In this letter, we consider a reconfigurable intelligent surface (RIS) assisted multiple-input multiple-output (MIMO) system in the presence of scattering objects. The MIMO transmitter and receiver, the RIS, and the scattering objects are modeled as mutually coupled thin wires connected to load impedances. We introduce a novel numerical algorithm for optimizing the tunable loads connected to the RIS. Compared with currently available algorithms, the proposed approach does not rely on the Neumann series approximation, but it optimizes the tunable load impedances alternately and one by one. At each iteration step, a closed-form expression for each impedance is provided by applying the Gram-Schmidt orthogonalization method. The algorithm is provably convergent and has a polynomial complexity with the number of RIS elements. Also, it is shown to outperform, in terms of achievable rate, two benchmark algorithms, which are based on a similar electromagnetic model, while requiring fewer iterations and a reduced execution time to reach convergence.

翻译：本文研究存在散射体条件下，可重构智能表面（RIS）辅助的多输入多输出（MIMO）系统。我们将MIMO发射机与接收机、RIS及散射体均建模为连接负载阻抗的互耦细导线。我们提出了一种用于优化RIS可调负载的新型数值算法。与现有算法相比，该方法不依赖诺伊曼级数近似，而是通过交替逐个优化可调负载阻抗。每次迭代中，采用格拉姆-施密特正交化方法为每个阻抗提供闭式解。该算法被证明可收敛，且复杂度随RIS单元数量呈多项式增长。同时，在可达速率方面，该算法优于两种基于相似电磁模型的基准算法，且所需迭代次数更少、收敛时间更短。