Lecture 8

SpreadSpectrumandOFDM

+Time Domain View (Sieve)

2

Channel

DirectSequenceSpreadSpectrum

+Spread Spectrum

n Usuallythespectrumofasignalisrelatedtothedata(symbol)raten Thenull-to-nullbandwidth@ 1/Tn T isthesymbolduration

n Spread-spectrumn Thespectrumismuchwiderthan1/Tn Thespreadingisachievedusinga“spreadingsignal”alsocalleda

“codesignal”or“spreadingcode”n Thereceiverusescorrelationormatchedfilteringtorecoverthe

originaldata

3

+Types of Spread Spectrum

n Direct-sequencespreadspectrum(DSSS)n Eachinformationsymbolis“chipped”intoapatternofsmallersymbols

n Thepatterniscalledthespread-spectrum“code”or“sequence”n ItisusedinIS-95,W-CDMA,cdma2000andIEEE802.11

n Frequencyhoppingspreadspectrum(FHSS)n Symbolsorpacketsaretransmittedondifferentfrequencycarrierseachtime

n Slowfrequencyhopping– thesamefrequencycarrierisusedoverseveralsymbolsorapacket(common)

n Fastfrequencyhopping– thefrequencycarrierischangedwithinasymbolperiod

n UsedinGSM,IEEE802.11(legacy)andBluetooth

4

+Systems using Spread SpectrumnDSSSisemployedin2GCDMAsystemsn IS-95,cdma2000

nDSSSisemployedinall3GcellularsystemsnUMTSandHSPA

nDSSSwasusedinlegacyIEEE802.11(WiFi)

5

+DSSS Modulation

n Theoriginaldatastreamis“chipped”upintoapatternofpulsesofsmallerduration

n Goodautocorrelationproperties

n Goodcross-correlationpropertieswithotherpatterns

n Eachpatterniscalledaspreadspectrumcodeorspreadspectrumsequence

6

Data Bit

“Spread” Bits

chip

1 2 3 4 5 6 7 8 9 10 11

PeriodicSpreadingCode

DataIn

SpreadingCodeIn

+DSSS details

n Insteadoftransmittingarectangularpulseforazerooraone,wetransmitasequenceofnarrowerrectangularpulses

n Thenarrowpulsesarecalled“chips”n Youoftenseereferencesto“chips/sec”insteadofbits/sec

n TheeasiestwayofcreatingaDSSSsignalistomultiplyoneperiodofthespreadingsequencewitheachdatasymboln Example:IEEE802.11

n Barkersequence:[111-1-1-11-1-11-1]n Totransmita“0”,yousend[111-1-1-11-1-11-1]n Totransmita“1”yousend[-1-1-1111-111-11]

n Sometimespartsofthespreadingsequencearemultipliedwiththedatasymbol

7

+Processing gain

n Definitionofprocessinggainn ThedurationofachipisusuallyrepresentedbyTcn ThedurationofthebitisTn TheratioT/Tc =N iscalledthe“processinggain”oftheDSSSsystem

n Theprocessinggainisalsotheratiobetweenthebandwidthofthespreadsignaltothebandwidthofthedatasignal

n Inmanycases,thisisalsotheratiooftheheightoftheautocorrelationpeaktothemaximumsideloben Thisratiodependsonthespreadingcodeproperties

8

+Operation of a DSSS Transceiver

9

Demodulationinvolvesaprocesscalled“correlation”

+Spectrum and Autocorrelation

10

Original signal

Spread Signal

⌧

⌧

Autocorrelationof Rectangle

Autocorrelationof Barker-11

PSD

PSD

E

E

fc +1T

fc �1T

fc �1Tc

fc +1Tc

f

f

+Autocorrelation properties of the Barker sequence

nThewidthofthemainlobeis2T/11n Aboutone-tenththewidthoftheautocorrelationoftherectangularpulse

nTheheightofthemainlobeis11timestheheightofthesidelobes

nTheratioofmainlobepeaktosidelobeisanimportantmeasureofhow“good”aspreadingcodeis

11

+7- Chip M-sequence

12

PeriodicAutocorrelation

Data Bit

Spreading Code

[1 -1 -1 1 -1 1 1 ]

Tschip

Ts

time time

-1

7

Ts

time

(a) (b)

