Transcript Performance Enhancement of the DSR by FEC

Orthogonal Frequency Division Multiplexing
(OFDM): Concept and System-Modeling
Klaus Witrisal
Signal Processing and Speech Communication Lab
Technical University Graz, Austria
VL: Mobile Radio Systems, Ch. 5: “Wideband Systems”
24-Nov-05
Outline
• Introduction
– What is OFDM?
– Multipath fading radio-channel
•
•
•
•
•
Principle of OFDM
OFDM Implementation and System Model
Advantages and Disadvantages
OFDM in Practice
Summary
What is OFDM?
• Modulation technique
– Requires channel coding
– Solves multipath problems
Transmitter:
Info
Source
Source
coding
e.g. Audio
Channel
coding /
interleaving
0110
OFDM
modulation
I/Q-mod.,
upconverter
01101101
Receiver:
Info
Sink
I/Q
PSD
Source
decoding
Decoding /
deinterleaving
RF
Radiochannel
PSD
f
Down*
converter,
-fc
I/Q-demod.
OFDM demodulation
I/Q
f
fc
RF
Multipath Propagation
• Reflections from walls,
etc.
• Time dispersive channel
– Impulse response:
p (t ) (PDP)
t [ns]
• Problem with high rate data
transmission:
– inter-symbol-interference
Multipath Radio Channel
Inter-Symbol-Interference
Transmitted signal:
Received Signals:
Line-of-sight:
Reflected:
The symbols add up
on the channel
 Distortion!
Delays
Multipath Radio Channel
Caractéristiques du canal
Outline
• Introduction
– What is OFDM?
– Multipath fading radio-channel
•
•
•
•
•
Principle of OFDM
OFDM Implementation and System Model
Advantages and Disadvantages
OFDM in Practice
Summary
Concept of parallel transmission (1)
Channel impulse
response
Time
1 Channel (serial)
Channels are transmitted
at different frequencies
(sub-carriers)
2 Channels
8 Channels
In practice: 50 … 8000
Channels (sub-carriers)
OFDM Technology
The Frequency-Selective Radio Channel
Power response [dB]
20
15
10
5
0
-5
-10
Frequency
• Interference of reflected (and LOS) radio waves
– Frequency-dependent fading
Multipath Radio Channel
Concept of parallel transmission (2)
Channel impulse
response
Time
Frequency
1 Channel (serial)
Frequency
2 Channels
Channel
transfer function
Signal is
“broadband”
Frequency
8 Channels
Frequency
Channels are
“narrowband”
OFDM Technology
Concept of an OFDM signal
Ch.1
Ch.2
Ch.3
Ch.4
Ch.5
Ch.6
Ch.7
Ch.8
Ch.9
Conventional multicarrier techniques
Ch.10
frequency
Ch.2 Ch.4 Ch.6
Ch.8 Ch.10
Ch.1 Ch.3 Ch.5
Ch.7 Ch.9
Saving of bandwidth
50% bandwidth saving
Orthogonal multicarrier techniques
Implementation and System Model
frequency
Outline
• Introduction
– What is OFDM?
– Multipath fading radio-channel
•
•
•
•
•
Principle of OFDM
OFDM Implementation and System Model
Advantages and Disadvantages
