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.
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