Multi-User Capacity Maximization for MIMO Gaussian Broadcast Channels

In this paper we consider the problem of maximizing the multi-user capacity of Gaussian multiple-input multiple-output (MIMO) broadcast channels (BC). This problem consists in finding the optimal users´ covariance matrices that maximize the multiuser capacity. These covariances represent, in the same time, the selection of users to transmit to, and their corresponding allocated power. To deal with this problem, many papers use iterative algorithms to provide the optimal solution. However, when the number of active users is high, these algorithms introduce a high order of complexity and suffer from memory drawback. Herein, we show that in a multi-user multi-antenna system, there exists a subset of active users that achieves a capacity close to the maximum, and that such iterative algorithms can be utilized considering a group of users instead of all active users. In addition, we present a new algorithm which makes a suboptimal selection of such group, referred to as the Best Group (BG). The proposed algorithm can be used jointly with any optimal power allocation algorithm in order to provide the covariances which maximize the multiuser capacity. Numerical results are provided and show that the BG selection is at least 5 times faster than other algorithms with a negligible reduction in the BC capacity.