- OFDM (Orthogonal Frequency Division Multiplexing) is a digital modulation technique that divides the available bandwidth into multiple orthogonal subcarriers. - Each subcarrier is modulated with a conventional modulation scheme at a low symbol rate, maintaining total data rates similar to conventional single-carrier modulation schemes in the same bandwidth. - OFDM has become popular for wireless networks and digital audio/video broadcasting due to its ability to cope with multi-path fading and resistance to intersymbol interference. It is used in technologies like WiFi, WiMAX, DVB, and LTE.

1. Introduction to OFDM
Fire Tom Wada
Professor, Information Engineering, Univ. of the Ryukyus
Chief Scientist at Magna Design Net, Inc
wada@ie.u-ryukyu.ac.jp
http://www.ie.u-ryukyu.ac.jp/~wada/
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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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3. Outline
• Background, history, application
• Review of digital modulation
• FDMA vs. Multi-carrier modulation
• Theory of OFDM
• Multi-path
• Summary
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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
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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
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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)
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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
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s t A f t
c k
( ) cos( )
    
2 
OFDM uses combination of ASK and PSK such as QAM, PSK

8. Symbol Waveform
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1 0 1 0 0
Digital Information
carrier
ASK
PSK
FSK
Symbol length

9. Multi bit modulation
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1 0 1 0 0
carrier
BPSK
1bit per symbol
QPSK
2bit per symbol
10 11 01 00 01
Symbol length

10. Mathematical expression
of digital modulation
• Transmission signal can be expressed as follows
• s(t) can be expressed by complex base-band signal
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]
)
Re[(
)
(
sin
,
cos
)
2
sin(
sin
)
2
cos(
cos
)
2
cos(
)
(
2 t
fc
j
k
k
k
k
k
k
c
k
c
k
k
c
e
jb
a
t
s
b
a
t
f
t
f
t
f
t
s


























( )
a jb e
k k
j fc t
 
2
( )
a jb
k k

ej fc t
2  Indicates carrier sinusoidal
Digital modulation
Digital modulation can be expressed by the complex number

11. Constellation map
• (ak + jbk) is plotted on I(real)-Q(imaginary) plane
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data
ak bk
00 π/4
01 3π /4
11 5π /4
10 7π /4
1
2
1
2

1
2

1
2

1
2

1
2
1
2
1
2
QPSK
I
Q

12. Quadrature Amplitude Modulation
(QAM)
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I
Q
I
Q
16QAM 64QAM

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
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( )
a jb
k k

I
Q

14. Frequency Division Multiple Access (FDMA)
• Old conventional method (Analog TV, Radio etc.)
• Use separate carrier frequency for individual transmission
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Radio
frequency
fｃ１ fｃ2 fｃ3 fｃN
Carrier frequency
Occupied BW
Channel
separation
Guard band

15. Japan VHF channel assignment
• Channel Separation =
6MHz
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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

16. Multi-carrier modulation
• Use multiple channel (carrier frequency) for one
data transmission
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data
cos( )
2 1
f t
cos( )
2 2
f t
cos( )
2f t
N
cos( )
2 1
f t
cos( )
2 2
f t
cos( )
2f t
N
LPF
LPF
LPF
data
DEMULTIPLEX
MULTIPLEX

17. Spectrum comparison for same data
rate transmission
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frequency
Single carrier
frequency
OFDM
frequency
Multi carrier

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

19. OFDM carriers
• OFDM carrier frequency is n・1/T
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Symbol period T
cos( )
2 1 0 1
 
   
f t
T
f
1
0 
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

20. Sinusoidal Orthogonality
• m,n: integer, T=1/f0
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cos( ) cos( )
( )
( )
sin( ) sin( )
( )
( )
cos( ) sin( )
2 2 2
0
2 2 2
0
2 2 0
0 0
0
0 0
0
0 0
0
 
 
 
mf t nf t dt
T
m n
m n
mf t nf t dt
T
m n
m n
mf t nf t dt
T
T
T
 







 







 



Orthogonal
Orthogonal
Orthogonal

21. A sub-carrier of f=nf0
• Amplitude and Phase will be digitally modulated
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a nf t b nf t
a b nf t
b
a
n n
n n n n
n
n
  
    
cos( ) sin( )
cos( ), tan
2 2
2
0 0
2 2
0
1
 
  
n cycles
t=0 t=T
Time

22. 8/8/2022 System Arch 2007 (Fire Tom Wada) 22
Base-band OFDM signal
 
s t a nf t b nf t
B n n
n
N
( ) cos( ) sin( )
 


