Monte-Carlo based random passive energy beamforming for reconfigurable intelligent surface assisted wireless power transfer*

Reconfigurable intelligent surface (RIS) employs passive beamforming to control the wireless propagation channel, which benefits the wireless communication capacity and the received energy efficiency of wireless power transfer (WPT) systems. Such beamforming schemes are classified as discrete and non-convex integer programming problems. In this paper, we propose a Monte-Carlo (MC) based random energy passive beamforming of RIS to achieve the maximum received power of electromagnetic (EM) WPT systems. Generally, the Gibbs sampling and re-sampling methods are employed to generate phase shift vector samples. And the sample with the maximum received power is considered the optimal solution. In order to adapt to the application scenarios, we develop two types of passive beamforming algorithms based on such MC sampling methods. The first passive beamforming uses an approximation of the integer programming as the initial sample, which is calculated based on the channel information. And the second one is a purely randomized algorithm with the only total received power feedback. The proposed methods present several advantages for RIS control, e.g., fast convergence, easy implementation, robustness to the channel noise, and limited feedback requirement, and they are applicable even if the channel information is unknown. According to the simulation results, our proposed methods outperform other approximation and genetic algorithms. With our methods, the WPT system even significantly improves the power efficiency in the nonline-of-sight (NLOS) environment.