Robust Hybrid Beamforming for Outage-Constrained Multigroup Multicast Mmwave Transmission with Phase Shifter Impairments

This article investigates robust hybrid beamforming design for outage-constrained multigroup multicast millimeter-wave (mmWave) transmission. The phase shifter impairments incorporated in the analog beamformer can impose negative damage on the Quality of Service (QoS) of users. To address this imperfect hardware problem, phase shifter impairments are modeled, and robust hybrid beamforming is formulated to maximize the worst-case signal-to-interference–plus-noise ratio (SINR). The digital beamformer and analog beamformer are jointly optimized based on an alternating optimization (AO) approach, where both the outage probability of users and the average transmit power at the base station (BS) are derived into closed-form expressions in each iteration. Moreover, the semidefinite programming (SDP) approach is resorted to handling the hybrid beamforming design. Based on the penalty and the successive convex approximation (SCA) approaches, we further propose a penalty-SCA-SDP-AO (PSSA) algorithm to address the constant-modulus constraint caused by phase shifters and the rank-one constraint introduced by the semidefinite form. Simulation results show that compared to the conventional nonrobust design, our robust hybrid beamforming design generally improves 40% nonoutage performance at least.