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IANTIANTUniversitt Hannover
Dr.-Ing. Van Duc Nguyen 1
OFDM
Orthogonal Frequency
Division Multiplexing
OFDM
Orthogonal Frequency
Division Multiplexing
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IANTIANTUniversitt Hannover
Dr.-Ing. Van Duc Nguyen 3
Current OFDM Systems
Current OFDM Systems
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IANTIANTUniversitt Hannover
Dr.-Ing. Van Duc Nguyen 4
Current OFDM systems: DABCurrent OFDM systems: DAB
Solution: Digital Audio Broadcasting (DAB)
CD-like quality even in the car.
Provides many services such as texts, pictures, and video in
radio.
Problems of analogue radio signals (FM, AM, etc.):B Low quality and poor services.
Some technical parameters:B 1.5 MHz bandwidth.
BUses OFDM technique with 192 1536 sub-carriers depending
on carrier frequency.BMaximal user data rate: 1.8 Mbit/s
BOperates in Germany at around 200 MHz and 1500 MHz.
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IANTIANTUniversitt Hannover
Dr.-Ing. Van Duc Nguyen 5
Current OFDM systems: DVB-TCurrent OFDM systems: DVB-T
Some technique parameters: 7.61 MHz bandwidth.
Uses OFDM technique with 1705 sub-carriers for 2k mode, and6817 sub-carriers for 8k mode.
Transmits MPEG-2 compressed video.
Maximal data speed up to 31 Mbit/s.
Problems of analogue video signals (PAL, SECAM,
NTSC, etc.):BHigh distortion, low resolution, low quality, and poor services
Solution: Digital Video Broadcasting (DVB-T)BRequires no cable, no satellite, smaller antenna.
BServiced in a wide range (home, garden, car).BMore services: Television, information, data.
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IANTIANTUniversitt Hannover
Dr.-Ing. Van Duc Nguyen 6
Current OFDM systems:
HiperLAN2/ IEEE 802.11.a
Current OFDM systems:
HiperLAN2/ IEEE 802.11.a
High Performance Local Area Network type 2
(HiperLAN2) is an ETSI standard of wireless LAN.
Some technical parameters:
20 MHz bandwidth.
Uses OFDM technique with 48 data
sub-carriers.
Operates at 5.2 GHz.
Allows up to 54 Mbit/s.
Allows adaptive modulation based on channel condition.
Use coherent modulation on each sub-carrier (BPSK,
QPSK, 16-QAM, and 64-QAM).
HiperLAN2-Terminal
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IANTIANTUniversitt Hannover
Dr.-Ing. Van Duc Nguyen 7
OFDM PrincipleOFDM Principle
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IANTIANTUniversitt Hannover
Dr.-Ing. Van Duc Nguyen 8
Single Carrier System (1)Single Carrier System (1)
Data transmission uses only one carrier frequency.
Frequency
Power spectral density
B
0f
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IANTIANTUniversitt Hannover
Dr.-Ing. Van Duc Nguyen 9
Single Carrier System (2)Single Carrier System (2)
Due to multi-path transmission, intersymbol interference is
introduced in the received signal.
The ratio of the maximal time delay of the channel to the
symbol duration is
SC
maxSC
TR
=
max
SCT
Theoretical view on the DVB-T scenario:
The total bandwidth of the system , which could
have an approximated symbol duration .
The maximal time delay of the channel would
then lead to the ratio
7.61MHzB =
SC 1/T B
max 224 s =
maxSC
SC
1704RT
=
The channel impulse response affects many symbols.
Equalization is complicated and computationally demanding.
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IANTIANTUniversitt Hannover
Dr.-Ing. Van Duc Nguyen 10
Multi-carrier System (1)Multi-carrier System (1)
The data stream is transmitted on parallel channels with asmaller bandwidth .
Instead of just one carrier frequency, many sub-carrier
frequencies are used.
CN
Intelligent solution: Division of bandwidth B into several subbands
MCnf
sf
sf
Frequency
Power spectral
density
B
0fLMCf LMCf +
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IANTIANTUniversitt Hannover
Dr.-Ing. Van Duc Nguyen 11
Multi-carrier System (2)Multi-carrier System (2)
The spacing between two sub-carrier frequencies:
The symbol duration is larger than before:
The ratio of the maximal time delay of the channel to the symbol
duration
C
sN
B
f =
CSCMC NTT =
MC
maxMC
TR
=
The channel impulse response affects just a few symbols.
