This work investigates the modeling and optimization of beyond diagonal reconfigurable intelligent surface (BD-RIS), which generalizes conventional RIS with diagonal phase shift matrices and provides additional flexibility for manipulating wireless channels, in wideband communication systems. Specifically, we start from the signal modeling of the BD-RIS-aided orthogonal frequency division multiplexing (OFDM) system, which bridges the time-domain and frequency-domain channels, and explicitly shows the frequency dependence of the BD-RIS response. We next characterize the frequency dependence of the BD-RIS response based on circuit models. Benefiting from the admittance parameter analysis, we model individually each tunable admittance component of BD-RIS and derive an approximated linear expression with respect to the frequency of the transmit signals. With the proposed signal model for the BD-RIS-aided OFDM system and the frequency-dependent BD-RIS model, we propose algorithms to optimize the BD-RIS and the power allocation at the transmitter to maximize the average rate for a BD-RIS-aided OFDM system. Finally, simulation results show that BD-RIS outperforms conventional RIS in the OFDM system. More importantly, the impact of wideband modeling of BD-RIS on the system performance becomes more significant as the circuit complexity of BD-RIS architectures increases.

翻译：本研究针对宽带通信系统中超对角可重构智能表面的建模与优化问题展开研究。超对角可重构智能表面通过推广传统对角相移矩阵型可重构智能表面，为无线信道调控提供了更高的灵活性。具体而言，我们首先建立了BD-RIS辅助正交频分复用系统的信号模型，该模型连接了时域与频域信道，并明确揭示了BD-RIS响应的频率依赖性。随后，我们基于电路模型对BD-RIS响应的频率依赖特性进行理论刻画。通过导纳参数分析，我们对BD-RIS的每个可调谐导纳元件进行独立建模，并推导出关于发射信号频率的近似线性表达式。基于所提出的BD-RIS辅助OFDM系统信号模型及频率相关BD-RIS模型，我们设计了联合优化BD-RIS配置与发射端功率分配的算法，以最大化BD-RIS辅助OFDM系统的平均速率。仿真结果表明，在OFDM系统中BD-RIS性能优于传统RIS。更重要的是，随着BD-RIS架构电路复杂度的增加，其宽带建模对系统性能的影响变得更为显著。