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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/
10/1/2015
1
What is OFDM?
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OFDM
=Orthogonal Frequency Division Multiplexing
Many orthogonal sub-carriers are multiplexed
in one symbol
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What is the orthogonal?
How multiplexed?
What is the merit of OFDM?
What kinds of application?
2
Outline
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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？
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State-of-the-art high bandwidth digital communication
start using OFDM
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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
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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
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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,
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Three type digital modulation:

s(t )  A  cos(2  f c  t  k )
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ASK : Amplitude Shift Keying
PSK : Phase Shift Keying
FSK : Frequency Shift Keying
OFDM uses combination of ASK and PSK such as QAM, PSK
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Symbol Waveform
Digital Information
1
0
1
0
0
carrier
ASK
PSK
FSK
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Symbol length
8
Multi bit modulation
carrier
1
0
1
0
0
10
11
01
00
01
BPSK
1bit per symbol
QPSK
2bit per symbol
Symbol length
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Mathematical expression
of digital modulation

Transmission signal can be expressed as follows
s (t )  cos(2  f c  t   k )
 cos k  cos(2  f c  t )  sin  k  sin(2  f c  t )
ak  cos k , bk  sin  k
s (t )  Re[(ak  jbk )e j 2fct ]

s(t) can be expressed by complex base-band signal (ak
e
j 2fct
(ak  jbk )
 jbk )e j 2fct
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
1
2
1

2
1

2
1
2
1
2
1
2
1

2
1

2
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QPSK
Q
I
11
Quadrature Amplitude Modulation
(QAM)
16QAM
64QAM
Q
Q
I
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I
12
Summary of digital modulation
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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
(ak  jbk )
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Plot of the coefficients gives
the constellation map
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Q
I
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Frequency Division Multiple Access
(FDMA)
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Old conventional method (Analog TV, Radio etc.)
Use separate carrier frequency for individual
transmission
Occupied BW
fｃ１
Carrier frequency
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Channel
separation
fｃ2
fｃ3
fｃN
Radio
frequency
Guard band
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Japan VHF channel assignment
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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Channel Separation =
6MHz
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Multi-carrier modulation
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Use multiple channel (carrier frequency) for
one data transmission
LPF
cos(2f 1t )
LPF
cos(2f 2 t )
cos(2f 2 t )
MULTIPLEX
DEMULTIPLEX
data
cos(2f 1t )
data
LPF
cos(2f N t )
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cos(2f N t )
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Spectrum comparison for
same data rate transmission
Multi carrier
Single carrier
OFDM
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frequency
frequency
frequency
17
OFDM vs. Multi carrier
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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
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Condition of the orthogonality will be explained later
Each 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 T
1
f0 
T
cos(2 1 f 0  t  1 )
cos(2  2  f 0  t  2 )
cos(2  3  f 0  t  3 )
cos(2  4  f 0  t  4 )
cos(2  5  f 0  t  5 )
cos(2  6  f 0  t  6 )
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Sinusoidal Orthogonality
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m,n: integer, T=1/f0
T
 ( m  n)
0 cos(2mf 0t )  cos(2nf 0t )dt   2
 0　(m  n)
T
T
 ( m  n)
0 sin(2mf 0t )  sin(2nf 0t )dt   2
 0　(m  n)
T
T
 cos(2mf t )  sin(2nf t )dt 0
0
0
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0
Orthogonal
Orthogonal
Orthogonal
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A sub-carrier of f=nf0
an  cos(2nf 0t )  bn  sin(2nf 0t )
 an  bn cos(2nf 0t  n ), n  tan
2