The impairment of intersymbol interference (ISI) is significantly
reduced, but the system is more sensitive to the time variations
of the channel.
and hence SCMC RR
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IANTIANTUniversitt Hannover
Dr.-Ing. Van Duc Nguyen 12
OFDM
(Orthogonal FrequencyDivision Multiplexing)
OFDM
(Orthogonal FrequencyDivision Multiplexing)
Due to the overlapping of the sub-carriers in the frequency domain,
a higher spectral efficiency is achieved. The sub-carriers have to be orthogonal so that they do not disturb each
other.
Intersymbol interference can be perfectly eliminated by using a so-called guard interval.
Frequency
Power spectral
density
B
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IANTIANTUniversitt Hannover
Dr.-Ing. Van Duc Nguyen 13
OFDM ModulationOFDM Modulation
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IANTIANTUniversitt Hannover
Dr.-Ing. Van Duc Nguyen 14
OFDM ModulationOFDM Modulation
OFDM signal before inserting guard interval:
S
equencecoder
Demultiplexer
Subchannel
modulator
Subchannel
modulator
Subchannel
modulator
Insertguardinterv
al
( ) ( ) ( ) tn
k
L
Ln
nk
k
k kTtsdtmtmsj
=
0, e==
=
=
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IANTIANTUniversitt Hannover
Dr.-Ing. Van Duc Nguyen 15
Arrangement of Data
Symbols in Frequency andTime Domain
Arrangement of Data
Symbols in Frequency andTime Domain
OFDM symbol
Time
Frequ
ency
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IANTIANTUniversitt Hannover
Dr.-Ing. Van Duc Nguyen 16
Orthogonal PrincipleOrthogonal Principle
Each sub-carrier is orthogonal to the others within the
OFDM symbol interval
( )( )
( )( )
( )( ) ( )
( )( ) ( ) ( )
0 0
ss s
0 0
0
s
0
1 1
jj j
1
j j 2 1 j 2
s s
C0
e e e
1 1e e e
j j
0 for with , ,
for
k T k T
p q tp t q t
kT kT
k T
p q t p q k p q k
kT
dt dt
p q p q
p qp q N k
T p q
+ +
+
+
=
= =
=
=
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IANTIANTUniversitt Hannover
Dr.-Ing. Van Duc Nguyen 17
Guard Interval Principle (1)Guard Interval Principle (1)
To maintain the received signal in the sinus form, a copy of the tailsignal is inserted at the front.
This copy is named guard interval whereas its length must be longerthan the maximal time delay of the channel: to prevent ISI.
Received signal from two paths:
maxG T
Guard
interval
thk
time
Useful interval
Caused by the propagation delay
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IANTIANTUniversitt Hannover
Dr.-Ing. Van Duc Nguyen 18
Guard Interval Principle (2)Guard Interval Principle (2)
Format of an OFDM symbol with guard interval:
CP Useful symbol
-TG T00
OFDM system with sufficient guard interval length:
The intersymbol interference is entirely eliminated and the
orthogonality between sub-carriers is maintained.
Simple channel estimation and equalization is possible. But the spectral efficiency is degraded by a factor (as
redundancy is added):
0
G
T
T=
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IANTIANTUniversitt Hannover
Dr.-Ing. Van Duc Nguyen 19
Basic Impulse
with Guard Interval
Basic Impulse
with Guard Interval
( )0 G 0for
0 otherwise
s T t Ts t
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IANTIANTUniversitt Hannover
Dr.-Ing. Van Duc Nguyen 20
OFDM DemodulationOFDM Demodulation
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IANTIANTUniversitt Hannover
Dr.-Ing. Van Duc Nguyen 21
Received Signal after
Multipath Propagation
Received Signal after
Multipath Propagation
For simplification, no additive noise is considered
( )m t ( , )h t
( , )H j t
( )u t
Transmitted signal Received signal
The received signal after multi-path transmission:
( ) ( ) ( , )u t m t h t = max
sj ( )
,
0
( , ) ( )eL
n t kT
k n
k n L
d h t s t kT d
+
= =
=
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IANTIANTUniversitt Hannover
Dr.-Ing. Van Duc Nguyen 22
OFDM DemodulatorOFDM Demodulator
Remove
G
uardinterval
Seq
uencedecoder
Multiplexer
Subchannel
demodulator
Subchannel
demodulator
Subchannel
demodulator
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IANTIANTUniversitt Hannover
Dr.-Ing. Van Duc Nguyen 23
Removal of Guard IntervalRemoval of Guard Interval
Illustration of removing the guard interval:
After removing the guard interval, it is valid:
( ) ( )tkTutkTu +=+ 0 kTt
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IANTIANTUniversitt Hannover
Dr.-Ing. Van Duc Nguyen 24
Received Symbol after Sub-
channel Demodulator (1)
Received Symbol after Sub-
channel Demodulator (1)
After removing the guard interval, and integration within the
useful interval, the received symbol becomes:
( )( )
{ }
( )
0
s
0
0 max
s s 0
0
1
j
,0
1
-j j ( )( )
, 00 0
1 e
1( , ) ( )e e
k T
l t
k l k
kT
k T Ln n l t kT
k nn LkT
d u t dt T
d h t s t kT d dt T
+
+
=
=
=
If is valid, ISI is completely eliminated.G maxT
0 0
s 0
0 0
( 1) ( 1)^
j( ) ( )0 0, , s , s
,0 0
ICIU,,
: interference part: useful part
( , ) ( , ) e
k T k T Ln l t kT
k l k l k n
n L n l kT kT
k lk ldd
s sd d H l t dt d H n t dt
T T
+ +
=
= +
144444444244444444314444244443
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IANTIANTUniversitt Hannover
Dr.-Ing. Van Duc Nguyen 25
Received Symbol after Sub-
channel Demodulator (2)
Received Symbol after Sub-
channel Demodulator (2)
For time invariant channel:
No intercarrier interference (see proof)
Received symbol is disturbed only by one complex channel
coefficient (linear distortion) (see proof)
( ) ( , )H j H j t =
, 0 , s ( )k l k l d s d H jl =
In the presence of additive noise:
, 0 , s , ( )k l k l k l d s d H jl n= +
Only one-tap equalizer is required!
