  Hybrid beamforming (HBF) is an attractive technology for practical massive
multiple-input and multiple-output (MIMO) millimeter wave (mmWave) systems.
Compared with the fully-connected HBF architecture, the partially-connected one
can further reduce the hardware cost and power consumption. However, the
special block diagonal structure of its analog beamforming matrix brings
additional design challenges. In this paper, we develop effective HBF
algorithms for spectral efficiency maximization (SEM) in mmWave massive MIMO
systems with the partially-connected architecture. One main contribution is
that we prove the equivalence of the SEM problem and a matrix weighted sum mean
square error minimization (WMMSE) problem, which leads to a convenient
algorithmic approach to directly tackle the SEM problem. Specifically, we
decompose the equivalent WMMSE problem into the hybrid precoding and hybrid
combining subproblems, for which both the optimal digital precoder and combiner
have closed-form solutions. For the more challenging analog precoder and
combiner, we propose an element iteration based algorithm and a manifold
optimization based algorithm. Finally, the hybrid precoder and combiner are
alternatively updated. The overall HBF algorithms are proved to monotonously
increase the spectral efficiency and converge. Furthermore, we also propose
modified algorithms with reduced computational complexity and finite-resolution
phase shifters. Simulation results demonstrate that the proposed HBF algorithms
achieve significant performance gains over conventional algorithms.
