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EM based Multiuser detection in Fading Multipath Environments

EM based Multiuser detection in Fading Multipath Environments. Mohammad Jaber Borran, Željko  akareski, Ahmad Khoshnevis, and Vishwas Sundaramurthy. Outline. Motivation Time-frequency representation Channel modeling. Outline (continued). Expectation Maximization algorithm

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EM based Multiuser detection in Fading Multipath Environments

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  1. EM based Multiuser detection in Fading Multipath Environments Mohammad Jaber Borran, Željko akareski, Ahmad Khoshnevis, and Vishwas Sundaramurthy

  2. Outline • Motivation • Time-frequency representation • Channel modeling

  3. Outline(continued) • Expectation Maximization algorithm • EM algorithm based detector • Performance comparison • Conclusions and future work

  4. Multipath • Fading • MAI Environment • Noise

  5. Time-Frequency RepresentationWhat is TFR? • A 2-D signal representation • Facilitates signaling by exploiting multipath and Doppler • Identifies Doppler as another dimension for diversity

  6. Tc M 1/T t Doppler -M Multipath Canonical Coordinates Canonical basis corresponding to the uniform grid L

  7. Channel ModelingRequirements • Multipath environment • Independent paths • Rayleigh fast fading

  8. Channel ModelingOur approach • Jakes’ model for individual paths • Independence assured by having: Spacing >> Tcoh ( ~ ) • Random delays for different multipath components • Canonical representation

  9. Channel ModelingCharacterization • Linear time-varying system n(t) s(t) x(t) r(t) + h(t, ) • Represented by its impulse response h(t, )

  10. Incorporate the canonical model into h(t, ) Channel ModelingCharacterization • The output r(t) determined as :

  11. Channel ModelingCharacterization • Spreading function H(, ) • Canonical finite-dimensional representation : where

  12. In our case Channel ModelingCharacterization • Bandlimited approximation of H(, )

  13. Channel ModelingCharacterization where Ei(t) : Jakes’ model rep. for path i

  14. EM AlgorithmIntroduction • Goal: • K-dim problem, direct approach is difficult. • Define complete data, i.e. y, such that

  15. EM AlgorithmIntroduction (cnt’d) and • Since y is unavailable, • b is unknown,

  16. EM AlgorithmIterative Nature, Decomposition • Provides an iterative method for ML estimation: • E step: Compute U(b,b(n)) • M step: • K 1-dim problems (with suitable complete data) • The value of b(0) is important.

  17. New Multiuser Detection SchemeComplete Data • The log-likelihood function • Define complete data, y(t) = (y1(t), …, yK(t)), as

  18. New Multiuser Detection SchemeIterative Expression, Special Cases • Defining • Assuming • bk=1  Multistage • bk=0  Time-Frequency RAKE receiver

  19. New Multiuser Detection SchemeBlock Diagram b(0) b(1) b(n-1) b(n) ... sgn I-b sgn I-b sgn + + b b ... TF RAKE + MRC MAI Estimation & Cancellation MAI Estimation & Cancellation ... r(t) HHz

  20. Simulation Results(3 paths, Bd=100Hz, 5 users, User 4)

  21. Simulation Results(3 paths, Bd=100Hz, 5 users, User 3)

  22. Conclusion • Canonical representation + EM algorithm  New Detector for Fast Fading Multipath Env. • Two special cases: TF RAKE and MultiStage • Outperforms TF RAKE and MultiStage • For rapid convergence use appropriatebk

  23. Future work • Theoretical error probability analysis • Near-Far resistance analysis • Optimum value for bk • Extension to asynchronous case

  24. That’s all Folks!

  25. Signal model Cross correlation matrix where

  26. New Multiuser Detection SchemeExpectation Calculation Step • The new log-likelihood function • It can be shown that

  27. Canonical RAKE • The coordinates for each symbol of a particular user are computed by:

  28. Simulation Results(3 paths, Bd=100Hz, 5 users, User 1)

  29. Simulation Results(3 paths, Bd=100Hz, 5 users, User 2)

  30. Simulation Results(3 paths, Bd=100Hz, 5 users, User 5)

  31. Simulation Results(3 paths, Bd=200Hz, 5 users, User 1)

  32. Simulation Results(3 paths, Bd=200Hz, 5 users, User 2)

  33. Simulation Results(3 paths, Bd=200Hz, 5 users, User 3)

  34. Simulation Results(3 paths, Bd=200Hz, 5 users, User 4)

  35. Simulation Results(3 paths, Bd=200Hz, 5 users, User 5)

  36. Channel Modeling Visualization of

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