11/2/2009 1

Introduction to OFDMFire Tom Wada

Professor, Information Engineering, Univ. of the RyukyusChief Scientist at Magna Design Net, Inc

wada@ie.u-ryukyu.ac.jphttp://www.ie.u-ryukyu.ac.jp/~wada/

11/2/2009 2

What is OFDM?

OFDM=Orthogonal Frequency Division Multiplexing

Many orthogonal sub-carriers are multiplexed in one symbol

What is the orthogonal?How multiplexed?What is the merit of OFDM?What kinds of application?

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Outline

Background, history, applicationReview of digital modulationFDMA vs. Multi-carrier modulationTheory of OFDMMulti-pathSummary

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Why OFDM is getting popular？

State-of-the-art high bandwidth digital communication start using OFDM

Terrestrial Video Broadcasting in Japan and EuropeADSL High Speed ModemWLAN such as IEEE 802.11a/g/nWiMAX as IEEE 802.16d/e

Economical OFDM implementation become possible because of advancement in the LSI technology

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Japan Terrestrial Video Broadcasting service

ISDB-T (Integrated Services Digital Broadcasting for Terrestrial Television Broadcasting)Service starts on 2003/December at three major cities (Tokyo, Nagoya, Osaka)Full service area coverage on 20065.6MHz BW is divided into 13 segments (~430KHz BW)HDTV: 12 segmentsMobile TV : 1 segmentSDTV: 4 segment Analog Service will end 2011

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Brief history of OFDM

First proposal in 1950’sTheory completed in 1960’sDFT implementation proposed in 1970’sEurope adopted OFDM for digital radio broadcasting in 1987OFDM for Terrestrial Video broadcasting in Europe and JapanADSL, WLAN(802.11a)

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Digital modulation basicsDigital modulation modulates three parameters of sinusoidal signal. A, θk fc,

Three type digital modulation: ASK : Amplitude Shift Keying PSK : Phase Shift Keying FSK : Frequency Shift Keying

s t A f tc k( ) cos( )= ⋅ ⋅ ⋅ +2π θ

OFDM uses combination of ASK and PSK such as QAM, PSK

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Symbol Waveform 1 0 1 0 0Digital Information

carrier

ASK

PSK

FSK

Symbol length

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Multi bit modulation

1 0 1 0 0

carrier

BPSK

1bit per symbol

QPSK

2bit per symbol

10 11 01 00 01

Symbol length

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Mathematical expression of digital modulationTransmission signal can be expressed as follows

s(t) can be expressed by complex base-band signal

])Re[()(

sin,cos)2sin(sin)2cos(cos

)2cos()(

2 tfcjkk

kkkk

ckck

kc

ejbats

batftf

tfts

⋅+=

==⋅⋅⋅−⋅⋅⋅=

+⋅⋅=

π

θθπθπθ

θπ

　

　

( )a jb ek kj fc t+ ⋅2π

( )a jbk k+e j fc t2π ⋅ Indicates carrier sinusoidal

Digital modulation

Digital modulation can be expressed by the complex number

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Constellation map (ak + jbk) is plotted on I(real)-Q(imaginary) plane

data ak bk

00 π/4

01 3π /4

11 5π /4

10 7π /4

12

12

−12

−12

−12

−12

12

12

QPSK

I

Q

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Quadrature Amplitude Modulation (QAM)

I

Q

I

Q

16QAM 64QAM

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Summary of digital modulationType of modulation: ASK,PSK,FSK,QAMOFDM uses ASK,PSK,QAMDigital modulation is mathematically characterized by the coefficient of complex base-band signal

Plot of the coefficients givesthe constellation map

( )a jbk k+

I

Q

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Frequency Division Multiple Access (FDMA)

Old conventional method (Analog TV, Radio etc.)Use separate carrier frequency for individual transmission

Radio frequency

fｃ１ fｃ2 fｃ3 fｃNCarrier frequency

Occupied BWChannel

separation

Guard band

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Japan VHF channel assignment

Channel Separation = 6MHz

Channel number Frequency (MHz)

