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2
Conventional Equalization
Equalizer DecoderSoft OutputFrom Receiver
Filter
Hard Output
Possible Equalizer Types:
•Linear Equalizer
•Decision Feedback Equalizer (DFE)
•Maximum A posteriori Probability (MAP) Equalizer
•Soft-output Viterbi (MLSE) Equalizer
Possible Decoder Types:
•Maximum A posteriori Probability (MAP) Decoder
•Viterbi (MLSE) Decoder
![Page 3: 1 Iterative Equalization and Decoding John G. Proakis proakis@neu.edu COMSOC Distinguished Lecture Tour](https://reader036.vdocuments.site/reader036/viewer/2022062307/5514f837550346935c8b603d/html5/thumbnails/3.jpg)
3
Turbo Principle / Turbo Coding
Turbo Encoder:
• Parallel concatenated recursive systematic convolutional encoders
• Encoders separated by an interleaver
d(n)
b(n)
D D+
cs(n)
cp1(n)
D D
cp2(n)
d`(n)
Puncturer and P
/S converter
Encoder 1
Encoder 2
+
+
+
Turbo Decoder:
• Two Soft-Input Soft-Output (SISO) decoders separated by interleavers
• SISO modules can be
• SOVA
• MAP
• Extrinsic information passed between modules
SISODecoder 1
SISODecoder 2
xp1
xs
xp2
Le
21
Le
12
Ld
![Page 4: 1 Iterative Equalization and Decoding John G. Proakis proakis@neu.edu COMSOC Distinguished Lecture Tour](https://reader036.vdocuments.site/reader036/viewer/2022062307/5514f837550346935c8b603d/html5/thumbnails/4.jpg)
4
Serially Concatenated Systems
Serially Concatenated Coding:
• Serial concatenated (recursive) convolutional encoders
• Encoders separated by an interleaver
Encoder 1d(n)
c(n) c’(n) b(n)
Encoder 2
Coded Transmission over Multipath Channels:
• (recursive) convolutional encoder
• Interleaved bits mapped to symbols
• Symbols passed through a multipath channel
Encoderd(n)
c(n) c’(n) Symbol
Mapper
Multipath
Channel
x(n)
r(n)
![Page 5: 1 Iterative Equalization and Decoding John G. Proakis proakis@neu.edu COMSOC Distinguished Lecture Tour](https://reader036.vdocuments.site/reader036/viewer/2022062307/5514f837550346935c8b603d/html5/thumbnails/5.jpg)
5
Channel Model / Precoding
Multipath Channel Model:• Received signal:
•Rate 1/1 convolutional code
D
Xh1(n)
D
Xh2(n)
D
XhL-1(n)
Xh0(n)
+
+w(n)
x(n)
r(n)
)()()()(0
nwlnxnhnrL
l
l
Precoded System:• Iteration gain only possible with recursive inner code (channel) [1], [2]• Recursive rate 1/1 precoder is employed before transmission• Most common precoder: Differential encoder
D
Xh1(n)
D
Xh2(n)
D
XhL-1(n)
Xh0(n)
+
+w(n)
x(n)
r(n)
y(n)
y(n-1)
![Page 6: 1 Iterative Equalization and Decoding John G. Proakis proakis@neu.edu COMSOC Distinguished Lecture Tour](https://reader036.vdocuments.site/reader036/viewer/2022062307/5514f837550346935c8b603d/html5/thumbnails/6.jpg)
6
Iterative Equalization and Decoding (Turbo Equalizer)
ConvolutionalEncoder Symbol
MapperMultipathChannel
dn cn c’n xn rn
MAPDecoder+
MAPEqualizer
+ChannelEstimator
r
LD
e(c’) LD
e(c) LD(c)
LD(d)
LE
e(c)LE
e(c’)LE(c’)
-
-
• Data bits are convolutionally encoded and interleaved• M-ary PSK modulated signals transmitted through a multipath channel, which is treated as an encoder
