  As a key enabling technology for 5G wireless, millimeter wave (mmWave)
communication motivates the utilization of large-scale antenna arrays for
achieving highly directional beamforming. However, the high cost and power
consumption of RF chains stands in the way of adoption of the optimal
fullydigital precoding in large-array systems. To reduce the number of RF
chains while still maintaining the spatial multiplexing gain of large-array,
hybrid precoding architecture has been proposed for mmWave systems and received
considerable interest in both industry and academia. However, the optimal
hybrid precoding design has not been fully understood, especially for the
multi-user MIMO case. This paper is the first work that directly addresses the
nonconvex hybrid precoding problem of mmWave multi-user MIMO systems (without
any approximation) by using penalty dual decomposition (PDD) method. The
proposed PDD method have a guaranteed convergence to KKT solutions of the
hybrid precoding problem under a mild assumption. Simulation results show that,
even when both the transmitter and the receivers are equipped with the fewest
RF chains that are required to support multi-stream transmission, hybrid
precoding can still approach the performance of fully-digital precoding in both
the infinite resolution phase shifter case and the finite resolution phase
shifter case with several bits quantization.
