Lecture 7 - sis.pitt.edu · Block interleaving n After codewords are created, the bits in the...

Lecture 7

TraditionalTransmission(Narrowband)SmallScaleFading– TimeVariation

+ Communication Issues and Radio Propagation

Fading Channels

Large Scale

Fading

Path-Loss &

Shadowing

Impacts Coverage

Small Scale

Fading

Time Variation

Time Dispersion

Angular Dispersion

Impactssignaldesign,receiverdesign,coding,BER

2

+Small scale fading

n Multipath=severaldelayedreplicasofthesignalarrivingatthereceiver

n Fading=constructiveanddestructiveaddingofthesignals

n Changeswithtime

n Resultsinpoorsignalquality

n Digitalcommunicationsn Highbiterrorrates

amplitudeloss

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5−1.5

−1

−0.5

0

0.5

1

1.5

Time in Seconds

Ampl

itude

Path 1Path 2Sum

3

+Summary

102.4 102.5 102.6 102.7 102.8 102.9−130

−125

−120

−115

−110

−105

−100

Distance from Base Station in Logarithmic Scale

Pow

er in

dB

Linear Fit of RSS in dB to log(distance)Slope is the distance-power gradient

Large Scale FadingHistogram of Deviations is Shadow Fading

Small Scale FadingHistogram of Deviations is Multipath Fading

Fourier Transform of Deviations is Doppler Spectrum

4

+ Small scale fading amplitude characteristics

n AmplitudesareRayleighdistributedn Worstcasescenario– resultsinthepoorestperformance

n Inline-ofsightsituationstheamplitudeshaveaRiceandistributionn StrongLOScomponenthasabetterperformancen WeakLOScomponenttendstoaRayleighdistribution

nOtherdistributionshavebeenfoundtofittheamplitudedistributionn Lognormaln Nakagami

5

+

z

f Z(z

)

�

0.6065�

Rayleigh, Rician and Lognormal PDFsI0(x)isthemodifiedBesselfunctionofthefirstkindoforderzero

fRay(r) =r

�2exp

✓� r2

2�2

◆, r � 0

fRic(r) =r

�2exp

✓�r2 +K2

2�2

◆I0

✓Kr

�2

◆, r � 0,K � 0

fLN(r) =1p

2⇡�2rexp

✓� (ln(r)� µ)2

2�2

◆

6

+Time variation of the channel

nTheradiochannelisNOTtimeinvariantn Movementofthemobileterminaln Movementofobjectsintheinterveningenvironment

nHowquicklydoesthechannelfade(change)?n Foratimeinvariantchannel,thechanneldoesnotchange

– thesignallevelisalwayshighorlown Fortimevariantchannels,itisimportanttoknowtherate

ofchangeofthechannel(orhowlongthechannelisconstant)

n MaximumDopplerfrequencyfm =fc v/c v isthevelocityofthemobile(orspeedofchangesintheenvironment)

7

+Fade rate and fade duration

n Thesignal“level”isthedBaboveorbelowtheRMSvalue

n Faderatedetermineshowquicklytheamplitudechanges(frequencyà DopplerSpectrum)

n Fadedurationtellsushowlongthechannelislikelytobe“bad”

n Designerrorcorrectingcodesandinterleavingdepthstocorrecterrorscausedbyfading

“level”

6crossingsofthe“level”in30seconds

timeunderthe“level”

packet

0 30 time

8

+Fade rate and duration

rmsmR rrrrrfN / )exp(22

=-= pLevelcrossingrate:

Averagefadeduration:

rmsm

rrrfrr / 2

1)exp(2

=--

=p

tfm =maximumDopplershift=fc v/c

v isthemobilevelocityc isthespeedoflightfc isthecarrierfrequency

9

+Coherence Time

n Howlongcanyouconsiderthechanneltobeconstantintime?

n WrittenasTcn Pleasedon’tconfusethiswiththe“chipduration”thathasthesamesymbol

n Examplen v=100km/h

n At900MHz,fm isabout83.3Hzn Thechannelchanges“could”occur83.3timesasecondn Tc=2.1ms