• Received signals are jointly equalized and decoded in a turbo structure• First proposed by Douillard, et.al [3], where SOVA modules are employed• Bauch extended the idea by employing MAP modules [4]
![Page 7: 1 Iterative Equalization and Decoding John G. Proakis proakis@neu.edu COMSOC Distinguished Lecture Tour](https://reader036.vdocuments.site/reader036/viewer/2022062307/5514f837550346935c8b603d/html5/thumbnails/7.jpg)
7
Time-invariant Test Channel
0.688
0.460
0.227
0.460
0.227
Impulse Response Frequency Response
t
• Proakis C channel [5]
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8
Low Complexity Alternative Equalizers: DFE and MLSE
• Performance of DFE and MLSE over the Proakis C channel [5]
Bit error rate performance [5]
![Page 9: 1 Iterative Equalization and Decoding John G. Proakis proakis@neu.edu COMSOC Distinguished Lecture Tour](https://reader036.vdocuments.site/reader036/viewer/2022062307/5514f837550346935c8b603d/html5/thumbnails/9.jpg)
9
Iterative Equalization and Decoding Performance
• Iterative equalization and decoding with MAP modules• Recursive systematic convolutional encoder with R=1/2, K=5, • Time-invariant 5 tap channel with a spectral null (Proakis C [5])• Equalizer has perfect knowledge of the channel • Block length 4096
Bit error rate performance of turbo equalizer [4]
![Page 10: 1 Iterative Equalization and Decoding John G. Proakis proakis@neu.edu COMSOC Distinguished Lecture Tour](https://reader036.vdocuments.site/reader036/viewer/2022062307/5514f837550346935c8b603d/html5/thumbnails/10.jpg)
10
Hard Iterative DFE and MAP Decoding
Forward
Filter
Feedback
Filter
Symbol
Detector
+
MAP
DecoderInput from
receiver filter
DFE withhard input feedback
kI
kI~
Hard encodedsymbols
OutputData
• During the first pass, symbol detector output is passed to the feedback filter• After the first pass, hard encoded symbol output of the decoder is used in the feedback filter
![Page 11: 1 Iterative Equalization and Decoding John G. Proakis proakis@neu.edu COMSOC Distinguished Lecture Tour](https://reader036.vdocuments.site/reader036/viewer/2022062307/5514f837550346935c8b603d/html5/thumbnails/11.jpg)
11
Performance of Hard Iterative DFE and MAP decoder
• BPSK modulation• R=1/2, K=7 convolutional coding• Block length 2048• Channel Proakis C
12 12.5 13 13.5 14 14.5 15 15.510
-6
10-5
10-4
10-3
10-2
10-1
100
Eb/N0 (dB)
PB
ER
Performance of Hard Iterative DFE(K1=K2=4) in Coded BPSK System
First iteration K=7 Second iteration K=7Third iteration K=7 Fourth iteration K=7
![Page 12: 1 Iterative Equalization and Decoding John G. Proakis proakis@neu.edu COMSOC Distinguished Lecture Tour](https://reader036.vdocuments.site/reader036/viewer/2022062307/5514f837550346935c8b603d/html5/thumbnails/12.jpg)
12
Soft Iterative DFE and MAP Decoding
Forward
Filter
Feedback
Filter
Decision
Device
+
MAP
Decoder
DFE withhard input feedback
kI
Soft encodedsymbols
OutputData