1 90-96

2 96-102

3 102-108

4 170-176

5 176-182

6 182-188

7 188-194

8 192-198

9 198-204

10 204-210

11 210-216

12 216-222

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Multi-carrier modulationUse multiple channel (carrier frequency) for one data transmission

data

cos( )2 1πf t

cos( )2 2πf t

cos( )2πf tN

cos( )2 1πf t

cos( )2 2πf t

cos( )2πf tN

LPF

LPF

LPF

data

DEM

ULTIPLEX

MU

LTIPLEX

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Spectrum comparison for same data rate transmission

frequencySingle carrier

frequencyOFDM

frequencyMulti carrier

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OFDM vs. Multi carrierOFDM is multi carrier modulationOFDM sub-carrier spectrum is overlappingIn FDMA, band-pass filter separates each transmissionIn OFDM, each sub-carrier is separated by DFT because carriers are orthogonal

Condition of the orthogonality will be explained laterEach sub-carrier is modulated by PSK, QAM

Thousands of PSK/QAM symbol can be simultaneously transmitted in one OFDM symbol

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OFDM carriers

OFDM carrier frequency is n・1/T

Symbol period Tcos( )2 1 0 1π θ⋅ ⋅ ⋅ +f t

Tf 10 =

cos( )2 2 0 2π θ⋅ ⋅ ⋅ +f tcos( )2 3 0 3π θ⋅ ⋅ ⋅ +f tcos( )2 4 0 4π θ⋅ ⋅ ⋅ +f t

cos( )2 5 0 5π θ⋅ ⋅ ⋅ +f t

cos( )2 6 0 6π θ⋅ ⋅ ⋅ +f t

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Sinusoidal Orthogonality

m,n: integer, T=1/f0

cos( ) cos( ) ( )

( )

sin( ) sin( ) ( )

( )

cos( ) sin( )

2 2 20

2 2 20

2 2 0

0 00

0 00

0 00

π π

π π

π π

mf t nf t dtT m n

m n

mf t nf t dtT m n

m n

mf t nf t dt

T

T

T

⋅ = =

≠

⎧⎨⎪

⎩⎪

⋅ = =

≠

⎧⎨⎪

⎩⎪

⋅ =

∫

∫

∫

　

　

　

　

Orthogonal

Orthogonal

Orthogonal

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A sub-carrier of f=nf0

Amplitude and Phase will be digitally modulated

a nf t b nf t

a b nf t ba

n n

n n n nn

n

⋅ − ⋅

= + + = −

cos( ) sin( )

cos( ), tan

2 2

2

0 0

2 20

1

π π

π φ φ　

n cycles

t=0 t=T

Time

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Base-band OFDM signal

{ }s t a nf t b nf tB n nn

N

( ) cos( ) sin( )= −=

−

∑ 2 20 00

1

π π

Ｔn=0n=1n=2n=3n=4n=5n=6

sB(t)

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How an,bn are caluculated from sB(t)- Demodulation Procedure -

According to the sinusoidal orthogonality, an,bn can be extracted.In actual implementation, DFT(FFT) is usedN is roughly 64 for WLAN, thoudand for Terrestrial Video Broadcasting

{ }

{ }

s t kf t dt

a nf t kf t dt b nf t kf t dt

T a

s t kf t dt T b

B

T

n n

TT

n

N

k

B k

T

( ) cos( )

cos( ) cos( ) sin( ) cos( )

( ) sin( )

⋅

= −

=

− =

∫

∫∫∑

∫

=

−

2

2 2 2 2

2

22

00

0 0 0 0000

1

00

π

π π π π

π

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Pass-band OFDM signal

SB(t) is upcoverted to pass-band signal S(t)fc frequency shift

{ } { }[ ]s t a f nf t b f nf tn c n cn

N

( ) cos ( ) sin ( )= + − +=

−

∑ 2 20 00

1

π π

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Actual OFDM spectrum

fｃ＋ｋｆ０fｃ＋(ｋ-1)ｆ０ fｃ＋(ｋ+1)ｆ０

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OFDM power spectrum

Total Power spectrum is almost square shape

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OFDM signal generation

Direct method needsN digital modulatorsN carrier frequency generator

Not practical

In 1971, method using DFT is proposed to OFDM siganal generation

{ } { }[ ]s t a f nf t b f nf tn c n cn

N

( ) cos ( ) sin ( )= + − +=

−

∑ 2 20 00

1

π π

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OFDM signal generation in digital domain

