Multi-Functional RIS: Signal Modeling and Optimization

In this paper, a multi-functional reconfigurable intelligent surface (MF-RIS) assisted non-orthogonal multiple access multiuser network is investigated. In contrast to existing studies assuming that the amplitude and phase shift coefficients of the refraction and reflection can be adjusted independently, we propose a practical model for the MF-RIS, where the refraction and reflection coefficients are highly coupled. Then, we investigate a sum-rate maximization problem by jointly optimizing the transmit beamforming and MF-RIS coefficients, subject to the coupled amplitude and phase shift constraints. To address the formulated non-convex problem, we propose an efficient iterative algorithm based on the fractional programming theory. Finally, numerical results show that: 1) The coupled MF-RIS scheme is superior to the simultaneous transmitting and reflecting RIS (STAR-RIS) and single-functional RIS (SF-RIS) schemes under the same power budget; 2) The performance gap between the ideal MF-RIS and coupled MF-RIS decreases with the increase of the total power budget.