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）作为一种新型泛化RIS架构，近期被提出，具备更优的波束调控灵活性和大范围覆盖扩展能力。然而，BD-RIS中超越对角的数学模型不可避免地给波束赋形设计引入了额外优化挑战。本文推导出最大化用户间有效信道增益和的BD-RIS无源波束赋形矩阵闭式解，并进一步提出一种计算高效的两阶段波束赋形框架，联合设计基站有源波束赋形与BD-RIS无源波束赋形，以提升BD-RIS辅助多用户多天线网络的和速率。数值结果表明，与现有最优算法相比，所提算法在实现更高和速率的同时，所需计算时间更少。该算法为BD-RIS辅助无线网络中实用波束赋形设计奠定了基础。