Flow-Level Stability of Channel-Aware Scheduling Algorithms

Information-theoretic results show that multi-user multi-antenna systems provide potentially huge capacity gains. However, these results assume sophisticated coding techniques and perfect channel state information which may require a prohibitive amount of feedback. This has led to a search for practical transmission schemes and ways to reduce the amount of channel feedback 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 near-orthogonal users. In order to further quantify the latter observation, we study a Gaussian broadcast channel with two transmit antennas and K statistically identical users 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. In particular, we consider a scheme that picks the user with the largest channel gain, and selects a second user from the next L- 1 strongest ones to form the best pair, taking channel angles into account as well. We prove that the rate gap converges to 1/(L-1) when the total number of users K tends to infinity. Allowing L to increase with K, it may be deduced that transmitting to a properly chosen pair of users is asymptotically optimal, while dramatically reducing the feedback overhead and operational complexity. Numerical experiments show that the asymptotic results are remarkably accurate, even for a relatively moderate number of users.