Active-RIS Enhances the Multi-User Rate of Multi-Carrier Communications

This paper explores a multi-user multi-carrier system leveraging an active reconfigurable intelligent surface (RIS), where the joint design of the RIS's programmable reflecting elements and the subcarrier-wise beamformers at the base station is investigated. To overcome the limitation of the conventional design, which aims solely at sum-rate maximization resulting in zero rates for some users across all sub-carriers and thus failing to boost all users rates, we propose the two alternative designs: one maximizing the geometric mean of the users' rates (GM-rate maximization) and the other maximizing the soft users' minimum rate (soft max-min rate optimization). However, they pose challenges as large-scale nonconvex problems, rendering convex-solver computational approaches impractical. To tackle this, we develop iterative computational procedures based on closed-form expressions of scalable complexity. Extensive simulations demonstrate the substantial benefits of these novel designs in significantly enhancing multi-user rates. Notably, under the same power budget, the active-RIS-assisted multi-carrier system achieves approximately twice the minimum user-rate or sum rate compared to RIS-less or passive-RIS-assisted counterparts.