 2 2
0 0
0
1
 
Ｔ
n=0
n=1
n=2
n=3
n=4
n=5
n=6
sB(t)

23. How an,bn are calculated 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
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 
 
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
T
T
n
N
k
B k
T
( ) cos( )
cos( )cos( ) sin( )cos( )
( ) sin( )

 

 







2
2 2 2 2
2
2
2
0
0
0 0 0 0
0
0
0
1
0
0

   


24. Pass-band OFDM signal
• SB(t) is upcoverted to pass-band signal S(t)
• fc frequency shift
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   
 
s t a f nf t b f nf t
n c n c
n
N
( ) cos ( ) sin ( )
   


 2 2
0 0
0
1
 

25. Actual OFDM spectrum
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fｃ＋ｋｆ０
fｃ＋(ｋ-1)ｆ０ fｃ＋(ｋ+1)ｆ０

26. OFDM power spectrum
• Total Power spectrum is almost square shape
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27. OFDM signal generation
• Direct method needs
N digital modulators
N carrier frequency generator
 Not practical
• In 1971, method using DFT is proposed to OFDM
signal generation
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   
 
s t a f nf t b f nf t
n c n c
n
N
( ) cos ( ) sin ( )
   


 2 2
0 0
0
1
 

28. OFDM signal generation in digital domain
• Define complex base-band signal u(t) as follows
• Perform N times sampling in period T
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 
s t u t
u t d e d a jb
B
n
j nf t
n
N
n n n
( ) Re ( )
( ) ,

   


 2
0
1
0

u
k
Nf
d e d e
d e k N
n
j nf
k
Nf
n
N
n
j
nk
N
n
N
n
j
N
nk
n
N
0
2
0
1 2
0
1
2
0
1
0
0
0 1 2 1





    
 





  






 

 

( , , , , )

u(k) = IFFT (dn) = IFFT(an + jbn)

29. OFDM modulator
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M
A
P
S
/
P
I-DFT
P
/
S
Real
cos( )
2f t
C
ＢＰＦ
generated
0~dＮ－１
AIR
Bit
stream
Imag
sin( )
2f t
C

30. OFDM demodulation
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   
 
  )
(
2
1
)
2
sin(
)
2
cos(
2
1
)]
2
cos(
)
(
[
)
(
2
sin
)
(
2
cos
)
(
1
0
0
0
1
0
0
0
t
s
t
nf
b
t
nf
a
t
f
t
s
LPF
t
nf
f
b
t
nf
f
a
t
s
I
N
n
n
n
C
N
n
c
n
c
n



















    )
(
2
1
)
2
cos(
)
2
sin(
2
1
]
)
2
sin(
)
(
[
1
0
0
0 t
s
t
nf
b
t
nf
a
t
f
t
s
LPF Q
N
n
n
n
C 



 





u t s t js t d e
I Q n
j nf t
n
N
( ) ( ) ( )
   


 2
0
1
0

dn = FFT(u(k))

31. OFDM demodulator (Too simple)
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T
u
n
e
r
S
/
P
DFT
P
/
S
A
/
D
LPF
Channel
cos( )
2f t
C
π/2
LPF
D
E
M
A
P
Bit
Stream

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
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Time
Symbol period
T=1/f０

33. Multi-path
• Delayed wave causes interference
Base Station
Mobile
Reception
Path 2
Path 3
Direct Path
Building
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34. Multi-pass effect
• Inter symbol interference (ISI) happens in Multi-path condition
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T=1/f０
Symbol k
Symbol k-1 Symbol k+1
Sampling Period
No multi-path
Sampling Period
Multi-path
Direct
Delayed

35. Guard Interval Tg
• By adding the Gurard Interval Period, ISI can be avoided
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OFDM symbol(1/f0)
Copy signal
Tg
Tg
Direct
Delayed
OFDM symbol (1/f0)
Tg
Sampling Period

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
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37. Multiple Frequency Network
• Frequency
utilization is low
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Area 1
Area 2
Area 3
Area 4
f１
f2
f3
f1

38. Single Frequency Network
• If multi-path
problem is solved,
SFN is possible
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Area 1
Area 2
Area 3
Area 4
f１
f１
f１
f1

39. That’s all for introduction
• Feature of OFDM
1. High Frequency utilization by the square spectrum
shape
2. Multi-path problem is solved by GI
3. Multiple services in one OFDM by sharing sub-
carriers (3 services in ISDB-T)
4. SFN
5. Implementation was complicated but NOW possible
because of LSI technology progress
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