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

2. 2 Ger man Aerospace Center 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. 3 Ger man Aerospace Center System Model: OFDM System with Iterative Receiver

4. 4 Ger man Aerospace Center Frame Structure Burst transmission Rectangular grid Pilot distance in frequency direction: N l =10 Pilot distance between OFDM symbols: N k =10

5. 5 Ger man Aerospace Center 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 S n,l by the expectations (soft symbol and soft variance):

6. 6 Ger man Aerospace Center Channel Estimation (CE) Filtering localized estimates yields final estimates of the complete CSI: where ω n’,l’,n,l,(i) is the shift-variant 2-D impulse response of the filter. T n,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. 7 Ger man Aerospace Center 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. 8 Ger man Aerospace Center EXIT Charts A-priori L-values: independent Gaussian random variable Probability density function of L A A-priori mutual information monotonically increasing, reversible function of σ A

9. 9 Ger man Aerospace Center EXIT Charts Steps for EXIT chart computation 1. Variance of a-priori L-values from a-priori information 2. A-priori L-value 3. Input a-priori L-value and simulated “channel”-value to component 4. Measure extrinsic information at output of component with histogram estimator

10. 10 Ger man Aerospace Center 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. 11 Ger man Aerospace Center BERT Chart A-priori L-values: independent Gaussian random variable Probability density function of L A A-priori BER monotonically increasing, reversible of σ A

12. 12 Ger man Aerospace Center BERT Charts Steps for BERT chart computation 1. Variance of a-priori L-values from a-priori BER 2. A-priori L-value 3. Input a-priori L-value and simulated “channel”-value to component 4. Measure extrinsic BER at output of component by hard decision

13. 13 Ger man Aerospace Center Comparison of EXIT and BERT Charts BERT chart computation 1. Variance of a-priori L-values 2. A-priori L-value 3. Input a-priori L-value and simulated “channel”-value to component 4. Measure extrinsic BER / information at output of component EXIT chart computation

14. 14 Ger man Aerospace Center Simulation Results: Scenario Bandwidth4.004 MHz Subcarriers1001 FFT length1024 Sampling duration T spl 3.1 ns Guard interval T GI 205 T spl Subcarrier spacing Δf4 kHz OFDM symbols / Frame101 ModulationQPSK, linear mapping CodingConv. code, R=1/2, (23,37) Information bits99986 Interleaver length199980 Interleaver typerandom Pilot spacing frequency10 Pilot spacing time10 f D,max 0.025Δf ≈ 100 Hz τ max 20 μs τ rms 0.001 τ max time … Exponential Channel model with Jakes’ Doppler fading

15. 15 Ger man Aerospace Center Simulation Results: AWGN Channel BERT Acronyms: PCE: perfect channel estimation DMOD: demodulator DCOD: decoder

16. 16 Ger man Aerospace Center Simulation Results: AWGN Channel EXIT Acronyms: PCE: perfect channel estimation DMOD: demodulator DCOD: decoder

17. 17 Ger man Aerospace Center Simulation Results: Exponential Channel Histogram of L-values at demodulator output No Gaussian distribution of L-values

18. 18 Ger man Aerospace Center 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. 19 Ger man Aerospace Center 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. 20 Ger man Aerospace Center 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. 21 Ger man Aerospace Center 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!