The reflection characteristics of a reconfigurable intelligent surface (RIS) depend on the phase response of the constituent unit cells, which is necessarily frequency dependent. This paper investigates the role of an RIS constituting unit cells with different phase-frequency profiles in a wide-band orthogonal frequency division multiplexing (OFDM) system to improve the achievable rate. We first propose a mathematical model for the phase-frequency relationship parametrized by the phase-frequency profile's slope and phase-shift corresponding to a realizable resonant RIS unit cell. Then, modelling each RIS element with $b$ control bits, we propose a method for selecting the parameter pairs to obtain a set of $2^b$ phase-frequency profiles. The proposed method yields an RIS design that outperforms existing designs over a wide range of user locations in a single-input, single-output (SISO) OFDM system. We then propose a low-complexity optimization algorithm to maximize the data rate through the joint optimization of (a) power allocations across the sub-carriers and (b) phase-frequency profile for each RIS unit cell from the available set. The analysis is then extended to a multi-user multiple-input single-output (MISO) OFDM scenario. Numerical results show an improvement in the coverage and achievable rates under the proposed framework as compared to single-slope phase-frequency profiles.

翻译：可重构智能表面（RIS）的反射特性依赖于其组成单元相位响应，而该响应必然与频率相关。本文研究了在宽带正交频分复用（OFDM）系统中，由不同相位-频率分布的单元构成的RIS对提升可达速率的机理。首先，针对可实现的谐振式RIS单元，提出了由相位-频率分布斜率和相移参数化的相位-频率关系数学模型。随后，通过设定每个RIS单元具备b个控制比特，提出了一种选择参数对的方法，以获得包含2^b种相位-频率分布的集合。该方法设计的RIS在单输入单输出（SISO）OFDM系统中，于广泛的用户位置范围内优于现有设计方案。进一步提出低复杂度优化算法，通过联合优化（a）子载波间的功率分配与（b）可用集合内各RIS单元的相位-频率分布，实现数据速率最大化。随后将分析扩展至多用户多输入单输出（MISO）OFDM场景。数值结果表明，与单斜率相位-频率分布相比，所提框架在覆盖范围和可达速率方面均有显著提升。