(c)

chiptime

+Autocorrelation

n Considerthespreadingsequencen [1-1-11-111]

13

1 -1 -1 1 -1 1 1

1 -1 -1 1 -1 1 1 Result:1x-1+-1x1+-1x1=-3

Aperiodicautocorrelation

1 -1 -1 1 -1 1 1

1 -1 -1 1 -1 1 1 1 -1 -1 1 -1 1 1

Result:1x-1+-1x1+-1x1+1x1+-1x-1+1x-1+1x1=-1

Periodicautocorrelation

+Example in a two-path channel

n Randomdatasequenceoftendatabitsn Spreadingby11chipsusingaBarkerpulse

n Twopathchannelwithinter-pathdelayof17chips>bitduration

n Multipathamplitudesn Mainpath:1n Secondpath:1.1

n Justforillustration!

n Reality:n Manymultipathcomponentsn Rayleighfadingamplitudesn Noise!

14

+Data and Channel

15

10 20 30 40 50 60 70 80 90 100 110-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 0 0 0 0 0011 1

+

0 20 40 60 80 100 120-15

-10

-5

0

5

10

15

20

25

Output without spreading16

0 20 40 60 80 100 120-15

-10

-5

0

5

10

15

Without Multipath With Multipath

Output of a Matched Filter

Errorsintroducedbythechannel

0 0 0 0 1 1 0 0 1 00 0 0 0 1 1 0 0 1 0

Signalaftercorrelationissampledatgreenlines

+

0 20 40 60 80 100 120-15

-10

-5

0

5

10

15

Output with spreading17

Without Multipath With Multipath

Output of a Matched Filter

0 20 40 60 80 100 120-15

-10

-5

0

5

10

15

Errorsintroducedbythechannelareremoved

0 0 0 0 0 0011 1 0 0 0 0 0 0011 1

+Summary of DSSS and Combatting Multipath

18

Data Bit

Ts

chip

Ts

time

time

Intersymbol Interference

Symbol 1 Symbol 2

Reduced Intersymbol Interference& In-band Diversity

Traditional Transmission

DSSS Transmission

Channel

+The RAKE receiver

n ObservethepeaksinthechanneloutputinthepreviousslidesthatareNOTsampled(Peaksthatarenotatthegreenverticalline)n Theycontainthe“same”informationasthesampledpeaks– butthese

peaksaredelayed!

n ARAKEreceiverconsistsofatappeddelay-linethatsamplesthesepeaks

n Eachpeakusuallysuffersindependentfadingn ThisisaformofdiversityinherentlyavailableinDSSSsystems

n InIS-95systemstheRAKEreceiverhasthree“fingers”n Itcansamplethreesuchpeakssimultaneouslyn A4thfingerisusedtolistentoadjacentcellsforRSSmeasurementsand

tosupportsofthand-offn Themobilestationistemporarilyconnectedtomorethanonebasestation

19

+Principle of RAKE Receiver

n Stepsn Multipleversionsofasignalarrivemorethanonechipinterval apartn Receiverattemptstorecoversignalsfrommultiplepathsandcombinethem

n Thismethodachievesbetterperformancethansimplyrecoveringdominantsignalandtreatingremainingsignalsasnoise

20

+CDMA/DSSS Summary

+CDMA Properties: Near-Far Problemn ACDMAreceivercannotsuccessfully

de-spreadthedesiredsignalinahighmultiple-access-interferenceenvironment

n Unlessatransmitterclosetothereceivertransmitsatpowerlowerthanatransmitterfartheraway,thefartransmittercannotbeheard

n Powercontrolmustbeusedtomitigatethenear-farproblem

n Mobilestransmitatsuchpowerlevelstoensurethatreceivedpowerlevelsareequalatbasestation

n Powercontrolandchannelproblems!

