  This paper proposes an asymptotically optimal hybrid beamforming solution for
large antenna arrays by exploiting the properties of the singular vectors of
the channel matrix. It is shown that the elements of the channel matrix with
Rayleigh fading follow a normal distribution when large antenna arrays are
employed. The proposed beamforming algorithm is effective in both sparse and
rich propagation environments, and is applicable for both point-to-point and
multiuser scenarios. In addition, a closed-form expression and a lower-bound
for the achievable rates are derived when analog and digital phase shifters are
employed. It is shown that the performance of the hybrid beamformers using
phase shifters with more than 2-bits resolution is comparable with analog phase
shifting. A novel phase shifter selection scheme that reduces the power
consumption at the phase shifter network is proposed when the wireless channel
is modeled by Rayleigh fading. Using this selection scheme, the spectral
efficiency can be increased as the power consumption in the phase shifter
network reduces. Compared to the scenario that all of the phase shifters are in
operation, the simulation results indicate that the spectral efficiency
increases when up to 50% of phase shifters are turned off.
