Transcript Turbo Codes at WVU

Iterative Channel Estimation
for Turbo Codes
over Fading Channels
Matthew C. Valenti
Assistant Professor
Dept. of Comp. Sci. & Elect. Eng.
West Virginia University
Morgantown, WV 26506-6109
[email protected]
This work supported by ONR award
N00014-00-1-0655
Overview
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Turbo codes.
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Methods for detecting turbo codes over
fading channels.
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Practical problems over fading channels.
DPSK-based
Pilot-based
Improved pilot-symbol techniques
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Iterative channel estimation and decoding
Turbo Codes
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Features:
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Parallel Code Concatenation

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Nonuniform interleaving
Recursive systematic encoding

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Can also use a serial concatenation
Usually RSC convolutional codes are used.
Can use block codes.
Iterative decoding algorithm.
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Optimal approaches: BCJR/MAP, SISO, log-MAP
Suboptimal approaches: max-log-MAP, SOVA
Turbo Encoder
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The data is encoded twice by two (usually)
identical RSC encoders
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A nonuniform interleaver changes the ordering of
bits at the input of the second encoder.
MUX can increase code rate from 1/3 to 1/2.
Systematic Output
Input
Encoder
#1
xi
MUX
Nonuniform
Interleaver
Length L
Encoder
#2
Parity
Output
Constraint length K
Recursive Systematic Convolutional
(RSC) Encoder
Iterative Decoding
Deinterleaver
Extrinsic
Information
Extrinsic
Information
systematic
data
parity
data
Decoder
#1
Interleaver
Decoder
#2
DeMUX
APP
for
hard bit
decisions
Interleaver

One decoder for each elementary encoder.
 Estimates the a posteriori probability (APP) of each data bit.
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Extrinsic Information is derived from the APP.
Each decoder uses the Log-MAP algorithm.
The Extrinsic Information is used as a priori
information by the other decoder.
Decoding continues for a set number of iterations.
Turbo Codes
for Fading Channels

Many channels of interest can be modeled as a
frequency-flat fading channel.
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Because of the time-varying nature of the channel, it
is necessary to estimate and track the channel.
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Fading: channel is time-varying
Flat: all frequencies experience same attenuation
Channel estimation is difficult for turbo codes because they
operate at low SNR.
The goal of this study is to develop channel
estimation techniques that take into account
the iterative nature of the decoder.
Basic System Model
dj
turbo
encoder
xi
channel
interleaver
symbol
mapper
pulse shaping
filter
s (t )
pilot symbols
fading
r (t )
Gaussian
1
Rc ( )  J 0 (2f d )
2
channel
estimator
2 *
cˆk
ˆ 2
zk
symbol
demapper
channel
deinterl.
turbo
decoder
dˆ j
Decoded
data
receiver
filter
rk
c(t )  X (t )  jY (t )
n(t )
channel
s (t )
r (t ) matched
Clarke/Jakes model:
AWGN
c(t )
transmitter
Input
data
Channel Estimation
for Turbo Codes

The turbo decoding algorithm requires accurate
estimates of channel parameters.
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Branch metric:  (si  si 1 )  ln P[di ]  zis xis  zip xip
zi 
2
ri ci*

