  In this paper, we investigate the combination of non-orthogonal multiple
access and millimeter-Wave communications (mmWave-NOMA). A downlink cellular
system is considered, where an analog phased array is equipped at both the base
station and users. A joint Tx-Rx beamforming and power allocation problem is
formulated to maximize the achievable sum rate (ASR) subject to a minimum rate
constraint for each user. As the problem is non-convex, we propose a
sub-optimal solution with three stages. In the first stage, the optimal power
allocation with a closed form is obtained for an arbitrary fixed Tx-Rx
beamforming. In the second stage, the optimal Rx beamforming with a closed form
is designed for an arbitrary fixed Tx beamforming. In the third stage, the
original problem is reduced to a Tx beamforming problem by using the previous
results, and a boundary-compressed particle swarm optimization (BC-PSO)
algorithm is proposed to obtain a sub-optimal solution. Extensive performance
evaluations are conducted to verify the rational of the proposed solution, and
the results show that the proposed sub-optimal solution can achieve a
near-upper-bound performance in terms of ASR, which is significantly improved
compared with those of the state-of-the-art schemes and the conventional mmWave
orthogonal multiple access (mmWave-OMA) system.
