lecture 13 of dm

8/16/2019 Lecture 13 of Dm

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Lecture13 1

Lecture 13

Introduction to OFDM

Ref: OFDM_intro.pdf


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Lecture13 2

• Orthogonal frequency division multiplexing (OFDM) is well-nown to !e

effective against multipath distortion" #t is a multicarrier communication

scheme$ in which the !andwidth of the channel is divided into su!carriersand data sym!ols are modulated and transmitted on each su!carrier

simultaneously

• %y inserting guard time that is longer than the delay spread of the channel$

an OFDM system is a!le to mitigate intersym!ol interference (#)"

• Orthogonal frequency division multiplexing (OFD!" #hich is a

modulation technique for multicarrier communication systems" is a

promising candidate for $% systems since it is less suscepti&le to

intersym&ol interference introduced in the multipath environment

• 'he idea of multicarrier communications is to divide the total signal&and#idth into num&er of su&carriers and information is transmitted

on each of the su&carriers


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Lecture13 3

• )nli*e the conventional multicarrier communicationscheme in #hich spectrum of each su&carrier is non+overlapping and &andpass filtering is used to extract thefrequency of interest" in OFD the frequency spacing

&et#een su&carriers is selected such that the su&carriersare mathematically orthogonal to each other 'hespectra of su&carriers overlap each other &ut individualsu&carrier can &e extracted &y &ase&and processing'his overlapping property ma*es OFD more spectral

efficient than the conventional multicarriercommunication scheme


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Lecture13 $

Generation of OFDM Symbols

• , &ase&and OFD sym&ol can &e generated in the

digital domain &efore modulating on a carrier for

transmission

• 'o generate a &ase&and OFD sym&ol" a serial of

digiti-ed data stream is first modulated using common

modulation schemes such as the phase shift *eying

(./0! or quadrature amplitude modulation (,!

• 'hese data sym&ols are then converted from serial+

toparallel (/.! &efore modulating su&carriers


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• &u!carriers are sampled with sampling rate N/

Ts $ where N is the num!er of su!carriers and

Ts is the OFDM sym!ol duration"

• 'he frequency separation !etween two

adacent su!carriers is N *π "

• Finally$ samples on each su!carrier are

summed together to form an OFDM sample"


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• +n OFDM sym!ol generated !y an N -su!carrier

• OFDM system consists of N samples and the m-th

sample of an OFDM sym!ol is

where X n is the transmitted data sym!ol on the n-th

su!carrier"


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Lecture13 5

• is equivalent to the N -point inverse discrete Fourier

transform (#DF') operation on the data sequence with

the omission of a scaling factor"

• in practice$ the #FF' is performed on the data sequenceat an OFDM transmitter for !ase!and modulation and

the FF' is performed at an OFDM receiver for !ase!and

demodulation"


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Lecture13 6

• Finally$ a !ase!and OFDM sym!ol is

modulated !y a carrier to !ecome a !andpass

signal and transmitted to the receiver"

• #n the frequency domain$ this corresponds to

translating all the su!carriers from !ase!and to

the carrier frequency simultaneously"


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Lecture13 7

a ,-su!carrier OFDM transmitter and the process of generating

one OFDM sym!ol"


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Lecture13 18

Intersymbol and Intercarrier Interference

• 9n a multipath environment" a transmitted sym&ol ta*esdifferent times to reach the receiver through differentpropagation paths

• From the receiver:s point of vie#" the channel introduces

• time dispersion in #hich the duration of the receivedsym&ol is stretched

• ;xtending the sym&ol duration causes the currentreceived sym&ol to overlap previous received sym&ols

and results in intersym&ol interference (9/9!• 9n OFD" 9/9 usually refers to interference of an OFD

sym&ol &y previous OFD sym&ols


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• 'his means that at the maximum of eachsu&carrier spectrum" all the spectra of othersu&carriers are -ero

• 'he receiver samples data sym&ols on individualsu&carriers at the maximum points anddemodulates them free from any interferencefrom the other su&carriers

• 9nterference caused &y data sym&ols onad


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Lecture13 13

• 'he orthogonality of a su&carrier #ith respect to othersu&carriers is lost if the su&carrier has non-ero spectralvalue at other su&carrier frequencies

