  This letter investigates the hybrid analog and digital beamforming (HBF)
design for multiuser millimeter wave (mmWave) communication systems based on
the minimum mean square error (MMSE) criterion. Using the alternating
minimization method, the hybrid precoder of the base station (BS) and the
hybrid combiners of the users are alternatively optimized. It is shown that
both the optimized digital precoder of the BS and the digital combiners of the
users have closed-form expressions, and their corresponding analog ones can be
efficiently obtained via generalized eigen-decomposition. Simulation results
show that the proposed MMSE HBF scheme has fast convergence and performs close
to the fully digital beamforming.
