Iterative Demodulation and Decoding of DPSK Modulated Turbo Codes over Rayleigh Fading Channels Bin Zhao, Ph.D. student Matthew Valenti, Assistant Professor Dept. of Comp. Sci. & Elect. Eng. West Virginia University

Introduction With coherent detection, turbo codes have remarkable performance in AWGN and fading channels. However with non-coherent or partially coherent detection, severe penalty in energy efficiency occurs [Hall & Wilson]: 3.5 dB loss in energy efficiency with differentially detected DPSK. 6~7dB loss in energy efficiency with non-coherently detected FSK. Possible solutions to achieve near coherent detection performance under unknown fading channels: Pilot symbol assisted modulation [Valenti & Woerner] Trellis based modulation with per survivor processing (PSP) “Turbo DPSK” [Hoeher & Lodge] Only convolutional codes considered to date for turbo DPSK. We extend the concept of turbo DPSK by cascading turbo outer codes with an accumulator inner code.

Extended Turbo DPSK Structure Code polynomials (1,13/15) UMTS interleaver for turbo code. -- 640 data bits. S-random channel interleaver. Soft-output, trellis- based APP demodulator for DPSK. Iterative decoding and demodulation.

A Simple Analytical Tool for Extended Turbo DPSK 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: code rate = 1/2 rate Es/No Eb/No ½ 0.5 dB 3.5 dB ⅓ -1.3 dB

Extended Turbo DPSK in AWGN Channel Rate 1/3 code. 3 dB energy gap between turbo codes with differentially detected DPSK and coherent BPSK. 2.5 dB energy gap between extended turbo DPSK and coherent turbo codes 0.5 dB processing gain from iterative decoding and APP demodulation. 2.5 dB 3 dB

Extended Turbo DPSK in AWGN Channel Rate ½ code. ~2.5 dB energy gap between turbo codes with differentially detected DPSK and coherent BPSK. 1.75 dB energy gap between extended turbo DPSK and coherent turbo codes. ~0.75 dB processing gain with iterative decoding and APP demodulation. Why does the gap close? Rate ½ and ⅓ extended turbo DPSK perform essentially the same at 3.5 dB, which matches our prediction. However, the coherently detected turbo code performs worse at rate ½ than at rate ⅓. 1.75 dB 2.5 dB

Extended Turbo DPSK in Fading Channel Rate 1/3 code in fully interleaved Rayleigh flat-fading channel. Energy gap between turbo codes with DPSK and coherent BPSK expands to 4.25 dB. Energy gap between extended turbo DPSK and turbo codes expands to 3.75 dB. ~0.5 dB processing gain with iterative decoding and APP demodulation. Why is the gap so large? The energy gap between BPSK and DPSK is much larger in fading than it is in AWGN. 3.75 dB 4.25 dB

Extended Turbo DPSK in Fading Channel Rate ½ code in fully interleaved Rayleigh flat-fading channel. 3.5 dB energy gap between turbo codes with DPSK and coherent BPSK. 3 dB energy gap between extended turbo DPSK and turbo codes. ~0.5dB processing gain with iterative decoding and APP demodulation. Unlike AWGN case, extended turbo DPSK requires ~1 dB more SNR in fading at rate ⅓ than at rate ½. 3 dB 3.5 dB

Conclusions and Future Work Extended turbo DPSK performs considerably worse than turbo codes with BPSK modulation and coherent detection (both coherently detected). The energy inefficiency of extended turbo DPSK results from a large energy gap between BPSK and DPSK modulation at low Es/No where turbo codes typically operate. At higher code rates, the energy gap deceases significantly in both AWGN and fading channels. An analytical tool is developed to predict the performance of extended turbo DPSK. In particular, the minimum SNR required for the iterative decoding structure to converge can be reliably predicted. Higher rate (higher than ½ ) extended turbo DPSK will be studied to better confirm our conclusions. Per-survivor based DPSK demodulation will be applied to estimate the channel information for turbo codes under unknown fading channels. The analytical tool we developed will be further studied to predict the performance of more generalized code concatenation schemes. e.g. serial concatenated convolutional codes. Further results to appear at the 2001 Asilomar Conference on Signals, Systems, and Computers (invited paper).