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 .

3

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

5

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

6

NTk

jL

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

7

1

0

/2)(1)}({)(

N

k

NknjekXN

kXIDFTNnx

1,...,1,0),(

1,...,1,),()(

NnnxNgNgnnNx

nxg

The received baseband signal

, n = 0 , 1 , … , N-1

: additive white Gaussian noise (AWGN)

: circular convolution

, k = 0 ,1, … ,N-1

)()()()( nwNnhnxny

)(nw

)()()(

)}({1)(

kWkHkX

nyDFTN

kY

8

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

NTKaTklj

lF

eF

TlKgh

NkegkH

NkkHkHkH

1

1

)(2

)()(

1,...,1,0,)(

1,...,1,0),()()(

aKlg

1max

TKM

a

9

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,][

10

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

11

The pilot subcarriers arrangement

12

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

fDNS

}1,...,1,0,)(|)({ SmmDmpmpP f

13

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((

NmlKapj

lmP eF)(2

,][

14

The FTCA-MMSE Estimator(Minimu mean-square error)

where"ˆ 1

,1

, WgFWXHgFYXH ppppepppPLS

PLSHHHgMMSE HRRgPLSPLSPLS ,

1ˆ,ˆˆ,

ˆˆ,,,

HPgg

HPLSHg FRHgER

PLS ,,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

NHFFFFHHFFFFHE

HHEN

B

HHHHH

eHee

)))(())(((

1

11

16

PLSHHHg

MMSEMMSEFTCA

HRFR

FgH

PLSPLSPLS ,1

ˆ,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

18

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

19

Τmax=0.64us

20

Τmax=0.64us , L=10

21

Τmax=0.64us , L=10 , Ka=0.72

22

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.

25