Robust Hybrid Beamforming Design for Multi-RIS Assisted MIMO System With Imperfect CSI

Reconfigurable intelligent surface (RIS) has been developed as a promising approach to enhance the performance of fifth-generation (5G) systems through intelligently reconfiguring the reflection elements. However, RIS-assisted beamforming design highly depends on the channel state information (CSI) and RIS’s location, which could have a significant impact on system performance. In this paper, the robust beamforming design is investigated for a RIS-assisted multiuser millimeter wave system with imperfect CSI, where the weighted sum-rate maximization problem (WSM) is formulated to jointly optimize transmit beamforming of the BS, RIS placement and reflect beamforming of the RIS. The considered WSM maximization problem includes CSI error, phase shifts matrices, transmit beamforming as well as RIS placement variables, which results in a complicated nonconvex problem. To handle this problem, the original problem is divided into a series of subproblems, where the location of RIS, transmit/reflect beamforming and CSI error are optimized iteratively. Then, a multiobjective evolutionary algorithm is introduced to gradient projection-based alternating optimization, which can alleviate the performance loss caused by the effect of imperfect CSI. Simulation results reveal that the proposed scheme can potentially enhance the performance of existing wireless communication, especially considering a desirable trade-off among beamforming gain, user priority and error factor.