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TDMA, FDMA, and CDMATDMA, FDMA, and CDMA Telecomunicazioni
Undergraduate course in Electrical EngineeringUniversity of Rome La Sapienza
Rome, Italy2007-2008
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2
TTime ime DDivision ivision MMultiple ultiple AAccess (TDMA)ccess (TDMA)
Each user is allowed to transmit only within specified timeintervals (Time Slots). Different users transmit in differents TimeSlots.When users transmit, they occupy the whole frequency bandwidth(separation among users is performed in the time domain).
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TDMA : TDMA : FrameFrame StructureStructure
TDMA requires a centralized control node, whose primary function isto transmit a periodic referencereference burstburst that defines a frame andforces a measure of synchronization of all the users.The frame so-defined is divided into time slots, and each user isassigned a Time Slot in which to transmit its information.
TF
TS
Frame
Time Slot
Ref
eren
ceB
urst
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TDMA : Frame StructureTDMA : Frame Structure
User 1 User 2 User 3
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5
TDMA : TDMA : guardguard timestimes
Since there are significant delays between users, each user receivesthe reference burst with a different phase, and its traffic burst istransmitted with a correspondingly different phase within the time slot.There is therefore a need for guardguard timestimes to take account of thisuncertainty.Each Time Slot is therefore longer than the period needed for theactual traffic burst, thereby avoiding the overlap of traffic burst even inthe presence of these propagation delays.
misalignment misalignment
with guard time without guard time
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6
TDMA : TDMA : preamblepreamble
Since each traffic burst is transmitted independently with an uncertainphase relaive to the reference burst, there is the need for a preamblepreambleat the beginning of each traffic burst.The preamble allows the receiver to acquire on top of the coarsesynchronization provided by the reference burst a fine estimate oftiming and carrier phase.
preamble information
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7
TDMA: TDMA: referencereference transmittertransmitter schemescheme
S STXSLOW IN
FAST OUT TDMAcoder
PulseShaper
Mod
Codegenerator
Digitalsignal BUFFER
Carriergenerator
fP
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8
TDMA: TDMA: a case a case studystudy
0 1 2 3 4 5 6 7 8 9 10
x 10-3
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
TIME
A
M
P
L
I
T
U
D
E
( )( ) ( ) ( )! "#=k
jk
j kTtats
Digital signal of user j
Sequence of equally spacedbinary antipodal symbols
ak(j) : k-th binary antipodal
symbol generated by user j
T : time period between symbols
Userj s(j)(t)
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9
TDMA: a case studyTDMA: a case study
( )( )ts jSLOW IN
FAST OUT
BUFFER
( )( )ts jC
Compressed signal
The symbols of the original signalare organized in groups of Nbpssymbols. Each group is transmittedin a single Time Slot of duration TS.Time Slots are organized in framesof duration TF.
0 1 2 3 4 5 6 7 8 9 10
x 10-3
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
TIME
A
M
P
L
I
T
U
D
E
0 1 2 3 4 5 6 7 8 9 10
x 10-3
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Signal after compression
TIME [s]
AMPLITUDE [V]
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10
TDMA: a case studyTDMA: a case study
0 1 2 3 4 5 6 7 8 9 10
x 10-3
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
TIME
A
M
P
L
I
T
U
D
E
0 1 2 3 4 5 6 7 8 9 10
x 10-3
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Signal after compression
TIME [s]
AMPLITUDE [V]
( )( ) ( ) ( )! !=
+ ""#=m
N
1kFC
jmNk
jC
bps
bpsmTkTtats
( )( ) ( ) ( )! "#=k
jk
j kTtats
TC : time interval between symbolsafter compression
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11
TDMA: a case TDMA: a case studystudy
TDMAcoder
Codegenerator
TDMA Coded Signal
The position in time of each group ismodified according to the TDMA code,which is assigned to the user.
In other words, the TDMA code indicateswhich slot inside each frame must beoccupied by the user.
