Optimal Passive Beamforming for Reconfigurable Intelligent Surface-Assisted Communications with Discrete Phase Shifts

This letter presents an optimal phase shift configuration method for Reconfigurable Intelligent Surfaces (RISs) with discrete phase shifts to maximize the passive beamforming gain. Specifically, based on theoretical analysis, the multi-ary phase shift optimization problem is first transformed into an equivalent binary phase shift problem. Although it is still a non-convex optimization problem, the optimal solution can be found indirectly through the linear search (LS) for the optimal phase of the superimposed channel. Accordingly, the LS algorithm is designed, in which iterative operations are adopted to ensure the linear computational complexity. The simulation results verify that the proposed LS algorithm achieves the globally optimal passive beamforming, which outperforms existing excellent algorithms. Furthermore, it is also revealed that a 3-bit quantized phase shifter can obtain sufficiently good performance relative to the ideal continuous phase shifter.