Simple Feedback Design and Beamforming for RIS-Assisted Systems

In a reconfigurable intelligent surface (RIS)-assisted communication system, optimizing the transmit beamforming of the active antenna array and the reflect beamforming of the passive phase shifters at the RIS require knowledge of the channel. Accurately estimating channels in such systems is a challenging task. We propose an algorithm that eliminates the need for channel estimation in these systems. The goal is to maximize the achievable rate at a single-antenna receiver in a system with a multiple-antenna transmitter. The problem is nonconvex, but closed-form solutions in systems with full channel state information can be found by using alternating optimization. We provide a low-complexity algorithm for active beamforming at the transmitter using rounds of single-bit feedback and passive beamforming at the RIS using tree-structured vector quantizers. Our results show that these algorithms asymptotically achieve the performance of a system with full channel state information available at both the transmitter and the RIS controller.