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This paper considers a reconfigurable intelligent surface (RIS) aidedorthogonal frequency division multiplexing (OFDM) relaying system, andinvestigates the joint design of RIS passive beamforming and subcarriermatching under two cases, where Case-I ignores the source-RIS-destinationsignal, while Case-II explores this signal for rate enhancement. We formulate amixed-integer nonlinear programming (MINIP) problem to maximize the sumachievable rate of all subcarriers by jointly optimizing the passivebeamforming and subcarrier matching. To solve this problem, we first develop abranch-and-bound (BnB)-based alternating optimization algorithm for attaining anear-optimal solution. Then, a low-complexity difference-of-convexpenalty-based algorithm and learning-to-optimize approach are also proposed.Finally, simulation results demonstrate that the RIS-assisted OFDM relayingsystem achieves a substantial achievable rate gain as compared to that withoutRIS since RIS recasts the subcarrier matching and balances the signal-to-noiseratio (SNR) among different subcarrier pairs.

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