lecture 9 - home page - university of pittsburgh · lecture 9 traffic engineering for circuit...
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Lecture 9
TrafficEngineeringforCircuitSwitchedConnections
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+Traffic Engineering
nCells- deployalargenumberoflow-power basestations- eachhavingalimitedcoveragearea
nReusethespectrumseveraltimesintheareatobecoveredtoincreasecapacity
n Issues:n Capacity(trafficload)inacellnOnemeasure=numberofcommunicationchannels thatareavailable
n Performancen Callblockingprobability,handoffdroppingprobability,throughputetc.
n Interference
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+GSM Logical Channels
nNoRFcarrierortimeslotisreservedforaparticulartaskexcepttheBCCHn Anytimeslotonanycarriercanbeusedforalmostanytaskn Framingstructurehastobemaintained
nChannelsareoftwotypes:n TrafficChannels(TCH)
n Voiceat13kbpsn Dataat9.6,4.8or2.4kbps
n ControlChannels(CCH)n Broadcast,CommonandDedicated
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+Broadcast Control Channels (Unidirectional)nBCCH(BroadcastControlChannel)
n Usedtotransmitcellidentifier,availablefrequencieswithinandinneighbouring cells,options(likeFH)etc.
n Continuallyactive“beacon”n Hastwosub-channels
nFCCH(FrequencyCorrectionChannel)n Usesafrequencycorrectionburst
nSCH(SynchronizationChannel)n Timesynchronizationinformation
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+ALOHA
n Transmitwheneveryouwantn Ifyouareacknowledged,everythingisfinen Otherwiseretransmitpackets
n Lowthroughput(18%)
n Slottedversionsareslightlybettern Transmissionattemptscantakeplaceonlyatdiscretepointsoftime
Computer A
Computer Btime
t t+x t+F t+x+F
collision
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+Use of ALOHA in Cellular Networks
nTosetupacall,MSs initiallyemployslottedALOHAtosendsomeinformationtotheBSn Called“randomaccesschannel”orsomethingsimilarn InLTE,apreambleistransmitted(uniqueormaycollide)
n Ifsuccessful,theyare“assigned”afrequencychannelandtimeslotorspread-spectrumcode
n Ifunsuccessful,theytryagainnMSgivesupifrepeatedtriesfail
n Collisions(congestion),poorchannelquality,etc.
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+Common Control Channels (Unidirectional)n Usedforallconnectionsetuppurposes
n Thepagingchannel(PCH)isusedforpagingamobilewhenitreceivesacall
n Therandomaccesschannel(RACH)isusedbytheMStosetupacalln SlottedALOHAontheRACH
n Accessgrantchannel(AGCH)isusedbytheBTStoallocateachanneltotheMSn ThiscanbeaTCH(startusingvoice)n OraSDCCH(negotiatefurtherforconnectionsetup)
SDCCH:StandalonededicatedCCH
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+Dedicated Control Channels (Bidirectional)n AslongasaMShasnotestablishedaTCH,itwilluseastand-alonededicatedcontrolchannel(SDCCH)forsignalingandcallsetupn Authenticationn Registration,etc.
n EachTCHhasaSlowAssociatedControlChannel(SACCH)n Exchangesysteminformationlikechannelquality,powerlevels,etc.
