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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
Forillustrationonly;Nottoscale
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
Forillustrationonly;Nottoscale
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
Source:IntroductiontoWirelessSystemsbyP.M.Shankar,JohnWiley&Sons,2002
+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
Source:IntroductiontoWirelessSystemsbyP.M.Shankar,JohnWiley&Sons,2002
+Equalization Concepts
n Inwirelessnetworksequalizersmustbeadaptiven Channelisusually
unknownandtimevarying
n Equalizerstrackthetimevariationandadapt
n Equalizerisusuallyimplementedatbaseband
Channel
Equalizer
54
Source:IntroductiontoWirelessSystemsbyP.M.Shankar,JohnWiley&Sons,2002
+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
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