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
a brief overview of Sprite;
prior work that motivated our cache design;
the basic structure of the Sprite caches;

3. Outline (continued) Expectation Maximization algorithm
EM algorithm based detector
Performance comparison
Conclusions and future work
a brief overview of Sprite;
prior work that motivated our cache design;
the basic structure of the Sprite caches;

4. Environment
Multipath
Noise
MAI
Fading

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

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

7. Channel Modeling Requirements
Multipath environment
Independent paths
Rayleigh fast fading

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

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

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

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

12. Channel Modeling Characterization
Bandlimited approximation of H(, )
In our case

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

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

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

16. EM Algorithm Iterative 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 Scheme Complete Data
The log-likelihood function
Define complete data, y(t) = (y1(t), …, yK(t)), as

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

19. New Multiuser Detection Scheme Block Diagram
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 appropriate bk

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 Scheme Expectation 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