  Millimeter-wave (mmWave) technology is one of the most promising candidates
for future wireless communication systems as it can offer large underutilized
bandwidths and eases the implementation of large antenna arrays which are
required to help overcome the severe signal attenuation that occurs at these
frequencies. To reduce the high cost and power consumption of a fully digital
mmWave precoder and combiner, hybrid analog/digital designs based on analog
phase shifters are often adopted. In this work we derive an iterative algorithm
for the hybrid precoding and combining design for spatial multiplexing in
mmWave massive multiple-input multiple-output (MIMO) systems. To cope with the
difficulty of handling the hardware constraint imposed by the analog phase
shifters we use the alternating direction method of the multipliers (ADMM) to
split the hybrid design problem into a sequence of smaller subproblems. This
results in an iterative algorithm where the design of the analog
precoder/combiner consists of a closed form solution followed by a simple
projection over the set of matrices with equal magnitude elements. It is
initially developed for the fully-connected structure and then extended to the
partially-connected architecture which allows simpler hardware implementation.
Furthermore, to cope with the more likely wideband scenarios where the channel
is frequency selective, we also extend the algorithm to an orthogonal frequency
division multiplexing (OFDM) based mmWave system. Simulation results in
different scenarios show that the proposed design algorithms are capable of
achieving performances close to the optimal fully digital solution and can work
with a broad range of configuration of antennas, RF chains and data streams.