22

Base station

+CDMA Deployment Issues

nRadioplanninginCDMAsystemsisdifferentfromstandardTDMA/FDMAsystemsn Reuseisdefineddifferentlyn Capacitycalculationsaredifferent

23

+Network planning for CDMA

nThereisnoconceptofco-channeloradjacentchannelinterferencen Interferencearisesfromusersinthesamecellandfromneighboringcells

n Codingandspreadspectrumplayaveryimportantroleinthemitigationofinterference

n InsteadofdefininganSr basedonsignalstrength,itismorecommontouseavalueofEb/It thatprovidesagiven“qualityofsignal”n Usuallythisisthevaluethatprovidesaframeerrorrateof1%– thisprovidesagoodMOSforvoice

n ThequantityIt isthetotalinterference

24

+More on Eb/It

nThevalueofEb/Itdependsgreatlyonn Propagationconditionsn Transmitpowersoftheinterferingusersn SpeedoftheMSn Numberofmultipathsignalsthatcanbeusedfordiversity

nCellbreathingn TheboundaryofaCDMAcellisnotfixedanddependsonwheretheEb/It isreached

n Capacitymustbeoffloadedtoothercarrierstoovercomethiseffect

25

+Coverage holes in CDMA

nPowercontrol,softhandoffandRSSthresholdsplayaveryimportantroleinthedesignn IftoomanyBSs(orsectors)coveranarea,thismaycreatea“coveragehole”

n Usually,notmorethanthreeBSsorsectorsshouldcoveranarea

26

Single CDMA Cell

Multiple CDMA Cells

High interference

holeSoft

handoffregions

+Approach

n Somewhatsimplified,butworksingeneralforM usersinacell

n Letusconsiderthereverselink(uplink)n Therearetwocomponentsoftheinterference

n Owncellinterference- Ion Othercellinterference– Ioc

n Assumingperfectpowercontrol,theowncellinterferenceisgivenby:

Io =(M-1)Svfn S istheaveragepowerreceivedfromeachoftheM mobilestationsn Thereverselink “activityfactor”isvf

n Theactivityfactorisameasureof whatfractionoftimeatransmissionoccurs

27

+Other Cell Interference

n Interferencefromothercellsfluctuatesasafunctionoftheload

n TheaveragevalueIoc canbeexpressedasfollowsIoc =f MSvf

n Assumptionisthatallothercellsaresimilartothecurrentcell

n Thefactorf indicatesfractionofothercellreceivedpowercomparedtotheown-cellreceivedpower

n Insomeways,f isameasureofthereusefactor

n Thefactorf dependsonthesizeofthegivencell,thepathlossexponent,shadowfadingdistribution,softhandoffparameters,etc.

28

+Approach (II)

n Totalinterferenceisgivenby:Itotal =Io +Ioc =[(1+f)M-1]vf S=[M/h - 1]vf S

n Herethetermh referstothe“reuseefficiency”n Supposethereisimperfectpowercontrol,wecanrepresentthisbyafactorhc

Itotal =[M/h - 1]vf (S/hc)

n Ingeneral,therequiredSIRmustbesmallerthantheobservedSIR

(Eb/It)req <(SIR)systemn Ignorethermalnoise

n ThedesiredsignalhasapowerS multipliedbythe“processinggain”Gp

29

+Approach (III)

n Proceedingfurther,weget:

n SolvingforMweget:

nMmax iscalledthe“polepoint”orasymptoticcellcapacity

30

Eb

It=

[M/h - 1]vf (S/hc)

SGp=

[(1+f)M-1]vfS/hc

SGp

M =1

1+fGphc

(Eb/It)vf (1+f)+

Mmax = 1Gphc

(Eb/It)vf (1+f)+

+Cell Loading and Pole Point in IS-95

n Cellloadingn Ameasureofthetotalinterferenceinthesystemcomparedtothermalnoise

n Representedbythequantityr =M/Mmax

n Youcanshowthatitisalsoapproximatelyequaltotheratioofthetotalinterferencetothethermalnoise

n Samplecalculationn Let(Eb/It)reqd =6dB=4,R =9.6kbps,Rc = 1.2288Mcps,hc =0.8,vf =0.5,f =0.67

n Then,thepolepointorMmax willbe:n Mmax =1+ (1.2288´ 106/9.6´ 103)(0.8/(4´ 0.5´ [1+0.67])=1+30.65= 32

n Ifa3sectorantennaisused,typically,thegainincapacityisbyafactorof2.55sothatthepolepointis: 31.65´ 2.55=81

31

+Comparison with AMPS/TDMA

n InAMPS,eachserviceproviderhas12.5MHzBWn Witha3sectorantenna,wecanhaveafrequencyreuseof7n Thereare30kHzchannelspervoicecalln Numberofchannels/cell=

