Performance Evaluation of Performance Evaluation of Weight-Based ICI-Weight-Based ICI-Cancellation Scheme in Cancellation Scheme in OFDM SystemsOFDM Systems

Jyh-Horng Wena, Jia-Wei Liub, Gwo-Ruey Leec and Cheng-Yi Hsiehd

指導教授：溫志宏 教授報告者 : 謝承毅

1

OutlineOutlineIntroductionICI Mechanism of Standard OFDM

SystemsICI Self-Cancellation SchemeThe Proposed Weight-Based ICI

Self-Cancellation SchemeSimulation ResultsConclusion

2

IntroductionIntroduction

For orthogonal frequency-division multiplexing (OFDM) communication systems, the frequency offsets in mobile radio channels distort the orthogonality between subcarriers resulting in intercarrier interference(ICI).

The ICI self-cancellation scheme is a simple way for ICI reduction.

3

ICI Mechanism of Standard ICI Mechanism of Standard OFDM SystemsOFDM Systems

Fig.1 Block diagram of the FFT-based OFDM systems ICI canceling mapping:

(1) (0)

(3) (2)

( 1) ( 2)

( 1) ( ) , 0, 2,4,..., 2

i i

i i

i i

i i

X X

X X

X N X N

X k X k k N

1 1

2 1 2

3 2 3

1

1

Differential coding:

( ) ( )

( ) ( ) ( )

( ) ( ) ( )

( ) ( ) ( )

( ) ( ) , =1

( ) ( ) ( ) , =2,3,...

i i i

i i

i i i

X k D k

X k X k D k

X k X k D k

X k X k D k

X k D k i

X k X k D k i

Serial

Data

InputS/P

SignalMapping

IFFT P/SAdding Cyclic Prefix

D/AUp

Converter

Channel

DownConverter

A/DRemoving

Cyclic Prefix

S/PFFTSignal

De-mappingP/S

Serial

Data

Output

Differential Coding

ICI Canceling Mapping

ICI Canceling

Demapping

Differential Decoding

ICI Self-Cancellation

Scheme

DifferentialEncoding

4

The transmitted signal in time domain can be written as1

2 /

0

1( ) ( )

Nj kn N

i ik

x n X k eN

and the received signal in time domain can be written as 2 /( ) ( ) ( ) ( ) j n N

i i i iy n x n h n w n e The corresponding frequency domain response could be

obtained by FFT, which gives1

0

1

0,

( ) ( ) ( ) ( ) ( ), 0,1,2,... 1

( ) ( ) (0) ( ) ( ) ( ) ( )

N

i i i ik

N

i i i i ik k m

Y m X k H k C k m W m m N

X m H m C X k H k C k m W m

and C(k – m) denotes the ICI coefficient between the mth and the kth subcarriers, which could be expressed as

1(1 )( )sin( ( ))

( )sin( ( ))

j k mNk m

C k m eN k m

N

, /offsetf f

Inter-carrier interference

Desired signal

The discrete-time channel response of slow fading channel could be expressed as1

,0

( ) ( )L

i l il

h n h n l

5

We assume that X(k) is zero mean and statistically independent with H(k).We further assume E[| H(k)|2]=1 .Therefore, the CIR can be derived as

2

12

0,

2

2

(0)

( )

.N

k k m

m

CCIR

C k m

E S m

E I m

The desired received signal power can be represented as

2 2 2 2( ) ( ) ( ) (0)i iE S m E X m E H m C

and the ICI power is

1

2 2 2 2

0,

( ) ( ) ( )N

i ik k m

E I m E X k E H k C k m

6

Assume the transmitted symbols are constrained so that X(1) =-X(0), X(3) = -X(2),…,X(N-1)= -X(N-2), then the received signal on subcarrier m becomes

1

0

2

0

2

0

2

0

( ) ( ) ( ) ( ) ( )

( ) ( ) ( ) ( 1) ( 1 ) ( )

( ) ( ) ( ) ( 1 ) ( )

( ) ( ) (0) (1) ( ) ( ) ( ) ( 1 ) ( )

N

i i i ik

N

i i i ikeven

N

i i ikeven

N

i i i i ikevenk m

m k k C k m m

k k C k m k C k m m

k k C k m C k m m

m m C C k k C k m C k m m

WY X H

WX H H

WX H

WX H X H

2

0

( 1) ( ) ( ) ( 1) (0) ( ) ( ) ( 1) ( ) ( 1)N

i i i i i ikevenk m

m m m C N C k k C k m C k m mWY X H X H

Similarly, the m+1-th subcarrier signal is expressed as

In such a case, the ICI coefficient is denoted as

'( ) ( ) ( 1 )C k m C k m C k m

ICI Self-Cancellation ICI Self-Cancellation SchemeScheme

7

1

0,

'( ) ( ) ( 1),

( ) 2 ( ) ( 1 ) ( 1)

