Beyond-diagonal reconfigurable intelligent surface (BD-RIS) has been proposed recently as a novel and generalized RIS architecture that offers enhanced wave manipulation flexibility and large coverage expansion. However, the beyond-diagonal mathematical model in BD-RIS inevitably introduces additional optimization challenges in beamforming design. In this letter, we derive a closed-form solution for the BD-RIS passive beamforming matrix that maximizes the sum of the effective channel gains among users. We further propose a computationally efficient two-stage beamforming framework to jointly design the active beamforming at the base station and passive beamforming at the BD-RIS to enhance the sum-rate for a BD-RIS aided multi-user multi-antenna network.Numerical results show that our proposed algorithm achieves a higher sum-rate while requiring less computation time compared to state-of-the-art algorithms. The proposed algorithm paves the way for practical beamforming design in BD-RIS aided wireless networks.

翻译：超越对角可重构智能表面（BD-RIS）作为一种新型且泛化的RIS架构，最近被提出以增强波束操控灵活性并实现更大范围的覆盖扩展。然而，BD-RIS中的超越对角数学模型不可避免地给波束成形设计带来了额外的优化挑战。本文推导了BD-RIS无源波束成形矩阵的闭式解，可最大化用户间有效信道增益之和。我们进一步提出了一种计算高效的两阶段波束成形框架，通过联合设计基站处的有源波束成形与BD-RIS处的无源波束成形，以提升BD-RIS辅助多用户多天线网络的总和速率。数值结果表明，与现有先进算法相比，所提算法在实现更高总和速率的同时，所需计算时间更少。该算法为BD-RIS辅助无线网络的实际波束成形设计铺平了道路。