(12.5´ 106 /30´ 103)´ (1/7)=57

n InthecaseofIS-136,witha3sectorantenna,wecanhaveafrequencyreuseof4n Each30kHzchannelcancarry3voicecallsn Numberofchannels/cell=

(12.5´ 106 /30´ 103)´ (1/4)´ 3=312.5

n WhatwasthepolepointofIS-95?n 81percarrierpercellsectorn With8cdma carriersina12.5MHzbandwidth,wecanhaveupto648

channelspercellsectorn With10cdma carriersina12.5MHzbandwidth,wecanhaveupto 810

channelspercellsector

32

+Remarks

n Rangesofvaluesn Powercontrolinefficiencyhc variesbetween0.7and0.85n Voiceactivityfactorvf variesbetween0.4and0.6n Theothercellinterferencef variesbetween0.56and1.28forapathlossexponentof4andastandarddeviationofshadowfadingof6to10dB

33

+Other issues

n ForwardLinkn Wehavetobeworriedaboutthepilot,sync,pagingandtrafficchannelsinIS-95and

manymoreincdma2000andUMTSn Thestrengthofthepilotchanneleffectivelydeterminesthesizeofthecelln Interferenceisfromclustersofhighpowertransmittersratherthanmanydistributedlow

powertransmittersn Designshouldtrytomaketheforwardandreverselinkcapacitiesasclosetooneanother

aspossiblen Thiswillreducetheamountofunnecessaryinterferenceandenablesmoothhandoffs

betweencells

n PNSequenceReusen Howcloselyshouldthesamepilotoffsetsbeused?(laterwhenwedoIS-95)

n Howdoesthelinkbudgetaffectthecapacity?

n Howdoessofthandoffaffectthecapacity?

34

+Frequency Domain View (Gate)

35

OR

OrthogonalFrequencyDivisionMultiplexing

Channel

+Diversity (continued) – Frequency Hoppingn Traditional

n Transmitter/receiverpaircommunicateonafixedfrequencychannel.

n FrequencyHoppingIdean Noise,fadingandinterferencechangewithfrequencybandintimen Movefrombandtoband

n Timespentonasinglefrequencyistermedthe“dwelltime”

nOriginallydevelopedformilitarycommunicationsn Spendashortamountoftimeinonefrequencybandn Preventinterceptionorjamming

36

+

DevelopedduringWWIIbyactressHedyLammar andclassicalcomposerGeorgeAntheil

Patentgiventogovernment

Frequency Hopping Spread Spectrum

37

+Frequency Hopping Spread Spectrumn Twotypesofsystems

n SlowHoppingn Dwelltimelongenoughtotransmitseveralbitsinarow(timeslot)

n FastHoppingn Dwelltimeontheorderofabitorfractionofabit(primarilyformilitarysystems)

n Transmitterandreceivermustknowhoppingpatternoralgorithmthatdeterminesthepatternbeforecommunications.n Cyclicpattern – bestforlownumberoffrequenciesandcombatingsmall-scale

fading:n Examplewithfourfrequencies:f4,f2,f1,f3,f4,f2,f1,f3,….

n Randompattern – bestforlargenumberoffrequencies,combatingco-channelinterference,andinterferenceaveragingn Examplewithsixfrequencies:f1,f3,f2,f1,f6,f5,f4,f2,f6,…n Userandomnumbergeneratorwithsameseedatbothends

38

+Frequency Hopping concept

39

ABC

One Period of Sequence = 1 0 0 1 0 1 1

0 01

10 0

110

111

1 01

11 0

1 00

1 0 0

ABC

t7

t6

t5

t4

t3

t2

t1

t0

CLK

CLK

f4

f1

f3

f7

f6

f5

f2

f4

fc

f1

f2

f3

f4

f5

f6

f7

frequ

ency

cha

nnel

s

time

+Combatting Time Dispersion

Rec

eive

d SN

R

frequencyTransmission

Lost Here

Hop Frequencies

Retransmission Here Successful

+Example Systems

nGSM(2GCellular)nVeryslowhopping

nOriginalIEEE802.11nSlowhopping

nBluetoothnAlsoslowhoppingover79frequencieseach1MHzwide

nPerpackethopping

41R

ecei

ved

SNR

frequency

……

2.402 GHz

2.480 GHz

1 MHz

Collision Different Users

+How do you utilize the entire bandwidth?

