Beyond Diagonal Reconfigurable Intelligent Surfaces for Multi-Carrier RF Wireless Power Transfer

Radio frequency (RF) wireless power transfer (WPT) is promising for promoting sustainability in future wireless systems, but its low end-to-end power transfer efficiency is a critical challenge. For this, reconfigurable intelligent surfaces (RISs) can be leveraged to enhance efficiency by providing nearly passive beamforming gains. Beyond diagonal (BD) RIS is a new RIS variant offering greater performance benefits than traditional diagonal RIS (D-RIS), though its potential for RF-WPT remains unexplored. Motivated by this, we consider a single-input single-output BD-RIS-aided RF-WPT system and we formulate a joint beamforming and waveform optimization problem aiming to maximize the harvested power at the receiver. We propose an optimization framework relying on successive convex approximation, alternating optimization, and semi-definite relaxation. Numerical results show that increasing the number of transmit sub-carriers or RIS elements improves the harvested power. We verify by simulation that BD-RIS leads to the same performance as D-RIS under far-field line-of-sight conditions (in the absence of mutual coupling), while it outper-forms D-RIS as the non-line-of-sight components dominate.