Beamforming and Waveform Optimization for RF Wireless Power Transfer with Beyond Diagonal Reconfigurable Intelligent Surfaces

Radio frequency (RF) wireless power transfer (WPT) is a promising technology to seamlessly charge low-power devices, but its low end-to-end power transfer efficiency remains a critical challenge. To address the latter, low-cost transmit/radiating architectures, e.g., based on reconfigurable intelligent surfaces (RISs), have shown great potential. Beyond diagonal (BD) RIS is a novel branch of RIS offering enhanced performance over traditional diagonal RIS (D-RIS) in wireless communications, but its potential gains in RF-WPT remain unexplored. Motivated by this, we analyze a BD-RIS-assisted single-antenna RF-WPT system to charge a single rectifier, and formulate a joint beamforming and multi-carrier waveform optimization problem aiming to maximize the harvested power. We propose two solutions relying on semi-definite programming for fully connected BD-RIS, a successive convex approximation (SCA)-based beamforming approach, and an efficient low-complexity iterative method relying on SCA. Numerical results show that the proposed algorithms converge and that adding transmit sub-carriers or RIS elements improves the harvesting performance. We show that the transmit power budget impacts the relative power allocation among different sub-carriers depending on the rectifier's operating regime, while BD-RIS shapes the cascade channel differently for frequency-selective and flat scenarios. Finally, we verify by simulation that BD-RIS and D-RIS achieve the same performance under pure far-field line-of-sight conditions (in the absence of mutual coupling). Meanwhile, BD-RIS outperforms D-RIS as the non-line-of-sight components of the channel become dominant.