Low Complexity RIS Update in OFDM Systems via RIS Element Allocation

In this paper, we propose reconfigurable intelligent surface (RIS) element allocation algorithms that maximize the minimum rate or sum rate in a multi-user (MU)-multiple-input single-output (MISO)-orthogonal frequency division multiplexing (OFDM) system aided with an RIS. Specifically, we first propose multiple metrics, which represent the minimum rate and sum rate, depending solely on the channel. We then propose multiple convex optimization algorithms to maximize the proposed metrics by updating the RIS matrix, validating that the metrics indeed represent the desired objectives successfully. Through the metrics, only a single RIS matrix update is required, contrast to existing works using alternating optimization. Finally, since the aforementioned optimization algorithms still suffer from high complexity, we propose RIS element allocation algorithms that update the RIS matrix to maximize the metrics with minimal complexities. Simulation results show that the RIS element allocation algorithms achieve remarkable performances close to existing benchmarks and exhaustive search with low complexities.