  Non-orthogonal multiple access (NOMA) and millimeter wave (mmWave) are two
key enabling technologies for the fifth-generation (5G) mobile networks and
beyond. In this paper, we consider mmWave NOMA systems with max-min fairness
constraints. On the one hand, existing beamforming designs aiming at maximizing
the spectrum efficiency (SE) are unsuitable for the NOMA systems with fairness
in this paper. On the other hand, previous work on about mmWave NOMA mostly
depends on full knowledge of channel state information (CSI) which is extremely
difficult to obtain accurately in mmWave communication systems. To address this
problem, we propose a heuristic hybrid beamforming design based on the
statistical CSI (SCSI) user grouping strategy. An analog beamforming scheme is
first proposed to integrate the whole cluster users to mitigate the
inter-cluster interference in the first stage. Then two digital beamforming
designs are proposed to further suppress the interference based on SCSI. One is
the widely used zero forcing (ZF) approach and the other is derived from the
signal-to leakage-plus-noise ratio (SLNR) metric extended from orthogonal
multiple access (OMA) systems. The effective gains fed back from the users are
used for the power allocation. We introduce the quadratic transform (QT) method
and bisection approach to reformulate this complex problem so as to rend it
solvable. Simulation results show that our proposed algorithms outperform the
previous algorithms in term of user fairness.
