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Introduction to OFDM. Fire Tom Wada Professor, Information Engineering, Univ. of the Ryukyus Chief Scientist at Magna Design Net, Inc [email protected] http://www.ie.u-ryukyu.ac.jp/~wada/. What is OFDM?. OFDM =Orthogonal Frequency Division Multiplexing - PowerPoint PPT Presentation
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04/22/23 1
Introduction to OFDM
Fire Tom WadaProfessor, Information Engineering, Univ. of the
RyukyusChief Scientist at Magna Design Net, Inc
[email protected]://www.ie.u-ryukyu.ac.jp/~wada/
04/22/23 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?
04/22/23 3
Outline
Background, history, application Review of digital modulation FDMA vs. Multi-carrier modulation Theory of OFDM Multi-path Summary
04/22/23 4
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
04/22/23 5
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
04/22/23 6
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)
04/22/23 7
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
04/22/23 8
Symbol Waveform 11 00 11 00 00Digital InformationDigital Information
carriercarrier
ASKASK
PSKPSK
FSKFSK
Symbol lengthSymbol length
04/22/23 9
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
04/22/23 10
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
04/22/23 11
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
04/22/23 12
Quadrature Amplitude Modulation (QAM)
II
II
16QAM16QAM 64QAM64QAM
04/22/23 13
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
04/22/23 14
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
04/22/23 15
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
04/22/23 16
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
04/22/23 17
Spectrum comparison for same data rate transmission
frequencyfrequencySingle carrierSingle carrier
frequencyfrequencyOFDMOFDM
frequencyfrequencyMulti carrierMulti carrier
04/22/23 18
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
04/22/23 19
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
04/22/23 20
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
04/22/23 21
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
04/22/23 22
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)
04/22/23 23
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
04/22/23 24
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
04/22/23 25
Actual OFDM spectrum
ff ｃｃ＋ｋ＋ｋｆｆ００
ff ｃｃ＋＋ (( ｋｋ --
1)1) ｆｆ００
ff ｃｃ＋＋ (( ｋｋ+1)+1) ｆｆ００
04/22/23 26
OFDM power spectrum
Total Power spectrum is almost square shape
04/22/23 27
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
04/22/23 28
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) )
04/22/23 29
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
04/22/23 30
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))
04/22/23 31
OFDM demodulator (Too simple)
TTuunneerr
SS//PP
DFTDFTPP//SS
AA//DD
LPFLPF
ChannelChannelcos( )2f tC
π/2π/2
LPFLPF
DDEEMMAAPP
Bit Bit StreamStream
04/22/23 32
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
04/22/23 33
Multi-path Delayed wave causes interference
Base Station
MobileReception
Path 2
Path 3
Direct Path
Building
04/22/23 34
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
04/22/23 35
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
04/22/23 36
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
04/22/23 37
Multiple Frequency Network
Frequency utilization is low
Area 1Area 1
Area 2Area 2
Area 3Area 3
Area 4Area 4
ff１１
f2f2
f3f3
f1f1
04/22/23 38
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
04/22/23 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
