Optimized UL RS DesignOZCL Sequences.docx
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Optimized UL RS DesignOZCL Sequences.docx
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OptimizedULRSDesignOZCLSequences
3GPPTSG-RANWG1#48bisR1-072053
Kobe,Japan,May7-11,2007
Source:
Sharp
Title:
OptimizedULRSDesign-OZCLSequences
AgendaItem:
7.11.2
Documentfor:
DiscussionandDecision
1.Introduction
Inaprevioussubmission[1]SharpproposedtheuseofOptimizedZadoff-Chu-Like(OZCL)sequencesfortheULdemodulationreferencesignals.InthissubmissionSharppresentsupdatedresultsthatverifytheperformanceimprovementsforOZCLsequences.
OZCLsequencesoffersignificantgainsforULRSusecomparedtoextendedZadoff-Chu(EZC)sequencesandtruncatedZadoff-Chu(TZC)sequences.asthiscontributionshows.
BasedontheseresultsandthepropertiesofOZCLsequences,SharprecommendstheuseofthesesequencesforULRSdemodulationsignalsforE-UTRA,atleastforshorterlengthsequences(length12-36).WebelieveourapproachrepresentsthebestwaytoactuallyobtainsequencesthataredesignedtomeettherequirementsofE-UTRA:
lowerPAPRandcubicmetric,lowercross-correlation,andbetterperformancewithsequencesofdifferentlengths.
Inadditiontofocusingonthe12-subcarriercase,whichrepresentsthemoststringentre-userequirements,wepresentlinklevelsimulationresultsforthecasewherethereare12and36subcarriersassignedconcurrently,aswellascommentsoncomplexityandanoverallcomparisonwithcyclicallyextendedZadoff-Chu(EZC)sequencesandtruncatedZadoff-Chu(TZC)sequences.
InthefollowingsectionwewillsummarizethecomparisonbetweenOZCLsequencesandTZC/EZCsequences.Wewillthenreviewthealgorithmusedtodesignthesequencesasdescribedin[1],andpresentupdatedlinksimulationresults.Followingthatwewilldescribeimplementationconsiderations.WewillthensummarizeourcomparisonwithTZC/EZCsequences.
2.
SummaryPerformanceComparison
Basedonresultsandconsiderationsdiscussedinthefollowingsections,wecansummarizetheperformancepropertiesofOZCLsequencescomparedtoextendedandtruncatedZCsequenceswecanmakethefollowingtables:
Table1SummarycomparisonofpropertiesbetweenOZCLandTZC/EZC
Criterion
OZCLSequences
TZC/EZCSequences
MedianCorrelation
Lower
Higher
Storage
Higher(but2Kbyteswithlength12)
Lower
ComputationalComplexity
AboutthesameifPAPRoptimizationisdoneinreal-time
MoreifOZCLsequencePAPRoptimizationnotdoneinrealtime.
Cross-correlationperformance
Alwaysbetter
Alwaysworse
Performancefor1RB
Substantiallybetterfor4RSpersector;alwaysbetterfor2RSpersectoratmedianSINRs.
SubstantiallyworseforRSpersector,alwaysworsefor2RSpersectoratmedianSINRs.
CM/PAPR
PAPRoptimizationallowsadirecttrade-offbetweensequencecross-correlationperformanceandPAPR/CM,andthisoptimizationcreatessequenceswithlessaveragecross-correlationthanTZC/EZCsequences.
Sequenceselectionistheoptimizationmethod;limitsthenumberofusablesequences,NodeBmayneedtore-assignsequencesbasedontransmittedpower[16].
SequenceHopping
PerformanceadvantagesshouldstillbebetterthanTZC/EZCsequences
Neededforcross-correlationperformance
FrequencyHopping
Notaproblem
Notaproblem
Table2MedianSINRPerformance
Sequence
Length12Sequences
Length36equences,
4sequences/sector
Length12and
Length36Sequences,
4Sequencespersector
2Sequences/sector
4Sequences/sector
SINR
∆OZCL
SINR
∆OZCL
SINR
∆OZCL
OZCL
0.06dB
-
-4.19dB
-
0.29dB
-
-3.84dB
(36&12)
-4.67dB
(3x12&12)
TZC
-0.35dB
-0.29dB
-5.44dB
-1.25dB
0.05dB
-0.24dB
-4.97dB(36&12)
EZC
-1.07dB
-1.01dB
-6.42dB
-2.23dB
-5.62dB
-5.34dB
-
Table3CM/PAPR
Sequence
Max.RawCM,dB
Length12
Length36
OZCL
3.32dB
2.45
TZC
5.19dB
4.33
EZC
3.86dB
4.54
3.
OptimizedULRSDesignAlgorithmandSimulationResults
In[1]weproposedasetofOZCLsequencesthatareidenticaltoZadoff-Chusequenceswhenthenumberofthesequencelengthischosentobeaprimenumber.
However,whentheZadoff-Chusequencelengthisnotaprimenumber,theOZCLsequencesderivedfromapplicationoftheproposeddesignalgorithmwillbeoptimizedandhavesignificantlyimprovedmeancorrelationbetweenanytwopairsofsequencescomparedtoextendedortruncatedZadoff-Chusequences.Theresultingsequenceshavethefollowingproperties:
Property1:
Theyareminimallycorrelated.
Property2:
Theyhaveconstantmodulus.
Property3:
Theirsubsetsareorthogonalornearlyorthogonal,
Property4:
Theirsubsetsarecyclicshiftsofeachother.