58

3

101081

360010310100

×=

××

×=

c

m

ff

10

+Performance in Mobile Wireless Channelsn Wirelesschannelconditionsinclude

n Attenuationn Multipathn Fadingn Interference

n Ifthechannelisaffectedbymultipathandfading,performanceisdifferentfromthatinAWGNchannels

n Ideallywestillwantn Verylowbiterrorratesatlowsignaltonoiseratiosundermultipathandfadingn Robustundermultipathandfading

n Doesnotdegraderapidlyiftheconditionschangen Practically,weneedanincreaseincomplexity/cost,bandwidth,and/orpower

toovercometheeffectsofmultipathandfading

11

+Performance in “Flat” Rayleigh Fading Channel

0 5 10 15 20 25 30 35 40 45 5010−6

10−5

10−4

10−3

10−2

10−1

Average SNR per Bit in dB

Aver

age

Bit E

rror r

ate

35 dB

Ps =1

2erfc (

p�b)

Ps =1

2

✓1�

r�̄b

1 + �̄b

◆⇡ 1

4�̄b

(AWGN - Non-fading)

(Flat Rayleigh-fading)

BPSK

12

+ Performance in Flat Rayleigh Fading Channelsn TheBERisnowafunctionofthe“average”Eb/N0

n ThefallinBERislinearnotexponential!

n LargepowerconsumptiononaveragetoachieveagoodBERn 30dBisthreeordersofmagnitudelarger

time

� b

�̄b

average

High and low that is close to 0�b Pe

Low and high that is close to maximum of 0.5�b Pe

13

+What is diversity?

n Idea:Sendthesameinformationoverseveral“uncorrelated”formsn Notallrepetitionswillbelostinafade

n Typesofdiversityn Timediversity– repeatinformationintimespacedsoastonotsimultaneouslyhave

fadingn Errorcontrolcoding!

n Frequencydiversity– repeatinformationinfrequencychannelsthatarespacedapartn FrequencyhoppingspreadspectrumandOFDM

n Spacediversity– usemultipleantennasspacedsufficientlyapartsothatthesignalsarrivingattheseantennasarenotcorrelatedn Usuallydeployedinallbasestationsbutharderatthemobilen TransmitdiversityandMIMO

n Polarizationdiversity

14

+Example of Diversity

nNotethatfadesareNOTalignedintime

nRecoveringinformationfromatleastonediversitybranchhasabetterchance

0 10 20 30 40 50 60 70 80 90 10010−3

10−2

10−1

100

0 10 20 30 40 50 60 70 80 90 10010−3

10−2

10−1

100

0 10 20 30 40 50 60 70 80 90 10010−3

10−2

10−1

100

0 10 20 30 40 50 60 70 80 90 10010−3

10−2

10−1

100

�b

�b

time

Threshold �b

Acceptable BER

Unacceptable BER

Diversity Branch 1

Diversity Branch 2

15

+Performance with diversity

n Ifthereisidealdiversity,theperformancecanimprovedrastically

n Therearedifferentformsofdiversitycombining

n Maximalratiocombiningn Difficulttoimplement

n Equalgaincombiningn Easytoimplement

n Selectiondiversityn Easytoimplement

n Problemsn Bandwidth!

BPSKwithM ordersofdiversity

16

+Frequency Hopping and Diversity

n Noticethatretransmissionsarelikelytosucceed

n EachtransmissionoccupiesaBW<coherenceBW R

ecei

ved

SNR

frequencyTransmission

Lost Here

Hop Frequencies

Retransmission Here Successful

17

(later)

+Error control coding

n Codingisaformofdiversityn Transmitredundantbits

usingwhichyoucanrecoverfromerrors

n Theredundantbitshaveapatternthatenablesthisrecovery

n Typesofcodingn Blockcodes(n,k)n Convolutional codesn Trelliscodedmodulationn Turbocodes

n Ideaof“coderate”Rcn Tradeoffs

Block Encoder

k bit data block n bit codeword

n-k parity check bits

k databits

18

+Motivation for Error Control Codingn Wecannotderivetheperformanceoferrorcontrolcodeshere

n Exampleofa(24,12)Golay coden Rayleighfadingchannel

n BFSKwithtwoordersofdiversity

n BFSKwithGolay code

19

+ Operation of block codes and interleaving

n Blockcodescancorrectuptoterrorsinablockofn bitsn Thevalueoft dependsonthecodedesign

