Reconfigurable Intelligent Surface Assisted OFDM Relaying: Subcarrier Matching with Balanced SNR

This paper considers a reconfigurable intelligent surface (RIS) aided orthogonal frequency division multiplexing (OFDM) relaying system, and investigates the joint design of RIS passive beamforming and subcarrier matching under two cases, where Case-I ignores the source-RIS-destination signal, while Case-II explores this signal for rate enhancement. We formulate a mixed-integer nonlinear programming (MINIP) problem to maximize the sum achievable rate of all subcarriers by jointly optimizing the passive beamforming and subcarrier matching. To solve this problem, we first develop a branch-and-bound (BnB)-based alternating optimization algorithm for attaining a near-optimal solution. Then, a low-complexity difference-of-convex penalty-based algorithm and learning-to-optimize approach are also proposed. Finally, simulation results demonstrate that the RIS-assisted OFDM relaying system achieves a substantial achievable rate gain as compared to that without RIS since RIS recasts the subcarrier matching and balances the signal-to-noise ratio (SNR) among different subcarrier pairs.