Outline

1. Transfer Chart Analysis of Iterative OFDM Receivers with Data Aided Channel EstimationStephan Sand, Christian Mensing, and Armin DammannGerman Aerospace Center (DLR)3rd COST 289 Workshop, Aveiro, Portugal, 12th July

2. Outline • System model • Frame structure • Channel estimation (CE) • Extrinisic information transfer (EXIT) Charts • Bit-error rate transfer (BERT) Charts • Comparison of BERT and EXIT charts • Simulation results • Conclusions & outlook

3. System Model: OFDM System with Iterative Receiver

4. Frame Structure • Burst transmission • Rectangular grid • Pilot distance in frequency direction: Nl=10 • Pilot distance between OFDM symbols: Nk=10

5. Channel Estimation (CE) • Initial iteration (i=0) only pilot symbols: • Pilot aided channel estimation (PACE) • Afterwards (i>0) additionally data estimates: • Pilot and data aided iterative channel estimation (ICE) • Localized estimates for the channel transfer function at pilot or data symbol positions, i.e., the least-squares (LS) estimate: • Replacing unknown Sn,l by the expectations (soft symbol and soft variance):

6. Channel Estimation (CE) • Filtering localized estimates yields final estimates of the complete CSI:where ωn’,l’,n,l,(i) is the shift-variant 2-D impulse response of the filter. Tn,l is the set of initial estimates that are actually used for filtering. • Filter design: • Knowledge of the Doppler and time delay power spectral densities (PSDs) optimal 2-D FIR Wiener filter • Separable Doppler and time delay PSDs two cascaded 1-D FIR Wiener filters perform similar than 2-D FIR Wiener filter

7. EXIT Charts • Benefits • Mutual information flow between inner and outer receiver • Independent computation for inner and outer receiver • Arbitrary combination of inner and outer receiver • Prediction of “turbo cliff“ position and BER possible • Assumptions • Log-likelihood ratio values (L-values): Gaussian distributed random variables • Interleaver depth large: uncorrelated L-values

8. EXIT Charts • A-priori L-values: independent Gaussian random variable • Probability density function of LA • A-priori mutual information monotonically increasing, reversible function of σA

9. EXIT Charts Steps for EXIT chart computation • Variance of a-priori L-values from a-priori information • A-priori L-value • Input a-priori L-value and simulated “channel”-value to component • Measure extrinsic information at output of component with histogram estimator

10. BERT Charts • Benefits • BER flow between inner and outer receiver • Independent computation for inner and outer receiver • Arbitrary combination of inner and outer receiver • Prediction of “turbo cliff“ position and BER possible • Assumptions • Log-likelihood ratio values (L-values): Gaussian distributed random variables • Interleaver depth large: uncorrelated L-values

11. BERT Chart • A-priori L-values: independent Gaussian random variable • Probability density function of LA • A-priori BER monotonically increasing, reversible of σA

12. BERT Charts Steps for BERT chart computation • Variance of a-priori L-values from a-priori BER • A-priori L-value • Input a-priori L-value and simulated “channel”-value to component • Measure extrinsic BER at output of component by hard decision

13. Comparison of EXIT and BERT Charts EXIT chart computation BERT chart computation • Variance of a-priori L-values • A-priori L-value • Input a-priori L-value and simulated “channel”-value to component • Measure extrinsic BER / information at output of component

14. Simulation Results: Scenario Exponential Channel model with Jakes’ Doppler fading … time

15. Simulation Results: AWGN Channel BERT Acronyms: • PCE: perfect channel estimation • DMOD: demodulator • DCOD: decoder

16. Simulation Results: AWGN Channel EXIT Acronyms: • PCE: perfect channel estimation • DMOD: demodulator • DCOD: decoder

17. Simulation Results: Exponential ChannelHistogram of L-valuesat demodulator output No Gaussian distribution of L-values

18. Simulation Results: Exponential Channel BERT Acronyms: • PCE: perfect channel estimation • ICE: iterative channel estimation • DMOD: demodulator • DCOD: decoder BERT: DCOD too pessimistic due to Gaussian assumption!

19. Simulation Results: Exponential Channel EXIT Acronyms: • PCE: perfect channel estimation • ICE: iterative channel estimation • DMOD: demodulator • DCOD: decoder ICE system trajectory dies out: independence assumption violated

20. Simulation Results: Exponential Channel BER Plot Acronyms: • PACE: pilot aided channel estimation • PCE: perfect channel estimation • ICE: iterative channel estimation • DMOD: demodulator • DCOD: decoder @ 7dB: ICE reaches PCE after 5 iterations

21. Conclusions & Outlook • Iterative receiver including pilot and data aided channel estimation • BERT and EXIT charts: • simpler computation of BERT charts • direct prediction of BERs in BERT charts • Simulation results indicate: • BERT charts too pessimistic due to Gaussian assumption of decoder • EXIT charts more robust against Gaussian assumption • ICE reaches PCE after a few iterations • Outlook: • A-posteriori feedback in ICE to improve convergence Thank you!