OFDM in Practice
Summary
Generating the OFDM signal (1)
• Symbol (QPSK) of sub-carrier i at time k
– Other symbol-alphabets can be used as well (BPSK, m-QAM)
• Baseband signal is generated by DSP
sBB,i ,k (t )  w(t  kT )  xi,k  exp j 2 if (t  kT )
Window function
xi,k
Sub-carrier
Im
Re
Spectrum of the modulated data symbols
• Rectangular Window
of duration T0
• Has a sinc-spectrum
with zeros at 1/ T0
Magnitude
T0
• Other carriers are put
in these zeros
•  sub-carriers are
orthogonal
Frequency
N sub-carriers:
sBB,k (t )  w(t  kT )
N 1
j 2 if ( t  kT )
x
e
 i ,k
i 0
resembles
IDFT!
Generating the OFDM signal (2)
xn
serial-toparallel
x0,k
x1,k
IDFT
(IFFT)
xN-1,k
xi,k
parallelto-serial
sn
sN-1,k
N data symbols:
(in frequencydomain)
s0,k
s1,k
Base-band
signal
Im
(time-domain)
Re
Idea of Guard Interval (GI)
Insertion of guard interval (cyclic prefix):
1 OFDM symbol
FFT-part
Channel impulse response (shorter than GI):
t
Cyclic convolution of transmitted signal
with channel impulse response
 multiplication in frequency-domain
Introduction
time
Amélioration OFDM
Une communication « normale » aurait besoin de répéter l’intervalle
de garde après chaque symbole alors qu’en OFDM, cet intervalle
n’est ajouté qu’après un symbole OFDM (des milliers de symboles
d’information).
GT
Delay
OFDM Symbol
Delay
Delay
GT
SYM
GT
GT
SYM
Delay
OFDM Symbol
Delay
GT
SYM
Delay
GT
SYM
OFDM System Model
• Multiplication of data symbols with (complex-valued)
channel transfer-function:
x-N/2,k
xN/2-1,k
h-N/2,k
n-N/2,k
y-N/2,k
hN/2-1,k
yi  xi hi  ni
nN/2-1,k
yN/2-1,k
Introduction
OFDM Block Diagram
Transmitter
0110
Symbol
mapping
(modulation)
010101001
Receiver
Decoding /
deinterleaving
power spectrum magnitude [dB]
Channel
coding /
interleaving
OFDM
modulation
(IFFT)
I/Q
I/Q
Guard
interval
OFDM spectrum for NFFT = 128, Nw in = 12, Nguard = 24, oversampling = 1
10
N symbols
0
-10
1 OFDM symbol
-20
-30
-40
-50
symbol de-60
mapping
0.2
(detection)
Channel 0.1
impulse
Channel response:
est.
FFT-part
Guard
-40 OFDM
-20
0
20
f
[MHz]
demod.
interval
time domain signal (baseband)
(FFT)
removal
I/Q
40
I/Q
Time sync.
0
-0.1
0
20
40
Introduction
-0.2
60
time
imaginary
real
60
80
100
120
sample nr.
140
160
180
200
Interprétation de l’OFDM
Considérons un système de transmission mono-antenne sur un canal
multi-trajets :
La réponse impulsionnelle du canal s’étend sur L+1 symboles: 0, 1, …, L
x(n)
Canal
y(n)
h(n)
L
y (n)  x(n) * h(n)   h(m) x(n  m)
m 0
L
y (n  1)  x(n  1) * h(n)   h(m) x(n  m  1)
m 0
L
y(n  M )  x(n  M ) * h(n)   h(m) x(n  m  M )
m 0
La mise en matrice
h0 h1 hL 0