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IANTIANTUniversitt Hannover
Dr.-Ing. Van Duc Nguyen 26
Implementation of an
OFDM Modulator and
Demodulator
Implementation of an
OFDM Modulator and
Demodulator
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IANTIANTUniversitt Hannover
Dr.-Ing. Van Duc Nguyen 27
Modulator (1)Modulator (1)
The k-th OFDM symbol is:
( ) sj0 , eL
n t
k k n
n L
m t s d
=
= ( )0 01kT t k T < +for
The signal is sampled with the sampling interval:
0a
C
Tt
N= where
It can be proven that
( )C
C
1j2
0 a 0 ,
0
eN
nl N
k k n
n
m kT lt s d
=
+ =
or
( ){ } {0 a C 0 ,ID TF k k nl nm kT lt N s d + =
C0,1, 2, , 1 ;l N k= Kfor
C 2 1N L= +
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IANTIANTUniversitt Hannover
Dr.-Ing. Van Duc Nguyen 28
Modulator (2)Modulator (2)
The OFDM modulator can be implemented by using an IFFT.
Demultip
lexer
Sequence
coder
IFFT
Multiplexer
Insertguard
interval
D/Aconverter
OFDM modulator
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IANTIANTUniversitt Hannover
Dr.-Ing. Van Duc Nguyen 29
OFDM Demodulator (1)OFDM Demodulator (1)
The received symbol is
( )
( ) 0s
0
1
j
,
0 0
1
e
k T
n t
k n k
kTd u t dt T s
+
= After sampling, it can be proven that
( )C
C
1j2
, 0 a0 0
1 eN
nl N
k n k
l
d u kT lt N s
=
= + for C0,1, 2, , 1;n N k= K
or
{ } ( ){ }, 0 a0
DFT1 k n k ld u kT lt
N s= +
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IANTIANTUniversitt Hannover
Dr.-Ing. Van Duc Nguyen 30
Implementation of an OFDM
Demodulator
Implementation of an OFDM
Demodulator
The OFDM demodulator can be effectively implemented
by using an FFT.
OFDM demodulator
Demultiplex
er
A/D
converter
Removeguard
interval
Sequencedec
oder
Multiplexe
r
FFT
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IANTIANTUniversitt Hannover
Dr.-Ing. Van Duc Nguyen 31
OFDM SpectrumOFDM Spectrum
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IANTIANTUniversitt Hannover
Dr.-Ing. Van Duc Nguyen 32
OFDM Spectrum (1)OFDM Spectrum (1)
It can be proven that the averaged power spectral density of theOFDM signal is the sum of function.
( ) ( )( )2s sj si 2L
mm
n L
TE T n =
=
Spectrum of the sub-carriers can overlap.
2si ( )
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OFDM Spectrum (2)OFDM Spectrum (2)
500 400 300 200 100 0 100 200 300 400 50050
45
40
35
30
25
20
15
10
5
0
5
mm
(j)[dB]
/s
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IANTIANTUniversitt Hannover
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OFDM Spectrum (3)OFDM Spectrum (3)
185 190 195 200 205 210 215 22030
25
20
15
10
5
0
mm
(j)[dB]
/s
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IANTIANTUniversitt Hannover
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EqualizationEqualization
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IANTIANTUniversitt Hannover
Dr.-Ing. Van Duc Nguyen 36
Equalization (1)Equalization (1)
Assumptions:
The guard interval is sufficiently long
The channel is time-invariant within an OFDM symbol
and non-frequency selective within a sub-carrier spacing.
