Using LMS weighting value as the CSI for soft decision

Viterbi decoder

Advisor : Yung-An Kao

Student : Chi-Ting Wu

2005.01.28

Outline

• Introduction • Block diagram• Formula computation• Simulation results• Conclusion

Introduction

• For Viterbi decoder, we view different sub-carriers in the same channel condition

• Actually, different sub-carrier suffers different channel condition

• Using the CSI for each sub-carriers• long train symbol? What else?• equalizer weighting values !!

Block diagram

Convolutional Encoder

Random Data Bits

Interleaver Constellation mapping IFFT

Add cyclic prefix

Add preamble

Radio front

Channel

Sample(20 MHz)

Remove cyclic prefixFFT

Frequency domain

equalizer

Constellation demapping

De-interleaver

Viterbi Decoder

Received Data Bits

CSI from long train symbol

CSI from long train symbol

and LMS weighting value

Formula computation

• According to the Central Limit Theorem, after we transmit lots of symbols, they all seems like Gaussian distribution

• The likelihood function

will become

1 2 3( ) ( ; ) ( ; ) ( ; ) ( ; )nL f x f x f x f x

2

2

( )

21( )

2

x

f x e

22

1

1 1( ) ( ) exp{ ( ) }

22

nn

ii

L x

Formula computation

22

1

1 1ln ( ) ln( ) ( )

22

n

ii

L n x

,

,

2

2 2

2 2

2

k l

k l

jk

k k

k N

k Nk kj

k

H er s

H

Hr s

H e

,

, 2 2

k ljk

k l

k N

H ew

H

The received signal after phase compensation is

,

* *

*2 2

( )

( )k l

k k k k

jk

k k k

k N

w H S n

H eH S n

H

And we know that the weighting value is

Formula computation

kr

,* **

2 2

2

2 22 2

( )( ) ([ ( )] / )

k ljkk k k k

k k k kk k N

k k k

kk N k N

H ew H S nabs abs H S n S

S H

H H n

SH H

We want the same weighting value for

Therefore, we use the weighting value :

And we take the expected value

2 2

2 2 22 2 2[ ]k k kk

kk N k N k N

H H HnE

SH H H

Simulation ~ interleaver

500 symbols

100 times average

1:1:15 dB

CFO=0.01

No SFO

Trms=50ns

4 bit quantization

No weighting value

Simulation ~ quantization

100 symbols

100 times average

1:1:15 dB

CFO=0.01

No SFO

Trms=50ns

No weighting value

Simulation ~ weighted CSI

500 symbols

100 times average

1:1:15 dB

CFO=0.01

No SFO

Trms=50ns

4 bit quantization

With interleaver

Simulation ~ weighted CSI

1000 symbols

100 times average

1:1:15 dB

CFO=0.01

No SFO

Trms=50ns

4 bit quantization

With interleaver

Conclusion

• Weighting values added should has better performance

• Some dimension problems should take notice