Reconfigurable intelligent surface (RIS) architectures not limited to diagonal phase shift matrices have recently been considered to increase their flexibility in shaping the wireless channel. One of these beyond-diagonal RIS or BD-RIS architectures leads to a unitary and symmetric RIS matrix. In this letter, we consider the problem of maximizing the signal-to-noise ratio (SNR) in single and multiple antenna links assisted by a BD-RIS. The Max-SNR problem admits a closed-form solution based on the Takagi factorization of a certain complex and symmetric matrix. This allows us to solve the max-SNR problem for SISO, SIMO, and MISO channels.

翻译：近年来，为提升无线信道塑造的灵活性，学术界开始关注超越对角相移矩阵的可重构智能表面（RIS）架构。其中一种超越对角RIS（BD-RIS）架构具有单位且对称的RIS矩阵。本文研究在BD-RIS辅助的单天线与多天线链路中最大化信噪比（SNR）的问题。该最大信噪比问题可通过特定复数对称矩阵的Takagi分解得到闭式解，从而实现SISO、SIMO和MISO信道中最大信噪比问题的求解。