Codebook-Based Self-Sustainable RIS: Optimal Splitting Schemes and Power Allocation

This paper studies the codebook-based configuration of a reconfigurable intelligent surface (RIS) that extends the coverage of a base station (BS) while utilizing energy harvesting to facilitate self-sustainable operation. For a given coverage area, we design a RIS codebook and propose a mathematical framework for analyzing the efficiency of three common energy harvesting schemes: power splitting (PS), element splitting (ES), and time splitting (TS). Thereby, we use a tile-based architecture at the RIS to exploit the advantages of both radio-frequency (RF) combining and direct-current (DC) combining. Moreover, we account for deterministic and random transmit signals for beam training and data transmission, respectively, and show their impact on the RF-DC conversion efficiencies at the rectifiers. Our main objective is to minimize the average transmit power at the BS by jointly optimizing the splitting ratio for the incident signal at the RIS and the power allocated to each RIS codeword. While the optimal power allocation is derived analytically, we show that the optimal splitting ratio can be determined by performing a grid search over a single optimization variable. Our performance evaluation reveals that the efficiency of the optimized splitting schemes depends on the adopted power consumption model and the number of tiles at the RIS. In particular, our results show that depending on the system parameters a different splitting scheme will achieve the lowest transmit power at the BS.