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Perfect channel state information (CSI) is challenging to obtain due to the limited signal processing capability at the intelligent reflection surface (IRS). This is the first work to study the worst-case robust beamforming design for an IRS-aided multiuser multiple-input single-output (MU-MISO) system under the assumption of imperfect CSI. We aim for minimizing the transmit power while ensuring that the achievable rate of each user meets the quality of service (QoS) requirement for all possible channel error realizations. With unit-modulus and rate constraints, this problem is non-convex. The imperfect CSI further increases the difficulty of solving this problem. By using approximation and transformation techniques, we convert the optimization problem into a squence of semidefinite program (SDP) subproblems that can be efficiently solved. Numerical results show that the proposed robust beamforming design can guarantee the required QoS targets for all the users.
Zhou et al. (2020) studied this question.