A Closed Form Approximation of the Sum Rate of Random Beamforming with Multiple Codebooks and its Application to Control of the Number of Codebooks

In this letter, a closed form approximation of the sum rate of random beamforming with multiple codebooks is derived. It is also proved that signal to interference plus noise ratios (SINRs) over different codeboks are independently distributed on the contrast to existing belief on dependence of SINRs. Through numerical simulation, it is shown that the derived approximation is tightly matched to the actual sum rate, and control of the number of codebooks based on the closed form approximation achieves near optimal sum rate performance.