n Hammingcodescancorrectoneerrorn Iftheminimumdistance ofthecodeisdmin,thenthecodecan

n Correctt =ë(dmin – 1)/2û errorsn Detectdmin – 1errors

n Iftherearemorethant errors,theerrorscannotbeusuallycorrected

n Inradiochannelswesee“bursts”oferrorsthatmayresultinmorethantbitsinablockofn bitsbeinginerror

n Inordertocorrectthesebursterrors,itiscommonto“interleave”thebits

n Aftercodingn Beforetransmitting

20

+What does coding get you?

n Considerawirelesslinkn Probabilityofabiterror=qn Probabilityofcorrectreception=p =1- qn Inablockofk bitswithnoerrorcorrection

n P(word correctlyreceived)=pk

n P(word error)=1– pk

n Witherrorcorrectionoft bitsinblockofn bits

)correct word(1)error word(

)()correct word(0

PP

qpin

P iint

i

-=

÷÷ø

öççè

æ= -

=å

21

+What does coding get you?

n Exampleconsider(7,4)HammingCodewhenBER= q =.01,p =0.99n Inablockof4bitswithnoerrorcorrectionn P(word correctlyreceived)=pk =.9606n P(word error)=1– pk =0.04n Witherrorcorrectionof1bitinblockof7bits

n Getanorderofmagnitudeimprovementinworderrorrate

002.0) (1) (

998.0)(17

)() ( 167

0

=−=

=""#

$%%&

'+=""

#

$%%&

'= −

=∑

correctwordPerrorwordP

qppqpin

correctwordP iint

i

22

+Impact of fading and coding

n Problem:n An(n,k)blockcodeconsistsofcodewordsthataren-bitslongn Itcancorrectt biterrorswithinthisblockofnbits.

n Whathappensifthereisaburstofnoiseorfadeandtherearemorethantbitsinerror?n Wehavelookedatthe“average”effectofcodingn Wehaveignoredthetimevariationofthechannelsofar

n Idea:n Errorsinwirelesschannelsoccurinburstsn Iftheerrorscanbespreadovermanycodewordstheycanbecorrected

23

+Block interleaving

n Aftercodewords arecreated,thebitsinthecodewords areinterleavedandtransmitted

n Thisensuresthataburstoferrorswillbedispersedoverseveralcodewords andnotwithinthesamecodeword

n Needsbufferingatthereceivertocreatetheoriginaldata

n Theinterleavingdepthdependsonthenatureofthechannel,theapplicationunderconsideration,etc.

24

+Convolutional Codes

n Thereisafinitestatemachinewithmemory(Kunits)thatgeneratesanencodedoutputfromaserialinputdata

n Decodingisachievedviaa“tree”ora“trellis”bychoosingthemostlikelypathwithinthetreeortrellis

n Softdecodingispossiblen Adecisiononabitismadebasedonavarietyofsignallevels

andnotasinglethreshold

n Convolutional codesaremorepowerfulthanblockcodesbuttheyrequirealargerredundancy

n Rate1/3and½codesareusedinGSMandCDMAn Datarateisreducedbyhalfortwo-thirdswiththesecodes

25

+Performance with Convolutional Codes

n Graphisnottoscale,butonlytogiveyouanidea

n Theplotisina flatRayleighfadingchannel

n Youcanseethatwithroughlytwoordersofdiversity,codingisfarmoreefficient 10-4

Pe

AverageEb/N0 indB

40261614

BFSK– NoDiversity

BFSK– 2ordersofdiversity

Rate1/2ConvolutionalCode,K=3,K=4,K=5

Forillustrationonly;Nottoscale

26

+The search for the perfect code

nTurboCoden Concatenationofcodeswithinterleaving

n Followedbyaniterativealgorithmfordecodingn Usesoftdecisionstomakethedecodingpowerful

n Insteadofcountingdifferencesinbitpositions,distanceprobabilitiesareused

n Thesearecalledprobabilisticcodes forthisreasonunliketypicalblockandconvolutionalcodesthatarecalledalgebraiccodes

nUsedin3Gcellular(UMTS)standard

27

+Turbocode Performance

n OnceacriticalvalueofEb/N0 isreached,theBERwithturbocodingdropsrapidly

n AtPe = 10-5,theturbocode islessthan0.5dBfromShannon’stheoreticallimitn Needsalargeblocklengthn Needsalargenumberofiterations

n ItdisplaysanerrorfloortypicallyatPe =10-6 orson Thedashedcurveishaltedinthefigure