n AFastAssociatedControlChannel(FACCH)isusedtoexchangesimilarinformationurgently(duringhandoffforinstance)
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+Framing Scheme in GSM (Traffic Channels)1 2 3 4 2048
1 2 3 4 51
1 2 3 4 26
TB TBData(57bits) TS GPData(57bits)
1 2 3 5 6 7 8
Hyperframe:3hours28min53.76s
Superframe:6.12s
TrafficMultiframe:120ms
Frame:4.615ms
Slot:577µs
Framingschemeisimplementedforencryptionandidentifyingtimeslots
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+Framing Scheme in GSM (Control Channels)1 2 3 4 2048
1 2 3 4 26
1 2 3 4 51
TB TBData(57bits) TS GPData(57bits)
1 2 3 5 6 7 8
Hyperframe:3hours28min53.76s
Superframe:6.12s
ControlMultiframe:235.4ms
Frame:4.615ms
Slot:577µs
Framingschemeisimplementedforencryptionandidentifyingtimeslots
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+One Time Slot (typical)
nAtimeslotlasts577µs (546.5µs ofdataand30.5µs ofguard-time)
nBitsperslot=3+57+1+26+1+57+3+8.25=156.25
nBitrate=156.25/577µs =270.79kbps
TB TBData(57bits) TS
TB:TailBits(3bits)TS:TrainingSequence(26bits)GP:GuardPeriod(8.25bits)
GP
Flags
Data(57bits)
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+Traffic Channel
n 20msofvoice(260bits@13kbps)isconvertedto456bitsafterCRCandconvolutional encoding
n Effectivedatarate=22.8kbps
n 456bits=8× 57bitsn (Reminder:atimeslothastwo57bitunitsseparatedbyatrainingsequence)
n VoicesamplesareinterleavedandtransmittedontheTCH
n DataandControlbitsarealsoencodedtoendupwith456bitsover20ms
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GSM Coding for Voice Traffic
n Class1a:CRCandconvolutionalcodingn 3-biterrordetection&errorcorrection
n Class1b:convolutionalcoding
n Class2:noerrorprotection
*tailbitstoperiodicallyresetconvolutionalcoder
(2,1,5)convolution
coder
260bits/20ms
=13kb/s
50class1abits
132class1bbits
78class2bits
456bits/20ms=22.8kb/s
Channelencoder
3-bitCRC
53bits
Bitinter-leaver
378bits
4tailbits*
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+Example: Mobile Initiated Call in 2G GSM MessageName Category
1.ChannelRequest RRM
2.ImmediateAssignment RRM
3.CallEstablishmentRequest CM
4.AuthenticationRequest MM
5.AuthenticationResponse MM
6.CipheringCommand RRM
7.CipheringReady RRM
8.SendDestinationAddress CM
9.RoutingResponse CM
10.AssignTrafficChannel RRM
11.TrafficChannel Established RRM
12.Available/BusySignal CM
13.CallAccepted CM
14.ConnectionEstablished CM
15.InformationExchange voicebits
Security
Related
TrafficChannel=Circuit
Thisisallcontrolsignaling
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+IS-95 Forward Channel
OneForwardCDMALink,1.25MHzinthe869-894MHzbands
Pilot Synch PCH 1
PCH 7
Code 1
CodeN
CodeP
CodeS
Code55
W0 W32 W1 W7 W8 W63
Fundamental Code Channel
Data
Mobile PowerControl
Subchannel
Fundamental Code Channel
Data
Mobile PowerControl
Subchannel
SupplementaryCode Channel
Data
The1.25MHzchannelisobtainedbycombining41AMPSchannelseach
havinga30kHzbandwidth
Forward traffic channel with one code
Forward traffic channel with multiple codes
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+The IS-95 Forward Link (I)
nTherearefourtypesoflogical channelsn TheyarecreatedbyusingorthogonalWalshcodes
nBroadcastchannelswithoutpowercontroln PilotChannel(assignedWalshcodeW0)n SynchChannel(assignedWalshcodeW32)n PagingChannel– PCH(upto7innumber)
nDedicatedchannelswithpowercontroln Forwardtrafficchannels– FTCH(many)
n Fundamentalcodechanneln Uptosevensupplementalcodechannels
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Basic Spreading Procedure on the Forward Channel in IS-95n Symbolsaregeneratedatdifferentrates
n Forthespreadsignaltobeat1.2288Mcps,theincomingstreammustbeat:1.2288x106/64=19.2kbps
n Whathappensiftheincomingstreamisatalowerrate?n Example:Incomingstreamisat4.8kbpsn Numberofchipsperbit=1.2288x106/4.8x103 =256
BasebandFilter
BasebandFilter
IPNat1.2288Mcps
QPNat1.2288Mcps
1.2288Mcps
WalshCode
LogicalChannelDependentSymbols
WhatisthisDSSSScheme?
