ICI Mitigation for Pilot-Aided OFDM Mobile Systems Yasamin Mostofi, Member, IEEE and Donald C. Cox,...

ICI Mitigation for Pilot-Aided OFDM Mobile SystemsYasamin Mostofi, Member, IEEE and Donald C. Cox, Fellow, IEEEIEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 4, NO.2, MARCH 2005

老師：高永安學生：蔡育修

Outline

Introduction System model Piece-Wise Linear Approximation

Method I

Method II Mathematical Analysis and Simulation Result Noise/Interference Reduction Simulation Results and Conclusion

Introduction

Transmission in a mobile communication environment is impaired by both delay and Doppler spread.

As delay spread increases, symbol duration should also increase.

reasons---1.near-constant channel in each frequency subband. 2.prevent ISI.

OFDM system become more susceptible to time-variations as symbol length increases. Time-variations introduce ICI. be mitigated to improve the performance.

We introduce two new methods to mitigate ICI. Both methods use a piece-wise linear model to approximate channel time-variations.

System model

: the transmitted data point in the th frequency subband

: the received data point in the th frequency subbandi

i

X i

Y i

Assume perfect timing synchronizaton

21

0

0 1 1j kiNN

i kk

X x e i N

is the cyclic prefix vector with length G(assume the length of

the channel is always less than or equal to G)

0 -1 2

: the time duration of

p

p N G i

x

x i x i G

T

one OFDM symbol after adding the guard

interval.

ths

s

th

: the channel tap at time instant

is the sampling period

for - 1 and 0 1 represents the channel

tap in the guard and data interval.

ik

ik

h k t i T

T T N G

h G i i N k

0

0 1 3

: a cyclic shift in the base

: a sample of additve white Gaussian noise

N

Gi

i k ii kk

N

i

y h x w i N

N

w

The channel output y

1

,0 ,1

th

21

0

0 1 4

Define as the FFT of the channel tap with respect to time-

variant:

0 & 0

N

N

i i i i d ii dd

ICI

m

j ukNu N

m mu

Y H X H X W i N

F m

F k h e m G

2

,0

1

1 0 , N-1

j m i dGN

i d mm

k N

H F d e i dN

The FFT of sequence y

2

,00

1

0

where

1

j miGave N

i mm

Nuave

m mu

H h e

h N h

Furthermore,

Pilot Extraction

We insert equally spaced pilots, , at subchannels /

for 0 -1 il iL P l i N L

i L

An estimate of Hi,0 can then be acquired at pilot：

,0 ,0

21

,0

0

0 1 5

: ICI at th subcarrier

Through an IFFT of length , the estimate of :

1

i ilili li

li li

i i

avek

j ikLaveL

lik

i

I WYH H i L

P P

I l

L h

h H eL

0 -1 6k L

In the absence of mobility, L pilots would have been enough to estimate the channel.

However, in the presence of Doppler, due to the ICI term,

using them for data detection results in poor perfor-mance.

This motivates the need to mitigate the resultant ICI.

Piece-Wise Linear Approximation We approximate channel time-variations with a piece-

wise linear model with a constant slope over the time duration T.

2thFor the channel tap, E is minimized for 1

2save

k k

Nk h h s

12

Nave

kkh h

For normalized Doppler of up to 20%, linear approxi-

mation is a good estimate of channel time-variations.

We will derive the frequency domain relationship.

Therefore, we approximate

1

2

th

1 0 -1 72

: the slope of the k channel tap in the OFDM symbol

Ni

k k k s

k

Nh h i T i N

8

where , and are 1 vectors

y x w

y x w N

midh M A������������������������������������������

������������������������������������������

Then,

we will have

12

k-m

,

0 & - -1 =

0 else

,

0 & - -1 =

0

N

N

N

k m

k m

h k m G N k m N G

k m

k m G N k m N G

midh

A

1

else

M is a diagonal matrix with diagonal elements of M ,

for 12k s

k k

NT k k N

Futhermore,

1 1 12 2 2

0 1

0 1

9

where

diag ... 0 ... 0

diag ... 0 ... 0

N N N

G

G

Y X X W

FFT h h h

FFT

mid slope

mid

slope

H C H

H

H

��������������������������������������������������������

n,m

2

k

where is the FFT of

1 0

= 1 0.5 0

n m

j k

Ns

BB

N

kB T N e

k

C

An FFT of y：

To solve for X, both Hmid and Hslope should be estimated.

