Robust Beamforming for Reconfigurable Intelligent Surface-Assisted Multi-Cell Downlink Transmissions

In this article, we comprehensively investigate robust beamforming schemes for reconfigurable intelligent surface (RIS)-assisted multi-cell downlink transmissions in the presence of channel estimation error (CEE), where an RIS is deployed at the joint boundary of multiple cells to assist downlink transmissions to cell-edge users. Specifically, we study a unified robust beamforming framework to maximize the minimum achievable rate or the coverage probability of cell-edge users with a bounded or a statistical CEE model. The bounded and statistical CEE models characterize the absolute robustness and statistical robustness demands of RIS-assisted cell-edge users. In particular, we reformulate the non-convex robust beamforming problem into two sub-problems, i.e., the optimal transmit beamforming at the base station (BS) and the optimal phase shifts at the RIS, which are alternately optimized. Moreover, we apply S-Procedure and Bernstein-type inequality to transform non-convex bounded and statistical CEE constraints into convex forms. Consequently, the BS transmit beamforming sub-problem and the RIS phase shifts sub-problem can be solved by a novel penalty-based method. Finally, the two sub-problems are iteratively optimized via a bisection-based strategy to obtain the joint robust beamforming. Simulation results demonstrate that the proposed robust beamforming scheme can converge rapidly and outperform reference schemes in the presence of CEE. Moreover, our proposed penalty-based method achieves better performance than that of the conventional semidefinite relaxation method.