Beyond-diagonal reconfigurable intelligent surface (BD-RIS) has garnered significant research interest recently due to its ability to generalize existing reconfigurable intelligent surface (RIS) architectures and provide enhanced performance through flexible inter-connection among RIS elements. However, current BD-RIS designs often face challenges related to high circuit complexity and computational complexity, and there is limited study on the trade-off between system performance and circuit complexity. To address these issues, in this work, we propose a novel BD-RIS architecture named Q-stem connected RIS that integrates the characteristics of existing single connected, tree connected, and fully connected BD-RIS, facilitating an effective trade-off between system performance and circuit complexity. Additionally, we propose two algorithms to design the RIS scattering matrix for a Q-stem connected RIS aided multi-user broadcast channels, namely, a low-complexity least squares (LS) algorithm and a suboptimal LS-based quasi-Newton algorithm. Simulations show that the proposed architecture is capable of attaining the sum channel gain achieved by fully connected RIS while reducing the circuit complexity. Moreover, the proposed LS-based quasi-Newton algorithm significantly outperforms the baselines, while the LS algorithm provides comparable performance with a substantial reduction in computational complexity.

翻译：超对角可重构智能表面（BD-RIS）因其能够泛化现有可重构智能表面（RIS）架构，并通过RIS单元间的灵活互连提供增强性能，近期引起了广泛的研究关注。然而，当前的BD-RIS设计常面临电路复杂度和计算复杂度高的挑战，且关于系统性能与电路复杂度之间权衡的研究有限。为解决这些问题，本文提出了一种名为Q-茎连接RIS的新型BD-RIS架构，该架构融合了现有单连接、树连接和全连接BD-RIS的特性，有助于在系统性能与电路复杂度之间实现有效权衡。此外，我们提出了两种算法来设计Q-茎连接RIS辅助多用户广播信道的RIS散射矩阵，即一种低复杂度的最小二乘（LS）算法和一种基于LS的次优拟牛顿算法。仿真结果表明，所提架构能够在降低电路复杂度的同时，达到全连接RIS所实现的和信道增益。此外，所提出的基于LS的拟牛顿算法显著优于基线方法，而LS算法在显著降低计算复杂度的同时提供了可比的性能。