Matrix C is fixed matrix and Hmid is readily available.

So we show how to estimate Hslope with our two methods.

Method I： ICI Mitigation Using Cyclic Prefix

2

1

10

where

, 1 1 2

: the transmitted cyclic prefix of the previous OFDM

G

pP

G i

i j G

prep

p

prep

y p w

i j h i G j G

xp

x

x

Q

Q

������������������������������������������

��������������

0 1 G

symbol

... ��������������

The output prefix vector

2

12

11

where

, for 1 & 1 2

, for 12

Re 1: 1

Re 2 :

mat

G

mat

ppp

N

i j G

s

t

t

p

y p w

i j h i G j G

Ni i T i G i G

v p G

v p G

R D X

R

D

X

��������������������������������������������������������

��������������

��������������

Rev J : reverses the order2,

of elements through of vector J

Re : 2t

i j

i j

v p G G

��������������

Then,

Equations (9) and (11) provide enough information to solve for X.

We use a simpler iterative approach to solve for X.

Method II： ICI Mitigation Utilizing Adjacent Symbols This can be done by utilizing either the previous symbol

or both adjacent symbols.

A constant slope is assumed over the time duration of

T+(N/2)*Ts for the former and T for the latter.

2

2

1 , 12 2

1

0

where

: the slope of the th channel tap in region 2

simiarly, , the slope in region 1

N Nnext

rk k

k

r

k

r

k

h hk G

T

k

Estimate of the slopes in region 2：

Utilizing two slopes introduces a minor change in (8).

1 1 2 2

1

method

where

: channel slope matrix in the region 1 2

, & 0 1 , 2

0

II

m

r r r r

r th

r

y x w

m m

Ni j i j i

i jelse

midh M A M A

A

MM

������������������������������������������

2

, & 1 , 2

0

r

Ni j i j i N

i jelse

MM

1 1 2 2method

: diagonal matrix for the slopes of the region

1 2

II

m

r r r rslope slope

r thslope

Y X X W

m

m

midH C H C H

H

��������������������������������������������������������

It can be easily shown the frequency domain relationship

1

2

r

22 2

s

r

22 2

s

,

1 1.5

1 1 =T

1

4 8

,

1 1.5

1 1 =T

n m

j n m j n mN N

n m

j n m j n mN N

n m

n m

e N e

Nn m

n m

n m

e N e

C

C

1

4 8

Nn m

Method I and Method II can handle considerably higher

delay and Doppler spread at the price of higher compu-

tation complexity.

Mathematical Analysis and Simulation Result We define SIRave as the ratio of average signal power

to the average interference power.

Our goal is to calculate SIRave when ICI is mitigated and

compare it to the that of the “no mitigation” case.

Noise/Interference Reduction

if 0, 0 -1ave ave

k kh Threshold h k L

Estimated channel taps are compared with a Threshold.

Let MAV represent the tap with maximum absolute value.

All the estimated taps with absolute values smaller than

MAV/γ for some γ>=1 will be zeros.

Simulation Results

System parameters

The power-delay profile of channel#1 has two main taps

that are separated by 20μs.

The power-delay profile of channel#2 has two main clus-

ters with total delay of 36.5μs.

Each channel tap is generated as Jakes model.

To see how ICI mitigation methods reduce the error floor.

in the absence of

noise for both channels.

To see the effect of noise for fd,norm = 6.5%

To see how ICI mitigation methods reduce the required

received SNR for achieving a Pb = 0.2.

Conclusion

Both methods used a piece-wise linear approximation to

estimate channel time-variations in each OFDM symbol.

These methods would reduce average Pb or the required

received SNR to a value close to that of the case with no

Doppler.

The power savings become considerable as fd,norm incre-

ases.