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+Channelization, Scrambling, and Error Correction Codesn CDMAsystemsuseavarietyofcodesforspreadingthesignal
n ChannelizationCodesn WalshcodesandOVSFcodesn Usedtoseparateusertransmissionsinthesamecellontheforwardlink
n Usedtoseparatemultiplesignalsofsame useronreverselinksin3Gsystems
n ScramblingCodes(PNcodes)n M-sequences,Goldsequences,Kasami sequencesn Usedtoseparatesignalsonthereverselinkfrommultipleusersn Usedtoseparatesignalsfromdifferentbasestationsontheforwardlink
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ToQPSKModulator
BasebandFilter
BasebandFilter
IPilotPNat1.2288Mcps
QPilotPNat1.2288Mcps
1.2288Mcps
WalshCodeW0
All0s
Pilot Channel
n ItiscontinuouslytransmittedbyaBSontheforwardlinkn Likea“beacon”(CompareBCCH)n ActsasthereferencesignalforallMSsn Usedindemodulationandcoherentdetection
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+The Pilot Channel (II)
n ItcarriesNOinformationbutitisaveryimportantsignal
n Ithas4-6dBhighertransmitpowerthananyotherchannel
n Thetransmitpowerofthepilotchannelisconstant(Nopowercontrol)
n TheIandQPNsequencesn AregeneratedusingaLFSRoflengthm =15n Theperiodis215 – 1=32767
n Anextrazeroisaddedafterarunlengthof14zerosoncewithintheperiodn Intime,oneperiodis32768 × 0.8138µs =26.67msn Numberofrepetitions/second=1/26.67 × 10-3 =37.5n Numberofrepetitionsin2seconds=75
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+PN Sequences are generated using Linear Feedback Shift Registers (LFSRs)
XORgateMultiplication
PolynomialRepresentation:ci {0,1}2
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+Use of the PN sequences in IS-95
nThePNsequencesaredefinedbythefollowingLFSRsn PNI(X) =X15 +X13 +X9 +X7 +X5 +1n PNQ(X)=X15 +X12 +X11 +X10 +X6 +X5 +X4 +X3 +1
nAllbasestationsusethesamePNsequencesbutwithadifferent“offset”
nTheoffsetsarebymultiplesof64chipsn Totalnumberofpossibleoffsets=32768/64=512n Durationof64chips=64´ 0.8138x 10-6 =52µs
n Lighttravels3´ 108 m/s =>15630m in52µs
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+More on the Offset
nThebasestationsinIS-95arecompletelysynchronizedusingGPSn Transmittedchipsonthedownlinkareallsynchronizedfromallbasestations
n TheBaseStation“SystemTime”issynchronizedtoa“UniversalCoordinatedTime”orUTCn UTCislooselywhatusedtobeGMTn Thetimeisspecifiedintermsofa24hourcyclen SystemtimeisnotthesameasUTCbecauseitdoesnotincludeleapseconds
nTheWalshcodesareusedwithoutanyoffsetn TheyarealignedsuchthatthefirstbitalwaysstartsattheevensecondintheIS-95system
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+The Synch Channel
n ThesynchchannelislockedtotheoffsetofthePN-sequenceusedinthepilotchanneln Itcontainsinformationpertinenttotheassociatedbasestationn MScanretrievetheinformationforsubsequentuse
n TheveryfirstbitsdemodulatedbytheMSarefromthesynchchanneln Importantinsynchronizingtothebasestationn Example1:ReversePNcodeshavezerooffsetrelativetoevennumberedsecondsofthesystemtime
n Example2:MSmustsynchitslongcodegeneratorwiththeoneusedattheBS
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+The Paging Channel
nTransmitscontrolinformationtotheMSn Pagemessagetoindicateincomingcalln Systeminformationandinstructions
n Handoffthresholdsn Maximumnumberofunsuccessfulaccessattemptsn Listofsurroundingcells(howaretheyidentified?)n Channelassignmentmessages
n Acknowledgmentstoaccessrequests
n Itoperatesateither4.8kbpsor9.6kbpsn Itispassedthrougharate½convolutionalencodertogoupto9.6kbpsor19.2kbps
n Iftheoutputis9.6kbps,itisrepeatedtogoupto19.2kbps
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+The forward traffic channel
nCarriesusertrafficandcontrolmessagestospecificMSsn DedicatedexclusivelytooneMS
nCancarrytrafficatdifferentratesn RateSet1
n 1.2kbps,2.4kbps,4.8kbpsand9.6kbpsn IdealtosupportQ-CELPthatvariesthevoicecoderate(maximumof8kbps)basedonthevoiceactivity
n UsedprimarilyinIS-95n RateSet2
n 1.8kbps,3.6kbps,7.2kbpsand14.4kbpsn Idealtosupportbettervoicequalityatamaximumof13kbpsn SuggestedforPCS(butalsoallowedinIS-95)
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+Coding of the speech signal