0 2 4 6 8 10 1210-6

10-5

10-4

10-3

10-2

10-1

100

Eb/N0 in dB

P e

Shannon’slimitforrate1/2coding


Turbocode

Uncoded

AWGN

28

+Turbocode Performance in a Flat Rayleigh Fading ChannelnSomeresultswithinterleavingand“sideinformation”

nSeeE.K.HallandS.G.Wilson,“DesignandAnalysisofTurbocodesonRayleighFadingChannels,”IEEEJSAC,Feb.1998

Eb/N0

0 1 2 3 4 5

Pe

10-1

10-2

10-3

10-4

10-5


capacity

Smallblocklength

Largerblocklength

29

Transmit Diversity: AlamoutiScheme

n Providesclosetotwoordersofdiversityn Itis3dBworsethanidealreceivediversitybecausethetwotransmitantennassplitthetotalpower

n IfthereareM receiveantennas,youcangetdiversityoforder2Minthesameway

n Worksforanycomplexmodulationscheme

n Canthinkofitasa“space-timecode”n Usedin3Gsystems

BPSK- CoherentDetection

30 30

+Alamouti’s Scheme in a 2×1 system

nSendsymbolsinspaceandtimeasshownbelow

31

Transmitter

+

nCombiningscheme

nWhatdoweget?

nSimilarly

Alamouti’s Scheme in a 2×1 system (2)

Twoordersofdiversity

32

+MIMO Diversity

n Idean Useboth transmitandreceivediversity!

nConsidertheAlamouti schemeinthe2×2MIMOsystemn Sendtwosymbolsintwosymbolperiodsn Bothreceiveantennasareusedtodetectthetransmittedsymbols

nQuestionsnWhatisthedatarate?nWhatisthebenefit?(seenext)

33

+Alamouti’s Scheme in a 2×2 system

nReceiveantenna1gets:

nReceiveantenna2gets:

nReceivercombinessignalsthisway:

r0 = h11s0 + h21s1 + n0

r1 = �h11s�1 + h21s

�0 + n1

r2 = h12s0 + h22s1 + n0

r3 = �h12s�1 + h22s

�0 + n3

s̃0 = h�11r0 + h21r�1 + h�12r2 + h22r

�3

s̃1 = h�21r0 � h11r�1 + h�22r2 � h12r

�3

34

+What do you end up with?

� Youhaveboth transmitandreceivediversity

s̃0 =��2

0 + �21 + �2

2 + �23

⇥s0 + h�11n0 + h21n

�1 + h�12n2 + h22n

�3

s̃1 =��2

0 + �21 + �2

2 + �23

⇥s1 � h11n

�1 + h�21n0 � h12n

�3 + h�22n2

Youget4ordersofdiversity!

35

+Space-Time Block Coding

nGeneralizationofAlamouti codesforanynumberoftransmitantennas

n Parameters:n N transmitantennas(space)n k timeslots(time)n m symbols

nRateofthecodeisR =m/k

n Idea:Transmita“block”ofNk symbolswithredundanciesinspaceandtimen Eachantennausesonly1/N ofthetotalpower

Lecture6 ©PrashantKrishnamurthy 36

+Impact of Time Dispersion

37

+

0 5 10 15 20 25 30 35 40 45 5010−6

10−5

10−4

10−3

10−2

10−1

γb in dB

Bit

Erro

r Rat

e1

2erfc

s1

1/�b + 0.1

!

1

2erfc (

p�b)

No ISIWith ISI

Performance in Frequency Selective Channels

nFigureshowsimpactofISIinnon-fadingchannels

n Ifyouincludefading,thingsgetworse

n Increasingpowerhasnoeffect!!

