Per-survivor Based Detection of DPSK Modulated High Rate Turbo Codes Over Rayleigh Fading Channels

1
Per-survivor Based Detection ofDPSK Modulated
High Rate Turbo Codes Over Rayleigh Fading
Channels

• Bin Zhao and Matthew C. Valenti
• Lane Dept. of Comp. Sci. Elect. Eng.
• West Virginia University
• Morgantown, WV

This work funded by the Office of Naval Research
under grant N00014-00-0655
2
Outline of Talk

• Background
• Iterative channel estimation and decoding.
• Turbo DPSK (Hoeher Lodge).
• Extended turbo DPSK
• Replace code in turbo DPSK with turbo code.
• Analytical tool to predict location of
  waterfall.
• Performance in AWGN and fading with perfect CSI
• Performance in unknown fading channels using
  PSP-based processing.
• Conclusions

3
Iterative Channel Estimation

• Pilot-symbol filtering techniques
• Valenti and Woerner Iterative channel
  estimation and decoding of pilot symbol assisted
  turbo codes over flat-fading channels, JSAC,
  Sept. 2001.
• Li and Georghiades, An iterative receiver for
  turbo-coded pilot-symbol assisted modulation in
  fading channels, Comm. Letters, April 2001.
• Trellis-based techniques
• Komninakis and Wesel, Joint iterative channel
  estimation and decoding in flat correlated
  Rayleigh fading channels, JSAC, Sept. 2001.
• Hoeher and Lodge, Turbo DPSK Iterative
  differential PSK demodulation and channel
  decoding, Trans. Comm., June 1999.
• Colavolpe, Ferrari, and Raheli, Noncoherent
  iterative (turbo) decoding, Trans. Comm., Sept.
  2000.

4
Turbo DPSK Structure

• From Hoeher/Lodge.
• K6 convolutional code.
• Block interleaver 20 frames.
• Trellis-based APP demodulation of DPSK with
  perfect CSI.
• In flat fading channels, per-survivor processing
  and linear prediction are applied to estimate the
  channel information.
• Iterative decoding and APP demodulation.

5
APP Demodulator for DPSK

• Can use BCJR algorithm to coherently detect
  trellis-based DPSK modulation.
• Only 2 state trellis when perfect CSI available.
• With unknown CSI apply linear prediction and
  per-survivor processing to estimate the channel
  information.
• Requires an expansion of the DPSK code-trellis.
• Complexity of APP demodulator is exponentially
  proportional to the order of linear prediction.
• PSP algorithm must be modified to produce
  soft-outputs.

6
Construction of Super-Trellis
?0
?0
S0

• Use a sliding window to combine multiple adjacent
  stages of simple DPSK trellis to construct the
  super-trellis of APP demodulator.
• Number of adjacent stages equals the order of the
  linear predictor.
• Complexity of super-trellis is exponentially
  proportional to the order of linear prediction.

?1
?1
S1
?0
?0
Window 1
Window 2
7
Branch Metric of APP Demodulation in Correlated
Fading Channel with PSP

• Channel LLR y and estimated channel input
• Prediction coefficient and Gaussian noise
  
• Prediction residue

8
Extended Turbo DPSK Structure

• Code polynomials (1,23/35)
• UMTS interleaver for turbo code.
• Rate compatible puncturing pattern.
• Block channel interleaver.
• Per-survivor based APP demodulation for
  correlated fading channels.
• Iterative decoding and demodulation.

9
Performance in AWGN Channel with Perfect CSI
0
10

• Framesize 1024 bits
• The energy gap between turbo code and extended
  turbo DPSK
• The energy gap decreases as the rate increases
  except for the rate 8/9 case.
• Why?

extended turbo DPSK
turbo code (coherent BPSK)
-1
10
-2
10
Rate Energy Gap
8/9 2 dB
4/5 1 dB
4/7 1.5 dB
1/3 2.5 dB
-3
10
BER
4/5
-4
4/7
10
8/9
1/3
-5
10
-6
10
1 dB
2.5 dB
-7
10
-6
-4
-2
0
2
4
6
8
Es/No in dB
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Analytical Tool Convergence Box

• Similar to the tunnel theory analysis.
• S. Ten Brink, 1999.
• Suppose Turbo decoder and APP demodulator ideally
  transform input Es/No into output Es/No.
• APP demodulator
• DPSK ? BPSK
• Turbo code decoder
• Turbo Code ? BPSK
• Convergence box shows minimum SNR required for
  converge.
• corresponds to the threshold SNR in the tunnel
  theory.
• convergence box location

0
10
-1
10
coherentDPSK
-2
BPSK
r ?turbo code
10
BER
-3
10
10 iterations
1 iteration
rate Es/No Eb/No
1/2 0.5 dB 3.5 dB
1/3 -1.3 dB 3.5 dB
-6
-4
-2
0
2
4
6
8
Es/No in dB
11
Performance in Fading Channelr 4/5 case

• BT0.01
• Block interleaver improves the performance of
  turbo code by about 1.5 dB.
• With perfect CSI, the energy gap between turbo
  code and extended turbo DPSK is 3 dB.
• For extended turbo DPSK, differential detection
  works better than per-survivor based detection
• Reason A 1 local iteration of turbo decoding is
  sub-optimal.
• Reason B the punctured outer turbo code is too
  weak.

12
Performance in Fading Channel r 1/3 case

• Per-survivor based detection loses about 1 dB to
  perfect CSI case.
• Per-survivor based detection has 1 dB gain over
  extended turbo DPSK with differential detection.
• Increasing the trellis size of APP demodulator
  provides a decreasing marginal benefit.

13
Performance in Fading Channel r 4/7 case

• With perfect CSI, the energy gap between turbo
  code and extended turbo DPSK is around 2.5 dB.
• Per-survivor based detection loses about 1 dB to
  perfect CSI case.
• Per-survivor based detection has 1 dB gain over
  extended turbo DPSK with differential detection.
• Increasing the trellis size of APP demodulator
  provides a decreasing marginal benefit.

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Conclusions

• Extended turbo DPSK turbo code DPSK
  modulation.
• Performs worse than turbo codes with BPSK
  modulation and coherent detection.
• However, the gap in performance depends on code
  rate.
• Large gap if code rate too low or too high.
• Convergence box predicts performance.
• Extended turbo DPSK suitable for PSP-based
  detection.
• PSP about 1 dB worse than extended DPSK with
  perfect CSI.
• For moderate code rates, PSP is 1 dB better than
  differential detection.
• However, if code rate too high, PSP can be worse
  than diff. detection.
• Performance can be improved by executing multiple
  local iterations of turbo decoding per global
  iteration (future work).

15
Future Work

• Search for optimal puncturing patterns for
  extended turbo DPSK.
• Search for a better modulation structure for
  turbo codes with a convergence region comparable
  or even better than that of BPSK modulated turbo
  codes.
• Further develop analytical tools that leverage
  the concepts of Gaussian density evolution and
  convergence boxes of extended turbo DPSK in the
  error-cliff region.