Soft decisions of the decoder is combined with the soft outputs of the DFE:
2
2
+
kI
Soft APPfrom lastiteration
Hard detectedsymbols
)ˆ( kIL
![Page 13: 1 Iterative Equalization and Decoding John G. Proakis proakis@neu.edu COMSOC Distinguished Lecture Tour](https://reader036.vdocuments.site/reader036/viewer/2022062307/5514f837550346935c8b603d/html5/thumbnails/13.jpg)
13
Histogram of DFE Output
-4 -3 -2 -1 0 1 2 3 40
100
200
300
400
500
600
700
E qua lizer Output va lues
Dis
trib
uta
tion
of E
qu
ali
zer
Ou
tpu
t Va
lue
s
F i rs t Itera tion, S NR=12, K =3
-5 0 50
200
400
600
800
1000
1200
1400
1600
1800
2000
E qua lizer Output va lues
Dis
trib
uta
tion
of
Eq
ua
lize
r O
utp
ut V
alu
es
F i rs t Itera tion, S NR=20, K =3
The histogram of equalizer estimated output for SNR = 12 dB
The histogram of equalizer estimated output for SNR = 20 dB
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14
Modified Soft Iterative DFE and MAP Decoding
Forward
Filter
Feedback
Filter
Decision
Device
+
MAP
Decoder
DFE withhard input feedback
kI
Soft encodedsymbols
OutputData
+
-
Only extrinsic information is passed to the DFE from the decoder
Re
Im
22
2
22
2
Variance Estimator
Variance Estimator
+ +kI
Soft APPfrom lastiteration
Hard detectedsymbols
Conversion
to LLR
![Page 15: 1 Iterative Equalization and Decoding John G. Proakis proakis@neu.edu COMSOC Distinguished Lecture Tour](https://reader036.vdocuments.site/reader036/viewer/2022062307/5514f837550346935c8b603d/html5/thumbnails/15.jpg)
15
Performance of Soft Iterative DFE and MAP Decoder
• Recursive systematic convolutional encoder with R=1/2, K=5, • Time-invariant 5 tap channel with a spectral null (Proakis C [5])• RLS updates at the DFE• Block length 4096• BPSK modulation
![Page 16: 1 Iterative Equalization and Decoding John G. Proakis proakis@neu.edu COMSOC Distinguished Lecture Tour](https://reader036.vdocuments.site/reader036/viewer/2022062307/5514f837550346935c8b603d/html5/thumbnails/16.jpg)
16
Performance of Soft Iterative DFE and MAP Decoder
• Recursive systematic convolutional encoder with R=1/2, K=5, • Time-invariant 5 tap channel with a spectral null (Proakis C [5])• RLS updates at the DFE• Block length 4096• QPSK modulation
![Page 17: 1 Iterative Equalization and Decoding John G. Proakis proakis@neu.edu COMSOC Distinguished Lecture Tour](https://reader036.vdocuments.site/reader036/viewer/2022062307/5514f837550346935c8b603d/html5/thumbnails/17.jpg)
17
Iterative Linear MMSE Equalization and Decoding
SISO Linear MMSE Equalizer [6]:
• Known channel:
• Received signal:
• Likelihood ratio for MMSE estimator output, :
• Channel matrix:
• MMSE estimator output:
where,
211 ,,1,, MMMkhk
2
1
M
Mkkknkn xhz
nx
)()(
1Pr
1Prln
1|ˆ1|ˆ
ln)(
nnMMSEe
xL
n
n
xL
nn
nnn
MMSE
x
x
xxp
xxpxL
21
2
1
11
211
0
0
0
00
0
1
1
1
MM
M
M
MM
MMM
hh
h
h
hh
hhh
H
xn
znn
Hnn mx mzcˆ
)(2
1tanh
),cov(),cov(12
nnxn
nnzn
nnH
nnN
n
xLxEm
EE
x
xHzm
xHxxHIc