( ) ( )ts jTDMA
0 1 2 3 4 5 6 7 8 9 10
x 10-3
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Signal after compression
TIME [s]
AMPLITUDE [V]
0 1 2 3 4 5 6 7 8 9 10
x 10-3
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
TIME [s]
AMPLITUDE [V]
( )( )ts jCfrom the
buffer
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12
TDMA: a case TDMA: a case studystudy
0 1 2 3 4 5 6 7 8 9 10
x 10-3
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Signal after compression
TIME [s]
AMPLITUDE [V]
0 1 2 3 4 5 6 7 8 9 10
x 10-3
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
TIME [s]
AMPLITUDE [V]
( ) ( ) ( ) ( )( )! !=
+ """#=m
N
1kFS
jmC
jmNk
jTDMA
bps
bpsmTTckTtats
cm(j) : TDMA code assigned to
user j for the m-th frame
( )( ) ( ) ( )! !=
+ ""#=m
N
1kFC
jmNk
jC
bps
bpsmTkTtats
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S(j)TX(t)
PulseShaper
Mod
Carriergenerator fP
TDMA: a case studyTDMA: a case study
Transmitted signalat RadioFrequencies
All users adopt the samecarrier frequency fp formodulating the base-band signal
0 1 2 3 4 5 6 7 8 9 10
x 10-3
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
TIME [s]
AMPLITUDE [V]
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014
-100
-50
0
50
100
TIME [s]
AMPLITUDE [V]
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014
-100
-50
0
50
100
TIME [s]
AMPLITUDE [V]
from
the
TDMA co
der( ) ( )ts jTDMA
( )( )ts jbbBase-bandsignal
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14
TDMA: a case TDMA: a case studystudy
( ) ( ) ( ) ( )( )! !=
+ """#=m
N
1kFS
jmC
jmNk
jTDMA
bps
bpsmTTckTtats
( ) ( ) ( ) ( )( ) ( )( )jP0jTDMATX
jTX tf2sin)t(gtsP2ts !+"#=
g0(t) : energy-normalizedimpulse response of thePulse Shaper. It hasunitary energy.
PTX : transmitted powerfP : carrier frequency
ϕ(j) : istantaneous phase
For the sake of simplifying the notation,let us consider the simple case of BPSK(in phase carrier modulation)
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TDMA: a case TDMA: a case studystudy
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014
-100
-50
0
50
100
TIME [s]
AMPLITUDE [V]
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016
-15
-10
-5
0
5
10
15
Time [s]
Amplitude [V]
( ) ( )ts jRX
( ) ( )ts jTX
Received signal afterpropagation over atwo-paths channel
BEWARE!
At risk for multi userinterference!
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TDMA: a case TDMA: a case studystudy
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016
-15
-10
-5
0
5
10
15
Time [s]
Amplitude [V]
0 1 2 3 4 5 6 7 8 9 10
x 10-3
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
TIME [s]
AMPLITUDE [V]
Receivedwaveform
Front-end filteringFront-end filtering
DemodulationDemodulation
SamplingSampling
Threshold detectionThreshold detection
Receivedbinaryantipodalsignal
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17
FFrequency requency DDivision ivision MMultiple ultiple AAccess (FDMA)ccess (FDMA)
Each user transmits with no limitations in time, but using only aportion of the whole available frequency bandwidth.Different users are separated in the frequency domain.
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18
FDMA vs. TDMAFDMA vs. TDMA
Frequency division is very simple: all transmitters sharing themedium have output power spectra in non-overlapping bands.
Many of the problems experienced in TDMA due to differentpropagation delays are eliminated in FDMA.
The major disadvantage of FDMA is the relatively expensive andcomplicated bandpass filters required.
TDMA is realized primarily with much cheaper logic functions.
Another disadvantage of FDMA is the rather strict linearityrequirement of the medium.
