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Hybrid beamforming (HBF) is an attractive technology for practical massivemultiple-input and multiple-output (MIMO) millimeter wave (mmWave) systems.Compared with the fully-connected HBF architecture, the partially-connected onecan further reduce the hardware cost and power consumption. However, thespecial block diagonal structure of its analog beamforming matrix bringsadditional design challenges. In this paper, we develop effective HBFalgorithms for spectral efficiency maximization (SEM) in mmWave massive MIMOsystems with the partially-connected architecture. One main contribution isthat we prove the equivalence of the SEM problem and a matrix weighted sum meansquare error minimization (WMMSE) problem, which leads to a convenientalgorithmic approach to directly tackle the SEM problem. Specifically, wedecompose the equivalent WMMSE problem into the hybrid precoding and hybridcombining subproblems, for which both the optimal digital precoder and combinerhave closed-form solutions. For the more challenging analog precoder andcombiner, we propose an element iteration based algorithm and a manifoldoptimization based algorithm. Finally, the hybrid precoder and combiner arealternatively updated. The overall HBF algorithms are proved to monotonouslyincrease the spectral efficiency and converge. Furthermore, we also proposemodified algorithms with reduced computational complexity and finite-resolutionphase shifters. Simulation results demonstrate that the proposed HBF algorithmsachieve significant performance gains over conventional algorithms.

Partially-Connected Hybrid Beamforming for Spectral Efficiency Maximization via a Weighted MMSE Equivalence