IdeainIEEE802.11g/a

=OFDM!

+Orthogonal Frequency Division Multiplexingn Ideainfrequencydomain:

n Coherencebandwidthlimitsthemaximumdatarateofthechanneln Senddatainseveralparallelsub-channelseachatalowerdatarateand

differentcarrierfrequency

n Ideaintimedomain:n Byusingseveralsub-channelsandreducingthedatarateoneach

channel,thesymboldurationineachchannelisincreasedn Ifthesymboldurationineachchannelislargerthanthemultipathdelay

spread,wehavefewerrors

n OFDMenablesn Spacingcarriers(sub-channels)ascloselyaspossiblen ImplementingthesystemcompletelyindigitaleliminatinganalogVCOs

43

+What is OFDM?

nModulation/Multiplexingtechnique

nUsualtransmissionn Transmitssinglehigh-ratedatastreamoverasinglecarrier

nWithOFDMnMultipleparallellow-ratedatastreamsn Low-ratedatastreamstransmittedonorthogonalsubcarriers

n Allowsspectraloverlapofsub-channels

44

+OFDM Remarks

n ItisNOTanewtechnologybuthasfoundnewimportancebecauseofapplicationsn DSLmodemswherethechannelisnotuniformn Digitalaudioandvideobroadcastn WirelessLANapplications

n IEEE802.11aandHIPERLAN-2

n FastimplementationusingFFT’sisnowpossible

n Canbeadaptive(usedin802.11a)

n Problemsn Synchronizationbetweencarriersn Peak-to-averagepower(PAP)ratios

n Requireslinearamplifiers

45

+OFDM Advantages

nBandwidthefficiency

nReductionofISIn Needssimplerequalizers

nRobusttonarrowbandinterferenceandfrequencyselectivefading

nPossibilityofimprovingchannelcapacityusingadaptivebitloadingovermultiplechannels

46

+OFDM in frequency and time domains

47

n Noteorthogonality inbothdomainsn Whatisone“OFDMsymbol”?

Frequency

Power Spectrum

sub-carrier

single carrier

4 Carriers Spanning the Bandwidth of One Carrier

Channel

Bc

frequency

Fourier transform of symbol

time

AmplitudeSub-Carriers

+OFDM Signal/Symbol

48

Df

+OFDM Symbol

n OneOFDM“symbol”lastsforsayTs secondsn Thesymbolconsistsofthesumoftheindividualsymbolsfromthemanysub-carriersn Example:ConsiderQPSKoneachcarrier

n Ingeneraln ForN subchannels,theN samplesofthei-th transmittedOFDMsymbolcanbewritten

as

49

IFFTComplexNumber

+Guard Time and Cyclic Prefix

n GuardtimeeliminatesISIiflargerthanexpecteddelayspreadoccurs

n Iftheguardtimehasnosignal,intercarrierinterference(ICI)mayoccurn ICIislikeacrosstalkbetweensubcarriers

n AcyclicprefixeliminatesICIn EnsuresthatdelayedreplicasofOFDMsymbolsalwayshaveintegernumberofcycleswithintheFFTinterval

n Maintainsorthogonalitybetweensubcarriersn Cyclicprefixisremovedatthereceiver

50

+OFDM Transmission – basic system

n N consecutivecomplexsymbolsareconvertedintoagroupofNparalleldatastreams,whichthenaremodulatedoverorthogonalsubcarriers

51

ChannelEncoding

SymbolMapping

SerialtoParallel

N-PointIFFT

ParallelToSerial

Guard/CPInsertion

ChannelDecoding

ParalleltoSerial Detector N-Point

FFTSerialtoParallel

Guard/CPRemoval

RadioChannel+AWGN

+Adaptive OFDM

52

frequency

|H(f)|

+Channel Partitioning for Multicarrier Modulation

n Asthechannelisfrequencyselective,itmakessensetosplitthechannelintoseveralsmallerpartsn EachsmallerchunkisnowanAWGNchannel

n EachAWGNchannelprovidesadifferent SNR

n Question:Howdoweallocatetransmitpowers/modulationschemestoeachchunk?Whatisthemostoptimal?

