  Hybrid precoding is a cost-effective approach to support directional
transmissions for millimeter wave (mmWave) communications. While existing works
on hybrid precoding mainly focus on single-user single-carrier transmission, in
practice multicarrier transmission is needed to combat the much increased
bandwidth, and multiuser MIMO can provide additional spatial multiplexing
gains. In this paper, we propose a new hybrid precoding structure for multiuser
OFDM mmWave systems, which greatly simplifies the hybrid precoder design and is
able to approach the performance of the fully digital precoder. In particular,
two groups of phase shifters are combined to map the signals from radio
frequency (RF) chains to antennas. Then an effective hybrid precoding algorithm
based on alternating minimization (AltMin) is proposed, which will alternately
optimize the digital and analog precoders. A major algorithmic innovation is a
LASSO formulation for the analog precoder, which yields computationally
efficient algorithms. Simulation results will show the performance gain of the
proposed algorithm. Moreover, it will reveal that canceling the interuser
interference is critical in multiuser OFDM hybrid precoding systems.
