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Using LMS weighting value as the CSI for soft decision
Viterbi decoder
Advisor : Yung-An Kao
Student : Chi-Ting Wu
2005.01.28
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Outline
• Introduction • Block diagram• Formula computation• Simulation results• Conclusion
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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 !!
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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
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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
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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
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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
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Simulation ~ interleaver
500 symbols
100 times average
1:1:15 dB
CFO=0.01
No SFO
Trms=50ns
4 bit quantization
No weighting value
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Simulation ~ quantization
100 symbols
100 times average
1:1:15 dB
CFO=0.01
No SFO
Trms=50ns
No weighting value
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Simulation ~ weighted CSI
500 symbols
100 times average
1:1:15 dB
CFO=0.01
No SFO
Trms=50ns
4 bit quantization
With interleaver
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Simulation ~ weighted CSI
1000 symbols
100 times average
1:1:15 dB
CFO=0.01
No SFO
Trms=50ns
4 bit quantization
With interleaver
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Conclusion
• Weighting values added should has better performance
• Some dimension problems should take notice