1 / 37

Recent Advances in Iterative Parameter Estimation

Recent Advances in Iterative Parameter Estimation. Cédric Herzet and Luc Vandendorpe Université catholique de Louvain, Belgium. Most estimators rely on the maximum-likelihood criterion. Unbiased Estimation mean is equal to the actual parameter Efficient

larya
Download Presentation

Recent Advances in Iterative Parameter Estimation

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Recent Advances in Iterative Parameter Estimation Cédric Herzet and Luc Vandendorpe Université catholique de Louvain, Belgium

  2. Most estimators rely on the maximum-likelihood criterion Unbiased Estimation mean is equal to the actual parameter Efficient It reaches the smallest mean square error

  3. Classical estimators operate in non-data-aided (NDA) mode Suboptimal if the sequence is coded All sequences are assumed equiprobable

  4. BER for BICM transmission with phase estimation NDA The estimation quality leads to BER degradation Perf. Sync

  5. We resort to the iterative methods to solve the ML problem Good performance We expect the method to converge to the ML solution Low complexity Each iteration must have a low computational load

  6. The EM algorithm enables an efficient search of the ML solution It is robust Converges under mild conditions to the ML solution It might converge slowly Depends on the quantity of missing information Easy to maximize

  7. BER for BICM transmission with phase estimation NDA Perf. Sync

  8. BER for BICM transmission with phase estimation NDA EM Perf. Sync

  9. BER for BICM transmission with phase estimation NDA EM Increase the number of iterations required to achieve converge Perf. Sync

  10. Synchronization based on the factor graph framework

  11. We apply the SP algorithm to the ML estimation problem The likelihood function may be viewed as the marginal of this probability

  12. The considered factor graph has two main parts Only depends on synchronization parameters Synchronization Only depends on transmitted symbols Symbol detection

  13. Symbol detection part transmits symbol extrinsic probabilities Synchronization Symbol extrinsic probabilities (= turbo receiver, BCJR decoder…) Symbol detection

  14. The synchronization part transmits a modified likelihood function Synchronization Modified likelihood function Symbol detection

  15. The extrinsic probabilities are used as a priori information Transmitted message : where extrinsic probability (from detection part)

  16. The synchronization message is approximated by a delta function We compute a « well-chosen » point of the likelihood function Synchronization Parameter estimate Symbol detection

  17. We solve a ML problemat each SP iteration Easier to compute due to the particular factorization of the a priori information:

  18. BER for BICM transmission with phase estimation NDA EM Perf. Sync

  19. BER for BICM transmission with phase estimation NDA Do not increase significantly the receiver complexity EM SP Perf. Sync

  20. The EM approach drops some information about the parameter maximized by the SP approach maximized by the EM approach

  21. Theoretical lower bounds for soft synchronizer performance

  22. Soft synchronizers consider a modified statistical model The symbol a priori knowledge is assumed to come from a soft information vector e

  23. We can compute the CRB related to the modified statistical model CRB related to the observation of a particular vector e

  24. We derive a lower bound valid for a soft information distribution Soft Modified Cramer-Rao Bound: easy to compute in practice…

  25. MSE for BICM transmission with phase estimation The soft synchronizers can reach the MCRB after only a few iterations… SMCRB MCRB

  26. MSE for BICM transmission with phase estimation NDA Do not take the code structure into account ! SMCRB MCRB

  27. MSE for BICM transmission with phase estimation NDA Do not take fully benefit from the available soft information EM MCRB

  28. MSE for BICM transmission with phase estimation NDA The SP approach enables to operate very close to the SMCRB SP EM MCRB

  29. Semi-analytical performance analysis of turbo-equalization schemes

  30. The considered receiver is made up with three blocks Turbo equalizer Received samples BER MAP decoder Channel estimator MMSE/IC equalizer Assumptions : BPSK, one user

  31. We want to calculate the equalizer outputs as functions of the inputs MMSE/IC equalizer Goal : find analytical expressions of functions f1 and f2

  32. Variance of LLR at equalizer output vs.estimation error variance 4 dB 5-tap Porat channel Calculations fit simulations very well simulations calculations

  33. The MAP decoder behavior is simulated MAP decoder f is simulated Finally, the BER may be expressed as a function of the equalizer inputs, notably the estimation error variance

  34. BER vs. estimation error variance The BER degradation is accurately predicted by calculations 4 dB 5-tap Porat channel simulations calculations

  35. Cooperations andprospective researches • Any problems related to parameter estimation: • Channel estimation • Time-varying parameters • … • Receiver design based on factor graphs • Analytical performance analysis (BER, CRB,…)

  36. Thank you for your attention !

  37. BER for BICM transmission

More Related