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Switch-based hybrid network is a promising implementation for beamforming inlarge-scale millimetre wave (mmWave) antenna arrays. By fully exploiting thesparse nature of the mmWave channel, such hybrid beamforming reduces complexityand power consumption when compared with a structure based on phase shifters.However, the difficulty of designing an optimum beamformer in the analog domainis 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 formassive MIMO communications in mmWave bands. We first propose a method fordecoupling the joint optimization of analog and digital beamformers byconfining the problem to a rank-constrained subspace. We then approximate thesolution through two approaches: norm maximization (SHD-NM), and majorization(SHD-QRQU). In the norm maximization method, we propose a modified sequentialconvex programming (SCP) procedure that maximizes the mutual information whileaddressing the mismatch incurred from approximating the log-determinant by aFrobenius norm. In the second method, we employ a lower bound on the mutualinformation by QR factorization. We also introduce linear constraints in orderto include frequently-used partially-connected structures. Finally, we show thefeasibility, and effectiveness of the proposed methods through severalnumerical examples. The results demonstrate ability of the proposed methods totrack closely the spectral efficiency provided by unconstrained optimalbeamformer and phase shifting hybrid beamformer, and outperform a competitorswitch-based hybrid beamformer.

Switch-based Hybrid Beamforming for Massive MIMO Communications in mmWave Bands