![Page 18: 1 Iterative Equalization and Decoding John G. Proakis proakis@neu.edu COMSOC Distinguished Lecture Tour](https://reader036.vdocuments.site/reader036/viewer/2022062307/5514f837550346935c8b603d/html5/thumbnails/18.jpg)
18
Iterative Linear MMSE Equalization and Decoding
sHmzc
sssHHDIc
Hs
D
m
H
xn
xnn
Hnn
xn
Hn
Nn
TMNxMNx
xNMn
xNMn
xNMnn
TxNMn
xNMn
xNMn
xn
nxn
mx
m
mmmdiag
mmm
xLm
ˆ
)(
010
)(1)(1)(1
)(2
1tanh
122
)(1)(1
221
2
1
2211
221111
221111
Steps to compute symbol estimates with the Linear MMSE equalizer:
Soft output calculation assuming Gaussian distributed estimates:
nHn
n
nnn
MMSEe
nHnn
Hnnnn
Hnnnn
xxxL
xxE
xxE
cs
sc
sc
sc
1
ˆ2ˆ2)(
1|ˆ
1|ˆ
2
)1(
2)1(2
)1(
)1(
![Page 19: 1 Iterative Equalization and Decoding John G. Proakis proakis@neu.edu COMSOC Distinguished Lecture Tour](https://reader036.vdocuments.site/reader036/viewer/2022062307/5514f837550346935c8b603d/html5/thumbnails/19.jpg)
19
Performance of SISO MMSE Linear Iterative Equalizer
• Recursive systematic convolutional encoder with R=1/2, K=5, • Time-invariant 5 tap channel with a spectral null (Proakis C [5])• Equalizer has perfect knowledge of the channel • Block length 4096
![Page 20: 1 Iterative Equalization and Decoding John G. Proakis proakis@neu.edu COMSOC Distinguished Lecture Tour](https://reader036.vdocuments.site/reader036/viewer/2022062307/5514f837550346935c8b603d/html5/thumbnails/20.jpg)
20
Comparison of System Performances
• Recursive systematic convolutional encoder with R=1/2, K=5, • Time-invariant 5 tap channel with a spectral null (Proakis C [5])• BER results after 6 iterations• Block length 4096
![Page 21: 1 Iterative Equalization and Decoding John G. Proakis proakis@neu.edu COMSOC Distinguished Lecture Tour](https://reader036.vdocuments.site/reader036/viewer/2022062307/5514f837550346935c8b603d/html5/thumbnails/21.jpg)
21
Experimental Study of Iterative Equalizers
ChannelProbe
TrainingSymbols
InformationSymbols
DeadTime
![Page 22: 1 Iterative Equalization and Decoding John G. Proakis proakis@neu.edu COMSOC Distinguished Lecture Tour](https://reader036.vdocuments.site/reader036/viewer/2022062307/5514f837550346935c8b603d/html5/thumbnails/22.jpg)
22
Joint MMSE Equalization and Turbo Decoding
FeedbackFilter
MAPDecoder 1 Demapper
&S/P
Converter
AdaptiveAlgorithm
DecisionDevice
x(n)
x(n)~
e-j(n)
e(n)
x(n)^
y(n)
xs
xp2
Le
12
Ld
2(n)
Le
12
TrainingSymbols
ForwardFilter +x
+
xp1
MAPDecoder 2
Lp2 Lp1
![Page 23: 1 Iterative Equalization and Decoding John G. Proakis proakis@neu.edu COMSOC Distinguished Lecture Tour](https://reader036.vdocuments.site/reader036/viewer/2022062307/5514f837550346935c8b603d/html5/thumbnails/23.jpg)
23
• Soft output of the DFE:
•RLS algorithm is used to track channel variation:
Decision Feedback Equalizer (DFE)
)(~)()()()(ˆ nnnnnx HH xwyw bf
)(ξ)(~)()1()(
)(ξ)()()1()(
))(~)1()()1(()()(ξ
))1()()()1((λ)(
)()1()(λ
)()1()(
1-
nnnnn
nnnnn
nnnnnxn
nnnnn
nnn
nnn
HH
H
H
xPww
yPww
xwyw
PykPP
yPy
yPk
bb
ff
bf
• Noise variance estimate: 222 ))(~)()()(()(λ)1()1(λσ)(σ nnnnnxnn HH xwyw bf