( ) ( ) ( )j ; j ; for 1H t H kT kT t k T = < +
( ) ( ) ( ) ( )s s s1 1j ; j ; for 2 2H t H n t n n = < +
The channel coefficient associated with sub-carriern
and OFDM symbol kcan be written by:
( ) ( )( )
( ) ( )s s s
1
j ; j ; for1 12 2
kT t k T
H t H n kTn n
< +
= < +
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IANTIANTUniversitt Hannover
Dr.-Ing. Van Duc Nguyen 37
Equalization (2)Equalization (2)
The demodulated symbol:
One-tap equalizer:( ), s ,j ;k n k nd H n kT d
=%
( ), ,s1
j ;k n k nd dH n kT= %
So for each sub-carrier only one complex coefficient is
needed for equalization.
Equalization much easier than in single carrier systems.
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IANTIANTUniversitt Hannover
Dr.-Ing. Van Duc Nguyen 38
Channel EstimationChannel Estimation
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IANTIANTUniversitt Hannover
Dr.-Ing. Van Duc Nguyen 39
Pilot Symbol PatternPilot Symbol Pattern
Transmitter: Pilot symbols can be inserted in time
and frequency domain.
Receiver: Remove pilot symbols to estimate the
channel transfer function of the channel.
An example ofpilot pattern:
fD
tD
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IANTIANTUniversitt Hannover
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Condition of Pilot DistanceCondition of Pilot Distance
Pilot distance in frequency domain is selecteddepending on the maximum Doppler frequency:
Pilot distance in time domain is selected depending
on the maximum time delay of the channel:
According to the sampling theorem:
D G
11
2 ( )t
t
rf D T T
= +
s max
1 1ff
rD f
=
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IANTIANTUniversitt Hannover
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Conventional Channel
Estimation Method
Conventional Channel
Estimation Method
Conventional channel estimation method is
performed by the two following steps:
The CTF at the position of pilot symbols is obtained by
dividing the received pilot symbol by the transmitted pilot
symbol:
The CTF at the position of data symbols is obtained by
interpolation of the estimated CTF in the first step.
,
,
,
k n
k n
k nH S
=
, ,interpol( )k n k nH H =%
IANT
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IANTIANTUniversitt Hannover
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Some Interpolation TechniquesSome Interpolation Techniques
Si:
Cubic:
0 5 10 151.5
1
0.5
0
0.5
1
1.5
t/ta
H(t)
a: an example for si interpolation
0 5 10 15
1.5
1
0.5
0
0.5
1
1.5b: an example for cubic interpolation
t/ta
H(t)
Original functionSampling pointInterpolated point (Si)
Original functionSampling pointinterpolated point (cubic)
1 1interpol( , )n n nx x x + =
1 1 2 3interpol( , , , )n n n n nx x x x x + + + =
IANTIANT
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IANTIANTUniversitt Hannover
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SynchronizationSynchronization
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What is Synchronization?What is Synchronization?
Frequency (transmitter) frequency (receiver).
Symbol timing (transmitter) symbol timing (receiver).
Transmitter Receiver
In general:
Frequency and time synchronization are required
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Frequency
Synchronization for OFDM
Frequency
Synchronization for OFDM
Problems:
Mismatch of the oscillators in transmitter and receiver or Doppler effect leads to a frequency shift.
Consequences:
The orthogonality of sub-carriers is not maintained. Causes intercarrier interference and degrades the
performance of the system.
OFDM system is sensible to a frequency offset.
IANTIANT Ti S h i ti
Ti S h i ti
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Time Synchronization
for OFDM
Time Synchronization
for OFDM
Problems:
Symbol timing at the receiver is unknown. FFT window position is unkown (symbol timing).
Propagation delay is unkown.
Consequences: FFT window position has to be estimated correctly.
Otherwise intersymbol interference appears and degrades the
performance of the system.
OFDM system is sensible to a time offset.
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IANTIANTUniversitt Hannover
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OFDM SystemOFDM System
Insert pilotsymbols
IFFTInsertguard
interval
analog
converter
Digital/
Radiochannel
Mod.in baseband
Additive noise
Analog/digital
converter
Removerguard
intervalFFT
Removepilot
symbols
EqualizationDem.
in baseband
Channelestimation
Destination
Source
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ConclusionConclusion
OFDM technique is robust against the multi-path
propagation interference. Easy to implement by an IFFT/FFT.
Requires only simple channel estimator and
one-tap equalizer.
High spectral efficiency.
OFDM is a powerful and flexible modulation
scheme which is a good candidate for Ad Hoc
networks