Iterative Equalization and Decoding. John G. Proakis [email protected] COMSOC Distinguished Lecture Tour. Conventional Equalization. Soft Output. Hard Output. Equalizer. From Receiver Filter. Decoder. Possible Equalizer Types: Linear Equalizer Decision Feedback Equalizer (DFE)
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Soft Output
Hard Output
Equalizer
From Receiver
Filter
Decoder
cs(n)
Puncturer and P/S converter
D
D
P
P1
P
cp1(n)
Encoder 1
P
SISO
SISO
Decoder 2
Decoder 1
D
D
d`(n)
+
+
+
+
cp2(n)
Encoder 2
Turbo Principle / Turbo Codingd(n)
b(n)
Le21
Le12
xp1
xs
xp2
Ld
P
c(n)
c’(n)
b(n)
d(n)
Encoder 1
Encoder 2
Serially Concatenated Systemsc(n)
c’(n)
Symbol
Mapper
d(n)
Encoder
x(n)
Multipath
Channel
r(n)
x(n)
x(n)
D
D
D
D
y(n)
h0(n)
h0(n)
h2(n)
h2(n)
hL1(n)
hL1(n)
w(n)
w(n)
r(n)
r(n)
D
D
X
X
X
X
X
X
X
X
h1(n)
h1(n)
+
+
+
+
Channel Model / Precodingdn
c’n
cn
xn
rn
Convolutional
Symbol
Multipath
P
Encoder
Mapper
Channel
LDe(c)
LD(c)
LDe(c’)
Channel
P1
+
Estimator
LE(c’)
LEe(c’)
LEe(c)
r
MAP
MAP
P
+
Equalizer
Decoder
LD(d)
Iterative Equalization and Decoding (Turbo Equalizer)

0.460
0.460
0.227
0.227
Timeinvariant Test Channelt
Impulse Response
Frequency Response
Bit error rate performance [5]
Bit error rate performance of turbo equalizer [4]
P1
P
+
Hard Iterative DFE and MAP DecodingOutput
Data
Input from
receiver filter
Forward
Filter
MAP
Decoder
Symbol
Detector
Hard encoded
symbols
DFE with
hard input
feedback
Feedback
Filter
P1
P
+
+
Soft Iterative DFE and MAP DecodingOutput
Data
Forward
Filter
MAP
Decoder
Soft encoded
symbols
DFE with
hard input
feedback
Feedback
Filter
Decision
Device
Soft decisions of the decoder is combined with the soft outputs of the DFE:
Hard detected
symbols
Soft APP
from last
iteration
The histogram of equalizer estimated output for SNR = 12 dB
The histogram of equalizer estimated output for SNR = 20 dB
P1
+
+
+
Modified Soft Iterative DFE and MAP DecodingOutput
Data
Conversion
to LLR
Forward
Filter
MAP
Decoder

Soft encoded
symbols
DFE with
hard input
feedback
Feedback
Filter
Decision
Device
Only extrinsic information is passed to the DFE from the decoder
Variance Estimator
Re
Im
+
Hard detected
symbols
Soft APP
from last
iteration
Variance Estimator
Steps to compute symbol estimates with the Linear MMSE equalizer:
Soft output calculation assuming Gaussian distributed estimates:
Probe
Dead
Time
Training
Symbols
Information
Symbols
Experimental Study of Iterative EqualizersP1
P
P
P
P1
MAP
MAP
Demapper
Decoder 1
Decoder 2
&
S/P
Converter
^
x(n)
Adaptive
Algorithm
~
x(n)
Decision
Feedback
Device
Filter
+
x
+
Forward
Filter
Training
Symbols
Joint MMSE Equalization and Turbo DecodingLe12
Le12
xp1
xs
xp2
Ld
Lp2
Lp1
s2(n)
e(n)
ejq(n)
y(n)
x(n)
channel
value
a priori
information
extrinsic
information
Number of states is reduced to 2(J1)
Survivor Paths
Discarded Paths
0
00
0
0
0
0
1
01
1
1
1
1
0
10
0
0
0
1
0
1
1
1
1
11
n4 n3 n2 n1 n
Path metric:
Survivor path:
hl (n)

Adaptive
Algorithm
DFE results for transducer 7.
Eye Pattern  Filter coefficients
PLL phase estimate  Bit error distribution
Channel impulse response estimate for transducer seven obtained using the channel probe
Comparison of received signal with the estimated received signal based on the channel estimate
Channel impulse response estimate for transducer seven obtained using adaptive channel estimator
[1] S. Benedetto, et.al., “Serial concatenation of interleaved codes: Design and performance analysis,” IEEE Trans. Info. Theory, vol. 42, pp. 409429, April 1998
[2] I. Lee, “The effect of a precoder on serially concatenated coding systems with ISI channel,” IEEE Trans. Commun., pp. 11681175, July 2001
[3] C. Douilard, et.al., “Iterative correction of intersymbol interference: Turboequalization,” European Transactions on Telecommunications, vol. 6, pp. 507511, Sep.Oct. 1995
[4] G. Bauch, H. Khorram, and J. Hagenauer, “Iterative equalization and decoding in mobile communications systems,” in Proc. European Personal Mobile Commun. Conf., pp. 307312
[5] J. Proakis, Digital Communications, McGrawHill Inc., 2001
[6] M. Tuchler, A. Singer, and R. Koetter, “Minimum mean squared error equalization using a priori information,” IEEE Trans. Signal Proc., vol. 50, pp. 673683, March 2002