In this paper, we consider a reconfigurable intelligent surface (RIS)-assisted multiple-input multiple-output communication system with multiple antennas at both the base station (BS) and the user. We plan to maximize the achievable rate through jointly optimizing the transmit precoding matrix, the receive combining matrix, and the RIS reflection matrix under the constraints of the transmit power at the BS and the unit-modulus reflection at the RIS. Regarding the non-trivial problem form, we initially reformulate it into an considerable problem to make it tractable by utilizing the relationship between the achievable rate and the weighted minimum mean squared error. Next, the transmit precoding matrix, the receive combining matrix, and the RIS reflection matrix are alternately optimized. In particular, the optimal transmit precoding matrix and receive combining matrix are obtained in closed forms. Furthermore, a pair of computationally efficient methods are proposed for the RIS reflection matrix, namely the semi-definite relaxation (SDR) method and the successive closed form (SCF) method. We theoretically prove that both methods are ensured to converge, and the SCF-based algorithm is able to converges to a Karush-Kuhn-Tucker point of the problem.

翻译：本文研究一种可重构智能表面辅助的多输入多输出通信系统，其中基站与用户端均配备多天线。我们旨在基站发射功率约束与RIS单元模反射约束下，通过联合优化发射预编码矩阵、接收合并矩阵及RIS反射矩阵来最大化可达速率。针对该非平凡问题形式，我们首先利用可达速率与加权最小均方误差之间的关联关系，将原问题重构为易于处理的形式。随后，对发射预编码矩阵、接收合并矩阵及RIS反射矩阵进行交替优化。特别地，最优发射预编码矩阵与接收合并矩阵以闭合形式求得。此外，针对RIS反射矩阵优化提出了两种计算高效的方法：半定松弛法与逐次闭合形式法。我们从理论上证明了两种方法均能确保收敛，且基于SCF的算法能够收敛至问题的Karush-Kuhn-Tucker点。