ICI mitigation in OFDM systems

2005/11/2 王治傑

2

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

3

System model

Assume the normalized length of the channel is always less than or equal to G in this paper

4

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

5

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

6

Simple pilot extraction

A rough estimation for . Here we insert L equally spaced pilot at li

avekh

7

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

8

Piecewise linear approximation Minimize

9

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

10

Piecewise linear approximation Hence

11

Piecewise linear approximation Frequency domain relationship:

12

Method 1: using CP

The output CP vector can be written as

Define

13

Method 1: using CP

Inserting into Q matrix ( )ikh

14

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

15

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

16

Method 2: utilizing adjacent symbols From the figure above

17

Method 2: utilizing adjacent symbols

18

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)

19

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,,

20

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

21

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

22

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

'

23

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

24

Solve the matrix inverse problem(3)

WXCHH

WXHCXHY

slopemid

slopemid

)(

YHCHHI

YCHHX

mid

A

slopemid

slopemid

111

1

)(

)(ˆ

YHAAIX mid132 )(ˆ