Orthogonal Frequency Division Multiplexing (OFDM): Concept and
System-Modeling
Klaus Witrisal
Signal Processing and Speech Communication LabTechnical 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
OFDM modulation
Source coding
I/Q-mod., up-
converter
I/Q RFChannel coding /
interleaving
Transmitter:
InfoSource
OFDM de-modulation
Source decoding
Down-converter,
I/Q-demod.I/Q RF
Decoding / deinter-leaving
Receiver:Radio-
channel
InfoSink
e.g. Audio 0110 01101101
fPSD
* fPSD
fc-fc
Multipath Radio Channel
Multipath Propagation
• Reflections from walls, etc.
• Time dispersive channel– Impulse response:
• Problem with high rate data transmission:– inter-symbol-interference
[ns]
p () (PDP)
Multipath Radio Channel
Inter-Symbol-Interference
Transmitted signal:
Received Signals:Line-of-sight:
Reflected:
The symbols add up on the channel
Distortion!
Delays
Outline
• Introduction– What is OFDM?– Multipath fading radio-channel
• Principle of OFDM• OFDM Implementation and System Model• Advantages and Disadvantages• OFDM in Practice• Summary
OFDM Technology
Concept of parallel transmission (1)
Channel impulse response
1 Channel (serial)
2 Channels
8 Channels
Time
In practice: 50 … 8000 Channels (sub-carriers)
Channels are transmitted at different frequencies (sub-carriers)
Multipath Radio Channel
The Frequency-Selective Radio Channel
• Interference of reflected (and LOS) radio waves– Frequency-dependent fading
-10
-5
0
5
10
15
20
Frequency
Power response [dB]
OFDM Technology
Concept of parallel transmission (2)
Channel impulse response
1 Channel (serial)
Channeltransfer function
Channels are “narrowband”
2 ChannelsFrequency
Frequency
8 ChannelsFrequency
FrequencyTime
Signal is “broadband”
Implementation and System Model
Concept of an OFDM signal
Ch.1
Ch.2 Ch.3 Ch.4 Ch.5 Ch.6 Ch.7 Ch.8 Ch.9 Ch.10
Saving of bandwidth
Ch.3 Ch.5 Ch.7 Ch.9Ch.2 Ch.4 Ch.6 Ch.8 Ch.10
Ch.1
Conventional multicarrier techniques
Orthogonal multicarrier techniques
50% bandwidth saving
frequency
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
)(2exp)()( ,,, kTtfijxkTtwts kikiBB
Re
Imxi,k
Window function Sub-carrier
resemblesIDFT!
Spectrum of the modulated data symbols
• Rectangular Window of duration T0
• Has a sinc-spectrum with zeros at 1/ T0
• Other carriers are put in these zeros
sub-carriers are orthogonal
Frequency
Magnitude
1
0
)(2,, )()(
N
i
kTtfijkikBB exkTtwts
N sub-carriers:
T0
Generating the OFDM signal (2)
serial-to-parallelxn
IDFT
(IFFT)
x0,k
x1,k
xN,k
parallel-to-serial
s0,k
s1,k
sN,k
sn
Re
Imxi,k
N data symbols:(in frequency-domain)
Base-band signal
(time-domain)
Introduction
Idea of Guard Interval (GI)
FFT-part
time
Insertion of guard interval (cyclic prefix):
Channel impulse response (shorter than GI):
t
1 OFDM symbol
Cyclic convolution of transmitted signal with channel impulse response
multiplication in frequency-domain
Guard interval (2) - Cyclic extension
System Proposal
OFDM Symbol Configuration (1)Transmitter pulse prototype w(t) Channel impulse response Receiver filter (implemented by FFT)
time
time
Prefix Postfix effective TX-time
kT
Twin Tguard TFFT
TFFT
excess delay time max
T
Introduction
OFDM System Model
• Multiplication of data symbols with (complex-valued) channel transfer-function:
x-N/2,k
h-N/2,k n-N/2,k
y-N/2,k
xN/2-1,k
hN/2-1,k nN/2-1,k
yN/2-1,k
iiii nhxy
Introduction
-60 -40 -20 0 20 40 60-50
-40
-30
-20
-10
0
10
f [MHz]
pow
er s
pect
rum
mag
nitu
de [
dB] OFDM spectrum for N
FFT = 128, N
w in = 12, N
guard = 24, oversampling = 1
0 20 40 60 80 100 120 140 160 180 200-0.2
-0.1
0
0.1
0.2time domain signal (baseband)
sample nr.
imaginaryreal
OFDM Block Diagram
OFDM modulation
(IFFT)
Channel coding /
interleaving
Guard interval
I/Q I/QSymbol mapping
(modulation)
Transmitter
N symbols
OFDM demod. (FFT)
Decoding / deinter-leaving
Guard interval removal
Time sync.
I/Q I/Q
symbol de-mapping
(detection)
Channel est.
ReceiverFFT-part
time
1 OFDM symbol
Channel impulse response:
0101010010110
Outline
• Introduction• Principle of OFDM• OFDM Implementation and System Model• Advantages and Disadvantages• OFDM System Design
– Parameter selection– Implementation Issues
• Summary and Applications
Introduction
Design of an OFDM System
Channel impulse
response
Guard intervallength
Channel Parametersare needed
x(4 … 10) FFTsymbollength
Nr. ofcarriers
Data rate;modulation
order
Other constraints:•Nr. of carriers should match FFT size
and data packet length
•considering coding and modulation schemes
OFDM System Design
OFDM Symbol Configuration (1)Transmitter pulse prototype w(t) Channel impulse response Receiver filter (implemented by FFT)
time
time
Prefix Postfix effective TX-time
kT
Twin Tguard TFFT
TFFT
excess delay time max
T
OFDM System Design
Spectral Shaping by Windowing
Design of an OFDM System
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.
DC–fs/2 fs/2
Transfer function oftransmitter/receiver
useable sub-carriers useable sub-carriers…, –1, 0, 1, … –N/2, … …, N/2–1
frequency
sub-carrierindex 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
OFDM Technology
Problems of OFDM (Research Topics)
• Synchronization issues:– Time synchronization
• Find start of symbols
– Frequency synchr.
• Find sub-carrier positions
• Non-constant power envelope– Linear amplifiers needed
• Channel estimation:
– To retrieve data
– Channel is time-variant
0 20 40 60 80 100 120 140 160 180 200-0.2
-0.1
0
0.1
0.2time domain signal (baseband)
sample nr.
imaginaryreal
f frequency offset
frequency
amplitude
Introduction
Correlation-based Frequency-sync.• Correlation of duplicated parts of OFDM signal
– e.g.: Cyclic prefix (Guard interval - GI):
Guard interval (M samples)
FFT-part (L samples)
conj.
conj.
... … (M times)
...
si:
• Peak at optimum position • Phase frequency-offset
• Received signal with f-offset:– Constant phase offset between samples spaced by L
1
0
*M
iLiiopt rrP
)/2exp( Nifjsr ii
Outline
• Introduction– What is OFDM?– Multipath fading radio-channel
• Principle of OFDM• OFDM Implementation and System Model• Advantages and Disadvantages• OFDM in Practice• Summary
Summary and Applications
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 – 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
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