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

Reconfigurable intelligent surface (RIS) is a promising solution to enhance the performance of wireless communications via reconfiguring the wireless propagation environment. In this paper, we investigate the joint design of RIS passive beamforming and subcarrier matching in RIS-assisted orthogonal frequency division multiplexing (OFDM) dual-hop relaying systems under two cases, depending on the presence of the RIS reflected link from the source to the destination in the first hop. Accordingly, we formulate a mixed-integer nonlinear programming (MINIP) problem to maximize the sum achievable rate over all subcarriers by jointly optimizing the RIS passive beamforming and subcarrier matching. To solve this challenging problem, we first develop a branch-and-bound (BnB)-based alternating optimization algorithm to obtain a near-optimal solution by alternatively optimizing the subcarrier matching by the BnB method and the RIS passive beamforming by using semidefinite relaxation techniques. Then, a low-complexity difference-of-convex penalty-based algorithm is proposed to reduce the computation complexity in the BnB method. To further reduce the computational complexity, we utilize the learning-to-optimize approach to learn the joint design obtained from optimization techniques, which is more amenable to practical implementations. Lastly, computer simulations are presented to evaluate the performance of the proposed algorithms in the two cases. Simulation results demonstrate that the RIS-assisted OFDM relaying system achieves sustainable achievable rate gain as compared to that without RIS, and that with random passive beamforming, since RIS passive beamforming can be leveraged to recast the subcarrier matching among different subcarriers and balance the signal-to-noise ratio within each subcarrier pair.