Transcript Slide 1

TURBO - CODING - 2006
4 International Symposium on Turbo Codes & Related Topics
6 International ITG-Conference on Source and Channel Coding
EM BASED MAP ITERATIVE CHANNEL ESTIMATION FOR TURBO CODED
SFBC-OFDM SYSTEMS
Hakan Doğan, Hakan Ali Çırpan, Erdal Panayırcı
Method
MAP Expectation/Maximization (EM) channel
estimation algorithm proposed for SFBC-Turbo
coded-OFDM and SFBC-Convolutionally codedOFDM sytems.
Principles
MAP-EM employs iterative channel estimation and
it improves receiver performance by re-estimating
the channel after each decoder iteration.
Advantages
MAP-EM approach considers the channel
variations as random processes and applies the
Karhunen-Loeve
(KL)
orthogonal
series
expansion. Complexity reduction by using optimal
truncation property.
Investigation
The performance merits of the iterative channel
estimator
Sensitivity of Turbo codes on channel estimation
errors.
The aim of this study is
The design of turbo receiver structures for
space-frequency block coded (SFBC-)
OFDM systems in unknown frequency
selective fading channels.
İstanbul University
Bilkent University
Electirical&Electronics Engineering
How it Works
First iteration
EM based channel estimator computes channel gains according to pilot symbols
Output of channel estimator is used SFBC demodulator
Equalized symbol sequence is passed through a channel interleaver and MAP decoder module
LLR of coded and uncoded bits are yielded
Next iteration
LLRs of coded bits are reinterleaved and passed through a nonlinearity (soft values calculated)
MAP-EM channel estimator iteratively estimate channel by taking received signal and interleaved soft value of transmitted symbols
which are computed bu outher channel decoder in the previous iteration.
Tx1
b( n)
Channel
C( n )

X( n)
SFBC
Encoder
Encoder

X 0 ( n) 


  X * ( n) 
1








X
(
n
)
Nc 2




*
 X N

( n) 
c 1

O
F
D
M
 X 1 ( n)



 X * ( n)

 0







 X N c 1 ( n ) 


*

 X Nc  2 ( n) 

O
F
D
M
Tx2
Received Signal Model
R e (n)   e (n)H1,e (n)   o (n)H 2,e (n)  We (n)
R o (n)    o† (n)H1,o (n)   e† (n) H 2,o ( n)  Wo ( n)
Channel Model
CH  

  E GG
†


Signal Model for Channel estimation
 R e (n)   e (n) o (n)   H1,e (n)   We (n) 
 R (n)      † (n)  † (n)   H (n)    W (n) 
e
 o   o
  2 ,e   o 
R(n)   (n)H(n)  W(n)












R1 ( n) 




RNc  2 ( n) 

RNc 1 ( n) 
R0 ( n)
Channel
Estimation
&
SFBC
OFDM
Demodulator
bˆ i (n)
Paralel
D(n)
-1
-to-
Z( n)
Decoder
Serial
ˆ (n)
X
MAP
nonlinear
function
 j (n)

EM Based Channel Estimation
ˆ
G
MAP  arg max p(G R)
G
Expectation Step

p  R G   E 
 p  R  , G 
H (n)   G (n)
†
Rx
ˆ
G
MAP  arg max 
 p(R G)  p  G 
G
Maximization Step
Taking derivatives with respect to G

 
        ˆ

( n) 
G1q 1     1  † ˆ e†( q ) R e (n)  ˆ o ( q ) R o ( n)
G q2 1
1
†
†( q )
o
R e (n)  ˆ e ( q ) R o
The optimal truncation property of KL reduces the amount of information required to
represent statistically dependent channel frequency response to minimum. Thus this
property can further reduce computational load on the channel estimation algorithm. if the
number of parameters in the expansion include dominant eigen values (Rank=8), we are able
to obtain a good approximation with a relatively small number of KL coefficients. For
instance, by replacing 256 x256 diagonal  with 8x8 diagonal  r decreases computational
complexity significiantly.
Simulations
Conclusion
Low Comlexity Turbo receiver structure was proposed for SFBC-Turbo
coded-OFDM in the case of MAP-EM Channel estimator.
Turbo coded receiver structure more sensitive to channel estimation errors
than convolutional coded receiver structure was shown.