An iterative water-filling algorithm for maximum weighted sum-rate of Gaussian MIMO-BC

We consider the maximization of weighted rate sum in Gaussian multiple-input-multiple-output broadcast channels. This problem is motivated by optimal adaptive resource allocation policies in wireless systems with multiple antenna at the base station. In fact, under random packet arrival and transmission queues, the system stability region is achieved by maximizing a weighted rate sum with suitable weights that depend on the queue buffer sizes. Our algorithm is a generalization of the well-known Iterative Multiuser Water-Filling that maximizes the rate sum under a total transmit power constraint and inherits from the latter its simplicity. We propose also a variation on the basic algorithm that makes convergence speed very fast and essentially independent of the number of users