This paper proposed new hybrid, analog-digital, beamforming for a multiusermillimeter wave (mm-wave) relay system. For this system, we consider a sum ratemaximization problem. The proposed hybrid beamforming is designed indirectly byconsidering a sum mean square error (MSE) minimization problem while utilizingthe solution of digital beamforming. To this end, we assume that the digitalbeamforming utilizes the well known block diagonalization (BD) approach. Underthis assumption, we solve our problem as follows: First, we formulate the sumrate maximization problem as the minimization of the MSE between the receivedsignal of the hybrid and digital beamforming designs. Then, we design thehybrid beamformings of the source, relay and each destination by leveragingcompressive sensing techniques. Simulation results confirm that the proposedhybrid beamforming design achieves performance very close to that of thedigital one. Furthermore, we have examined the effects of the number of radiofrequency (RF) chains and paths together, and the accuracy of angle of arrival(AoA) and angle of departure (AoD) estimators on the sum rate of the hybridbeamforming designs. Computer simulations reveal that the total sum rate of thehybrid beamforming increases when the number of RF chains and paths increase(or the accuracy of the AoA (AoD) estimator improves).
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