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With the severe spectrum shortage in conventional cellular bands, large-scale antenna systems in the mmWave bands can potentially help to meet the anticipated demands of mobile traffic in the 5G era. There are many challenging issues, however, regarding the implementation of digital beamforming in large-scale antenna systems: complexity, energy consumption, and cost. In a practical large-scale antenna deployment, hybrid analog and digital beamforming structures can be important alternative choices. In this article, optimal designs of hybrid beamforming structures are investigated, with the focus on an N (the number of transceivers) by M (the number of active antennas per transceiver) hybrid beamforming structure. Optimal analog and digital beamforming designs in a multi-user beamforming scenario are discussed. Also, the energy efficiency and spectrum efficiency of the N × M beamforming structure are …