Beyond Diagonal Reconfigurable Intelligent Surfaces in Wideband OFDM Communications: Circuit-Based Modeling and Optimization

TL;DR

This paper develops a frequency-dependent, circuit-based BD-RIS model for wideband OFDM and proposes a two-stage optimization framework that jointly designs the BD-RIS admittance and transmitter power. By mapping the BD-RIS scattering matrix to a frequency-dependent admittance matrix and modeling tunable admittances with lumped L-C networks, it captures realistic wideband behavior for group-connected and forest-connected architectures. Continuous- and discrete-valued admittance design methods are developed (quasi-Newton and greedy-codebook approaches, respectively), and a Jensen-based bound paired with water-filling enables tractable optimization. Numerical results show BD-RIS consistently outperforms conventional RIS, with larger gains for more complex BD-RIS architectures and when full wideband modeling is employed, underscoring the importance of circuit-aware design in wideband systems.

Abstract

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.

Figures (6)

• Figure 1: Diagram for the BD-RIS-aided SISO-OFDM system.
• Figure 2: Examples of a 6-element BD-RIS with (a) group-connected and (b) forest-connected reconfigurable admittance network of group size 3, and the equivalent circuit for each admittance.
• Figure 3: The susceptance as a function of (a) frequency and (b) the value of susceptance at the center frequency $f_\mathrm{c} = 2.4$ GHz with $L_1 = 2.5$ nH, $L_2 = 0.7$ nH, and $C\in[0.2,3]$ pF for a practical varactor diode.
• Figure 4: (a) The slope and (b) the intercept of equation (\ref{['eq:B_Bc']}) as a function of $\omega$; (c) the fitted result based on equation (\ref{['eq:fitted_model']}). The parameters $\alpha_j$, $\beta_j$, $\forall j\in\{1,2\}$ in the linear model (\ref{['eq:fitted_model']}) are set as $\alpha_1 = 2.0046\times10^{-10}$, $\alpha_2 = -1.9968$, $\beta_1 = 6.2775\times10^{-12}$, $\beta_2 = -0.0942$.
• Figure 5: Average rate versus transmit power $P$ with BD-RIS having different architectures ($M\in\{36,48\}$, $\bar{M}\in\{1,3,6\}$). The legend "WM" is short for wideband modeling; "GC" is short for group-connected; "FC" is short for forest-connected. For both "GC" and "FC" architectures, the case of $\bar{M}=1$ refers to the conventional RIS.