Fairness maximization and delay analysis for multi-antenna broadcast channels using random beamforming

A Multi-Input Multi-Output (MIMO) broadcast channel with large number (n) of users is considered. It is assumed each user either receives the minimum rate constraint of Rmin or remains silent. Accordingly, for the case of random beamforming, an user selection strategy together with a proper power allocation method is proposed, showing the maximum number of active users scales as Mlog(log(n))Rmin-θ(1) in the asymptotic case of n → ∞, where M   represents the number of transmit antennas. Noting the asymptotic sum-rate capacity of such channel is Mlog(log(n))Mlog(log(n)), the proposed method is able to approach the asymptotic sum-rate capacity within a constant gap. Moreover, it is shown the expected delay of this fair power allocation strategy behaves like RminMnlog(n)log(log(n))-θ(1)+ωnlog(log(n)), where the expected delay is defined as the minimum number of channel uses to make sure each user receives at least one packet. Accordingly, it is proved that for sufficiently large (k  ) number of channel uses, the average number of services received by a randomly selected user scales as kMlog(log(n))nRmin1+Olog(k)k.