3bis.multiplexing

8/10/2019 3bis.Multiplexing

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TDMA, FDMA, and CDMATDMA, FDMA, and CDMA

Telecomunicazioni

Undergraduate course in Electrical Engineering

University of Rome La Sapienza

Rome, Italy

2007-2008

NB --> I "case study" non sono parte delle domande d'esame.


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TTimeime DDivisionivision MMultipleultipleAAccess (TDMA)ccess (TDMA)

Each user is allowed to transmit only within specified time

intervals (Time Slots). Different users transmit in differents Time

Slots.

When users transmit, they occupy the whole frequency bandwidth

(separation among users is performed in the time domain).


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TDMA :TDMA : FrameFrameStructureStructure

TDMA requires a centralized control node, whose primary function is

to transmit a periodic referencereference burstburst that defines a frame and

forces a measure of synchronization of all the users.

The frame so-defined is divided into time slots, and each user is

assigned a Time Slot in which to transmit its information.

TF

TS

Frame

Time Slot

Reference

Burst


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TDMA : Frame StructureTDMA : Frame Structure

User 1 User 2 User 3


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TDMA:TDMA: referencereferencetransmittertransmitterschemescheme

S STXSLOWIN

FAST

OUTTDMAcoder

PulseShaper

Mod

Codegenerator

Digitalsignal

BUFFER

Carriergenerator

fP


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TDMA:TDMA: a casea 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( )( ) ( ) ( ) = kjk

j kTtats

Digital signal of userjSequ en ce o f equ a l l y spa ced

b i n a r y a n t i p o da l sy m b o l s

ak(j): k-th binary antipodal

symbol generated by userj

T: time period between symbols

Userj

s(j)(t)


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TDMA: a case studyTDMA: a case study

( )

( )ts j

SLOWIN

FASTO

UT

BUFFER

( )

( )ts j

C

Compressed signal

The sy m bo l s o f t h e o r i g i n a l s i g n a l

a r e o r g a n i zed i n g r o u p s o f Nb p s

sy m bo l s. Ea ch g r o u p i s t r a n sm i t t ed i n a si n g l e T im e Sl o t o f d u r a t i o n TS.

T im e Sl o t s a r e o r g a n i zed i n f r am es

o f d u r a t i o n T F.

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


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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

( )

( ) ( )

( ) =+ = m

N

1kFC

j

mNk

j

C

bps

bps mTkTtats

( )( ) ( ) ( ) = kjk

j kTtats

TC: time interval between symbolsafter compression


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TDMA: a caseTDMA: a case studystudy

TDMAcoder

Codegenerator

TDMA Coded Signal

The po si t i o n i n t im e o f ea ch g r o up i s

m od i f i ed a c co r d i n g t o t h e TDM A code,

w h i ch i s assi gn ed t o t h e user .

I n o t h er w o r d s, t h e TDM A code i n d i c a t es

w h i c h sl o t i n si d e ea ch f r am e m ust be

occu p i ed by t h e u ser .

( ) ( )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

( )( )ts jCfrom

the

buffe

r


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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

( ) ( ) ( ) ( )( =

+ =

m

N

1kFS

jmC

jmNk

jTDMA

bps

bpsmTTckTtats

cm(j): TDMA code assigned to

userjfor the m-th frame

( )( ) ( ) ( ) =

+ = m

N

1kFC

jmNk

jC

bps

bpsmTkTtats


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S(j)TX(t)Pulse

ShaperMod

Carriergenerator fP


Transmitted signalat RadioFrequencies

A l l u ser s adop t t h e sam eca r r i er f r eq uen c y f pfo r

m odu l a t i n g t h e ba se-

ban d si g n a l

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

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014

-100

-50

0

50

100

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014

-100

-50

0

50

100

from

the

TDM

Acoder

( ) ( )ts jTDMA

( )( )ts jbb Base-bandsignal


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( ) ( ) ( ) ( )( =

+ =

m

N

1kFS

jmC

jmNk

jTDMA

bps

bpsmTTckTtats

( ) ( ) ( ) ( )( ) ( )( jP0jTDMATXjTX tf2sin)t(gtsP2ts +=g0(t) : energy-normalizedimpulse response of thePulse Shaper. It hasunitary energy.

PTX: transmitted powerfP: carrier frequency

(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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0 0.002 0.004 0.006 0.008 0.01 0.012 0.014

-100

-50

0

50

100

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]

Am

plitude[V]

( ) ( )ts jRX

( ) ( )ts jTX

Received signal afterpropagation over atwo-paths channel

BEWARE!

At risk for multi userinterference!


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004 0.006 0.008 0.01 0.012 0.014 0.01

Time [s]

1 2 3 4 5 6 7 8 9 10

x 1

Receivedwaveform

F r o n t - en d f i l t er i n g F r o n t -en d f i l t er i n g

D emo d u l a t i o n D emo d u l a t i o n

S amp l i n g S amp l i n g

Th r esho l d det ect i o nTh r esho l d det ect i o n

Received

binaryantipodalsignal


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FFrequencyrequency DDivisionivision MMultipleultipleAAccess (FDMA)ccess (FDMA)

Each user transmits with no limitations in time, but using only a

portion of the whole available frequency bandwidth.

Different users are separated in the frequency domain.


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FDMA vs. TDMAFDMA vs. TDMA

Frequency division is very simple: all transmitters sharing the

medium 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 and

complicated bandpass filters required.TDMA is realized primarily with much cheaper logic functions.

Another disadvantage of FDMA is the rather strict linearity

requirement of the medium.