Noise variance:   2rE
Fading amplitude: ak  ck
Phase:  k  ck
(required for coherent detection)
2
No
2
b
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Because turbo codes operate at low SNR,
conventional methods for channel estimation
often fail.
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Therefore channel estimation and tracking is a
critical issue with turbo codes.
The Phase Ambiguity Problem
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If the receiver is operating at low SNR,
accurate estimates of the phase k will not
be available.
A proactive solution to the phase ambiguity
problem is required.
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Use DPSK.
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Differential detection
Multiple-symbol differential detection.
Use a pilot.
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Pilot tone.
Pilot symbol.
DPSK for Turbo Codes
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When differential detection is used with DSPK, a
severe performance loss occurs.
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~ 4.5 dB loss for turbo codes in Rayleigh fading
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Noncoherent combining loss.
Not a viable option.
However, multiple-symbol differential detection can be
used to approach coherent performance.
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P. Hoeher and J. Lodge
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“Turbo-DPSK”
Serial code concatenation
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Convolutional outer code
Accumulator inner code
Per-survivor processing and linear prediction
Globecom 98. & Trans. Comm. 99
Coherent Detection using
Pilot Symbols
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Coherent detection over Rayleigh fading channels
requires a pilot.
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Pilot tone
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TTIB: Transparent Tone in Band
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1984: McGeehan and Bateman
Pilot symbols
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PSAM: Pilot Symbol Assisted Modulation
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1987: Lodge and Moher; 1991: Cavers
PSAM has been shown to be more power efficient
than TTIB for turbo codes.
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L.-D. Jeng, Y.-T. Su, and J.-T. Chiang, “Performance of turbo
codes in multipath fading channels,” VTC 98.
Pilot Symbol Assisted
Modulation (PSAM)
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Pilot symbols:
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Known values that are periodically inserted into the
transmitted code stream.
Assists channel estimator located at the receiver.
Allows for coherent detection over channels that are
unknown and time varying.
segment #1
symbol
#1
symbol
#1
segment #2
symbol
#M-1
pilot
symbol
symbol
#1
symbol symbol
#M-1
#1
pilot symbols added here
symbol
#M-1
pilot
symbol
symbol
#M-1
Pilot Symbol
Assisted Decoding
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Pilot symbols are used to obtain initial channel
estimates.
After each iteration of turbo decoding, the bit
estimates are used to obtain new channel estimates.
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Decision-directed estimation.
Optimal channel estimator uses Wiener filter.
pilot symbols
y(t )
matched
filter
yn
channel
estimator
 2 *
 2 cˆn 
 ˆ 
y
(q )
k
pilot symbol
insertion
xˆ l( q )
channel
interleaver
(q)
symbol
demapper
xˆ (l q )
Tentative
estimates of
the code bits
nonlinear
function
channel
deinterl.
turbo
decoder
(q )
i
mˆ (i q)
Final estimates
of the data
Hard vs. Soft-Decision
Feedback
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Hard-decision feedback
xi( q )
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if (iq )  0
if (iq )  0
Valenti & Woerner
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R1
S
T1
1998 Electronics Letters, 1999 MILCOM
Soft-decision feedback
xi( q )
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F I
 tanhG J
H2 K
(q)
i
Sandell, Luschi, Strauch, Yan
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1998 Globecom (for convolutional coding & equalization)
Performance of
Pilot Symbol Assisted Decoding
1
10
DSPK: no estimates
PSAM: no feedback
PSAM: hard-decision feedback
PSAM: soft-decision feedback
BPSK: perfect estimates
0
10
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Simulation parameters:
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-1
10
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-2
Rayleigh flat-fading
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Correlated: fdTs = .005
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channel interleaving depth 50
Turbo code
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BER
10
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-3
10
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-4
10
-5
-6
10
1
2
3
4
5
6
Eb/No in dB
7
8
9
10
1250 S-Random interleaver
12 iterations of log-MAP
Pilot symbol spacing: M = 21
K = 61 channel estimator

10
r=1/2, Kc =4
Simple moving average.
Performance in Faster Fading
1
10
DSPK: no estimates
PSAM: no feedback
PSAM: hard-decision feedback
PSAM: soft-decision feedback
BPSK: perfect estimates
0
10
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Simulation parameters:
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-1
10
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-2
Rayleigh flat-fading
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Correlated: fdTs = .02
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channel interleaving depth 50
Turbo code
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BER
10
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-3
10
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-4
10
-5
10
-6
10
1
2
3
4
5
6
Eb/No in dB
7
8
9
10
r=1/2, Kc =4
1250 S-Random interleaver
12 iterations of log-MAP
Pilot symbol spacing: M = 11
Wiener filtering: K = 61
Performance Factors for
Pilot Symbol Assisted Decoding
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Performance is more sensitive to errors in estimates
of the fading process than estimates in noise
variance.
Pilot symbol spacing
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Type of channel estimation filter
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Want symbols close enough to track the channel.
However, using pilot symbols reduces the energy available
for the traffic bits.
Wiener filter provides optimal solution.
However, for small fd, a moving average is acceptable.
Size of channel estimation filter
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Window size of filter should contain about 4 pilot symbols.
Effect of Pilot Symbol Spacing
-1
10
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Simulation parameters:
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Rayleigh flat-fading
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fd Ts  0.02
-2
10
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BER
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-3
10
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-4
10
0
5
10
15
20
25
30
Pilot symbol spacing M
35
40
45
Solid line fdTs = .005
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Dotted line fdTs = .005
channel interleaving depth 50
r=1/2, Kc =4
1250 S-Random interleaver
12 iterations of log-MAP
Order K = 61 estimator
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hard-decision feedback
soft-decsion feedback
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Turbo code
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fd Ts  0.005
Correlated:
Moving average for slow fading
Wiener filter for fast fading
Eb/No = 4.5 dB
Future Work
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Compare coherent PSAM technique with
multiple-symbol DSPK technique.
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Incorporate adaptability
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In terms of performance and complexity.
Adaptive estimation filters (Kalman).
Adaptive pilot-symbol spacing.
Extend the results to higher order modulation
and trellis coded modulation.
Extend the results to the problems of symboltiming estimation and frame synchronization.
Conclusions
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Pilot symbol assisted decoding can be used to
achieve nearly coherent detection/decoding
of turbo codes.
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Iterative estimation/decoding improves
performance.
Good performance even with just hard-decision
feedback.
Iterative estimation can also be used for other
types of codes.