This paper addresses the problem of maximizing the capacity of a multiple-input multiple-output (MIMO) link assisted by a beyond-diagonal reconfigurable intelligent surface (BD-RIS). We maximize the capacity by alternately optimizing the transmit covariance matrix, and the BD-RIS scattering matrix, which, according to network theory, should be unitary and symmetric. These constraints make the optimization of BD-RIS more challenging than that of diagonal RIS. To find a stationary point of the capacity we maximize a sequence of quadratic problems in the manifold of unitary matrices. This leads to an efficient algorithm that always improves the capacity obtained by a diagonal RIS. Through simulation examples, we study the capacity improvement provided by a passive BD-RIS architecture over the conventional RIS model in which the phase shift matrix is diagonal.

翻译：本文研究了借助超对角可重构智能表面（BD-RIS）实现多输入多输出（MIMO）链路容量最大化的问题。我们通过交替优化发射协方差矩阵和BD-RIS散射矩阵来最大化容量。根据网络理论，该散射矩阵应为酉矩阵且对称。这些约束使得BD-RIS的优化比对角RIS更具挑战性。为找到容量的稳定点，我们在酉矩阵流形上最大化一系列二次规划问题，从而提出一种高效算法。该算法始终能提升对角RIS所获得的容量。通过仿真示例，我们研究了无源BD-RIS架构相较于传统相移矩阵为对角形式的RIS模型所带来的容量提升。