0 h h h
 y (n  1) 
0
1
L



0 0 




0  h h
 y (n  M  1)
0
1



 y (n  M )  M 11  0 0  h0
y ( n)
x ( n)


0
 x(n  1) 


 0



 0
 x(n  M ) 



hL 0

 x(n  M  1) 
h1 hL  M 1M 1 L 

x
(
n

M

L
)

 M 1 L1

Maintenant imaginer que nous avion ajouté un préfix cyclique au vecteur
d’entrée, c’est-à-dire que les
x(n  M 1)  x(n) , ... , x(n  M  L)  x(n  1  L)
On a donc ajouté L points (taille du filtre – 1) au début de la séquence.
Re-écriture matricielle
y ( n)
 h0


0
 y (n  1) 



0



h
 y (n  M  1)
 L


 y (n  M )  M 11  h1
h1 hL 0  0 
x ( n)


 x(n  1) 
h0 h1 hL  0 





  0



 x(n  M  1)
 0 0 h0 h1 



hL  0 0 h0  M 1M 1  x(n  M )  M 11
Matrice circulante
Propriété: Soit h une matrice circulante, W matrice de la FFT et WH
la matrice de IFFT. WhWH est une matrice diagonale avec des
éléments sur le diagonal étant la FFT de la première ligne de la
matrice h.
Pré-codage
Exploitons cette propriété pour dé-convoluer le signal et le canal.
Imaginez que le vecteur de symboles d’information X de taille N (ou
M+1) est à envoyer sur un canal multi-trajets.
On applique une IFFT avant d’envoyer sur le canal, puis on ajoute un
préfixe cyclique. La taille du vecteur à envoyer est maintenant N+Ng où
Ng<L.
Les N derniers échantillons reçus forme le vecteur y. On peut écrire
X  le vecteur d' information
x  W H X  le vecteur effectivement envoyé (la IFFT de x)
y  hx  hW H X  le vecteur effectivement reçu
En réception
On applique un FFT sur le signal reçu
Y  Wy  Whx  WhW H X  HX  diag FFT du canal X
x(n)
y(n)
Alors OFDM n’est qu’un précodage qui permet de diagonaliser un canal
multi-trajets.
N canaux parallèles indépendants
Y0  X 0 H 0  n0
Y1  X1H1  n1
YN 1  X N 1 H N 1  nN 1
La capacité équivalent est la somme des capacités individuelles.
Water-Filling peut être utilisé en émission si on connaît le canal en
émission.
Outline
•
•
•
•
•
Introduction
Principle of OFDM
OFDM Implementation and System Model
Advantages and Disadvantages
OFDM System Design
– Parameter selection
– Implementation Issues
• Summary and Applications
Design of an OFDM System
Data rate;
modulation
order
Channel
impulse
response
Channel
Parameters
are needed
Guard
interval
length
x(4 … 10)
FFT
symbol
length
Nr. of
carriers
Other constraints:
•Nr. of carriers should match FFT size
and data packet length
•considering coding and modulation schemes
Introduction
OFDM Symbol Configuration (1)
Transmitter pulse prototype w(t)
T
Twin
Tguard
TFFT
Prefix
effective TX-time
Postfix
time
kT
Channel impulse response
tmax
t excess delay time
Receiver filter (implemented by FFT)
TFFT
OFDM System Design
time
Spectral Shaping by Windowing
OFDM System Design
OFDM Symbol Configuration (2)
• Not all FFT-points can be used for data carriers
– Lowpass filters for AD- and DA-conversion
• oversampling required
– DC offsets; carrier feedtrough; etc.
Transfer function of
transmitter/receiver
–fs/2
–N/2, …
useable sub-carriers
DC
useable sub-carriers
…, –1, 0, 1, …
Design of an OFDM System
fs/2
…, N/2–1
frequency
sub-carrier
index i
Outline
• Introduction
– What is OFDM?
– Multipath fading radio-channel
•
•
•
•
•
Principle of OFDM
OFDM Implementation and System Model
Advantages and Disadvantages
OFDM in Practice
Summary
Advantages of OFDM
• Solves the multipath-propagation problem
– Simple equalization at receiver
• Computationally efficient
– For broadband systems more efficient than SC
• Supports several multiple access schemes
– TDMA, FDMA, MC-CDMA, etc.
• Supports various modulation schemes
– Adaptability to SNR of sub-carriers is possible
• Elegant framework for MIMO-systems
– All interference among symbols is removed
Problems of OFDM (Research Topics)
time domain signal (baseband)
0.2
•
Synchronization issues:
0.1
– Time synchronization
0
• Find start of symbols
-0.1
– Frequency synchr.
• Find sub-carrier positions
•
Non-constant power
envelope
-0.2
imaginary
real
0
20
40
60
80
100
120
sample nr.
140
160
180
200
amplitude
– Linear amplifiers needed
•
Channel estimation:
– To retrieve data
– Channel is time-variant
frequency
f frequency offset
OFDM Technology
Correlation-based Frequency-sync.
• Correlation of duplicated parts of OFDM signal
– e.g.: Cyclic prefix (Guard interval - GI):
s i:
Guard interval
FFT-part
(M samples)
(L samples)
...
…
conj.
(M times)
conj.
Popt 
M 1
*
r
 i ri  L
...

i 0
• Peak at optimum position
• Phase  frequency-offset
• Received signal with f-offset: ri  si exp( j 2 f i / N )
– Constant phase offset between samples spaced by L
Introduction
Outline
• Introduction
– What is OFDM?
– Multipath fading radio-channel
•
•
•
•
•
Principle of OFDM
OFDM Implementation and System Model
Advantages and Disadvantages
OFDM in Practice
Summary
Applications of OFDM
• Wireless LAN
– IEEE802.11a/g
– HYPERLAN
• DAB, DVB, etc.
– Digital Audio/Video Broadcasting
• xDSL (Digital Subscriber Line)
– uses Discrete Multitone (DMT)
Summary and Applications
Summary – Essential “Ingredients”
• IFFT & FFT
– For efficient implementation
• Guard interval insertion
– Obtaining simple equalization
– Removing all IS- & IC-interferences
• Error correction coding
– To restore bits that are lost on weak sub-carriers