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. From Hoeher/Lodge. K=6 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. Turbo DPSK Structure

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. 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. 0 S0 S0 1 S1 S1 0 0 S2 S2 1 S3 S3 0 Construction of Super-Trellis 0 0 S0 1 1 S1 0 0 Window 1 Window 2

7. Channel LLR y and estimated channel input Prediction coefficient and Gaussian noise Prediction residue Branch Metric of APP Demodulation in Correlated Fading Channel with PSP

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 extended turbo DPSK turbo code (coherent BPSK) • 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? -1 10 -2 10 -3 10 BER 4/5 -4 4/7 10 8/9 1/3 -5 10 -6 1 dB 10 2.5 dB -7 10 -6 -4 -2 0 2 4 6 8 Es/No in dB

10. Analytical Tool: Convergence Box 0 10 • 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: -1 10 coherentDPSK -2 BPSK r =⅓turbo code 10 BER -3 10 10 iterations 1 iteration -6 -4 -2 0 2 4 6 8 Es/No in dB

11. Performance in Fading Channel:r = 4/5 case • BT=0.01 • 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.

14. 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.