Throughput maximization for the multiuser MIMO broadcast channel

We consider the problem of maximizing the throughput (sum rate) of the Gaussian MIMO broadcast channel under a sum power constraint. Assuming that decision feedback precoding is used at the transmitter, this is a concave optimization problem. A computationally efficient algorithm has been proposed (Jorswieck, E. and Boche, H., WPMC, 2002), which successively performs iterative waterfilling and power control. This strategy is based on uplink/downlink duality. We expand those results, by providing necessary and sufficient conditions for when this dedicated strategy achieves the optimal sum capacity. For the low SNR regime, it is shown that the capacity achieving strategy is single user transmission over the channel with the largest maximal eigenvalue. Furthermore, we illustrate, by numerical simulations, the properties of the sum capacity without precoding.