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Improved Channel Estimation Based on Improved Channel Estimation Based on Parametric Channel Approximation Parametric Channel Approximation Modeling for OFDM SystemsModeling for OFDM Systems
IEEE TRANSATIONS ON BROADCASTING , VOL. 54 NO. 2 IEEE TRANSATIONS ON BROADCASTING , VOL. 54 NO. 2 JUNE 2008JUNE 2008
指導老師 : 王瑞騰 老師學 生 : 李裕銘
1
OUTLINEOUTLINEIntroductionSystem modelFraction Taps Channel
Approximation Estimations (FTCA)
Simulations and analysesConclusionsRererence
2
INTRODUCTIONINTRODUCTION In this paper, improved channel estimation
methods based on the parametric channel approximation model using pilot tones are proposed for the OFDM system .
The full-rank MMSE estimator has large computational complexity , and in parametric channel estimator can only be adopted in sparse multi-path fading channels.
In order to solve these problems lying in with the channel models , a parametric model is proposed . This model is called
“fraction taps channel approximation(FTCA)” channel model .
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Channel ModelChannel ModelChannel impulse response of the multi-path
fading channel
the complex gain of the i-th propagation path
the delay of the i-th propagation path
Frequency response
4
:
:
)()(1
i
i
i
L
ii
h
hh
L
i
fji
fj
ieh
dehfH
1
2
2)()(
Orthogonal frequency division Orthogonal frequency division multiplexing(OFDM) system multiplexing(OFDM) system modelmodel
Discrete-time baseband equivalent model of OFDM system
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OFDM channel frequency response
, k=0, 1, … , N-1 N : number of the subcarriers
k : subcarrier index
T : sampling interval
hi : the complex gain of the i-th propagationThe observed channel
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NT
kjL
ii
i
ehkH2
1
)(
1,...,1,0
)}({)(
Nn
kHIDFTNnh
Time domain signal
, n = 0 , 1, … , N-1
Ng : the number of samples in the guard interval
which satisfies Ng x T≧ τmax
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1
0
/2)(1
)}({)(N
k
NknjekXN
kXIDFTNnx
1,...,1,0),(
1,...,1,),()(
Nnnx
NgNgnnNxnxg
The received baseband signal
, n = 0 , 1 , … , N-1
: additive white Gaussian noise (AWGN)
: circular convolution
, k = 0 ,1, … ,N-1
)()(
)()( nwN
nhnxny
)(nw
)()()(
)}({1
)(
kWkHkX
nyDFTN
kY
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Fraction Taps Channel Approximation Fraction Taps Channel Approximation (FTCA) Estimations (FTCA) Estimations
The FTCA channel model
: fraction factor selected from (0,1] : complex gain of the l-th approximation M : number of approximation taps
M
lalF
M
l
NT
KaTklj
lF
eF
TlKgh
NkegkH
NkkHkHkH
1
1
)(2
)()(
1,...,1,0,)(
1,...,1,0),()()(
aK
lg
1max
TKM
a
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In matrix notation , the channel frequency response vector
and then , , k=0~N-1 and l=1~M
, k=0~N-1 and i=1~L
hWHFgHHH NeeF
TNHHH )1(),...,0(
TFFFF NHHHH )]1(),...,1(),0([
Teeee NHHHH )]1(),...,1(),0([
TMgggg ],...,,[ 21 T
Lhhhh ],...,,[ 21
NkjikN
ieW /2,][
NlkKjlk
aeF /2,][
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Based on the Least Square(LS) criterion
g = (FHF)-1FHH = (FHF)-1FHWNh
He : commonly very small and can be negligible when
Ka is properly selected .
FgHHHH FeF
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The pilot subcarriers arrangement
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In OFDM system , the S pilot subcarriers are assumed to be evenly inserted into the N transmission subcarriers
Let P denote the set that contains the position indexes of the S pilot tones
fD
NS
}1,...,1,0,)(|)({ SmmDmpmpP f
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The FTCA Estimators
where
, m=0,…,S-1 and l=1,…,M
Tp SpYpYY ))1(()),...,0((
ppepppp WHXgFXY ,
TP SpXpXpXdiagX ))1(()),...,1(()),0((
TeeePe SpHpHpHH ))1(()),...,1(()),0((,
TP SpWpWpWW ))1(()),...,1(()),0((
N
mlKapj
lmP eF)(2
,][
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The FTCA-MMSE Estimator(Minimu mean-square error)
where
"ˆ 1,
1, WgFWXHgFYXH ppppepppPLS
PLSHHHgMMSE HRRgPLSPLSPLS
,1
ˆ,ˆˆ,ˆˆ
,,,
HPgg
HPLSHg
FRHgERPLS
,,ˆ,)ˆ(
,
SeHPggP
HPLSPLSHH
IA
BFRF
HHERPLSPLS
)(
)ˆˆ(
2
,
,,1
ˆ,ˆ,,
1,...,1,0|))((| 2 SmmpXA15
The Average Channel Energy Approximation Error (ACEAE) Be
For the channel frequency response is achieve by
N
HFFFFHHFFFFHE
HHEN
B
HHHHH
eHee
)))(())(((
1
11
16
PLSHHHg
MMSEMMSEFTCA
HRFR
FgH
PLSPLSPLS,
1ˆ,ˆˆ,
ˆ
ˆ
,,,
The FTCA-LS Estimator
For the channel frequency response is achieve by
PLSHPP
HP
PHP
HPPP
HP
HPLS
HFFF
YXFFXXFg
,1
1
ˆ)(
)(ˆ
PLSHPP
HPLSLSFTCA HFFFFgFH ,
1 ˆ)(ˆˆ
17
FlowchartFlowchart
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PPLSP XHY ,
MMSEFTCAH ˆ
LSFTCAH ˆ
PPPLS YXH 1,
ˆ
M
Simulations and analysesSimulations and analysesIn the OFDM systemMulti-path slow fading channelCarrier frequency : 1GHzSignal bandwidth (BS) : 2.5MHzNumber of subcarriers (N) : 1024Number of samples in the guard interval
(Ng) : 32Sampling interval (T) : 0.4 us
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Τmax=0.64us
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Τmax=0.64us , L=10
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Τmax=0.64us , L=10 , Ka=0.72
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Τmax,A=1.6us , Τmax,E=6.4us , L=10 , Ka,E=0.72 , Ka,A=0.51
23
ConclusionsConclusionsAs compared to the observed channel
model , its dimension reduced, where the full-rank estimators using pilots tones can be adopted, and consequently, improves the channel estimation performance .
It eliminates the problem of multi-path delay estimation and can be adopted in a channel not restricted to a sparse mlti-path fading.
24
REFERENCESREFERENCES J.-J. van de Beek , O. Edfors , and M. Sandell , “On
channel estimation in OFDM systems,” in Proc. IEEE Vehicular Technology Conf. , Jul. 1995 , vol. 2 , pp. 815-819
B. Yang , K. B. Letaief , R. S. Cheng , and Z. Cao , “Channel estimation for OFDM transmission in multipath fading channeds based on parametric channel modeling,” IEEE Trans. Commun. , vol. 49 , pp.467-479 , Mar. 2001.
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