Fairness maximization in multi-antenna broadcast channels using random beamforming

A Multi-Input Multi-Output (MIMO) Broadcast Channel (BC) with large number (n) of users is considered. It is assumed each user either receives the minimum rate constraint of R_min or remains silent. Accordingly, for the case of random beamforming, a user selection strategy together with a proper power allocation method is proposed, showing the maximum number of active users scales as ^{M ln(ln(n))}/R_min -θ(1) in the asymptotic case of n → ∞, where M represents the number of transmit antennas. Noting the asymptotic sum-rate of such channel is M ln(ln(n)), the proposed method is able to approach the asymptotic sum-rate capacity within a constant gap.