Outage and Diversity Analysis of Opportunistic Beamforming over Rayleigh Channels

In a multiuser system, the multiuser diversity gain capitalizes primarily on the dynamic range of channel fluctuations. When the channel varies slowly, opportunistic beamforming using multiple antennas at the transmitter can be used to generate artificial temporal fading resulting in amplified multiuser diversity gain. When there exists a sufficient number of users in the system, opportunistic beamforming has been shown to achieve similar throughput as true beamforming but with much more limited feedback. In particular, it has been shown that the required number of users to achieve near true beamforming throughput on the number of transmit antennas is exponential when each user is equipped with single antenna. In this paper, a framework is presented to analyze the outage probability, diversity order and array gain of opportunistic beamforming over Rayleigh fading channels. First, we obtain an exact closed-form expression for the outage probability. Then, using some approximations, we show that the number of users must be at least the same as the number of transmit antennas in order to achieve full diversity. We quantify the array gain for the full diversity case and establish the dependence of the array gain on the number of users. Finally, we verify our analysis with numerical results.