Accurate Approximations and Asymptotic Results for the Sum-Rate of Random Beamforming for Multi-Antenna Gaussian Broadcast Channels

In this paper, we first present a new closed form approximation for the sum-rate of random beamforming. A generic curve fitting procedure is developed to make this approximation accurate for arbitrary signal-to-noise ratios (SNRs) and number of transmit antennas. Our analytical approach leads also to simple asymptotic formulas for high SNR or large number of antennas. Selected numerical results show that our proposed approximation leads to results that come very close to the exact sum-rate and that our asymptotic formulas converge to the exact values when the SNR or the number of antennas tend to high values.