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OFDM Transmission over WidebandChannel
Gwo-Ruey Lee
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Outlines
OFDM Transmission over Wideband Channel
The Time Dispersive Channel Model
Effects of Time Dispersive Channels on OFDM
Channel Estimation Time Domain Channel Estimation
Frequency Domain Channel Estimation
Equalization
Comparisons of Time- and Frequency- DomainEqualization
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The Time Dispersive Channel Model
A time-dispersive channel can be characterizedby its channel impulse response
where
is the number of multipath components
is the path gain of path i
is the path delay of path i
1
0
( ) ( ) ( )L
i i
i
h t t t
L
( )i t
i
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The Time Dispersive Channel Model
Each path gain is a complex random variablewith uniformly distributed phases and Rayleighdistributed magnitude.
The average power of each path decaysexponentially.
( )i
t
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The Time Dispersive Channel Model
The mathematical model for the time dispersivechannel is
where is the sampling period, and is
the root-mean-squared (RMS) delay spread.sT RMST
3/3
2 21 1(0, ) (0, )
2 2i i i
N j N
2 2
0i /s RMS
iT Te
2
0 1
/s RMS
T Te
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Effects of Time Dispersive Channels onOFDM
The phenomenon of multipath fading causesprevious symbol to interfere with the lattersymbol. This is known as the inter-symbol
interference (ISI).
The received signal is the convolution ofthe transmitted symbols and the discrete-time
channel impulse response.
ISI ISI ISI
1/1
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Channel Estimation
Channel estimation is the task of estimating thefrequency response of the radio channel thetransmitted signal travels before reaching thereceiver antenna.
The channel estimation can be performed using thetime domain approach and frequency domainapproach. Time domain channel estimation
Frequency domain channel estimation
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Time Domain Channel Estimation
This channel estimation is performed using the timedomain approach, before FFT processing of thetraining symbols.
In this, the channel impulse response instead of thechannel frequency response, is estimated.
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Time Domain Channel Estimation
The received time domain signals are
is the channel impulse response.
is the known symbol.
is noise.
nx
nw
nh
)1.4(;64,...,1, nwxhrnnnn
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Time Domain Channel Estimation
The time domain convolution can be expressed asa matrix vector multiplication.
The parameter Lis defined as the maximum
length of the impulse response, L
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Time Domain Channel Estimation
Then receive signal is expressed as
1
2
3
4
64
r
r
r
r
r
1 64 64 2
2 1 64 3
63 62 64
64 63 64 1
L
L
L
L
x x x
x x x
x x x
x x x
0
1
2
1L
h
h
h
h
1
2
3
4
64
w
w
w
w
w
n n nr h x w h wX
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Time Domain Channel Estimation
The least square (LS) estimate for ish
rXXXh HH
LS
1)(
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Frequency Domain Channel Estimation
This channel estimation is performed using thefrequency domain approach.
In this, the channel frequency response isestimated by using two repeat training sequences.
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Frequency Domain Channel Estimation
We get (4.2) from (4.1) through FFT transform,
If we have two repeat sequences,
k k k k R X H W
1, 1,
2, 2,
k kk
k
k kk
R WXR H
R WX
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W l h b
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Frequency Domain Channel Estimation
The least square (LS) estimate for eachis
,k LSH
1
, 1, 2,
1
2
H H
k LS k k k k k H X X X R R
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Comparisons of Time- and Frequency-Domain Equalization
Time-domain Equalization Frequency-domainEqualization
Convolution One-tap multiplication
High complexity
when Lis lager
Low complexity
when Lis small
No FFT Required FFT Required
nn rh
kk RH *
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Wi l T h b
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Wi l A T h L b
References
[1] L. Hanzo, W. Webb and T. Keller, Single- and multi-carrier quadratureamplitude modulation Principles and applications for personalcommunications, WLANs and broadcasting, John Wiley & Sons, Ltd, 2000.
[2] Mark Engels, Wireless Ofdm Systems: How to Make Them Work?KluwerAcademic Publishers.
[3] John Terry, Juha Heiskala, OFDM Wireless LANs: A Theoretical andPractical Guide, Sams.