  While mmWave bands provide a large bandwidth for mobile broadband services,
they suffer from severe path loss and shadowing. Multiple-antenna techniques
such as beamforming (BF) can be applied to compensate the signal attenuation.
We consider a special case of hybrid BF called per-stream hybrid BF (PSHBF)
which is easier to implement than the general hybrid BF because it circumvents
the need for joint analog-digital beamformer optimization. Employing BF at the
base station enables the transmission of multiple data streams to several users
in the same resource block. In this paper, we provide an offline study of
proportional fair multi-user scheduling in a mmWave system with PSHBF to
understand the impact of various system parameters on the performance. We
formulate multi-user scheduling as an optimization problem. To tackle the
non-convexity, we provide a feasible solution and show through numerical
examples that the performance of the provided solution is very close to an
upper-bound. Using this framework, we provide extensive numerical
investigations revealing several engineering insights.
