The transmit beamforming for millimeter wave systems has become a promising strategy to achieve higher spectral efficiency. The beamforming design for such systems stems out from various network optimization criterions that strike a balance between quality of service and energy/cost incurred to the system. We offer a simple and comprehensive solution to one of such key network optimization problems, namely transmit power minimization in multi-user millimeter wave system constrained on users' desired quality of service. The minimum transmit power beamforming vector is designed via hybrid analog and digital precoder that satisfies the practical hardware constraints. The crux of simplicity of the proposed algorithm lies in the fact that the analog beamforming could be solved via equal gain transmission method and the digital beamforming via zero forcing and Perron-Frobenius theorem. We also present simulation results of the proposed algorithms illustrating the performance gain comparable to computationally expensive fully digital and unconstrained beamforming algorithms.
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