Lecture 13 of Dm
Transcript of Lecture 13 of Dm
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Lecture 13
Introduction to OFDM
Ref: OFDM_intro.pdf
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• 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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• )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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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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• 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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• 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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a ,-su!carrier OFDM transmitter and the process of generating
one OFDM sym!ol"
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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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• '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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• ## 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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• 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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• 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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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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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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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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*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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/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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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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• '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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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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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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