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FDMA:FDMA: referencereferenceschemescheme

S STXPulse

ShaperMod

Codegenerator

Digitalsignal

Carriergenerator


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FDMA: a caseFDMA: a case studystudy

0 5 10

x 10-3

-1

-0.5

0

0.5

1

Generated bit st ream 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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( )( ) ( ) ( ) = kjk

j kTtats

( )( ) ( )( ) ( )tgtsts 0jj

bb =

( )

( )

( ) ( )

( )( )

( )

(

jj

P

j

bbTX

j

FDMA tftcf2sin)t(sP2ts ++=

Digital binary signal

Base-band signal

FDMA-coded signal

f : frequency spacing between adjacent users

c(j): FDMA code assigned to userjSTX

(j)(t)


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P r o p a g a t i o n P r o p a g a t i o n

D emo d u l a t i o n D emo d u l a t i o n

((De cod i n g Decod i n g ))

S amp l i n g S amp l i n g

Th r e sho l d Th r e s h o l d

de tec t i onde tec t i on

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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TDMA + FDMATDMA + FDMA

FDMA TDMA + FDMA


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TDMA + FDMA in GSM900 standardTDMA + FDMA in GSM900 standard


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CCodeode DDivisionivision MMultipleultipleAAccess (CDMA)ccess (CDMA)


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CDMA: basicCDMA: basic principlesprinciples

In CDMA each user is assigned a unique code sequence (spreading

code), which it uses to encode its data signal.

The receiver, knowing the code sequence of the user, decodes the

received signal and recovers the original data.

The bandwidth of the coded data signal is chosen to be much larger

than the bandwidth of the original data signal, that is, the encoding

process 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, provided

that each user has a unique code that has a sufficiently low cross-

correlation with the other codes.


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CDMACDMA schemesschemes

Direct Sequence CDMA (DS-CDMA)The original data signal is multiplied directly by the high chip rate

spreading code.

Frequency Hopping CDMA (FH-CDMA)The carrier frequency at which the original data signal is transmitted is

rapidly 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 are

decided by the spreading code.


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x(t) s(t)CODING

Cx

fre q ue nc y

Band of the original

signal

band of the coded signal

fre q ue nc y

Direct SequenceDirect SequenceSpread SpectrumSpread Spectrum


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Original signal

(band related to the bitrate)

Spreading sequence composed by

chips, with chiprate >> bitrate

Coded signal(band related to the chiprate)


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Signal1

Signal2

Coded signal

1

Coded signal

2

Sum of coded

signals 1and 2



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Received signal

code used for signal 1

multiplier

signal 1 decoded s ignal



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In FH-SS, the transmitter spreads the spectrum by continuously

jumping from one frequency channel to another

A larger number of intervals leads to a better spreading

Each user selectees the next frequency hop according to a code

(FH code)

Frequency Hopping Spread SpectrumFrequency Hopping Spread Spectrum


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Time-frequency occupation for a FH-SS signal

f0f1f2f3f4f5

f6f7f8f9

f

t

Dwell time

FH code period


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FH-SS signal robustness to a interferers at constant frequency

f0f1f2f3f4f5

f6f7f8f9

f

t

Interference limited

a un dwell time

Interferer atconstant frequency


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Coexistence of different FH-SS signals

f0f1f2f3f4

f5f6f7f8f9

f

t

Signal 2

Signal 1

If codes are well chosen (orthogonal) No interference!!


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CDMA : theCDMA : the partial correlation problempartial correlation problem

PartialPartial correlationscorrelationsamong encoded signals arise when no attempt

is made to synchronize the transmitters sharing the channel, or

when propagation delays cause misalignment even when

transmitters are synchronized.Partial correlations impede the receiver to totally cancel the

contributions of other users even in the presence of spreading

codes 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 the

spreading codes, but cannot be totally eliminated.

CDMA systemCDMA system capacitycapacity isis thusthus tipicallytipically limitedlimited byby thetheinterferenceinterferencefromfromotherotherusersusers,, ratherratherthanthanbybythermalthermalnoisenoise.


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CDMA : theCDMA : the near-far problemnear-far problem

If all the users transmit at the same power level, then the received

power is higher for transmitters closer to the receiving antenna.

Thus, transmitters that are far from the receiving antenna are at a

disadvantage 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 the

same for all transmitters.In other words, the nearby transmitters are assigned a lower

transmit power level than the far away transmitters.

Power control can be easily achieved in centralized access

schemes (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 STXCDMA coder(multiplier)

PulseShaper

Mod

Code

generator

Digitalsignal

Carrier

generator

fP

Transmitter


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DS-CDMA:DS-CDMA: referencereferenceschemescheme

Front-Endfilter and

demodulatorMultiplier Integrator

Code

generator

Received

signal

Receiver

SRX tothe

decis

or


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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 caseDS-CDMA: a case studystudy

( )( )ts j ( )[ ]kc j ( )

( )ts jDSCDMA

binary data signal Codeword DS-CDMA-coded signal


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Digital binary signal

( )( ) ( ) ( ) = kjk

j kTtats

( ) ( ) ( ) ( )[ ]( ) =

=k

N

1mC

jjk

jDSCDMA

DS

kTmTtmcats

DS-CDMA-coded signal

NDS: length of the codewordTC: chip time

( ) ( ) ( ) ( )( ) ( )( jP0jDSCDMATXjTX tf2sin)t(gtsP2ts +=

( ) ( ) ( ) ( ) ( )( ) ( ) ( ) ( )(=

==L

1l

jl

jTX

jl

jjTX

j tsthtstsRX

Transmittedsignal

Signal afterpropagation over amultipath channel

Spreading Signal


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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

Am

plitude[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

Amp

litude[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 and

demodulation

Signal obtained by directmultiplication of the base-

band signal with thespreading signal

Received sequence

after integration of theabove samples

3bis.multiplexing

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