![Page 24: 1 Iterative Equalization and Decoding John G. Proakis proakis@neu.edu COMSOC Distinguished Lecture Tour](https://reader036.vdocuments.site/reader036/viewer/2022062307/5514f837550346935c8b603d/html5/thumbnails/24.jpg)
24
MAP Decoding
• Maximize a posteriori probability:
• Decision variable written in the form of log-likelihood ratio:
1,,1,0),|( kiddP in y
S nn
S nn
pssssp
pssssp
n
n
dP
dPdn
)(/),,'(
)(/),,'(
1
1log
)|1(
)|1(log)(
yy
yy
y
y
![Page 25: 1 Iterative Equalization and Decoding John G. Proakis proakis@neu.edu COMSOC Distinguished Lecture Tour](https://reader036.vdocuments.site/reader036/viewer/2022062307/5514f837550346935c8b603d/html5/thumbnails/25.jpg)
25
MAP Decoding (BCJR Algorithm)
)|()(),(n nnn xypdPss
• State transition probability:
where ),( p
nsnn yyy ),( p
nsnn xxx
22n σexp
σ2
)(exp),(
pn
pn
snn
e
n
xyydLdss
S nenn
S nenn
ne
nn ssss
ssssdLyd
)(β),(γ)(α
)(β),(γ)(αlog)(
σ
2)(Λ
1
1
2
channelvalue
a prioriinformation
extrinsicinformation
![Page 26: 1 Iterative Equalization and Decoding John G. Proakis proakis@neu.edu COMSOC Distinguished Lecture Tour](https://reader036.vdocuments.site/reader036/viewer/2022062307/5514f837550346935c8b603d/html5/thumbnails/26.jpg)
26
• depends on the channel trellis defined by hl(n) with 2(L-1) states
•If xn-l for J<l<L-1 is known
MAP Equalizer
1
02
en )(
σ2
1exp),(γ
L
lln
ln xnhyss
11
02
en ˆ)()(
σ2
1exp),(γ
L
Jlln
lJ
lln
ln xnhxnhyss
),(γen ss
Number of states is reduced to 2(J-1)
![Page 27: 1 Iterative Equalization and Decoding John G. Proakis proakis@neu.edu COMSOC Distinguished Lecture Tour](https://reader036.vdocuments.site/reader036/viewer/2022062307/5514f837550346935c8b603d/html5/thumbnails/27.jpg)
27
Per-Survivor Processing
00
01
10
11 1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
n-4 n-3 n-2 n-1 n
33 ,Y nn
22 ,Y nn
11,Y nn
00 ,Y nn
n
Snmn
Sn
Sn
mmm SP Y|αYPath metric:
Survivor path: ]0,0,1,1[Y0 n
]1,0,1,1[Y2 n
0
1
1
0
Discarded Paths Survivor Paths
![Page 28: 1 Iterative Equalization and Decoding John G. Proakis proakis@neu.edu COMSOC Distinguished Lecture Tour](https://reader036.vdocuments.site/reader036/viewer/2022062307/5514f837550346935c8b603d/html5/thumbnails/28.jpg)
28
Channel Estimator
AdaptiveAlgorithm
+hl (n)(n)x y(n)
e(n)-
• Each survivor path has a separate channel estimator• The input to the channel estimator, , is the estimates within the survivors• RLS algorithm is employed
(n)x
![Page 29: 1 Iterative Equalization and Decoding John G. Proakis proakis@neu.edu COMSOC Distinguished Lecture Tour](https://reader036.vdocuments.site/reader036/viewer/2022062307/5514f837550346935c8b603d/html5/thumbnails/29.jpg)
29
Channel Estimator
• Initial channel estimate is based on the correlation of the preamble• RLS algorithm is employed to track the channel
• Noise variance estimate:
)(ξ)(ˆ)()1()(
))(ˆ)1(()()(ξ
))1()(ˆ)()1((λ)(
)(ˆ)1()(ˆλ
)(ˆ)1()(
1-
nnnnn
nnnyn
nnnnn
nnn
nnn
H
H
H
xPww
xw
PxkPP
xPx
xPk
222 )(ξλ)1()1(λσ)(σ nnn
