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This paper designs a novel hybrid (a mixture of analog and digital) beamforming and examines the relation between the hybrid and digital beamformings for downlink multiuser massive multiple input multiple output (MIMO) systems. We assume that perfect channel state information is available only at the transmitter and we consider the total sum rate maximization problem. For this problem, the hybrid beamforming is designed indirectly by considering a weighed sum mean square error (WSMSE) minimization problem incorporating the solution of digital beamforming which is obtained from the block diagonalization technique. The resulting WSMSE problem is solved by applying the theory of compressed sensing. The relation between the hybrid and digital beamformings is studied numerically by varying different parameters, such as the number of radio frequency (RF) chains, analog to digital converters (ADCs) and multiplexed symbols. Computer simulations reveal that for the given number of RF chains and ADCs, the performance gap between digital and hybrid beamformings can be decreased by decreasing the number of multiplexed symbols. Moreover, for the given number of multiplexed symbols, increasing the number of RF chains and ADCs will increase the total sum rate of the hybrid beamforming which is expected.

Beamforming for multiuser massive MIMO systems: Digital versus hybrid analog-digital