n Thespeechsignalsareencodedinto20ms framesn Theframescontain192bitsofspeechat9.6kbps
n Highvoiceactivityn Theframescontain24bitsat1.2kbps
n Backgroundnoiseorlowvoiceactivityn Theframescontain48&96bitsat2.4and4.8kbps
n Providesmoothtransitionbetweentheothertwodatarates
n Thereare8tailbitsintheframethatareusedtoresettheconvolutionalencoder
n At9.6kbpsand4.8kbpsthereisaCRCcodeaswelltoindicatethe“quality”oftheframen Framequalityindicator(12,10,8or6bits)n Onlydetectframeerrors
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+Frame Quality Indicator (FQI)
nInCDMA,theframeerrorratespecifiestherequiredSIRforthesystemnTypically1%or2%(dependingonrateset)
nTheFQIintheframeallowstheBStodetectwhetherornotaframeisinerror
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+
BBF
BBF
IPilotPNat1.2288Mcps
QPilotPNat1.2288Mcps
1.2288Mcps
WalshCodeWi
MUX
Long CodeDecimator
Long CodeGenerator
64:1
1.2288Mcps
LongCodeMask Long CodeDecimator
BlockInterleaver
SymbolRepetition
19.2ksps
ConvolutionalEncoder
VoiceTraffic
Rate1/2
24:1
PowerControlBits
800bps
19.2ksps
19.2ksps
800bps
Operation of the Forward Traffic Channel (Rate Set 1)
Uniqueforeachuser
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+Control signals and data over FTCHs
n IS-95supportstransmissionofn Signalingdataanduserdataoverthesameframen Primaryuserdata(voice)andsecondaryuserdata(e.g.Fax)overthesameframe
n Thisisallowedonlyforthe9.6kbpsframesn Onlyspeechcanbecarriedatlowerrates
n Dimandburstn Signalingorsecondaryuserdataoccupiespartoftheframealongwithspeech
n Blankandburstn Signalingorsecondaryuserdataoccupiestheentireframe
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ComparewithSACCHandFACCH
inGSM
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+
OneReverseCDMALink,1.25MHzinthe
824– 849MHz
AccessChannel
Fundamental Code Channel
Data
SupplementaryCode Channel
Data
AccessChannel
AccessChannel
AccessChannel
TrafficChannel
1
TrafficChannel
T
SupplementaryCode Channel
Data
SupplementaryCode Channel
Data
SupplementaryCode Channel
Data
Reverse CDMA Channel
ComparewithRACHAndAGCH
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+What is UMTS?
n UMTSstandsforUniversalMobileTelecommunicationsSystemn 3GcellularstandardintheUS,Europe,andAsia
n OutcomeofseveralresearchactivitiesinEuropen GeneratedtrialsystemsandbasicunderstandingofWCDMAn Assistedthestandardizationefforts
n Mostofthestandardizationworkwasfocusedin3GPPn 3GPPreferstothephysicallayerasUTRA– UMTSTerrestrialRadioAccessn Therearetwomodes– FDDandTDD
n UMTScansupportbothGSM-MAPandIS-41corenetworksn Anall-IPthirdalternativeis availablenow
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+UMTS Architecture
n TheUMTSSystemn Consistsofmanylogicalnetworkelementssimilartothe2Gsystemsn Logicalnetworkelementshave“openinterfaces”
n Therearethreecomponentsn UserEquipment(UE)n UMTSTerrestrialRadioAccessNetwork(UTRAN)n CoreNetwork(CN)
n HeavilyborrowsfromGSM
UserEquipment
UMTSTerrestrial
RANCore
Network
Uu Iu
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+Detailed Network Elements
USIM
ME
UE
Cu
Uu
NodeB
NodeB
NodeB
NodeB
RNC
RNC
MSC/VLR
SGSN
GMSC
GGSN
HLR
PLMNPSTN
Internet
Iu
IubIur
UTRAN CN
WCDMAAirInterface
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+Summary of WCDMA
n WCDMAissomewhatdifferentcomparedtoIS-95
n Itisa“wideband”directsequencespreadspectrumsystemn Supportsupto2Mbpsusing
n Variablespreadingn Multicode connections
n Thechiprateis3.84Mcpsn Approximatebandwidthis5MHzn Carrierspacingisonarasterof200kHzn Supportshigherdatarates/capacityn Increasedmultipathdiversity(proportionaltochipduration)
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+UTRA General Interface – II
n Higherlayerdataiscarriedintransportchannelsn Thedataiscarriedinchunkscalled“transportblocks”n Eachtransportchannelismappedtoaphysicalchannel(later)n Theframesare10mslong
n Atransportchannelhasn ATFI– TransportFormatIndicator
n Timedependentfieldn Containsparameters oftheassociatedtransportchannel
n TFI’sarecombinedintoTFCIsn TransportFormatCombinationIndicatorn TFCI’stellthereceiverwhattransportchannelsareactive
