ｽﾗｲﾄﾞﾀｲﾄﾙなし

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
System Arch 2007 (Fire Tom Wada)
1
What is OFDM?


OFDM
=Orthogonal Frequency Division Multiplexing
Many orthogonal sub-carriers are multiplexed
in one symbol




10/1/2015
What is the orthogonal?
How multiplexed?
What is the merit of OFDM?
What kinds of application?
System Arch 2007 (Fire Tom Wada)
2
Outline






Background, history, application
Review of digital modulation
FDMA vs. Multi-carrier modulation
Theory of OFDM
Multi-path
Summary
10/1/2015
System Arch 2007 (Fire Tom Wada)
3
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
10/1/2015
System Arch 2007 (Fire Tom Wada)
4
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
10/1/2015
System Arch 2007 (Fire Tom Wada)
5
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)
10/1/2015
System Arch 2007 (Fire Tom Wada)
6
Digital modulation basics

Digital modulation modulates three
parameters of sinusoidal signal.
A, θk fc,

Three type digital modulation:

s(t )  A  cos(2  f c  t  k )



ASK : Amplitude Shift Keying
PSK : Phase Shift Keying
FSK : Frequency Shift Keying
OFDM uses combination of ASK and PSK such as QAM, PSK
10/1/2015
System Arch 2007 (Fire Tom Wada)
7
Symbol Waveform
Digital Information
1
0
1
0
0
carrier
ASK
PSK
FSK
10/1/2015
Symbol length
System Arch 2007
(Fire Tom Wada)
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
10/1/2015
System Arch 2007 (Fire Tom Wada)
9
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
10/1/2015
System Arch 2007 (Fire Tom Wada)
10
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
10/1/2015
QPSK
Q
System Arch 2007 (Fire Tom Wada)
I
11
Quadrature Amplitude Modulation
(QAM)
16QAM
64QAM
Q
Q
I
10/1/2015
System Arch 2007 (Fire Tom Wada)
I
12
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
(ak  jbk )

Plot of the coefficients gives
the constellation map
10/1/2015
System Arch 2007 (Fire Tom Wada)
Q
I
13
Frequency Division Multiple Access
(FDMA)


Old conventional method (Analog TV, Radio etc.)
Use separate carrier frequency for individual
transmission
Occupied BW
fｃ１
Carrier frequency
10/1/2015
Channel
separation
fｃ2
fｃ3
fｃN
Radio
frequency
Guard band
System Arch 2007 (Fire Tom Wada)
14
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
10/1/2015

Channel Separation =
6MHz
System Arch 2007 (Fire Tom Wada)
15
Multi-carrier modulation

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 )
10/1/2015
cos(2f N t )
System Arch 2007 (Fire Tom Wada)
16
Spectrum comparison for
same data rate transmission
Multi carrier
frequency
Single carrier
frequency
OFDM
10/1/2015
frequency
System Arch 2007 (Fire Tom Wada)
17
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
simultaneously transmitted in one OFDM symbol
10/1/2015
System Arch 2007 (Fire Tom Wada)
18
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 )
10/1/2015
System Arch 2007 (Fire Tom Wada)
19
Sinusoidal Orthogonality

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
10/1/2015
0
System Arch 2007 (Fire Tom Wada)
Orthogonal
Orthogonal
Orthogonal
20
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
10/1/2015
t=T
System Arch 2007 (Fire Tom Wada)
21
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)
10/1/2015
System Arch 2007 (Fire Tom Wada)
22
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



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
10/1/2015
System Arch 2007 (Fire Tom Wada)
23
Pass-band OFDM signal


SB(t) is upcoverted to pass-band signal S(t)
fc frequency shift
N 1


s(t )   an cos2 ( f c  nf 0 )t  bn sin2 ( f c  nf 0 )t
n0
10/1/2015
System Arch 2007 (Fire Tom Wada)
24
Actual OFDM spectrum
fｃ＋(ｋ-1)ｆ０
10/1/2015
fｃ＋ｋｆ０
fｃ＋(ｋ+1)ｆ０
System Arch 2007 (Fire Tom Wada)
25
OFDM power spectrum

Total Power spectrum is almost square shape
10/1/2015
System Arch 2007 (Fire Tom Wada)
26
OFDM signal generation
N 1


s(t )   an cos2 ( f c  nf 0 )t  bn sin2 ( f c  nf 0 )t
n0

Direct method needs
N digital modulators
N carrier frequency generator
 Not practical

In 1971, method using DFT is proposed to
OFDM siganal generation
10/1/2015
System Arch 2007 (Fire Tom Wada)
27
OFDM signal generation in digital domain

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

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)
10/1/2015
System Arch 2007 (Fire Tom Wada)
28
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
10/1/2015
AIR
ＢＰＦ
System Arch 2007 (Fire Tom Wada)
29
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))
10/1/2015
System Arch 2007 (Fire Tom Wada)
30
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
10/1/2015
System Arch 2007 (Fire Tom Wada)
D
E
M
A
P
31
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
Time
Symbol period
T=1/f０
10/1/2015
System Arch 2007 (Fire Tom Wada)
32
Multi-path

Delayed wave causes interference
Pat h 2
Building
Direct Pat h
Pat h 3
Mobile
Recept ion
Base St at ion
10/1/2015
System Arch 2007 (Fire Tom Wada)
33
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

Inter symbol interference (ISI) happens in Multi-path condition
10/1/2015
System Arch 2007 (Fire Tom Wada)
34
Guard Interval Tg
Tg
OFDM symbol(1/f0)
Tg
Copy signal

By adding the Gurard Interval Period, ISI can be
avoided
Tg OFDM symbol (1/f0)
Direct
Delayed
Sampling Period
10/1/2015
System Arch 2007 (Fire Tom Wada)
35
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
10/1/2015
System Arch 2007 (Fire Tom Wada)
36
Multiple Frequency Network
f3
f１
f1
Area 3
Area 4
Area 1
f2

Area 2
10/1/2015
System Arch 2007 (Fire Tom Wada)
Frequency
utilization is low
37
Single Frequency Network
f１
f１
f1
Area 3
Area 4
Area 1
f１
Area 2
10/1/2015

If multi-path
problem is solved,
SFN is possible
System Arch 2007 (Fire Tom Wada)
38
That’s all for introduction

Feature of OFDM
1.
2.
3.
4.
5.
10/1/2015
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
System Arch 2007 (Fire Tom Wada)
39

Download Report