  The integration of non-orthogonal multiple access in millimeter-Wave
communications (mmWave-NOMA) can significantly improve the spectrum efficiency
and increase the number of users in the fifth-generation (5G) mobile
communication. In this paper we consider a downlink mmWave-NOMA cellular
system, where the base station is mounted with an analog beamforming phased
array, and multiple users are served in the same time-frequency resource block.
To guarantee user fairness, we formulate a joint beamforming and power
allocation problem to maximize the minimal achievable rate among the users,
i.e., we adopt the max-min fairness. As the problem is difficult to solve due
to the non-convex formulation and high dimension of the optimization variables,
we propose a sub-optimal solution, which makes use of the spatial sparsity in
the angle domain of the mmWave channel. In the solution, the closed-form
optimal power allocation is obtained first, which reduces the joint
optimization problem into an equivalent beamforming problem. Then an
appropriate beamforming vector is designed. Simulation results show that the
proposed solution can achieve a near-upper-bound performance in terms of
achievable rate, which is significantly better than that of the conventional
mmWave orthogonal multiple access (mmWave-OMA) system.
