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

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

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

Introduction -- Rate region for 2 user MAC

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

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

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

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

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

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

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

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