n Blindtransportformatdetection(BTFD)isalsopossiblen Usuallyhappensonlyontheforwardlink
n Therearetwotypesoftransportchannelsn Dedicatedtransportchannelsn Commontransportchannels
ControlSignaling
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+UTRA General Interface
Transport channel 1 Transport channel 2
Transport Block
Transport Block
TFI TFITransport Block
Transport Block Higher
PHYTFCI Coding & MUXing
TFI TFITransport Block + Error
Indication
Transport Block + Error
Indication
Higher
PHYTFCI Decoding &
DeMUXing
Transmitter
Receiver
PhysicalControl Channel
PhysicalData Channel
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+ Mapping of Transport Channels to Physical Channels
Broadcast Channel (BCH)Primary Common ControlPhysical Channel (PCCPCH)
Forward Access Channel (FACH) Secondary Common ControlPhysical Channel (SCCPCH)Paging Channel (PCH)
Random Access Channel (RACH)Physical Random AccessChannel (PRACH)
Dedicated Channel (DCH)Dedicated Physical Data Channel(DPDCH)Dedicated Physical Control Channel (DPCCH)
Downlink Shared Channel (DSCH)
Common PacketChannel (CPCH)
Physical Downlink SharedChannel (PDSCH)Physical Common PacketChannel (PCPCH)
Forward Only Reverse Only Both Reverse and Forward
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Random Access Channel
n BasedonslottedALOHAn 15accessslotsevery20msn Preamblesaretransmittedfor4096
chipsof5120chipsinanaccessslotn Followedbytheaccessmessage
n Messagehasadataandacontrolpartn Dataparthasavariablespreading
factorn Controlparthasafixedspreading
factorof256
Slot 1 Slot 2 Slot 3 Slot 4 Slot 5 Slot 15
20 ms
Preamble
4096 chipsPreamble Preamble Message Part = 1-2 10 ms frames
5120 chips
User Data – 10,20,40, 80 bits
Pilot – 8 bits
0 1 2 3 14
TFCI
Data part
Controlpart
10ms=2560chips
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Reverse DPCH Structure
n TheDPCCHcarriesphysicallayercontrolinformationn Ithasafixedspreadingfactorof
256
n TheDPDCHcarrieshigherlayerinformationn Spreadingfactorcanrange
between4and256
n TPC– TransmissionPowerControl
n FBI– FeedbackInformation
Data (voice bits)
Pilot
0 1 2 3 14
10 ms Frame = 38400 chips
TFCI FBI TPC
DPDCH
DPCCH
1 slot =2560 chips
Frame 1 Frame 2 Frame 72
Superframe = 720 ms
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+ Reverse multiplexing and channel coding chain in UMTS
CRC Attachment
Transport BlockConcatenation/ CodeBlock Segmentation
Channel Coding
Radio Frame Equalization
First Interleaving(20, 40, or 80 ms)
Radio Frame Segmentation Rate matching
Transport ChannelMultiplexing
Physical ChannelSegmentation
CRC Attachment
CRC AttachmentPhysical ChannelMapping
Second interleaving(10 ms)
DPDCH1 DPDCH2 DPDCHN
Other TransportChannels
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+More details
n Figureshowsreverselink
n Forwardlinkissimilar,butcontrolanduserdataareseparatedintime
n Includespowercontrolforsomechannels,andnotforothers
CRCEncoder
CRCEncoder Tr
ansp
ort
bloc
kCon
cate
natio
n or
se
gmen
tatio
nChannelCoder
Interleaver
RateMatcher
Tran
spor
t c
hann
elM
ultip
lexe
r
Tran
spor
t to
Ph
ysic
al c
hann
el
map
per
Interleaver
Transport Ch 1 Blk 1
Transport Ch 1 Blk 2
Transport Channel 2
Transport Channel 3
DPDCH1
DPCCH
Sepa
ratedincod
e
ReverseLinkExample
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+Reverse chain in UMTS details –In Atransportblockisreceivedfromthehigherlayers
n ACRCisattached(0,8,12,16or24bits)n Usedtoprovideerrorindicationtohigherlayers
n Thetransportblocksareeitherconcatenatedorsegmentedbasedontheirsizeascomparedtothechannelcodingblockn Twotypesofchannelcodingareprovided
n ½and1/3rateconvolutionalcodingn 1/3rateturbocoding
n Channelcodingisperformed
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+Reverse chain in UMTS details –IIn Radioframeequalization
n Ensuresthatdataisdividedintoequalsizedblockswhentransmittedovermany10msframes
n Dataispaddedwithzerostillitcanbedividedintoequalsizedblocksthatfitinaframe
n Firstinterleavingn Usedonlywhenthedelaybudgetisacceptablen Dependsonhowoftendataarrivesfromhigherlayers(calledthetransmissiontime