![Page 30: 1 Iterative Equalization and Decoding John G. Proakis proakis@neu.edu COMSOC Distinguished Lecture Tour](https://reader036.vdocuments.site/reader036/viewer/2022062307/5514f837550346935c8b603d/html5/thumbnails/30.jpg)
30
Channel impulse response estimate for transducer seven
obtained using the channel probe
DFE results for transducer 7.Eye Pattern - Filter coefficients
PLL phase estimate - Bit error distribution
Experimental Results
![Page 31: 1 Iterative Equalization and Decoding John G. Proakis proakis@neu.edu COMSOC Distinguished Lecture Tour](https://reader036.vdocuments.site/reader036/viewer/2022062307/5514f837550346935c8b603d/html5/thumbnails/31.jpg)
31
Experimental Results
Channel impulse response estimate for transducer seven
obtained using adaptive channel estimator
Comparison of received signal with the estimated received signal based on the
channel estimate
![Page 32: 1 Iterative Equalization and Decoding John G. Proakis proakis@neu.edu COMSOC Distinguished Lecture Tour](https://reader036.vdocuments.site/reader036/viewer/2022062307/5514f837550346935c8b603d/html5/thumbnails/32.jpg)
32
Experimental Results
• Sparse Channel with multipath delay in the order of 200 symbols• Length of the DFE or channel estimator filters cannot cover the channel• Sparse processing is needed
![Page 33: 1 Iterative Equalization and Decoding John G. Proakis proakis@neu.edu COMSOC Distinguished Lecture Tour](https://reader036.vdocuments.site/reader036/viewer/2022062307/5514f837550346935c8b603d/html5/thumbnails/33.jpg)
33
Results of DFE Turbo Decoder
Event Modulation DFE Iter1
Iter2
Iter3
Iter4
Iter5
0 QPSK 334 25 4 3 3 3BPSK 70 0
1 QPSK 488 80 56 49 47 49BPSK 22 0
2 QPSK 392 43 18 15 15 15BPSK 64 4 2 2
3 QPSK 374 27 17 12 11 11BPSK 51 0
4 QPSK 290 11 7 7 7 7BPSK 38 0
5 QPSK 121 2 0BPSK 20 0
6 QPSK 165 1 2 2 2 2BPSK 7 0
7 QPSK 247 6 2 2 2 2BPSK 1 0
8 QPSK 207 7 1BPSK 17 1 0
![Page 34: 1 Iterative Equalization and Decoding John G. Proakis proakis@neu.edu COMSOC Distinguished Lecture Tour](https://reader036.vdocuments.site/reader036/viewer/2022062307/5514f837550346935c8b603d/html5/thumbnails/34.jpg)
34
Results of Iterative DFE Turbo Decoder
Event Mod. DFE Iter1 Iter2 DFE Iter1 Iter2 DFE Iter1 Iter2 DFE Iter1 Iter2 DFE Iter1 Iter20 QPSK 334 25 4 140 1 2 133 1 1 138 1 1 139 1 11 QPSK 488 80 56 203 16 9 179 8 5 171 7 4 172 5 42 QPSK 392 43 18 186 7 7 177 6 6 173 6 6 173 6 63 QPSK 374 27 17 165 5 6 148 2 04 QPSK 290 11 7 139 5 5 131 3 3 129 3 3 129 3 35 QPSK 121 2 06 QPSK 165 1 2 73 1 1 75 2 07 QPSK 247 6 2 104 08 QPSK 207 7 1 89 0
![Page 35: 1 Iterative Equalization and Decoding John G. Proakis proakis@neu.edu COMSOC Distinguished Lecture Tour](https://reader036.vdocuments.site/reader036/viewer/2022062307/5514f837550346935c8b603d/html5/thumbnails/35.jpg)
35
Results of Iterative DFE MAP Decoder
Event Mod. DFE1 MAP1
DFE2 MAP2
DFE3 MAP3
DFE4 MAP4
DFE5 MAP5
DFE6 MAP6
0 QPSK 512 136 268 49 215 31 212 31 210 31 210 31/16BPSK 46 0
1 QPSK 307 0BPSK 40 0
2 QPSK 522 167 265 13 210 0BPSK 42 0
