Sum power iterative water-filling for multi-antenna Gaussian broadcast channels

We consider the problem of maximizing sum rate on a multiple-antenna downlink in which the base station and receivers have multiple-antennas. The optimum scheme for this system was recently found to be "dirty paper coding". Obtaining the optimal transmission policies of the users when employing this dirty paper coding scheme is a computationally complex nonconvex problem. We use a "duality" to transform this problem into a convex multiple access problem, and then obtain a simple and fast iterative algorithm that gives us the optimum transmission policies.