intervalorTTI)n IfdifferenttransportchannelshavedifferentTTI’s,theymustbetimealignedbefore
multiplexing
n Ratematchingn Thisissimilartothepuncturing/repetitionoperationsinIS-95n Itisusedtomatchthenumberofbitstobetransmittedtothenumberavailableona
singleframen TheTFCIcontainstheratematchingattribute
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+Reverse chain in UMTS details –IIIn Transportchannelmultiplexing
n Differenttransportchannelsaremultiplexedheren Spreadingcodesareusedtoseparatethechannelsn Serialmultiplexingisalsopossible
n SecondInterleavingn Alsocalledintra-frameinterleavingn Lastsfor10msn Appliedseparatelyforeachphysicalchannel
n Theoutputisamappingtoaphysicalchanneln Thenumberofbitsgivenforaphysicalchannelatthisstageisexactlyequaltothenumberthatthespreadingfactorofthatframecantransmit
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+Traffic Engineering (2)
nQuestions:n IfIwanttoplaceacall,whatistheprobabilitythatIwillNOTgetacommunicationchannel?n“Newcalladmission”
n IfIammovingfromcelltocell,whatistheprobabilitythatduringacall,IwillNOTfindacommunicationchannelinthenewcelltocontinuemycall?n“Handoffcalladmission”
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+Grade of Service
n Gradeofservicen Usually2%blockingprobabilityduringbusyhourn Busyhourmaybe
1. Busyhouratbusiestcell2. Systembusyhour3. Systemaverageoverallhours
n Givenc =T/Nc trafficchannelspercell– whatisthegradeofservice(GoS)?n HowmanyuserscanbesupportedforaspecificGoS?
n BasicanalysiscalledTrafficEngineeringorTrunkingn Sameascircuitswitchedtelephonyn UseErlang B andErlang CModels
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+Erlangs - 1
nLettherebec =T/Nc channelspercell
nInagiventimeperiod,supposethereareQusersmakingacalln IfQ =c,anynewcallwillbeblockedwithprobability1
n IfQ <c,thenyourcallmaygetachannel
nHowdowequantifythisbetter?nErlangs
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+Erlangs - 2
n Howdoyouestimatetrafficdistribution?n TrafficintensityismeasuredinErlangs
n OneErlang =completelyoccupiedchannelfor60minutes
n Examplesn 30kHzvoicechanneloccupiedfor30min/hourcarries0.5Erlangs
n 100callsinonehoureachlasting3minutes=100calls/hour× 3/60=5Erlangs
n Agner Krarup Erlang
n ScientistwiththeCopenhagenTelephoneCompany
n Studieddatafromavillage’stelephonecallstoarriveathisconclusions
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+More on Erlangs
n Lettrafficintensityperuser=Aun Au =averagecallrequestrate× averageholdingtime=l × th
n Totaltrafficintensity=trafficintensityperuser×numberofusers=Au × nu
n Example:n 100subscribersinacelln 20make1call/hourfor6min=>20× 1× 6/60=2En 20make3calls/hourfor½min=>20× 3× .5/60=0.5En 60make1call/hourfor1min=>60× 1× 1/60=1En 100usersproduce3.5Eloador35mE peruser
nu =20;l =1;th =6/60
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+Notation associated with queues
nWrittenasP/Q/R/Sn P:Descriptionofarrivingtrafficn Q:Descriptionofserviceratesortimesn R:Numberofserversn S:Numberofusersthatcanbeinthesystem(includesthosebeingservedandthosewaiting)
nM=>Markov(Poissonarrivaltimes,exponentialservicetimes)n Commonlyusedasitistractableanditfitsvoicecalls
n Ifthenumberofusersthatcanbeinthesystem(S)isinfinite,itisdroppedfromthenotation
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+Erlang B Model: M/M/c/c queue
n ToestimatetheperformanceofatrunkedsystemusetheErlang Bqueueing model
n Thesystemhasafinitecapacityofsize cn Customersarrivingwhenallservers(channels)busyaredropped
n Blockedcallsclearedmodel(BCC)(nobuffer)
n Assumptionsn c identicalservers(channels)processcustomersinparalleln CustomersarriveaccordingtoaPoissonprocess(averageofλ calls/s)n Customerservicetimesexponentiallydistributed(averageof1/μsecondspercall)
n Theofferedtrafficintensityisa =λ/μ inErlangs
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+Erlang B Formula or Blocking Formulan ProbabilityofacallbeingblockedB(c,a)
n Erlang Bformulacanbecomputedfromtherecursiveformula
nUsuallydeterminedfromtableorcharts
B(c, a) =ac
c!/
cX
n=0
an
n!
