  Millimeter wave (mmWave) systems will likely employ large antenna arrays at
both the transmitters and receivers. A natural application of antenna arrays is
simultaneous transmission to multiple users, which requires multi-user
precoding at the transmitter. Hardware constraints, however, make it difficult
to apply conventional lower frequency MIMO precoding techniques at mmWave. This
paper proposes and analyzes a low complexity hybrid analog/digital beamforming
algorithm for downlink multi-user mmWave systems. Hybrid precoding involves a
combination of analog and digital processing that is motivated by the
requirement to reduce the power consumption of the complete radio frequency and
mixed signal hardware. The proposed algorithm configures hybrid precoders at
the transmitter and analog combiners at multiple receivers with a small
training and feedback overhead. For this algorithm, we derive a lower bound on
the achievable rate for the case of single-path channels, show its asymptotic
optimality at large numbers of antennas, and make useful insights for more
general cases. Simulation results show that the proposed algorithm offers
higher sum rates compared with analog-only beamforming, and approaches the
performance of the unconstrained digital precoding solutions.
