Throughput maximization and optimal number of active users on the two transmit antenna downlink of a cellular system

This paper presents an analysis of the sum-capacity of the vector broadcast channel with two transmit antennas and K mobile users equipped with a single antenna. We derive the optimal power allocation on the dual sum-power multiple access channel. We show that in contrast to conventional water-filling, the number of users that are allocated power in order to maximize the mutual information can be a non-monotonic function of the total power for some channel realizations, and it can be larger than the number of transmit antennas. We give a geometrical interpretation of this phenomenon and we show simulation examples. We also show that despite the fact that more users than transmit antennas might need to be allocated with power in order to maximize the mutual information, constraining the number of active users to be no more than the number of transmit antennas incurs only a marginal loss in spectral efficiency both in terms of outage and ergodic capacity.