2
1
bn
an
Amplitude and Phase will be digitally modulated
n cycles
Time
t=0
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t=T
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Base-band OFDM signal
N 1
sB (t )   an cos(2nf 0t )  bn sin(2nf 0t )
n0
Ｔ
n=0
n=1
n=2
n=3
n=4
n=5
n=6
sB(t)
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How an,bn are caluculated from sB(t)
- Demodulation Procedure T
s
0
B
(t )  cos(2kf 0t )dt
N 1

  an  cos(2nf 0t ) cos(2kf 0t )dt  bn  sin(2nf 0t ) cos(2kf 0t )dt
n0
T
T
0
0

T
 ak
2

T
0
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sB (t ) sin(2kf 0t )dt 
T
bk
2
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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Pass-band OFDM signal
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SB(t) is upcoverted to pass-band signal S(t)
fc frequency shift
N 1
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s(t )   an cos2 ( f c  nf 0 )t  bn sin2 ( f c  nf 0 )t
n0
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Actual OFDM spectrum
fｃ＋(ｋ-1)ｆ０
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fｃ＋ｋｆ０
fｃ＋(ｋ+1)ｆ０
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OFDM power spectrum
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Total Power spectrum is almost square shape
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OFDM signal generation
N 1
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
s(t )   an cos2 ( f c  nf 0 )t  bn sin2 ( f c  nf 0 )t
n0
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Direct method needs
N digital modulators
N carrier frequency generator
 Not practical
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In 1971, method using DFT is proposed to
OFDM siganal generation
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OFDM signal generation in digital domain
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Define complex base-band signal u(t) as follows
sB (t )  Reu(t )
N 1
u(t )   d n  e j 2nf 0t , d n  an  jbn
n0
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Perform N times sampling in period T
 k 
u
 
 Nf 0 
N 1
d
n
n0
 j 2N 
  dn   e



n0
N 1
e
j 2 nf 0
k
Nf 0

N 1
d
n
e
j
2 nk
N
n0
nk
( k  0,1,2,, N  1)
u(k) = IFFT (dn) = IFFT(an + jbn)
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OFDM modulator
cos(2f C t )
Real
M
Bit
A
stream
P
S
/
P
I-DFT
P
/
S
Imag
sin(2f C t )
generated
0~dＮ－１
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AIR
ＢＰＦ
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OFDM demodulation
N 1
s(t )   an cos2 ( f c  nf0 )t bn sin2 ( f c  nf0 )t
n 0
1 N 1
1
LPF[ s(t )  cos(2f C t )]   an cos(2nf0t )  bn sin(2nf0t )  sI (t )
2 n 0
2
1 N 1
1
LPF[ s(t )   sin(2f C t )]   an sin(2nf0t )  bn cos(2nf0t )  sQ (t )
2 n 0
2
N 1
u(t )  sI (t )  jsQ (t )   d n  e
j 2 nf 0t
n0
dn = FFT(u(k))
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OFDM demodulator (Too simple)
LPF
Channel
T
u
n
e
r
cos(2f C t )
π/2
A
/
D
S
/
P
P
/
S
DFT
LPF
Bit
Stream
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D
E
M
A
P
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Summary of OFDM signal
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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
Time
Symbol period
T=1/f０
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Multi-path
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Delayed wave causes interference
Pat h 2
Building
Direct Pat h
Pat h 3
Mobile
Recept ion
Base St at ion
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Multi-pass effect
No multi-path
Symbol k-1
Symbol k
T=1/f０
Symbol k+1
Sampling Period
Multi-path
Direct
Delayed
Sampling Period
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Inter symbol interference (ISI) happens in Multi-path condition
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Guard Interval Tg
Tg
OFDM symbol(1/f0)
Tg
Copy signal
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By adding the Gurard Interval Period, ISI can be
avoided
Tg OFDM symbol (1/f0)
Direct
Delayed
Sampling Period
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Multi-path
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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
f3
f１
f1
Area 3
Area 4
Area 1
f2

Area 2
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Frequency
utilization is low
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Single Frequency Network
f１
f１
f1
Area 3
Area 4
Area 1
f１
Area 2
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If multi-path
problem is solved,
SFN is possible
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That’s all for introduction
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Feature of OFDM
1.
2.
3.
4.
5.
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High Frequency utilization by the square
spectrum shape
Multi-path problem is solved by GI
Multiple services in one OFDM by sharing subcarriers (3 services in ISDB-T)
SFN
Implementation was complicated but NOW
possible because of LSI technology progress
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