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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
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
f
PSD
*f
PSD
f c-f c
Multipath Radio Channel
Multipath Propagation
• Reflections from walls,etc.
• Time dispersive channel
– Impulse response:
• Problem with high rate data
transmission: – inter-symbol-interference
τ [ns]
p (τ ) (PDP)
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Multipath Radio Channel
Inter-Symbol-Interference
Transmitted signal:
Received Signals:
Line-of-sight:
Reflected:
The symbols add upon the channel
Æ 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 impulseresponse
1 Channel (serial)
2 Channels
8 Channels
Time
In practice: 50 … 8000
Channels (sub-carriers)
Channels are transmittedat 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]
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OFDM Technology
Concept of parallel transmission (2)
Channel impulseresponse
1 Channel (serial)
Channeltransfer function
Channels are“narrowband”
2 ChannelsFrequency
Frequency
8 Channels Frequency
Frequency Time
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)()( ,,, kT t f i j xkT t wt s k ik i BB −∆⋅⋅−= π
Re
Im xi,k
Window function Sub-carrier
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resemblesIDFT!
Spectrum of the modulated data symbols
• Rectangular Windowof duration T
0
• Has a sinc-spectrumwith zeros at 1/ T
0
• Other carriers are put
in these zeros
• Æ sub-carriers are
orthogonalFrequency
Magnitude
∑−
=
−∆−=
1
0
)(2
,, )()( N
i
kT t f i j
k ik BB e xkT t wt sπ
Nsub-carriers:
T0
Generating the OFDM signal (2)
serial-to-
parallel xn
IDFT
(IFFT)
x0,k
x1 ,k
x N,k
parallel-
to-serial
s0,k
s1 ,k
s N,k
sn
Re
Im xi,k
N data symbols:(in frequency-domain)
Base-bandsignal
(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 signalwith channel impulse response
Æ multiplication in frequency-domain
Guard interval (2) - Cyclic extension
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System Proposal
OFDM Symbol Configuration (1)Transmitter pulse prototype w(t )
Channel impulse response
Receiver filter (implemented by FFT)
time
time
Prefix Postfixeffective TX-time
k ⋅T
T win T guard T FFT
T FFT
τ excess delay timeτ 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
x N /2-1,k
h N /2-1,k n N /2-1,k
y N /2-1,k
iiii nh x y +=
OFDM Technology
OFDM Block Diagram
OFDM
modulation
(IFFT)
Channel
coding /
interleaving
Guard
interval
I/Q I/QSymbol
mapping
(modulation)
Transmitter
0101010010110
OFDM
demod.
(FFT)
Decoding /
deinter-
leaving
Guard
interval
removal
Time sync.
I/Q I/Q
symbol de-
mapping
(detection)
Channel est.
Receiver
RF modulation; TX antenna;Multipath channel;RX antenna;RF demodulation
Outline
• Introduction
• Principle of OFDM
• OFDM Implementation and System Model• Advantages and Disadvantages
• OFDM System Design
– Parameter selection
– Implementation Issues
• Summary and Applications
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Introduction
Design of an OFDM System
Channelimpulse
response
Guardintervallength
Channel
Parameters
are needed
x(4 … 10) FFTsymbollength
Nr. of carriers
Data rate;modulation
order
Other constraints:
•Nr. of carriers should match FFT sizeand 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 Postfixeffective TX-time
k ⋅T
T win T guard T FFT
T FFT
τ excess delay timeτ max
T
OFDM System Design
Spectral Shaping by Windowing
−60 −40 −20 0 20 40 60−90
−80
−70
−60
−50
−40
−30
−20
−10
0
10
OFDM spectrum for NFFT
= 64, Nguard
= 16, oversampling = 2
frequency in sub−carriers
p o w e r s p e c t r u m m
a g n i t u d e [ d B
]
Nwin
= 2
Nwin
= 0
Nwin
= 16
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 – f s/2 f s/2
Transfer function of
transmitter/receiver
useable sub-carriers useable sub-carriers
…, –1, 0, 1, … – N /2, … …, N /2–1
frequency
sub-carrier
index i
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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 domainsignal (baseband)
samplenr.
imaginaryreal
δ 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.
Σ
... … (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
i
Liiopt r r P
)/2exp( N i f jsr ii δ π =
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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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