• From the time domain perspective" the correspondingsinusoid no longer has an integer num&er of cycles#ithin the FF' interval


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Lecture13 1$

• ## occurs when the multipath channel varies over oneOFDM sym!ol time"

• .hen this happens$ the Doppler shifts on each multipathcomponent causes a frequency offset on the su!carriers$resulting in the loss of orthogonality among them"

• ## also occurs when an OFDM sym!ol experiences #"

'his situation can !e viewed from the time domain perspective$ in which the integer num!er of cycles foreach su!carrier within the FF' interval of the currentsym!ol is no longer maintained due to the phase

transition introduced !y the previous sym!ol"• Finally$ any offset !etween the su!carrier frequencies of

the transmitter and receiver also introduces ## to anOFDM sym!ol"


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Lecture13 1

• For an OFDM transmitter with N su!carriers$ if the

duration of a data sym!ol is Ts$ the sym!ol duration

of the OFDM sym!ol at the output of the transmitteris

• Tos= Ts . N

• 'hus if the delay spread of a multipath channel is

greater than Ts !ut less then Tos$ the data sym!ol in

the serial data stream will experience

frequency-selective fading

while the data sym!ol on each su!carrier willexperience only flat-fading"


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Lecture13 14


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• to further reduce the #$ a guard time is insertedat the !eginning of each OFDM sym!ol !eforetransmission and removed at the receiver !eforethe FF' operation"

• #f the guard time is chosen such that its durationis longer than the delay spread$ the # can !e

completely eliminated" %ut &till have selfinterference"


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Lecture13 16

Interference between OFDM Symbols

• Transmitted Signal

• Due to delay spread ISI occurs

Delay Spread

IOSI

OS1 OS2 OS3

• Solution could be guard interval between OFDM symbols


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•+lthough the guard time which has longer duration

than the delay spread of a multipath channel

can eliminate # completely$ the received sym!ol isstill interfered !y its replicas received from

multipath components"

•#n order to compensate this distortion$ a one-tap

channel equali/er is needed for each su!carrier"

•+t the output of FF' on the receiver side$ thesample at each su!carrier is multiplied !y the

coefficient of the corresponding channel equali/er"


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Lecture13 21

yclic !refi"

• 0eros used in the guard time can reduce interference !etween OFDM sym!ols (#O pro!lem)"

• Orthogonality of carriers is lost when multipath channels

are involved"

• yclic prefix can restore the orthogonality"


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yclic !refi"

• onvert a linear convolution channel into a circularconvolution channel"

• 'his restores the orthogonality at the receiver"

• 1nergy is wasted in the cyclic prefix samples"


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Lecture13 23

yclic !refi" Illustration

TosTg

yclic !refi"

OS 1 OS 2

OS1#OS2 $ OFDM Symbols

Tg % &uard Time Interval

Ts % Data Symbol !eriod

Tos % OFDM Symbol !eriod '( ) Ts


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Lecture13 2$

*ffect of t+e (umber of Subcarriers and

&uard Time Duration

• ,ssumptions>14, modulation scheme

a 4$+su&carrier OFD system

#ith a t#o+ray multipath channel

'he po#er of the second path is 4 d? lo#er

than the first one

@o noise is present at the receiver in order to

have a clear idea of the influence of 9/9 and9=9


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•'he influence of # can !e reduced !y increasing the

duration of an OFDM sym!ol" 'o quantify the influence$we define a measure as

2 3 delay spreadsym!ol duration•For a given !andwidth of an OFDM signal$ the sym!ol

duration is proportional to the num!er of su!carriers"•#f η is large$ a significant num!er of samples of individual

OFDM sym!ols are affected !y # 34 high %15"•#f 2 is small$ a small portion of the individual OFDM

sym!ols is affected !y # 34low %15"


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• 9t sho#s that 9/9 is more severe for the OFD

system #ith small num&er of su&carrierscompared #ith the one that has a large num&erof su&carriers

• OFD sym&ols #ith long duration are moreresilient to frequency+selective fading &ut moresensitive to time+selective fading 'ime+selectivefading results in the loss of orthogonality among

su&carriers


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/ummery

• 'he attraction of OFDM is mainly due to how the system

handles the multipath interference at the receiver"

