Recently, simultaneously transmitting and reflecting reconfigurable intelligent surfaces (STAR-RISs) have received significant research interest. The employment of large STAR-RIS and high-frequency signaling inevitably make the near-field propagation dominant in wireless communications. In this work, a STAR-RIS aided near-field multiple-input multiple-multiple (MIMO) communication framework is proposed. A weighted sum rate maximization problem for the joint optimization of the active beamforming at the base station (BS) and the transmission/reflection-coefficients (TRCs) at the STAR-RIS is formulated. The non-convex problem is solved by a block coordinate descent (BCD)-based algorithm. In particular, under given STAR-RIS TRCs, the optimal active beamforming matrices are obtained by solving a convex quadratically constrained quadratic program. For given active beamforming matrices, two algorithms are suggested for optimizing the STAR-RIS TRCs: a penalty-based iterative (PEN) algorithm and an element-wise iterative (ELE) algorithm. The latter algorithm is conceived for STAR-RISs with a large number of elements. Numerical results illustrate that: i) near-field beamforming for STAR-RIS aided MIMO communications significantly improves the achieved weighted sum rate compared with far-field beamforming; ii) the near-field channels facilitated by the STAR-RIS provide enhanced degrees-of-freedom and accessibility for the multi-user MIMO system; and iii) the BCD-PEN algorithm achieves better performance than the BCD-ELE algorithm, while the latter has a significantly lower computational complexity.

翻译：近期，同时发射和反射可重构智能表面（STAR-RIS）引起了广泛的研究兴趣。大型STAR-RIS的部署与高频信号传输不可避免地使得近场传播在无线通信中占据主导地位。本文提出了一种STAR-RIS辅助的近场多输入多输出（MIMO）通信框架，并构建了一个加权和速率最大化问题，以联合优化基站（BS）处的有源波束赋形与STAR-RIS处的传输/反射系数（TRCs）。该非凸问题通过基于块坐标下降（BCD）的算法求解。具体而言，在给定STAR-RIS TRCs的条件下，通过求解凸二次约束二次规划得到最优有源波束赋形矩阵；在给定有源波束赋形矩阵时，提出了两种优化STAR-RIS TRCs的算法：基于惩罚的迭代（PEN）算法和逐元素迭代（ELE）算法，其中后者专为具有大量元素的STAR-RIS设计。数值结果表明：i) 相较于远场波束赋形，STAR-RIS辅助MIMO通信中的近场波束赋形显著提升了加权和速率；ii) STAR-RIS支持的近场信道为多用户MIMO系统提供了增强的自由度与可达性；iii) BCD-PEN算法性能优于BCD-ELE算法，但后者具有显著更低的计算复杂度。