. Rhee, Degrees of freedom in wireless multiuser spatial multiplex
systemswithmultiple antennas, IEEE Trans. Commun.,vol.54, no.10, pp.1744
1753,Ot.2006.
[23℄ D.J.MazzareseandW. A.Krzymien, Throughputmaximizationandoptimal
num-ber of ative userson the two transmit antenna downlink of a ellularsystem, in
Pro. IEEEPai RimConf.onCommun., Comp. andSig. Proessing (PACRIM),
Vitoria,BC,Canada,Aug.2003.
[24℄ P. Bergman, Randomodingtheoremforbroadasthannelswithdegraded
ompo-nents, IEEE Trans.Inform. Theory,vol.19,no.3,pp.197207,Mar.1973.
[25℄ S.A.JafarandA.Goldsmith, Isotropifadingvetorbroadasthannels: Thesalar
upperbound andlossin degreesoffreedom, IEEE Trans. Inform. Theory, vol.51,
no.3,pp.848857,Mar.2005.
[26℄ A. Lapidoth, S. Shamai (Shitz), and M.Wigger, On theapaityof fading MIMO
broadast hannels with imperfet transmitter side-information, in Pro. of 43rd
[27℄ R.Zamir,S.Shamai(Shitz),andU.Erez, Nested linear/lattieodesforstrutured
multiterminal binning, IEEE Trans.Inform. Theory, vol.48, pp. 12501276, June
2002.
[28℄ T.Philosof,U.Erez,andR.Zamir, Combinedshapingandpreodingforinterferene
anellation at low SNR, in Pro. IEEE Int. Symp. Info. Th. (ISIT), Yokohama,
Japan,June2003.
[29℄ U. Erez and S. ten Brink, Approahing the dirty paperlimit for aneling known
interferene, in Pro. 41st. Allerton Conf. on Com., Cont. and Comp., Montiello
IL,USA,Ot. 2003.
[30℄ A.Bennatan,D.Burstein,G.Caire,andS.Shamai(Shitz),Superpositionodingfor
side informationhannels, in Pro. of Int. Symp. on Inform. Theory and Its Appl.
(ISITA), Parma,Italy,Ot. 2004.
[31℄ F.Boardi,F.Tosato,andG.Caire, PreodingShemesforthe MIMO-GBC, in
Pro. of Int.Zurih Sem.on Comm.(IZS'06), Zurih,Switzerland,Febr.2006.
[32℄ R. F. H. Fisher and C. H. Windpassinger, Improved MIMO preoding for
deen-tralized reeivers resembling onepts from lattieredution, in Pro. IEEE Glob.
Teleom. Conf.(Globeom),SanFraniso,CA,USA,De.2003.
[33℄ W. Yu and J. Cio, Trellis preoding for the broadasthannel, in Pro. IEEE
Glob. Teleom. Conf.(Globeom), SanAntonio,TX,USA,Nov.2001.
[34℄ C. Peel, B. Hohwald, and A. Swindlehurst, A vetor-perturbation tehnique for
near-apaitymulti-antennamulti-userommuniation-partI:hannelinversionand
regularization, IEEE Trans.Commun.,vol.53,no.1,pp.195202,Jan.2005.
[35℄ M.Airy,A.Forenza,R.W.HeathJr.,andS.Shakkottai,PratialCostapre-oding
for the multiple antenna broadast hannel, in Pro. IEEE Glob. Teleom. Conf.
(Globeom),Dallas,TX,USA,Nov.2004.
[36℄ C.Windpassinger,R.F.H.Fisher,andJ.B.Huber, Lattie-redution-aided
broad-astpreoding, IEEE Trans.Commun.,vol.52,pp.20572060,De.2004.
[37℄ R. F. H. Fisher and C. H. Windpassinger, Even-integer preoding for broadast
hannels, inPro.of 5thInt.ITG Conf.onSoureandCh.Coding(SCC),Munih,
Germany,Jan.2004.
[38℄ B. M. Hohwald, C.B. Peel, and A. L.Swindlehurst, A vetor-perturbation
teh-nique for near apaity multiantenna multiuser ommuniation - part II:
perturba-tion, IEEETrans.Commun.,vol.53,pp.537544,Mar.2005.
[39℄ M.Tomlinson, Newautomatiequalizeremployingmodulo arithmeti, Eletronis
Letters, vol.7,no.5/6,pp.138139,Mar.1971.
[40℄ M. Miyakawa and H. Harashima, A method of ode onversionfor adigital
om-muniationhannel with intersymbolinterferene, Trans.Inst. Eletron. Commun.
