11/5/2012 1

Introduction to OFDM

Fire Tom WadaProfessor, 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/

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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, application Review of digital modulation FDMA vs. Multi-carrier modulation Theory of OFDM Multi-path Summary

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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 Europe ADSL High Speed Modem WLAN such as IEEE 802.11a/g/n WiMAX 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 2006 5.6MHz BW is divided into 13 segments

(~430KHz BW) HDTV: 12 segments Mobile TV : 1 segment SDTV: 4 segment Analog Service will end 2011

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Brief history of OFDM

First proposal in 1950’s Theory completed in 1960’s DFT implementation proposed in 1970’s Europe adopted OFDM for digital radio

broadcasting in 1987 OFDM for Terrestrial Video broadcasting

in Europe and Japan ADSL, WLAN(802.11a)

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Digital modulation basics Digital 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( ) 2

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

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Symbol Waveform 11 00 11 00 00Digital InformationDigital Information

carriercarrier

ASKASK

PSKPSK

FSKFSK

Symbol lengthSymbol length

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Multi bit modulation

11 00 11 00 00

carriercarrier

BPSKBPSK

1bit per symbol1bit per symbol

QPSKQPSK

2bit per symbol2bit per symbol

1010 1111 0101 0000 0101

Symbol lengthSymbol length

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Mathematical expression of digital modulation

Transmission 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

ba

tftf

tfts

　

　

( )a jb ek kj fc t 2

( )a jbk ke j fc t2 Indicates carrier sinusoidalIndicates carrier sinusoidal

Digital modulationDigital modulation

Digital modulation can be expressed by the complex numberDigital 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

1

2

1

2

1

2

1

21

2

1

2

1

2

1

2

QPSKQPSK

II

QQ

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Quadrature Amplitude Modulation (QAM)

II

QQ

II

QQ

16QAM16QAM 64QAM64QAM

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Summary of digital modulation Type of modulation: ASK,PSK,FSK,QAM OFDM uses ASK,PSK,QAM Digital modulation is mathematically

characterized by the coefficient of complex base-band signal

Plot of the coefficients gives the constellation map

( )a jbk k

II

QQ

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Frequency Division Multiple Access (FDMA)

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

transmission

Radio Radio frequencyfrequency

ff ｃｃ

１１

ff ｃｃ

22

ff ｃｃ

33

ff ｃｃ

NNCarrier frequencyCarrier frequency

Occupied BWOccupied BWChannel Channel

separationseparation

Guard Guard bandband

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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 modulation Use multiple channel (carrier frequency)

for one data transmission

datadata

cos( )2 1f t

cos( )2 2f t

cos( )2f tN

cos( )2 1f t

cos( )2 2f t

cos( )2f tN

LPFLPF

LPFLPF

LPFLPF

datadata

DEM

ULT

IPLE

X

MU

LTIP

LEX

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Spectrum comparison for same data rate transmission

frequencyfrequencySingle carrierSingle carrier

frequencyfrequencyOFDMOFDM

frequencyfrequencyMulti carrierMulti carrier

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OFDM vs. Multi carrier OFDM is multi carrier modulation OFDM sub-carrier spectrum is overlapping In FDMA, band-pass filter separates each

transmission In OFDM, each sub-carrier is separated by

DFT because carriers are orthogonal Condition of the orthogonality will be explained

later Each sub-carrier is modulated by PSK, QAM

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

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OFDM carriers

OFDM carrier frequency is n ・ 1/T

Symbol period TSymbol period Tcos( )2 1 0 1 f t

Tf

10

cos( )2 2 0 2 f t

cos( )2 3 0 3 f t

cos( )2 4 0 4 f t

cos( )2 5 0 5 f t

cos( )2 6 0 6 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

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 tb

a

n n

n n n nn

n

cos( ) sin( )

cos( ), tan

2 2

2

0 0

2 20

1

　

n cyclesn cycles

t=0t=0 t=Tt=T

TimeTime

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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