3 QPSK 288 40 155 5 144 5 146 5 146 5 146 5/2BPSK 47 0
4 QPSK 238 5 119 0BPSK 36 0
5 QPSK 153 0BPSK 10 0
6 QPSK 208 9 81 0BPSK 6 0
7 QPSK 91 0BPSK 7 0
8 QPSK 282 15 109 5 101 0BPSK 16 0
![Page 36: 1 Iterative Equalization and Decoding John G. Proakis proakis@neu.edu COMSOC Distinguished Lecture Tour](https://reader036.vdocuments.site/reader036/viewer/2022062307/5514f837550346935c8b603d/html5/thumbnails/36.jpg)
36
Results for Iterative Map Equalizer Turbo Decoder
PK#
MOD. EquMap1
TurIter1
TurIter2
EquMap2
TurIter1
TurIter2
EquMap3
TurIter1
TurIter2
EquMap4
TurIter1
TurIter2
EquMap5
TurIter1
TurIter2
0 BPSK 21 00 QPSK 447 73 50 80 3 3 8 01 BPSK 7 01 QPSK 682 241 222 444 154 115 197 38 25 33 4 1 3 3 02 BPSK 8 02 QPSK 427 64 45 76 1 3 6 03 BPSK 14 03 QPSK 392 59 35 62 2 1 2 04 BPSK 16 04 QPSK 313 14 6 10 05 BPSK 05 QPSK 34 1 06 BPSK 2 06 QPSK 81 1 1 3 07 BPSK 07 QPSK 52 08 BPSK 4 08 QPSK 130 2 2 6 1 1 4 1 1 4 1 1 4 1 1
![Page 37: 1 Iterative Equalization and Decoding John G. Proakis proakis@neu.edu COMSOC Distinguished Lecture Tour](https://reader036.vdocuments.site/reader036/viewer/2022062307/5514f837550346935c8b603d/html5/thumbnails/37.jpg)
37
Results for Iterative MAP Equalizer MAP Decoder
PK#
MOD. EquMAP 1
DecMAP 1
EquMAP 2
DecMAP 2
EquMAP 3
DecMAP 3
0 BPSK 13 00 QPSK 600 333 212 38 29 01 BPSK 10 01 QPSK 407 88 33 02 BPSK 7 02 QPSK 643 415 313 95 32 03 BPSK 20 03 QPSK 294 9 6 04 BPSK 18 04 QPSK 327 34 19 05 BPSK 1 05 QPSK 85 06 BPSK 8 06 QPSK 113 07 BPSK 2 07 QPSK 77 08 BPSK 2 08 QPSK 277 14 1 0
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Conclusions
• Due to error propagation in the DFE, turbo decoder cannot provide performance improvement beyond the second iteration Error Floor
• Joint DFE and turbo decoding adds an additional loop to the system and lowers the error floor
• Joint channel estimator and iterative equalizer is able to decode packets with low SNR, which cannot be decoded with the DFE
• Tail cancellation is an effective way to reduce the computational complexity of the MAP equalizer
• If the channel is sparse, although the DFE filter lengths are short, the DFE is able to provide enough information to the turbo decoder
• A sparse DFE can be used to improve the performance of the DFE/MAP Decoder and the DFE/Turbo Decoder
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References
[1] S. Benedetto, et.al., “Serial concatenation of interleaved codes: Design and performance analysis,” IEEE Trans. Info. Theory, vol. 42, pp. 409-429, April 1998[2] I. Lee, “The effect of a precoder on serially concatenated coding systems with ISI channel,” IEEE Trans. Commun., pp. 1168-1175, July 2001[3] C. Douilard, et.al., “Iterative correction of intersymbol interference: Turbo-equalization,” European Transactions on Telecommunications, vol. 6, pp. 507-511, 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. 307-312[5] J. Proakis, Digital Communications, McGraw-Hill 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. 673-683, March 2002