In this paper, we focus on intelligent reflecting surface (IRS) assisted multi-antenna communications with transceiver hardware impairments encountered in practice. In particular, we aim to maximize the received signal-to-noise ratio (SNR) taking into account the impact of hardware impairments, where the source transmit beamforming and the IRS reflect beamforming are jointly designed under the proposed optimization framework. To circumvent the non-convexity of the formulated design problem, we first derive a closed-form optimal solution to the source transmit beamforming. Then, for the optimization of IRS reflect beamforming, we obtain an upper bound to the optimal objective value via solving a single convex problem. A low-complexity minorization-maximization (MM) algorithm was developed to approach the upper bound. Simulation results demonstrate that the proposed beamforming design is more robust to the hardware impairments than that of the conventional SNR maximized scheme. Moreover, compared to the scenario without deploying an IRS, the performance gain brought by incorporating the hardware impairments is more evident for the IRS-aided communications.
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