  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.
