Efficient scheduling of multi-user multi-antenna systems

The capacity region of the Gaussian multi-antenna broadcast channel was characterized recently in [19]. It was shown that a scheme based on Dirty Paper Coding [2] achieves the full capacity region when the transmitter has perfect channel state information. However, this scheme potentially involves considerable amounts of feedback and complex algorithms for coding and user selection. This has led to a quest for practical transmission schemes and ways to reduce the amount of channel state information required. In particular, it has been shown that when the total number of users is large, the sum capacity can be closely approached by transmitting to a small subset of nearorthogonal users. In order to further quantify the latter observation, we study a Gaussian broadcast channel with two transmit antennas and K statistically identical, independent users each with a single receive antenna. We obtain an exact asymptotic characterization of the gap between the full sum capacity and the rate that can be achieved by transmitting to a suitably selected pair of users. Specifically, we consider various simple schemes for user-pair selection that take into account the channel norms as well as the relative orientation of the channel vectors. We conclude that a scheme that picks the strongest user and selects a second user to form the best pair, is asymptotically optimal, while also being attractive in terms of feedback and operational complexity. Numerical experiments show that the asymptotic results tend to be remarkably accurate, and that the proposed scheme significantly outperforms a beam-forming strategy for a typical number of users.