Recently, user selection algorithms in combination with linear precoding have been proposed that achieve the same scaling as the sum capacity of the MIMO broadcast channel. Robust opportunistic beamforming, which only requires partial channel state information for user selection, further reduces feedback requirements. In this work, we study the optimality of the opportunistic norm-based user selection system in conjunction with hard SINR requirements under max-min fair beamforming transmit power minimization. It is shown that opportunistic norm-based user selection is asymptotically optimal, as the number of transmit antennas goes to infinity when only two users are selected in high SNR regime. The asymptotic performance of opportunistic norm-based user selection is also studied when the number of users goes to infinity. When a limited number of transmit antennas and/or median range of users are available, only insignificant performance degradation is observed in simulations with an ideal channel model or based on measurement data.
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