Robust Beamforming for RIS-Assisted Wireless Communications With Discrete Phase Shifts

In this letter, we study the robust beamforming design for the reconfigurable intelligent surface (RIS)-assisted communication systems from a multi-antenna access point (AP) to a single-antenna user under imperfect channel state information (CSI), where the RIS has only a finite number of phase shifts at each element. In particular, considering the cascaded AP-RIS-user channel estimation error, we aim to jointly optimize the transmit beamforming at the AP and discrete phase shifts of RIS to minimize the transmission power of AP, subject to a signal-to-noise ratio constraint at the user. To tackle the non-convex optimization problem, we decouple it into two subproblems and propose a novel alternative optimization framework. More specifically, the robust beamforming of AP is first obtained through S-Procedure and semidefinite relaxation. Then we recast the discrete phase shift constraint at RIS into an equivalent convex one, and propose an efficient algorithm to obtain a near optimal solution. Finally, the two subproblems are iteratively optimized to obtain joint robust beamforming. Simulation results show that the proposed scheme can approach the performance of the perfect CSI counterpart and substantially outperform traditional non-robust methods.