ThusthesetofOZCLsequencesis“basedon”GCL/CAZACsequences,butwiththeprovisothatthesequencesareoptimizedfortheLTEnumerologyandthusofferasignificantperformanceadvantagecomparedtoTZC/EZCsequences.In[2]itisshownthatifaWelchBoundEqualitysetofsequencesexist,thentheframe,ormatrixofsequences,mustbeaunitnormtightframe.Assuchwerestrictourselvestosequencesthatarebasedonaprojectiontothenearesttightframe,whichturnsouttobetheunitarypartofapolardecompositionoftheframe.NotethatTZCorEZCsequences,especiallyforlength12,donotpossessakeypropertythatatightframeimplies,namely,thatalleigenvaluesofitssingularvaluedecompositionarenotthesame.Thisislikelyonereasonthatcross-correlationpropertiesofTZC/EZCsequencesarewidelyvarying.
InthenextsectionwedemonstratethattheproposedOZCLsequenceshavesignificantenoughperformancegainstojustifytheiruseasULRS.
InAnnexAwedescribethealgorithmusedtocreatesuchsequencesindetail,basedonalternatingprojectionsontoconvexsetsandorthogonalmanifolds.
4.
PerformanceComparisonofOZCLwithtruncatedZCsequences
InwhatfollowsweshallmainlybaseresultsforcomparisonwithtruncatedZCsequences.Regardingcross-correlationperformance,EZCsequencesgenerallyperformworsethanTZCsequencesascanbeseenfromTable1,andthegainsofOZCLsequenceswithrespecttoEZCsequencesaregenerallygreaterthanwithTZCsequences.HencewefocusedonacomparisonwithTZCsequences.
TodeterminetherelativedifferenceOZCLsequences’performancewithrespecttoTZCsequences,weused,for2tiersofcells,with3sectorspercell,ageneticalgorithmbasedontheconceptsuggestedin[3].DetailsofthisalgorithmareinAnnexB.
4.1.Cross-correlationbetweenlength12sequences
InFigure1,weshow,forthe12sub-carriercase,thecomparisonofCDFofcross-correlationsoftheOZCLdesignedfromthealgorithmpresentedintheAnnexwith5000iterationsversustheTZCsequences,for84sequences,composedof7groupsof12OZCLsequences.Inaddition,thecross-correlationsof84EZCsequencesareshown.
Figure1Cross-CorrelationmagnitudeofOZCLsequencesversustruncatedsequencesfor84sequencesoflength12
FromtheabovecurvewhileOZCLsequenceshavegreatermaximumcorrelationbetterthantruncatedZCsequences;theaveragecorrelationmagnitudeis1.2dBlessthanTZCsequences;anditsmedianvalueis0.75dBbetterthanTZCsequences.
4.2.
Intercellinterferencewithlength12sequences
4.2.14sequencespersector
Nextweconsideredwhetheritispossibletoassignsequencestocellsandsectorsthatactuallyminimizethemultipleaccessinterference.Toanswerthatquestionweassigned4sequencestoeachof3sectorspercell,inatypical19hexagonalcellarrangement,using25iterationsofthegeneticassignmentalgorithmdescribedinAnnexB.ThesimulationincludedtheparametersofTable4,andtheCDFofreceivedSINRisdepictedinFigure2.ThemedianSINRofOZCLsequencesisseentobe1.25dBbetterthanforTZCsequencesatthemedian.
Inaddition,wecomparedtheperformanceofEZCsequenceswithOZCLsequences.TheEZCsequences,whilehavingbetterCMpropertiesthanTZCsequences,alsohaveworsecross-correlationproperties;theyareworsethanOZCLsequencesby2.9dBatthemedian.
Inthiscase,with4UEspersector,OZCLsequencesoutperformEZCsequencesbyover2.2dB.
4.2.12sequencespersector
Wehavealsoinvestigatedthesituationwhereonly2RSareassignedpersector.Inthatcase,regardingSINR,OZCLsequencesoutperformTZCandEZCsequencesby0.4dBand1.0dBrespectivelyatthemedian.
Thus,forlength12sequences:
∙OZCLsequenceshavebettercross-correlationpropertiesandSINRperformancethaneitherTZCorEZCsequences.
∙OZCLsequenceshavelowerCMthaneitherEZCorOZCLsequences.
∙IfthechoiceofsequencesisrestrictedtoEZCandTZCsequences,thereisapenaltypaidfortradingoffCMwithsequenceSINR,whereaswithOZCLsequencesitispossibletogetthebestbenefitsofEZCandTZCsequences.
Table4SimulationParameters
Parameter
Assumption
CellularLayout
Hexagonalgrid,19cellsites,3sectorspersite
CellISD
1732m
Distance-dependentpathloss
L=I+37.6log10(.R),Rinkilometers
I=128.1–2GHz
Shadowingfading
Log-normal,10dBstandarddeviation
Antennapattern(horizontal)
(For3-sectorcellsites
withfixedantennapatterns)
=70degrees,Am=20 dB
Userdistribution
Uniformlydroppedinsectorarea,4UEspersector
CarrierFrequency
2.0GHz
MinimumdistancebetweenUEandcell
>=35meters
MaximumUETXpowerincludingPAPRbackoff
24dBm
NoiseFigure
4dB
Powercontrol
Maintainreceivedsignalpowerasthatatcelledge
Figure2SINRof12-lengthOZCLsequencescomparedtoTZCsequences,4RSspersectorperRB
Figure3EZCversusOZCLsequenceSINR,4RSspersectorperRB
Figure4SINRdistribution,2RSpersectorperRB
4.3.Length36sequences
Inaddition,weinvestigatedthepropertiesoflength36sequences.Forsetsof108sequencesbrokeni
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