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7/31/2019 Thong Tinv Otu Yen

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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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Current OFDM Systems

Current OFDM Systems


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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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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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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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OFDM PrincipleOFDM Principle


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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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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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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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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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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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OFDM ModulationOFDM Modulation


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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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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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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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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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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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Basic Impulse

with Guard Interval

Basic Impulse

with Guard Interval

( )0 G 0for

0 otherwise

s T t Ts t


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OFDM DemodulationOFDM Demodulation


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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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OFDM DemodulatorOFDM Demodulator

Remove

G

uardinterval

Seq

uencedecoder

Multiplexer

Subchannel

demodulator

Subchannel

demodulator

Subchannel

demodulator


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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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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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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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Implementation of an

OFDM Modulator and

Demodulator

Implementation of an

OFDM Modulator and

Demodulator


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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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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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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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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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OFDM SpectrumOFDM Spectrum


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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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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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185 190 195 200 205 210 215 22030

25

20

15

10

5

0

mm

(j)[dB]

/s


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EqualizationEqualization


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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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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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Channel EstimationChannel Estimation


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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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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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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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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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SynchronizationSynchronization

IANTIANT


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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

IANTIANT


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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.

IANTIANT


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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

IANTIANT


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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

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