ＴＴn=0n=0n=1n=1n=2n=2n=3n=3n=4n=4n=5n=5n=6n=6

ssBB(t)(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 used N 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

Ta

s t kf t dtTb

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

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Pass-band OFDM signal

SSBB(t) is upcoverted to pass-band signal S(t)(t) is upcoverted to pass-band signal S(t) ffcc frequency shift frequency shift

s t a f nf t b f nf tn c n cn

N

( ) cos ( ) sin ( )

2 20 00

1

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Actual OFDM spectrum

ff ｃｃ＋ｋ＋ｋｆｆ００

ff ｃｃ＋＋ (( ｋｋ --

1)1) ｆｆ００

ff ｃｃ＋＋ (( ｋｋ+1)+1) ｆｆ００

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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

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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

10 　

uk

Nfd e d e

d e k N

n

j nfk

Nf

n

N

n

jnk

N

n

N

n

jN

nk

n

N

0

2

0

1 2

0

1

2

0

1

00

0 1 2 1

　 　 ( , , , , )

u(k) = IFFT (du(k) = IFFT (dnn) = IFFT(a) = IFFT(ann + jb + jbnn) )

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OFDM modulator

MMAAPP

SS//PP

I-DFTI-DFTPP//SS

RealReal

cos( )2f tC

ＢＰＦＢＰＦgeneratedgenerated

00~d~d Ｎ－１Ｎ－１

AIRAIR

Bit Bit streamstream

ImagImag

sin( )2f tC

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OFDM demodulation

)(2

1)2sin()2cos(

2

1)]2cos()([

)(2sin)(2cos)(

1

000

1

000

tstnfbtnfatftsLPF

tnffbtnffats

I

N

nnnC

N

ncncn

)(2

1)2cos()2sin(

2

1])2sin()([

1

000 tstnfbtnfatftsLPF Q

N

nnnC

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

n

N

( ) ( ) ( )

2

0

10

ddnn = FFT(u(k)) = FFT(u(k))

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OFDM demodulator (Too simple)

TTuunneerr

SS//PP

DFTDFTPP//SS

AA//DD

LPFLPF

ChannelChannelcos( )2f tC

π/2π/2

LPFLPF

DDEEMMAAPP

Bit Bit StreamStream

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Summary of OFDM signal Each symbol carries information Each symbol wave is sum of many sinusoidal Each sinusoidal wave can be PSK, QAM

modulated Using IDFT and DFT, OFDM implementation

became practical

TimeTime

Symbol periodSymbol periodT=1/fT=1/f ００

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Multi-path Delayed wave causes interference

Base Station

MobileReception

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/fT=1/f ００

Symbol kSymbol kSymbol k-1Symbol k-1 Symbol k+1Symbol k+1

Sampling PeriodSampling Period

No multi-pathNo multi-path

Sampling PeriodSampling Period

Multi-pathMulti-path Direct Direct

DelayedDelayed

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Guard Interval Tg

By adding the Gurard Interval Period, ISI can be avoided

OFDM symbol(1/fOFDM symbol(1/f00))

Copy signalCopy signal

TTgg

TTgg

DirectDirect

DelayedDelayed

OFDM symbol (1/fOFDM symbol (1/f00))TTgg

Sampling PeriodSampling Period

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Multi-path By adding GI, orthogonality can be maintained However, multi-path causes Amplitude and Phase

distortion for each sub-carrier The distortion has to be compensated by Equalizer

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Multiple Frequency Network

Frequency utilization is low

Area 1Area 1

Area 2Area 2

Area 3Area 3

Area 4Area 4

ff１１

f2f2

f3f3

f1f1

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Single Frequency Network

Area 1Area 1

Area 2Area 2

Area 3Area 3

Area 4Area 4

ff１１

ff１１

ff１１

f1f1

If multi-path problem is solved,SFN is possible

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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