Define complex base-band signal u(t) as follows

Perform N times sampling in period T

[ ]s t u t

u t d e d a jb

B

nj nf t

n

N

n n n

( ) Re ( )

( ) ,

=

= ⋅ = +=

−

∑ 2

0

10π 　

u kN f

d e d e

d e k N

n

j n f kN f

n

N

n

j nkN

n

N

n

jN

nk

n

N

0

2

0

1 2

0

1

2

0

1

00

0 1 2 1

⎛⎝⎜

⎞⎠⎟ = ⋅ = ⋅

= ⋅⎛

⎝⎜

⎞

⎠⎟ = −

=

−

=

−

=

−

∑ ∑

∑

π π

π

　　 ( , , , , )L

u(k) = IFFT (dn) = IFFT(an + jbn)

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OFDM modulator

MAP

S/P

I-DFTP/S

Real

cos( )2πf tC

ＢＰＦgenerated0~dＮ－１

AIR

Bit stream

Imag

sin( )2πf tC

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OFDM demodulation

{ } { }[ ]

{ } )(21)2sin()2cos(

21)]2cos()([

)(2sin)(2cos)(

1

000

1

000

tstnfbtnfatftsLPF

tnffbtnffats

I

N

nnnC

N

ncncn

=−=⋅

+−+=

∑

∑−

=

−

=

πππ

ππ

{ } { } )(21)2cos()2sin(

21])2sin()([

1

000 tstnfbtnfatftsLPF Q

N

nnnC =+=−⋅ ∑

−

=

πππ

u t s t js t d eI Q nj nf t

n

N

( ) ( ) ( )= + = ⋅=

−

∑ 2

0

10π

dn = FFT(u(k))

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OFDM demodulator (Too simple)

Tuner

S/P

DFTP/S

A/D

LPF

Channelcos( )2πf tC

π/2

LPF

DEMAP

Bit Stream

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Summary of OFDM signalEach symbol carries informationEach symbol wave is sum of many sinusoidalEach sinusoidal wave can be PSK, QAM modulatedUsing IDFT and DFT, OFDM implementation became practical

Time

Symbol periodT=1/f０

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Multi-path

Delayed wave causes interference

Base Stat ion

MobileRecept ion

Path 2

Path 3

Direct Path

Building

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Multi-pass effect

Inter symbol interference (ISI) happens in Multi-path condition

T=1/f０Symbol kSymbol k-1 Symbol k+1

Sampling Period

No multi-path

Sampling Period

Multi-path Direct

Delayed

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Guard Interval Tg

By adding the Gurard Interval Period, ISI can be avoided

OFDM symbol(1/f0)

Copy signal

Tg

Tg

Direct

Delayed

OFDM symbol (1/f0)Tg

Sampling Period

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Multi-pathBy adding GI, orthogonality can be maintainedHowever, multi-path causes Amplitude and Phase distortion for each sub-carrierThe distortion has to be compensated by Equalizer

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Multiple Frequency Network

Frequency utilization is low

Area 1

Area 2

Area 3

Area 4

f１

f2

f3

f1

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Single Frequency Network

Area 1

Area 2

Area 3

Area 4

f１

f１

f１

f1

If multi-path problem is solved,SFN is possible

11/2/2009 39

That’s all for introduction

Feature of OFDM1. High Frequency utilization by the square

spectrum shape2. Multi-path problem is solved by GI3. Multiple services in one OFDM by sharing sub-

carriers (3 services in ISDB-T)4. SFN5. Implementation was complicated but NOW

possible because of LSI technology progress