  This paper investigates the application of non-orthogonal multiple access
(NOMA) in millimeter wave (mmWave) communications by exploiting beamforming,
user scheduling and power allocation. Random beamforming is invoked for
reducing the feedback overhead of considered systems. A nonconvex optimization
problem for maximizing the sum rate is formulated, which is proved to be
NP-hard. The branch and bound (BB) approach is invoked to obtain the optimal
power allocation policy, which is proved to converge to a global optimal
solution. To elaborate further, low complexity suboptimal approach is developed
for striking a good computational complexity-optimality tradeoff, where
matching theory and successive convex approximation (SCA) techniques are
invoked for tackling the user scheduling and power allocation problems,
respectively. Simulation results reveal that: i) the proposed low complexity
solution achieves a near-optimal performance; and ii) the proposed mmWave NOMA
systems is capable of outperforming conventional mmWave orthogonal multiple
access (OMA) systems in terms of sum rate and the number of served users.
