Beyond-diagonal reconfigurable intelligent surfaces (BD-RISs), originally in the passive form, have attracted attention due to their benefits in enhanced wave manipulating through flexible inter-element connections and element arrangements. To mitigate the severe multiplicative fading, the concept of active BD-RISs with signal amplification capability has recently been proposed. Inspired by this, we investigate the hybrid transmitting and reflecting mode of active BD-RISs to achieve full-space coverage. We start by deriving a physics compliant communication model applying active BD-RIS with hybrid mode. We further propose novel architectures including reciprocal and non-reciprocal implementations with cell-wise single, group, and fully connections. We also develop a unified optimization framework for the joint transmit precoding and hybrid mode active BD-RIS design to maximize the sum rate of multi-user communication systems, which is applicable to all considered architectures. Numerical results demonstrate that, under the same total power budget, the proposed active BD-RIS with hybrid mode substantially outperforms active and passive simultaneous transmitting and reflecting RISs as well as passive BD-RISs with hybrid mode. This shows the synergy gain from inter-element connection, element arrangements, and active amplification.

翻译：超越对角线的可重构智能表面（BD-RIS）最初以无源形式出现，因其通过灵活的元件间连接与元件排布增强波操控能力的优势而备受关注。为缓解严重的乘性衰落效应，具备信号放大能力的主动BD-RIS概念近期被提出。受此启发，我们研究了主动BD-RIS的混合收发模式以实现全空间覆盖。首先，我们推导了适用于混合模式主动BD-RIS的物理兼容通信模型。进一步，我们提出了包含互易与非互易实现方案的新型架构，涵盖单元级单连接、组连接与全连接方式。同时，我们开发了面向多用户通信系统总和速率最大化的联合发射预编码与混合模式主动BD-RIS统一优化框架，该框架适用于所有考虑架构。数值结果表明，在相同总功率预算下，所提出的混合模式主动BD-RIS在性能上显著优于主动与被动同时收发可重构智能表面（STAR-RIS）以及混合模式无源BD-RIS。这揭示了元件间连接、元件排布与主动放大之间的协同增益效应。