• Multipath generates two effects6 frequency selective fading

and intersym!ol interference (#)"

• 'he 7flatness7 perceived !y a narrow-!and channel overcomes

the former$ and modulating at a very low sym!ol rate$ which

maes the sym!ols much longer than the channel impulse

response$ diminishes the latter"

• the insertion of an extra guard interval !etween consecutive

OFDM sym!ols can reduce the effects of # even more" 'hus$

an equali/er in the receiver is not necessary"


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/ummery

• 'here are two main draw!acs with OFDM$ the large

dynamic range of the signal (also referred as pea-to

average 89+5: ratio) and• its sensitivity to frequency errors"

• 'hese in turn are the main research topics of OFDM

in many research centers around the world


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•For a given signal &and#idth" the frequency

spacing &et#een su&carriers decreases as the

num&er of su&carrier increases

•'he small frequency separation &et#een t#o

su&carriers ma*es them more vulnera&le to the

9=9 due to the frequency offset introduced &y

the Doppler spread of the channel

/ummery


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Lecture13 33

/ummary

• For a given num&er of su&carriers" increasingguard time duration reduces 9/9 due to the

decrease in delay spread relative to the sym&ol

time" &ut reduces the po#er efficiency and

&and#idth efficiency• For a given signal &and#idth" increasing the

num&er of su&carriers increases the po#er

efficiency &ut also increases the sym&ol duration

and results in a system more sensitive to

Doppler spread


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Lecture13 3$

alculation of OFDM 9arameters

Assume:• R = !it rate$

• delay spread of a multipath channel 3 ;

• the guard time T g should &e at least t#ice the

delay spread T g 4 *;

• 'o minimi/e the signal-to-noise ratio (&?;


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Lecture13 3

• 'he frequency spacing !etween two adacent su!carriers @ f is6

@ f =1/T s

• For a given data rate R$ the num!er of information !its per

OFDM sym!ol BOS is6

BOS = RT s

•For a given B

os

and the num!er of !its per sym!ol persu!carrier R sub$ the num!er of su!carriers N is6

C-A+M"• 'he OFDM signal !andwidth is defined as

• BW = N Δf


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Lecture13 34

O&servation 1

• #ncreasing the sym!ol duration decreases the

frequency spacing !etween su!carriers" 'hus$ for a

given signal !andwidth$ more su!carriers can !eaccommodated" On the other hand$ for a given

num!er of su!carriers$ increasing the sym!ol duration

decreases the signal !andwidth"


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Lecture13 35

O&servation 2

• 9ncreasing the num&er of su&carriers increases thenum&er of samples per OFD sym&ol Ao#ever" it doesnot necessary imply that the sym&ol duration increases9f the OFD sym&ol duration remains the same" the

duration &et#een t#o samples decreases as a result• 'his implies the increase in the OFD signal &and#idth

• On the other hand" if the OFD signal &and#idth isfixed" then increasing the num&er of su&carriersdecreases the frequency spacing &et#een t#o

su&carriers" #hich in turn increases the sym&ol duration'he duration &et#een t#o samples remain the same inthis case


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Bindo#ing


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• /ynchroni-ation is a *ey issue in the design of aro&ust OFD receiver Time- and frequency-synchronization are paramount to respectivelyidentify the start of the OFD sym&ol and toalign the modulators: and the demodulators:

local oscillator frequencies• 9f any of these synchroni-ation tas*s is not

performed #ith sufficient accuracy" then theorthogonality of the su&+carriers is (partly! lost

'hat is" inter+sym&ol interference (9/9! and inter+carrier+interference (9=9! are introduced


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Lecture13 $$


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Lecture13 $

Serial

to

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,-

,($1

"-

"($1

IFFT

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to

Serial

.dd

!

/indowingD.

0F Section

Input

Symbols

OFDM Transmitter


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.Dand

0emove

!

Serial to

!arallelFFT

!arallel

to Serial

and

Decoder

,-

,($1

"-

"($1

Output

Symbols

OFDM 0eceiver


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lecture 13 of dm

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