Reconfigurable intelligent surfaces (RISs) allow controlling the propagation environment in wireless networks through reconfigurable elements. Recently, beyond diagonal RISs (BD-RISs) have been proposed as novel RIS architectures whose scattering matrix is not limited to being diagonal. However, BDRISs have been studied assuming continuous-value scattering matrices, which are hard to implement in practice. In this paper, we address this problem by proposing two solutions to realize discrete-value group and fully connected RISs. First, we propose scalar-discrete RISs, in which each entry of the RIS impedance matrix is independently discretized. Second, we propose vector-discrete RISs, where the entries in each group of the RIS impedance matrix are jointly discretized. In both solutions, the codebook is designed offline such as to minimize the distortion caused in the RIS impedance matrix by the discretization operation. Numerical results show that vector-discrete RISs achieve higher performance than scalar discrete RISs at the cost of increased optimization complexity. Furthermore, fewer resolution bits per impedance are necessary to achieve the performance upper bound as the group size of the group connected architecture increases. In particular, only a single resolution bit is sufficient in fully connected RISs to approximately achieve the performance upper bound.

翻译：可重构智能表面（RIS）通过可重构元件实现对无线网络传播环境的控制。近期提出的超对角RIS（BD-RIS）是一种散射矩阵不限于对角形式的新型RIS架构。然而，现有研究均假设BD-RIS采用连续值的散射矩阵，这在实践中难以实现。本文针对该问题提出两种解决方案以实现离散值的分组与全连接RIS。首先，我们提出标量离散化RIS方案，其中RIS阻抗矩阵的每个元素独立进行离散化处理。其次，提出向量离散化RIS方案，对RIS阻抗矩阵各组内元素进行联合离散化。两种方案均采用离线码本设计以最小化离散化操作对RIS阻抗矩阵造成的失真。数值结果表明，向量离散化RIS在增加优化复杂度的情况下可获得优于标量离散化RIS的性能。此外，随着分组连接架构的组尺寸增大，达到性能上限所需的单阻抗分辨率比特数随之减少。特别地，全连接RIS仅需单比特分辨率即可近似达到性能上限。