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19
FDMA: FDMA: referencereference schemescheme
S STXPulse
ShaperMod
Codegenerator
Digitalsignal
Carriergenerator
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20
FDMA: a case FDMA: a case studystudy
0 5 10
x 10-3
-1
-0.5
0
0.5
1
Generated bit stream for each user
0 0.005 0.01 0.015
-60
-40
-20
0
20
40
60
Signal after Pulse Shaping
0 0.005 0.01 0.015
-60
-40
-20
0
20
40
60
Signal after FDMA coding
( )( )ts j( )( )ts jbb
( ) ( )ts jFDMA
Digital binary signal Base-band signal FDMA-coded signal
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21
FDMA: a case FDMA: a case studystudy
( )( ) ( ) ( )! "#=k
jk
j kTtats
( )( ) ( )( ) ( )tgtsts 0jj
bb !=
( ) ( ) ( ) ( )( )( ) ( )( )jjP
jbbTX
jFDMA tftcf2sin)t(sP2ts !+"+#=
Digital binary signal
Base-band signal
FDMA-coded signal
Δf : frequency spacing between adjacent usersc(j) : FDMA code assigned to user j
STX(j)(t)
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22
FDMA: a case FDMA: a case studystudy
PropagationPropagation
DemodulationDemodulation((DecodingDecoding))
SamplingSampling
ThresholdThresholddetectiondetection
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018-60
-40
-20
0
20
40
Amplitude [V]
Received Signal after Demodulation (Decoding)
Transmitted
Received
-4 -2 0 2 4 6 8 10 12 14 16
-6
-4
-2
0
2
4
x 10-3 Samples of the received waveform
0 0.005 0.01 0.015 0.02
-8
-6
-4
-2
0
2
4
6
8
Time [s]
Amplitude [V]
-4 -2 0 2 4 6 8 10 12 14 16-0.5
0
0.5
1
1.5
Transmittedsignal at RF
Receivedbase-bandwaveform
Samples atthe receiveroutput
Receivedbinarystream
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23
TDMA + FDMATDMA + FDMA
FDMA TDMA + FDMA
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24
TDMA + FDMA in GSM900 standardTDMA + FDMA in GSM900 standard
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25
CCode ode DDivision ivision MMultiple ultiple AAccess (CDMA)ccess (CDMA)
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26
CDMA: basic CDMA: basic principlesprinciples
In CDMA each user is assigned a unique code sequence (spreadingcode), which it uses to encode its data signal.The receiver, knowing the code sequence of the user, decodes thereceived signal and recovers the original data.The bandwidth of the coded data signal is chosen to be much largerthan the bandwidth of the original data signal, that is, the encodingprocess enlarges (spreads) the spectrum of the data signal.
CDMA is based on spread-spectrum modulation.If multiple users transmit a spread-spectrum signal at the same time,the receiver will still be able to distinguish between users, providedthat each user has a unique code that has a sufficiently low cross-correlation with the other codes.
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27
CDMA CDMA schemesschemes
Direct Sequence CDMA (DS-CDMA)The original data signal is multiplied directly by the high chip ratespreading code.
Frequency Hopping CDMA (FH-CDMA)The carrier frequency at which the original data signal is transmitted israpidly changed according to the spreading code.
Time Hopping CDMA (TH-CDMA)The original data signal is not transmitted continuously. Instead, thesignal is transmitted in short bursts where the times of the bursts aredecided by the spreading code.
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x(t) s(t)CODING
Cx
frequencyBand of the original
signalband of the coded signal
frequency
Direct SequenceDirect Sequence Spread SpectrumSpread Spectrum
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29
Direct SequenceDirect Sequence Spread SpectrumSpread Spectrum
Original signal(band related to the bit rate)
Spreading sequence composed bychips, with chip rate >> bit rate
Coded signal(band related to the chip rate)
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30
Sign
al 1
Sign
al 2
Coded signal1
Coded signal2
Sum of codedsignals 1 and 2
Direct SequenceDirect Sequence Spread SpectrumSpread Spectrum
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31
Received signal
code used for signal 1
multiplier
signal 1 decoded signal
Direct SequenceDirect Sequence Spread SpectrumSpread Spectrum
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32
In FH-SS, the transmitter spreads the spectrum by continuouslyjumping from one frequency channel to another
A larger number of intervals leads to a better spreadingEach user selectees the next frequency hop according to a code(FH code)
Frequency Hopping Spread SpectrumFrequency Hopping Spread Spectrum
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33
Frequency Hopping Spread SpectrumFrequency Hopping Spread Spectrum
Time-frequency occupation for a FH-SS signal
f0
f1
f2
f3
f4
f5
f6
f7
f8
f9
f
t
Dwell time
FH code period
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34
Frequency Hopping Spread SpectrumFrequency Hopping Spread Spectrum
FH-SS signal robustness to a interferers at constant frequency
f0
f1
f2
f3
f4
f5
f6
f7
f8
f9
f
t
Interference limiteda un dwell time
Interferer atconstant frequency
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35
Frequency Hopping Spread SpectrumFrequency Hopping Spread Spectrum
Coexistence of different FH-SS signals
f0
f1
f2
f3
f4
f5
f6
f7
f8
f9
f
t
Signal 2Signal 1
If codes are well chosen (orthogonal) No interference!!
