1. Iterative Water-filling for Gaussian Vector Multiple Access Channel
Wei Yu, Wonjong Rhee, Stephen Boyd and John M. Cioffi
IEEE Trans. Inform., 2002
Presenters: Xingkai Bao and Zhenlei Shen

2. Outline Introduction Optimization for Sum Capacity
Multiple Access Channel
Rate region for 2 user MAC
goal
Optimization for Sum Capacity
Singer-user Water-filling
Multi-user Water-filling
Iterative Water-filling
Conclusion

3. Introduction -- Multiple Access Channel
Multiple uncoordinated transmitters send independent information to a common receiver

4. Introduction -- Rate region for 2 user MAC

5. Introduction -- Rate region for 2 user MAC
Constraint
Total power
Changing
Pentagon
Hull
Convex
Intersection
Water filling

6. Introduction --Goal
Find a numerical algorithm that can be used to efficiently compute the sum capacity achieving input distribution for a Gaussian vector multiple access channel

7. Optimization for sum capacity --Single-user water-filling
Solve
where
Orthogonal matrix

8. Optimization for sum capacity --Single-user water-filling
Step 1:
We can rewrite the problem as

9. Optimization for sum capacity --Single-user water-filling
Step 2:

10. Optimization for sum capacity --Single-user water-filling
Results

11. Optimization for sum capacity --Multi-user water-filling
Solve
where is the covariance matrix of the i’th user
Result

12. Thank you Welcome Zhenlei to present
The numerical algorithm of iterative waterfilling