Efficient scheduling of multi-user multi-antenna systems

capacity region of Gaussian multi-antenna broadcast channel was characterized recently in [19]. It was shown that a scheme based on Dirty Paper Coding [2] achieves full capacity region when 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 amount of channel state information required. In particular, it has been shown that when total number of users is large, sum capacity can be closely approached by transmitting to a small subset of near-orthogonal users. In order to further quantify 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 gap between full sum capacity and 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 channel norms as well as relative orientation of channel vectors. We conclude that a scheme that picks strongest user and selects a second user to form best pair, is asymptotically optimal, while also being attractive in terms of feedback and operational complexity.