[41℄ M.ShubertandH.Bohe,Solutionofthemultiuserdownlinkbeamformingproblem
withindividualSINRonstraints, IEEETrans.Vehi.Teh.,vol.53,no.1,pp.1828,
Jan.2004.
[42℄ M. Stojni, H. Vikalo, and B. Hassibi, Maximizingthe sum-rate of multi-antenna
broadasthannelsusinglinearpreproessing, IEEETrans.WirelessComm.,vol.5,
no.9,pp.23382342,Sept.2006.
[43℄ Z.TuandR.S.Blum,Multi-userdiversityforadirtypaperapproah, IEEEComm.
Lett.,vol.7,no.8,pp.370372,Aug.2003.
[44℄ M.SharifandB.Hassibi, Aomparisonoftime-sharing,DPC,andbeamformingfor
MIMObroadasthannelswithmanyusers, IEEETrans. Commun.,vol.55, no.1,
pp.1115,Jan.2007.
[45℄ Q.H.Spener,A.L.Swindlehurst,andM.Haardt,Zero-foringmethodsfordownlink
spatialmultiplexinginmultiuserMIMOhannels, IEEETrans.Sig. Proessing,vol.
52,no.2,pp.461471,Febr.2004.
[46℄ B.HohwaldandS.Viswanath,Spaetimemultipleaess: lineargrowthinthesum
rate, inPro.of40thAllertonConf.onCommun.,ControlandComput.,Montiello,
IL,USA,Ot.2002.
[47℄ A. Lapidoth, On the high-SNR apaity of non-oherent networks, IEEE Trans.
Inform.Theory,vol.51,no.9,pp.30253036,Sept.2005.
[48℄ W.ChoiJ.G.Andrews, Theapaitygainfrombasestationooperativesheduling
inaMIMODPCellularsystem, inPro.IEEEInt.Symp.Info.Th.(ISIT),Seattle,
WA, USA,July2006.
[49℄ L.Breiman,Onsomelimittheoremssimilartothear-sinlaw, TheoryofProbability
anditsAppl.,vol.10,1965.
[50℄ M.R.LeadbetterandH. Rootzen, Extremaltheoryforstohasti proesses, Ann.
Probab.,vol.16, pp.431478,1988.
[51℄ D.J. Love,R.W. Heath Jr.,W. Santipah,and M.L.Honig, Whatisthevalueof
limitedfeedbakforMIMOhannels?, IEEEComm.Mag.,vol.42,no.10,pp.5459,
Ot.2003.
[52℄ P. Ding, D. J.Love, and M. Zoltowski, Multiple antenna broadasthannels with
shape feedbak and limited feedbak, IEEE Trans. Sig. Proessing, vol.55, no. 7,
pp.34173428,July2007.
[53℄ P. Viswanath, D. N. Tse, and R. Laroia, Opportunisti beamforming using dumb
antennas, IEEE Trans.Inform. Theory, vol.48,no.6,pp.12771294,June2002.
[54℄ A. Narula, M. J. Lopez, M. D. Trott, and G. W. Wornell, Eient use of side
informationinmultiple-antennadatatransmissionoverfadinghannels, IEEEJour.
[55℄ S. Zhou,Z. Wang,andG. B.Giannakis, Quantifying thepowerlosswhentransmit
beamformingreliesonniteratefeedbak, IEEETrans.WirelessComm.,vol.4,no.
4,pp.19481957,July2005.
[56℄ K.Mukkavilli,A.Sabharwal,E.Erkip,andB.Aazhang,Onbeamformingwithnite
ratefeedbakinmultiple-antennasystems, IEEETrans.Inform.Theory,vol.49,no.
10,pp.25622579,Ot.2003.
[57℄ W. Santipah and M. Honig, Asymptoti apaity of beamforming with limited
feedbak, inPro. IEEEInt.Symp. Info.Th.(ISIT),Chiago,IL,USA,July2004.
[58℄ D.Love,R.W.HeathJr.andT.Strohmer,Grassmannianbeamformingfor
multiple-inputmultiple-outputwirelesssystems, IEEETrans.Inform.Theory,vol.49,no.10,
pp.27352747,Ot.2003.
[59℄ J. H. Conway, R. H. Hardin, and N. J. A. Sloane, Paking Lines, Planes, et.:
Pakings in Grassmannian Spaes, Journal of Exper. Math., vol. 5, pp. 139159,
1996.
[60℄ W. Santipah and M.Honig, Signature optimization forCDMA with limited
feed-bak, IEEETrans.Inform. Theory,vol.51,no.10,pp.34753492,Ot.2005.
feed-bak, IEEETrans.Inform. Theory,vol.51,no.10,pp.34753492,Ot.2005.