Iterative Water-Filling for Gaussian Vector Multiple Access Channels

W. Yu, W. Rhee, S. Boyd, and J. Cioffi

IEEE Transactions on Information Theory, 50(1):145-151, January 2004.
Short version appeared in Proceedings IEEE Symposium on Information Theory, Washington DC, June 2001, pages 322-322.

We develop an efficient iterative water-filling algorithm to find an optimal transmit spectrum for maximum sum capacity in a Gaussian multiple access channel with vector inputs and a vector output. The iterative algorithm converges from any starting point and reaches within (K-1)/2 nats per output dimension from the K-user sum capacity after just one iteration.