Beam Selection Gain from Butler Matrices

We consider a wireless transmission scenario, when a base station is endowed with a fixed beamforming network, where M antennas are employed at the base station to point beams to predetermined azimuthal angles. In our setting, a Butler matrix is deployed at the RF stage to form M beams, and then the best beam is selected for transmission. We derive the distribution of the beam selection gain for this scenario under a Rician channel assumption as a function of both the azimuthal location of the remote unit and the Rician A'-factor. Using some key properties of the noncentral chi-square distribution, we prove that beam selection outperforms antenna selection.