On Opportunistic Beamforming in Fast Fading Scenarios

We comment on the famous work GtOpportunistic beamforming using dumb antennasLt by P. Viswanath, D.N.C. Tse, and R. Laroia, from 2002. In that paper, it is argued that in an independent and fast fading environment, the opportunistic beamforming technique provides no performance gain. This assessment is based on the argument that the fading distribution of the equivalent channel, which is obtained through opportunistic beamforming, does not depend on the number of transmit antennas in independent and fast fading scenarios. In this paper, we show that this argument of the original work is based on a non-physical model of Rayleigh fading, and as a consequence, results in a wrong conclusion. In contrast, we show that there is beamforming gain to be obtained by the opportunistic beamforming technique even for independent and fast fading environments. For the case of uncoupled antennas, the amount of obtainable beamforming gain approaches - with probability one - the number of transmit antennas from below as the number of users approaches infinity.