introduction to ofdm - ie.u-ryukyu.ac.jpwada/system12/32-sysarc2012(ofdm).pdf · introduction to...
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11/5/2012 1
Introduction to OFDMFire Tom Wada
Professor, Information Engineering, Univ. of the RyukyusChief Scientist at Magna Design Net, Inc
[email protected]://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, 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
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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