  Switch-based hybrid network is a promising implementation for beamforming in
large-scale millimetre wave (mmWave) antenna arrays. By fully exploiting the
sparse nature of the mmWave channel, such hybrid beamforming reduces complexity
and power consumption when compared with a structure based on phase shifters.
However, the difficulty of designing an optimum beamformer in the analog domain
is prohibitive due to the binary nature of such a switch-based structure. Thus,
here we propose a new method for designing a switch-based hybrid beamformer for
massive MIMO communications in mmWave bands. We first propose a method for
decoupling the joint optimization of analog and digital beamformers by
confining the problem to a rank-constrained subspace. We then approximate the
solution through two approaches: norm maximization (SHD-NM), and majorization
(SHD-QRQU). In the norm maximization method, we propose a modified sequential
convex programming (SCP) procedure that maximizes the mutual information while
addressing the mismatch incurred from approximating the log-determinant by a
Frobenius norm. In the second method, we employ a lower bound on the mutual
information by QR factorization. We also introduce linear constraints in order
to include frequently-used partially-connected structures. Finally, we show the
feasibility, and effectiveness of the proposed methods through several
numerical examples. The results demonstrate ability of the proposed methods to
track closely the spectral efficiency provided by unconstrained optimal
beamformer and phase shifting hybrid beamformer, and outperform a competitor
switch-based hybrid beamformer.