53

NoisePSD/|H(f)|

Allocationofpower

Water-fillingalgorithmAllocatemoreenergywheretheSNRisbetter!

+Adaptive OFDM

n Improvechannelcapacityfurthern Changemodulationschemen Allocatingbits/powerpersubcarrieraccordingtothequalityofeachsubchannel

54

AOFDM Components

Channel Quality Estimator*

Set of Modulation Schemes

Adaptive Loading/Allocation Algorithm

+

+

+Adaptive Modulation

55

No transmission (0 bits)

BPSK (1 bit/symbol)QPSK (2 bits/symbol)

16-QAM (4 bits/symbol)8-QAM (3 bits/symbol)

Set of ModulationSchemes

+Adaptive Modulation on Parallel Channels

56

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Number of Subcarriers

SNR (dB) BW Efficiency

1 bit

2 bits

3 bits

4 bits

16

+Operation of Adaptive Algorithms

57

ChannelQuality

Estimator

Adaptive Algorithm

BitsAnd

Power

Subcarrier 1

Subcarrier 2

Subcarrier 3

Subcarrier N

Channel QualityInformation, e.g. SNR

time

Allocation

Based on optimal“Water-Filling”Power Distribution

+

Modulation Scheme Selection

+OFDM Based Wireless LANs – IEEE 802.11an OperatesintheU-NIIBand

n 5.15–5.25,5.25–5.35,and5.725–5.825GHz

n Providesmultipletransmissionmodes/ratesdependingonchannelconditions.n 6,9,12,18,24,36,48,and54Mbps

n 4digitalmodulations:BPSK,QPSK,16-QAM,64QAM

n Radiospectrumisdividedinto8separatesegments/channels,20MHzeach

n 52carriers(subchannels)perchanneln Eachsubcarrierhasbandwidthof~300kHzn 48fordatamodulation,and4forpilotsignal

58

+Recent Trends

nMIMOwithOFDMn IEEE802.11n,802.11acnDataratesgreaterthan100Mbps

nOFDMforwideareadataservicesn LTEandWiMax

nOtherPHYtechnologiesnUWBwithOFDMnMC-CDMA

+Revisiting “Data Rates” in Wireless

nHomeA/Vnetworksareexpectedtoneed1-10GbpsnAssumingaspectralefficiencyof1bps/Hz,weneedatleast1GHzofspectrumnHaveignoredtheeffectsofmultipathfading

nBruteforceapproachnMaynotmeetthetechnology,regulatoryandcostrequirements

nCanweincreasethebps/Hzinwirelesssystems?

60

+

Source:IEEESpectrum- July2004

Even

tualcon

vergen

ce

Edholm’s Law

n PhilEdholmn Nortel’sCTO

n ThreeTelecomCategoriesn Wirelinen Nomadic(Portable)n Wireless(Mobile)

n Dataratesincreaseexponentiallyn Thereisapredictabletimelagbetweenwirelessandwirelinesystems

61

+How can we increase data rates?

n Traditionalwaysn Reducethesymbolduration

n Needslargerbandwidthn Leadstoawidebandchannelandfrequencyselectivity-irreducibleerrorrates

n Increasethenumberofbits/symboln ErrorratesincreasewithM forthesameEb/N0

n MIMOsystemsn Thereisnoneedtoincreasethebandwidthorpower

n Butwhatarethelimitations?n Usemultipletransmit(Tx)andreceive(Rx)antennasn Increasesspectralefficiencytoseveraltensofbps/Hz

62

+What is MIMO?

n SofarwehaveconsideredSingleInputSingleOutputorSISOsystemsn Bothtransmitterandreceiverhave

oneantennaeachn Simplestformoftransceiver

architecture

n Singleinputmultiple-output(SIMO)systemsn Receiverhasmultipleantennas

n Multipleinputmultipleoutput(MIMO)systemsn Bothtransmitterandreceiverhave

multipleantennasn Strictly:EachantennahasitsownRF

chain(modulator,encoderandsoon)

63

+Performance enhancements due to MIMOnDiversitygainnAbilitytoreceivemultiplecopiesofthesignalwithindependentfading

nSpatialmultiplexinggainnSenddifferentinformationbitsoverdifferentantennasandrecovertheinformation

nInterferencereductionnReducetheregionofinterferencetherebyincreasingcapacity

64