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CDMA : the CDMA : the partial correlation problempartial correlation problem
PartialPartial correlationscorrelations among encoded signals arise when no attemptis made to synchronize the transmitters sharing the channel, orwhen propagation delays cause misalignment even whentransmitters are synchronized.Partial correlations impede the receiver to totally cancel thecontributions of other users even in the presence of spreadingcodes having low cross-correlation.In presence of partial correlations, the received signal is thereforeaffected by Multi User Interference.The partial correlations can be reduced by proper choice of thespreading codes, but cannot be totally eliminated.CDMA system CDMA system capacitycapacity isis thusthus tipicallytipically limitedlimited byby the theinterferenceinterference fromfrom otherother usersusers, , ratherrather thanthan byby thermalthermal noisenoise.
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CDMA : the CDMA : the near-far problemnear-far problem
If all the users transmit at the same power level, then the receivedpower is higher for transmitters closer to the receiving antenna.Thus, transmitters that are far from the receiving antenna are at adisadvantage with respect to interference from other users.This inequity can be compensated by using power controlpower control.Each transmitter can accept central control of its transmitted power,such that the power arriving at the common receiving antenna is thesame for all transmitters.In other words, the nearby transmitters are assigned a lowertransmit power level than the far away transmitters.Power control can be easily achieved in centralized accessschemes (e.g. third generation cellular networks), but is achallenging issue in distributed systems.
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DS-CDMA: DS-CDMA: reference schemereference scheme
S STX
CDMA coder(multiplier)
PulseShaper
Mod
Codegenerator
Digitalsignal
Carriergenerator
fP
Transmitter
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DS-CDMA: DS-CDMA: referencereference schemescheme
Front-Endfilter and
demodulatorMultiplier Integrator
Codegenerator
Receivedsignal
Receiver
SRX to the
decisor
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0 5 10
x 10-3
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Generated bit stream for each user
0 2 4 6 8
-1
-0.5
0
0.5
1
Assigned Codeword
0 0.005 0.01
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Binary signal after coding for each user
DS-CDMA: a case DS-CDMA: a case studystudy
( )( )ts j ( )[ ]kc j ( ) ( )ts jDSCDMA
binary data signal Codeword DS-CDMA-coded signal
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DS-CDMA: a case DS-CDMA: a case studystudy
Digital binary signal( )( ) ( ) ( )! "#=
k
jk
j kTtats
( ) ( ) ( ) ( )[ ] ( )! !=
""#=k
N
1mC
jjk
jDSCDMA
DS
kTmTtmcats
DS-CDMA-coded signal
NDS : length of the codewordTC : chip time
( ) ( ) ( ) ( )( ) ( )( )jP0jDSCDMATX
jTX tf2sin)t(gtsP2ts !+"#=
( ) ( ) ( ) ( ) ( )( ) ( ) ( ) ( )( )!=
"#$=%=L
1l
jl
jTX
jl
jjTX
j tsthtstsRX
Transmittedsignal
Signal afterpropagation over amultipath channel
Spreading Signal
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DS-CDMA: a case DS-CDMA: a case studystudy
0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01
-1
0
1
x 10-4 Received Signal after Demodulation
Amplitude [V]
0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01
-1
0
1
x 10-4 Received Signal after Code Multiplication
Amplitude [V]
0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.01
-5
0
5
x 10-4 Received Signal after Integration
Amplitude [V]
Received signal afterFront-End filtering anddemodulation
Signal obtained by directmultiplication of the base-band signal with thespreading signal
Received sequenceafter integration of theabove samples