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：本文研究了宽带通信系统中超对角可重构智能表面（BD-RIS）的建模与优化问题，该技术通过推广具有对角相移矩阵的传统RIS，为操控无线信道提供了额外灵活性。具体而言，我们首先建立了BD-RIS辅助正交频分复用（OFDM）系统的信号模型，该模型桥接时域与频域信道，并明确揭示了BD-RIS响应的频率依赖性。随后，基于电路模型刻画了BD-RIS响应的频率依赖特性。借助导纳参数分析，我们对BD-RIS的每个可调导纳组件进行独立建模，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依赖型BD-RIS模型，我们设计了优化算法，通过调整BD-RIS配置与发射端功率分配以最大化BD-RIS辅助OFDM系统的平均速率。最终仿真结果表明，在OFDM系统中BD-RIS性能优于传统RIS。更重要的是，随着BD-RIS架构电路复杂度的提升，宽带建模对系统性能的影响愈发显著。