Robust design of hybrid multicast beamforming with phase error in mmWave systems

This paper studies the robust beamforming design for multi-group multicast transmission with a hybrid analog and digital structure in millimeter wave (mmWave) communication systems. Unlike the conventional additive error model, we consider a novel multiplicative phase error model which is more suitable for capturing the channel uncertainty in mmWave systems. We adopt a partially-connected hybrid structure where each radio frequency (RF) chain is connected to an exclusive subset of antenna elements at the base station. The robust design problem is formulated to minimize the total transmit power while satisfying the outage constraint for each user's signal-to-interference-plus-noise ratio (SINR). We first utilize the alternating minimization method to optimize the analog and digital beamformers alternatively. Each of these two subproblems is then solved approximately by using the second-order Taylor expansion together with the Bernstein-type inequality. Simulation results show that the approximation is quite safe and the outage constraint can be well satisfied. It is also shown that the power performance of the proposed robust design is within 1dB close to the ideal case when the standard derivation of the channel phase error is within 5.7°.