38

+Multipath models for time dispersion

n Thetimedispersionintroducedbytheradiochannelcausesinter-symbolinterferenceanddegradestheperformance

n TheRMS“delayspread”posesalimitationonthemaximumdataratethatcanbesupportedoverachanneln Frequency“selective”fading(RMSdelayspread>symbolduration)

n Flatfading(RMSdelayspreadis<<symbolduration)

n Multipathmodelsarerequiredtocharacterize“wideband”systemsn TDMAwithhighdataratesn CDMAwithhighchipratesn WLANs(manyMbps)

39

+Time dispersion in a radio channel

n Timedomainview

n Therearemultipathcomponentsthatcancauseinter-symbolinterferenceifthesymboldurationissmallerthanthemultipathdelayspread

n Lineartimeinvariantimpulseresponse

n Frequencydomainview

n Therearemultipathcomponentsthatcancausenotchesinthefrequencyresponsen Thechannelhasa“coherencebandwidth” wherethecharacteristicsareconstant

n ThecoherencebandwidthlimitsthemaximumdataratethatcanbesupportedoverthechannelQ(⌧) =

LX

i=1

Pi�(t� ⌧i)

40

+Idea of Delay Spread

Coherencebandwidth ofthechannelisapproximately1/10trms

41

+

102.4 102.5 102.6 102.7 102.8 102.9−130

−125

−120

−115

−110

−105

−100

Distance from Base Station in Logarithmic Scale

Rec

eive

d Si

gnal

Stre

ngth

in d

Bm

Channel Impulse Response at a Given Time

Delay Spread over Distance

But,usually,weassumeaconstantRMSDelaySpreadforachannel

42

+The RMS Delay Spread

nTheRMSdelayspreadisafunctionofthePi andtinThelargertheRMSdelayspread,thesmalleristhedataratethatcanbesupportedoverthechannel

nRMSdelayspreadvariesbetweenafewmicrosecondsinurbanareastoafewnanosecondsinindoorareasn Higherdataratesarepossibleindoorandnotoutdoor!!

nThecoherencebandwidthdetermineswhetherasignalisnarrowbandorwideband

43

Example of RMS delay spread

Considerthepowerdelayprofilegivenhere

s 47.101.011.011.0

501.03121.01101.0

µ

τ

=++++

×+×+×+×+×=M

2

222222

s 82.401.011.011.0

501.03121.01101.0

µ

τ

=

++++

×+×+×+×+×=

τ RMS = 4.82−1.472 =1.39 µs

Bc =1

10×1.39= 72 kHz

44

+RMS delay spread

n MeasuredRMSdelayspreadvaluesn Indoorareas:30-300nsn Openareas:≈0.2µsn Suburbanareas:≈1µ sn Urbanareas:1-5µsn Hillyurbanareas:3-10µs

45

+Sample measurements – Office Areas

0 50 100 150 200 250 300 3500

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1 Fc = 1000 MHz / Peak value = -76.1097 dB

time (in ns)

0 50 100 150 200 250 300 3500

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1 Fc = 500 MHz / Peak value = -75.0557 dB

time (in ns)

1 GHz

500 MHz

46

+Narrowband and Wideband Signal

NarrowbandSignal WidebandSignal

47

Source:IntroductiontoWirelessSystemsbyP.M.Shankar,JohnWiley&Sons,2002

+Regions of “Influence”

n Dependingonthesymbolduration(orsignalbandwidth)andthechannelconditions,wemayseedifferentthingshappeninginaradiochannel

Cohe

renceBW

xT

CoherenceTime/T

Fast&Flat Slow&Flat

Fast&Freq.Sel.

Slow&Freq.Sel.

