  In millimeter wave (mmWave) systems, antenna architecture limitations make it
difficult to apply conventional fully digital precoding techniques but call for
low cost analog radio-frequency (RF) and digital baseband hybrid precoding
methods. This paper investigates joint RF-baseband hybrid precoding for the
downlink of multiuser multi-antenna mmWave systems with a limited number of RF
chains. Two performance measures, maximizing the spectral efficiency and the
energy efficiency of the system, are considered. We propose a codebook based RF
precoding design and obtain the channel state information via a beam sweep
procedure. Via the codebook based design, the original system is transformed
into a virtual multiuser downlink system with the RF chain constraint.
Consequently, we are able to simplify the complicated hybrid precoding
optimization problems to joint codeword selection and precoder design (JWSPD)
problems. Then, we propose efficient methods to address the JWSPD problems and
jointly optimize the RF and baseband precoders under the two performance
measures. Finally, extensive numerical results are provided to validate the
effectiveness of the proposed hybrid precoders.
