ｽﾗｲﾄﾞﾀｲﾄﾙなし

OFDM(2)
Matrix Based Simlation
Fire Tom Wada
Professor, Information Engineering, Univ. of the Ryukyus
Chief Scientist at Magna Design Net, Inc
[email protected]
http://www.ie.u-ryukyu.ac.jp/~wada/
10/1/2015
1
OFDM Modulator
Copy
to make Guard Interval
Bit
stream
M
A
P
S
/
P
IFFT
P
/
S
Tg
OFDM symbol (1/f0)
generated0~dＮ－１
10/1/2015
2
Multi-path channel
Tg
OFDM symbol (1/f0)
Pat h 2
Building
Direct Pat h
Mobile
Recept ion
Pat h 3
Base St at ion
Tg
10/1/2015
OFDM symbol (1/f0)
3
OFDM Demodulator
Remove Guard Interval
Tg
OFDM symbol (1/f0)
Noise
Bit
Stream
10/1/2015
S
/
P
DFT
D
E
M
A
P
P
/
S
Equalize
4
FFT matrix
 Y (0) 
 x(0) 




 Y (1) 
 x(1) 

FFT











 Y ( M  1) 
 x( M  1) 
 0
0
 Y (0) 
 0


 1
1 
 Y (1) 





M 



  0  ( M 1)
 Y ( M  1) 

1
M




 x(0) 


 x(1) 
 ( k 1)*( l 1) ; k  row, l  colum n




 x( M  1) 
 x(0) 
0


( M 1)
x
(
1
)









( M 1)*( M 1) 

 x( M  1) 


Here,   e
10/1/2015
j
2
M
5
IFFT matrix
 x(0) 
 Y (0) 
 Y (0) 






1
 x(1) 
 Y (1) 
 Y (1) 
( k 1)*( l 1)

IFFT


;
k

row
,
l

colum
n









M






 x( M  1) 
 Y ( M  1) 
 Y ( M  1) 
 0
 Y (0) 
0

0
 x(0) 





0
1
( M 1)
x
(
1
)
Y
(
1
)




1 














M 





0
( M 1)
( M 1)*( M 1) 

 
 x( M  1) 
 
 Y ( M  1) 


Here,   e
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j
2
M
6
Multi-path channel in Matrix
GI of n-1
Symbol n-1
GI of n
Symbol n
10/1/2015
7
If Multi-path delay is small than GI length

Channel Matrix is Cyclic Matrix!
10/1/2015
8
Two path Multi path Channel
Example
Base
Station
Receiver
Channel Impulse Response = [1, 0.5 , 0, 0]
Two path Multi path Channel
Example
 Y (0) 
 X (0) 




 Y (1) 
 X (1) 

FFT
*
Channel
*
IFFT
*
 Y ( 2) 
 X ( 2) 




 Y (3) 
 X (3) 
1
1  1
0
0 0.5 
1
1  X (0) 
 Y (0) 
1 1
1 1









1
2
3
1
2
3
Y
(
1
)
1



0
.
5
1
0
0
1



X
(
1
)
1
1










2

4

6
2
4
6
 Y ( 2) 

  0 0.5 1
0  4 1     X ( 2) 
4 1 








3
6
 9 
3
6
9 
Y
(
3
)
1



0
0
0
.
5
1
1



X
(
3
)








0
0
0  X (0) 
 Y (0)   H (0)

 


Y
(
1
)
0
H
(
1
)
0
0
X
(
1
)

 



 Y ( 2)   0
0
H ( 2)
0  X ( 2) 

 


0
0
H (3)  X (3) 
 Y (3)   0
If time domain channel matrix is cyclic, Frequency Domain Channel Matrix is
diagonal!
Additive Noise

 Y (0) 
 X (0)   noise(0) 



 


 Y (1) 
 X (1)   noise(1) 

 Y ( 2)   FFT * Channel* IFFT *  X ( 2)    noise( 2) 



 


X
(
3
)
noise
(
3
)
 Y (3) 





1
1  1
0
0 0.5 
1
1  X (0) 
1
1  noise(0) 
 Y (0) 
1 1
1 1
1 1













1
 2  3  0.5 1
0
0  1 1 1  2  3  X (1)  1 1  1  2  3  noise(1) 
 Y (1)  1 1 

2
 Y ( 2)   4 1  2  4  6  0 0.5 1
0  4 1  2  4  6  X ( 2) 
 4  6  noise( 2) 
4 1 











3
6
 9 
3
6
9 
3
6
 9 
Y
(
3
)
1



0
0
0
.
5
1
1



X
(
3
)
1



noise
(
3
)











0
0
0  X (0)   N (0) 
 Y (0)   H (0)

 

 

Y
(
1
)
0
H
(
1
)
0
0
X
(
1
)
N
(
1
)

 

 


 Y ( 2)    0



0
H ( 2)
0
X ( 2)
N ( 2) 

 

 

0
0
H (3)  X (3)   N (3) 
 Y (3)   0
10/1/2015
11
How to recover sending signal from receiver signal.
- EQUALIZE Ignore　Noise
0
0
0  X (0) 
 Y (0) 
 X (0)   H (0)



 


Y
(
1
)
X
(
1
)
0
H
(
1
)
0
0
X
(
1
)



 



FFT
*
Channel
*
IFFT
*

 Y ( 2) 
 X ( 2)   0
0
H ( 2)
0  X ( 2) 



 


Y
(
3
)
X
(
3
)
0
0
0
H
(
3
)
X
(
3
)



 


Then
 1

 H (0)
 X (0)  


0
X
(
1
)

 
 X ( 2)   

  0
 X (3)  

 0

10/1/2015
0
0
1
H (1)
0
0
1
H ( 2)
0
0

0 

 Y (0) 


0 
Y
(
1
)




0  Y ( 2) 
 Y (3) 
1 

H (3) 
12
HW5



Modify SCILAB program “71-MatrixOFDMSimulation1.sce”
to measure Symbol Error Rate vs S/N ratio
in M=16 OFDM with QPSK modulation
You can create Matlab program if you like.
Make Symbol Error Rate vs SN ratio






Vertical: SER in log scale
Horizontal: SN ratio 0dB, 1dB … to 15dB
Your report should contain your program and measured
data in Graph.
Dead Line : December End 2010
Please submit to TA: kano-san
[email protected]
10/1/2015
13

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