48


+Performance degradation and mitigation

Issue PerformanceAffected MitigationTechnique

ShadowFading

Coverage FadeMargin– Increasetransmitpower

ordecreasecellsizeTime

VariationBiterrorrate

PacketerrorrateErrorcontrolcoding

InterleavingFrequencyhopping

Diversity

TimeDispersion

Inter-symbolInterferenceand

IrreducibleErrorRates

EqualizationDS-SpreadSpectrum

OFDMDirectionalAntennas

49

+Radio Propagation Characterization

FadingChannels

LargeScaleFading SmallScaleFading

PathLossShadowFading TimeVariation TimeDispersion

AmplitudefluctuationsDistributionofamplitudesRateofchangeofamplitude

“DopplerSpectrum”

MultipathDelaySpreadCoherenceBandwidth

IntersymbolInterferenceCoverage

ReceiverDesign(coding)Performance(BER)

ReceiverDesign,PerformanceMaximumDataRates

50

+Time Dispersion (Revisited)

1100900 920 940 960 980 1000 1020 1040 1060 1080

-65

-100

-95

-90

-85

-80

-75

-70

Frequency in MHz

Pow

er

in d

Bm

Deep Fade at Specific Frequencies

51

+What does time dispersion do?

n Multipathdispersionorcoherencebandwidthresultsinirreducibleerrorrates

n Evenifthepowerisinfinitelyincreased,therewillbelargenumberoferrors

n Theonlymeansofovercomingtheeffectsofdispersionaretousen Equalizationn Directsequencespreadspectrum

n Orthogonalfrequencydivisionmultiplexing 5 10 15 20 25 30 35 40 45

10-6

10-5

10-4

10-3

10-2

10-1

100

Eb/N0

P e

Withtimedispersion

Withflatfading

Nosmallscalefading

Forillustrationonly,nottoscale

52

+Equalization

nAnequalizern Filterthatperformstheinverseofthechanneln Compensateforthedistortioncreatedbythefrequencyselectivitycausedbymultipathtimedispersion

n CombatsISI

n Equalizationn AnysignalprocessingthatreducestheimpactofISI

a

53


+Equalization Concepts

n Inwirelessnetworksequalizersmustbeadaptiven Channelisusually

unknownandtimevarying

n Equalizerstrackthetimevariationandadapt

n Equalizerisusuallyimplementedatbaseband

Channel

Equalizer

54


+Operating Modes of an Equalizer

n Twostepapproachtoequalization

n Trainingn Aknownfixed-lengthsequenceistransmittedforthereceiver’s

equalizerto‘train’onn Thissetstheparametersintheequalizer

n Trackingn Theequalizertracksthechannelchangeswiththehelpofthe

trainingsequencen Usesachannelestimatetocompensatefordistortionsinthe

unknownsequence

55

+Operating Modes (2)

n Trainingn Trainingsequenceistypicallyapseudorandomorfixedbinarypattern

n Needstobedesignedtoaccountfortheworstcaseconditionsn Fastestvelocity,largestdelayspread,deepestfades

n Enablesthereceivertosetitsfiltercoefficientsatnearoptimalvalues

n Requiresperiodictrainingn Whatisthemaximumamountoftimeyoucantransmitdatabeforetheequalizerhastobetrainedagain?

n Trackingn Userdataistransmittedimmediatelyaftertraining

56

+Operating Modes (3)

n Duringthetrainingstep,thechannelresponse,h(t)isestimated

n Duringthetrackingstep,theinputsignal,s(t),isestimated

Known Measured Unknown/Estimated

Training s(t) r(t) h(t)

Tracking h(t) r(t) s(t)

h(t)s(t) r(t)

57

+Types of Equalizers

nLineartransversalequalizer,Decisionfeedbackequalizer(DFE),andMaximumlikelihoodsequenceestimator(MLSE)

nEqualizerAlgorithmsn Zeroforcingalgorithm

n Theequalizerforcesthecombinedchannel-equalizerresponsetobezeroatt =±kT forallk exceptone

n Leastmeansquare(LMS)algorithmn Minimizesthemeansquareerrorbetweentheequalizeroutputanddesired

outputn Recursiveleastsquares(RLS)algorithm

n Usesadaptivesignalprocessingandtimeaverages

58

+Comments on Equalization

nDisadvantagesofequalizersnComplexity&powerconsumptionnNumericalerrors

nFractionallyspacedequalizersnUsetapsthatarespacedtosamplethesignalattheNyquist rateandnotthesymbolrate

nEqualizersareusedinNA-TDMA,GSMandHIPERLANnSC-FDMAusedontheLTEuplinkcanbethoughtofasfrequencydomainequalization

59

Lecture 7 - sis.pitt.edu · Block interleaving n After codewords are created, the bits in the...

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