( ) ( 1).

i i i

N

ik k even

i i

Y m Y m Y m

X k C k m C k m C k m

W m W m

The demodulation for self-cancellation is suggested to work in such a way that each signal at the (m + 1)-th subcarrier (m is even) is multiplied by −1 and then summed with the one at the m-th subcarrier. Then the resultant data sequence is used for making symbol decision. It can be represented as

The corresponding ICI coefficients then becomes

''( ) 2 ( ) ( 1 ) ( 1).C k m C k m C k m C k m

0 10 20 30 40 50 6010

-7

10-6

10-5

10-4

10-3

10-2

10-1

100

101

ε = 0.2

Subcarrier

Am

plitu

de o

f IC

I coeff

icie

nt

C(k-m)

C(k-m) - C(k+1-m)

2C(k-m) - C(k+1-m) - C(k-m-1)

Fig. 2 Comparison of C(k – m), C’(k – m) and C”(k – m)

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The Proposed Weight-Based ICI Self-The Proposed Weight-Based ICI Self-Cancellation SchemeCancellation Scheme

The received signal Yi’(m) could be represented as

'

1

0,

0, ,

( ) ( ) ( 1),

( ) ( )[ ( ) ( 1 ) ( 1) ( ) ]

( ) ( 1),

( ) ( ) (0) (1) ( 1) (0)

( ) ( )[ ( ) ( 1 ) ( 1) ( ) ]

i i i

N

i ik k even

i i

i i

N

i ik k even k m

Y m Y m Y m

X k H k C k m C k m C k m C k m

W m W m

X m H m C C C N C

X k H k C k m C k m C k m C k m

1

( ) ( 1), (9)i iW m W m

In (9), the weight, λ, is a real value between 0 and 1. Also, the summation of these weights is assumed to be 2, i.e.,

2

9

The CIR in the proposed scheme could be derived

2

12

0,,

2

2

(0) (1) 2 ( 1) (0)

( ) ( 1 ) 2 ( 1) ( )

,

m N

kk evenk m

X

I

C C C N CCIR

C k m C k m C k m C k m

The weighting values, λ and ρ, could be determined based on maximum CIR.

2 2 2 2

2 2

2 2 2 2

( / ) ( / )0

( )

( / ) ( / ) 0

m X I I X

I

X I I X

dCIR d d d d

d

d d d d

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90

0.5

1

abs(W

eig

hting v

alu

e)

λ

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.91

1.5

2

Normalize frequency offset

abs(W

eig

hting v

alu

e)

ρ

Fig. 3 The values of weight for the different frequency offsets 10

The mean and variance of the collected symbols could be derived.

The mean and variance of Mi ,SNR=1 11

1

2

1

2

0,

1

1

is numbers of OFDM symbol

is OFDM symbol index

( )

( 1)

S

ii

S

ii

Ni

im m even i

T MS

V M TS

S

i

Y mM

Y m

Simulation ResultsSimulation Results

Table I The simulation parameters for the proposed scheme

Total Number of Simulation 10240000

Number of Subcarrier 512

Samples in Cyclic Prefix 128

Modulation Type QPSK

Carrier Frequency 2.4GHz

Channel Model Six-Ray and AWGN

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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9-20

-10

0

10

20

30

40

50

60

Normalize frequency offset

CIR

Conventional OFDM

Zhao's schemeProposed scheme

Fig. 5 Performance comparison with Zhao’s scheme 13

0 1 2 3 4 5 6 7 8 910

-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

SNR(dB)

BE

R

AWGN ε = 0

Proposed scheme ε = 0.05

Zhao's scheme ε = 0.05Proposed scheme ε = 0.5

Zhao's scheme ε = 0.5

Fig. 6 Performance on the BER under the AWGN channel

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0 5 10 15 20 2510

-4

10-3

10-2

10-1

100

SNR(dB)

BE

R

Proposed scheme ε = 0.05

Zhao's scheme ε = 0.05Proposed scheme ε = 0.5

Zhao's scheme ε = 0.5

Fig. 7 Performance on the BER under the frequency selective fading channel

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ConclusionConclusionThe performances of CIR and BER

on the proposed schemes with a large frequency offset are better than that of Zhao’s scheme.

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