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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. Outline. System model Frame structure Channel estimation (CE)

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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

outline
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
frame structure
Frame Structure
  • Burst transmission
  • Rectangular grid
    • Pilot distance in frequency direction: Nl=10
    • Pilot distance between OFDM symbols: Nk=10
channel estimation ce
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):
channel estimation ce1
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
exit charts
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
exit charts1
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
exit charts2
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
bert charts
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
bert chart
BERT Chart
  • A-priori L-values: independent Gaussian random variable
  • Probability density function of LA
  • A-priori BER monotonically increasing, reversible of σA
bert charts1
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
comparison of exit and bert charts
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
simulation results scenario
Simulation Results: Scenario

Exponential Channel model with Jakes’ Doppler fading

time

simulation results awgn channel bert
Simulation Results: AWGN Channel BERT

Acronyms:

  • PCE: perfect channel estimation
  • DMOD: demodulator
  • DCOD: decoder
simulation results awgn channel exit
Simulation Results: AWGN Channel EXIT

Acronyms:

  • PCE: perfect channel estimation
  • DMOD: demodulator
  • DCOD: decoder
simulation results exponential channel histogram of l values at demodulator output
Simulation Results: Exponential ChannelHistogram of L-valuesat demodulator output

No Gaussian

distribution of

L-values

simulation results exponential channel bert
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!

simulation results exponential channel exit
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

simulation results exponential channel ber plot
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

conclusions outlook
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!