B(c, a) =a⇥B(c� 1, a)
c+ a⇥B(c� 1, a)
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+Example of Erlang B Calculation
nFor100userswithatrafficloadof3.5E,howmanychannelsareneededinacelltosupport2%callblocking?nUseErlang BtablesorchartsnWitha2%callblocking,weneed8channels
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+Sample Erlang B table
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+Erlang B Chart
10-1
100
101
102
10-3
10-2
10-1 1 2 3 5 7 9 15 25 35 95
Traffic load in E rlangs
prob
abilit
y of
block
ing
N: num ber of channels
8channels
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+Example: Using Erlang B for traffic engineering
nConsiderasingleanalogcelltowerwith56trafficchannelsnWhenallchannelsarebusy,callsareblockednCallsarriveaccordingtoaPoissonprocessatanaveragerateof1callperactiveuserperhour
nDuringthebusyhour¾oftheusersareactivenThecallholdingtimeisexponentiallydistributedwithameanof120seconds
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+Example: Continued
nWhatisthemaximumloadthecellcansupportwhileproviding2%callblocking?n FromtheErlang Btablewithc=56channelsand2%callblocking,themaximumload=45.9Erlangs
nWhatisthemaximumnumberofuserssupportedbythecellduringthebusyhour?n Loadperactiveuser=(1call/3600s)× (120s/call)=33.3mErlangs
n Numberofactiveusers=45.9/(0.0333)=1377n Totalnumberofusers=4/3numberactiveusers=1836
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+Another Example
nConsideranAMPSsystemwith30kHzchannels,4sectors/cell,frequencyreuseofNc =9,and12.5MHzofbandwidth.n Numberofchannels=12.5× 106/30×103 =416channels
n Say20arecontrolchannels=>totalnumberofvoicechannels=396
n Numberofchannels/cell=396/9=44n Numberofchannels/sector=44/4=11
n IfanIS-136systemisused,assuming3timeslotspercarrier,thenumberofchannels/sector=33
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+Example (Continued)
nFora2%blockingprobability,fromtheErlangBtables,themaximumtrafficloadisnForAMPS:5.84EnForIS-136:24.6E
nIftheaveragecalldurationis3minutes,andeachcallis3/60=0.05EnAMPScansupport5.84/0.05=116calls/hour/sector
n IS-136cansupport24.6/0.05=492calls/hour/sector
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+Handoff and Mobility
nAcallwilloccupyachannelaslongasauserisinthecelln Ifweassumecellresidencetimeisexponential,thenthechanneloccupancy=min(call holdingtime,cellresidencytime)
nAlsoexponentiallydistributed
nSimilarcalculationscanbedone,butweignoremobilityandhandoffhere
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+Traffic Engineering in CDMA
nItismorecomplicated!
nDeterminingErlangcapacityisnottrivialnOneapproximationistousethenumberofchannelsfromthe“polepoint”
nTobemoreaccurate,wehavetocharacterizetheimpactofcallarrivalsandholdingtimeontheinterference
nSeeforexample:A.M.ViterbiandA.J.Viterbi,“ErlangCapacityofaPowerControlledCDMASystem,”IEEEJSAC,Vol.11,No.6,August1993.
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