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ICI mitigation in OFDM systems
2005/11/2 王治傑
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Reference
Y. Mostofi, D.C. Cox, “ICI mitigation for pilot-aided OFDM mobile systems,” IEEE trans. on wireless communications, vol.4, Mar 2005.
W.G. Jeon, K.H. Chang and Y.S. Cho.”an equalization technique for OFDM systems in time-varying multipath channels,” IEEE trans. on communications, vol.47 Jan. 1999
“Iterative solutions of nonlinear equations in several variables,” academic press 1970
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System model
Assume the normalized length of the channel is always less than or equal to G in this paper
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System model
A constant channel is assumed over the time interval . for represents the kth channel tap in the guard and data interval respectively
The channel output can be expressed as follow:
ss TitTi )1( )(ikh 101 NiandiG
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System model
where
Furthermore
is the average of the mth tap over 0<t<N*Ts
1
0
)(1 N
u
um
avem h
Nh
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Simple pilot extraction
A rough estimation for . Here we insert L equally spaced pilot at li
avekh
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Piecewise linear approximation
For normalized Doppler of up to 20%, linear approximation is a good estimate of channel time-variations and the effect on correlation characteristics is negligible
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Piecewise linear approximation Minimize
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Piecewise linear approximation Assume , it can be easily seen that
F is minimized at s=N/2-1 or s=N/2. Therefore we approximate with the estimate of
We have . Then can be expressed as follows:
( )ikh
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Piecewise linear approximation Hence
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Piecewise linear approximation Frequency domain relationship:
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Method 1: using CP
The output CP vector can be written as
Define
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Method 1: using CP
Inserting into Q matrix ( )ikh
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Method 1: using CP
Recommended procedure Set the initial estimate of Hslope to zero
Estimate Hmid from pilots Solve for X Solve for ζ Use
to estimate Hslope
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Method 2: utilizing adjacent symbols
A constant slope is assumed over the time duration of T+(N/2)*Ts for the former and T for the latter
The former can handle lower Doppler values without processing delay while the latter would have a better performance
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Method 2: utilizing adjacent symbols From the figure above
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Method 2: utilizing adjacent symbols
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Solve the matrix inverse problem The bottleneck is to solve
which contains N simultaneous equations Also, it requires NxN matrix inversion and has
complexity O(N3)
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Solve the matrix inverse problem(1) The general solution are not adequate
Gauss-Jordan elimination Although it can raise accuracy by pivoting
Cholesky’s method Use iterative method
Jacobi iteration Gauss-Seidel
Sufficient condition: diagonally dominantNkkkkk aaaa ,2,1,,
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Solve the matrix inverse problem(2) Remove those less dominant ICI terms. Th
en transform the matrix H’ to a block-diagonal matrix H’’, e.g., Y=HX
1,11,10,1
1,11,10,1
1,01,00,0
NNNN
N
N
aaa
aaa
aaa
H
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Solve the matrix inverse problem(2)
1,12,11,1
1,1
0,
1,10,1
,01,00,0
2
2
2
2
00
0
0
0
NNNNNN
NN
aaa
a
a
aa
aaa
H
q
q
q
q
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Solve the matrix inverse problem(2) Then
qNA
A
A
H
1
1
0
0
0
XHY TqNXXXX '
1'1
'0
qnqnqnqnnqn
qnqnqnqn
qnn
nn
nnnn
nnnnnn
n
aaa
aa
a
a
aa
aaa
A
q
q
q
q
,1,,
,11,1
,
,
1,1,1
,1,,
2
2
2
2
00
0
0
00
Tqnnnn XXXX 1'
TqNYYYY '1
'1
'0 Tqnnnn YYYY 1
'
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Solve the matrix inverse problem(2) Finally, the size of the matrix inverse is lower
ed to (q+1) by (q+1)
This method is only available when the multipath fading channel is slowly time varying.
'1'nnn YAX
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Solve the matrix inverse problem(3)
WXCHH
WXHCXHY
slopemid
slopemid
)(
YHCHHI
YCHHX
mid
A
slopemid
slopemid
111
1
)(
)(ˆ
YHAAIX mid132 )(ˆ