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

•Switch-based hybrid networks provide a promising implementation for beamforming•Binary nature of the switch-based structure hinders design of analog beamformer•Decoupling and optimizing in a rank-constrained subspace is an effective method•Frobenius norm and QR lower bound can be used as effective surrogate cost functions•Any partially network can be designed by imposing suitable linear constraints Switch-based hybrid networks provide a promising implementation for beamforming in large-scale millimeter wave (mmWave) antenna arrays by reducing both complexity and power consumption. However, the design of the optimum beamformer in the analog domain is a difficult task due to the binary nature of the switch-based structure. In this work, we tackle this problem, proposing a new approach that decouples the joint optimization of the analog and digital beamformer and confines the problem to a rank-constrained subspace to give an approximate solution. We then describe two algorithms for solving the resulting optimization: the first employs norm maximization and the second utilizes majorization. In the norm maximization method, we present a modified sequential convex programming procedure that maximizes the mutual information while addressing the mismatch incurred from approximating the log-determinant by a Frobenius norm. The second method employs a lower bound on the mutual information by QR factorization. Furthermore, unlike previous approaches, we introduce a general strategy for dealing with partially-connected structures using linear constraints. We verify the effectiveness of the proposed methods through several numerical examples and show that they closely track the spectral efficiency provided by the unconstrained optimal beamformer while outperforming the switch-based design by unified greedy algorithm.