  Millimeter-wave communications is the most promising technology for
next-generation cellular wireless systems, thanks to the large bandwidth
available compared to sub-6 GHz networks. Nevertheless, communication at these
frequencies requires narrow beams via massive MIMO and beamforming to overcome
the strong signal attenuation, and thus precise beam-alignment between
transmitter and receiver is needed. The resulting signaling overhead may become
a severe impairment, especially in mobile networks with high users density.
Therefore, it is imperative to optimize the beam-alignment protocol to minimize
the signaling overhead. In this paper, the design of energy efficient joint
beam-alignment protocols for two users is addressed, with the goal to minimize
the power consumption during data transmission, subject to rate constraints for
both users, under analog beamforming constraints. It is proved that a bisection
search algorithm is optimal. Additionally, the optimal scheduling strategy of
the two users in the data communication phase is optimized based on the outcome
of beam-alignment, according to a time division multiplexing scheme. The
numerical results show significant decrease in the power consumption for the
proposed joint beam-alignment scheme compared to exhaustive search and a
single-user beam-alignment scheme taking place separately for each user.
