Iterative Channel Estimation for Turbo Codes over Fading Channels

1. Iterative Channel Estimationfor Turbo Codesover Fading Channels Matthew C. Valenti Assistant Professor Dept. of Comp. Sci. & Elect. Eng. West Virginia University Morgantown, WV 26506-6109 mvalenti@wvu.edu This work supported by ONR award N00014-00-1-0655

2. Overview • Turbo codes. • Practical problems over fading channels. • Methods for detecting turbo codes over fading channels. • DPSK-based • Pilot-based • Improved pilot-symbol techniques • Iterative channel estimation and decoding

3. Turbo Codes • Features: • Parallel Code Concatenation • Can also use a serial concatenation • Nonuniform interleaving • Recursive systematic encoding • Usually RSC convolutional codes are used. • Can use block codes. • Iterative decoding algorithm. • Optimal approaches: BCJR/MAP, SISO, log-MAP • Suboptimal approaches: max-log-MAP, SOVA

4. Turbo Encoder • The data is encoded twice by two (usually) identical RSC encoders • 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 MUX Parity Output Encoder #2 Nonuniform Interleaver Length L Constraint length K Recursive Systematic Convolutional (RSC) Encoder

5. Iterative Decoding • One decoder for each elementary encoder. • Estimates the a posteriori probability (APP) of each data bit. • 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. Deinterleaver Extrinsic Information Extrinsic Information Interleaver systematic data Decoder #1 Decoder #2 APP for hard bit decisions parity data DeMUX Interleaver

6. Turbo Codes for Fading Channels • Many channels of interest can be modeled as a frequency-flat fading channel. • Fading: channel is time-varying • Flat: all frequencies experience same attenuation • Because of the time-varying nature of the channel, it is necessary to estimate and track the channel. • 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.

7. Basic System Model turbo encoder channel interleaver symbol mapper pulse shaping filter Input data transmitter pilot symbols Clarke/Jakes model: fading AWGN channel Gaussian matched filter channel estimator receiver Decoded data symbol demapper channel deinterl. turbo decoder

8. Channel Estimationfor Turbo Codes • The turbo decoding algorithm requires accurate estimates of channel parameters. • Branch metric: • Noise variance: • Fading amplitude: • Phase:(required for coherent detection) • Because turbo codes operate at low SNR, conventional methods for channel estimation often fail. • Therefore channel estimation and tracking is a critical issue with turbo codes.

9. The Phase Ambiguity Problem • 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. • Use DPSK. • Differential detection • Multiple-symbol differential detection. • Use a pilot. • Pilot tone. • Pilot symbol.

10. DPSK for Turbo Codes • When differential detection is used with DSPK, a severe performance loss occurs. • ~ 4.5 dB loss for turbo codes in Rayleigh fading • Noncoherent combining loss. • Not a viable option. • However, multiple-symbol differential detection can be used to approach coherent performance. • P. Hoeher and J. Lodge • “Turbo-DPSK” • Serial code concatenation • Convolutional outer code • Accumulator inner code • Per-survivor processing and linear prediction • Globecom 98. & Trans. Comm. 99

11. Coherent Detection using Pilot Symbols • Coherent detection over Rayleigh fading channels requires a pilot. • Pilot tone • TTIB: Transparent Tone in Band • 1984: McGeehan and Bateman • Pilot symbols • PSAM: Pilot Symbol Assisted Modulation • 1987: Lodge and Moher; 1991: Cavers • PSAM has been shown to be more power efficient than TTIB for turbo codes. • L.-D. Jeng, Y.-T. Su, and J.-T. Chiang, “Performance of turbo codes in multipath fading channels,” VTC 98.

12. Pilot Symbol Assisted Modulation (PSAM) • Pilot symbols: • 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 segment #2 symbol #1 symbol #M-1 symbol #1 symbol #M-1 pilot symbol pilot symbol symbol #1 symbol #M-1 symbol #1 symbol #M-1 pilot symbols added here

13. Pilot Symbol Assisted Decoding • 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. • Decision-directed estimation. • Optimal channel estimator uses Wiener filter. pilot symbols channel estimator matched filter Tentative estimates of the code bits channel interleaver pilot symbol insertion nonlinear function symbol demapper channel deinterl. turbo decoder Final estimates of the data

14. Hard vs. Soft-Decision Feedback • Hard-decision feedback • Valenti & Woerner • 1998 Electronics Letters, 1999 MILCOM • Soft-decision feedback • Sandell, Luschi, Strauch, Yan • 1998 Globecom (for convolutional coding & equalization)

15. Performance of Pilot Symbol Assisted Decoding 1 10 • Simulation parameters: • Rayleigh flat-fading • Correlated: fdTs = .005 • channel interleaving depth 50 • Turbo code • r=1/2, Kc =4 • 1250 S-Random interleaver • 12 iterations of log-MAP • Pilot symbol spacing: M= 21 • K = 61 channel estimator • Simple moving average. DSPK: no estimates PSAM: no feedback PSAM: hard-decision feedback 0 PSAM: soft-decision feedback 10 BPSK: perfect estimates -1 10 -2 10 BER -3 10 -4 10 -5 10 -6 10 1 2 3 4 5 6 7 8 9 10 Eb/No in dB

16. Performance in Faster Fading 1 10 • Simulation parameters: • Rayleigh flat-fading • Correlated: fdTs = .02 • channel interleaving depth 50 • Turbo code • r=1/2, Kc =4 • 1250 S-Random interleaver • 12 iterations of log-MAP • Pilot symbol spacing: M= 11 • Wiener filtering: K = 61 DSPK: no estimates PSAM: no feedback PSAM: hard-decision feedback 0 PSAM: soft-decision feedback 10 BPSK: perfect estimates -1 10 -2 10 BER -3 10 -4 10 -5 10 -6 10 1 2 3 4 5 6 7 8 9 10 Eb/No in dB

17. Performance Factors for Pilot Symbol Assisted Decoding • Performance is more sensitive to errors in estimates of the fading process than estimates in noise variance. • Pilot symbol spacing • Want symbols close enough to track the channel. • However, using pilot symbols reduces the energy available for the traffic bits. • Type of channel estimation filter • Wiener filter provides optimal solution. • However, for small fd, a moving average is acceptable. • Size of channel estimation filter • Window size of filter should contain about 4 pilot symbols.

18. Effect of Pilot Symbol Spacing • Simulation parameters: • Rayleigh flat-fading • Correlated: • Solid line fdTs = .005 • Dotted line fdTs = .005 • channel interleaving depth 50 • Turbo code • r=1/2, Kc =4 • 1250 S-Random interleaver • 12 iterations of log-MAP • Order K = 61 estimator • Moving average for slow fading • Wiener filter for fast fading • Eb/No = 4.5 dB

19. Future Work • Compare coherent PSAM technique with multiple-symbol DSPK technique. • In terms of performance and complexity. • Incorporate adaptability • 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 symbol-timing estimation and frame synchronization.

20. Conclusions • Pilot symbol assisted decoding can be used to achieve nearly coherent detection/decoding of turbo codes. • Iterative estimation/decoding improves performance. • Good performance even with just hard-decision feedback. • Iterative estimation can also be used for other types of codes.