Downlink reconfigurable intelligent surface (RIS)-assisted multi-input-multi-output (MIMO) systems are considered with far-field, near-field, and hybrid-far-near-field channels. According to the angular or distance information contained in the received signals, 1) a distance-based codebook is designed for near-field MIMO channels, based on which a hierarchical beam training scheme is proposed to reduce the training overhead; 2) a combined angular-distance codebook is designed for mixed-far-near-field MIMO channels, based on which a two-stage beam training scheme is proposed to achieve alignment in the angular and distance domains separately. For maximizing the achievable rate while reducing the complexity, an alternating optimization algorithm is proposed to carry out the joint optimization iteratively. Specifically, the RIS coefficient matrix is optimized through the beam training process, the optimal combining matrix is obtained from the closed-form solution for the mean square error (MSE) minimization problem, and the active beamforming matrix is optimized by exploiting the relationship between the achievable rate and MSE. Numerical results reveal that: 1) the proposed beam training schemes achieve near-optimal performance with a significantly decreased training overhead; 2) compared to the angular-only far-field channel model, taking the additional distance information into consideration will effectively improve the achievable rate when carrying out beam design for near-field communications.

翻译：考虑了下行可重构智能表面（RIS）辅助的多输入多输出（MIMO）系统，涵盖远场、近场以及混合远近场信道。根据接收信号中包含的角度或距离信息：1）针对近场MIMO信道设计了基于距离的码本，并据此提出一种分层波束训练方案以降低训练开销；2）针对混合远近场MIMO信道设计了角度-距离联合码本，并据此提出一种两阶段波束训练方案，分别在角度域和距离域实现对齐。为在降低复杂度的同时最大化可达速率，提出一种交替优化算法以迭代方式进行联合优化。具体而言，通过波束训练过程优化RIS系数矩阵，基于均方误差（MSE）最小化问题的闭式解获得最优合并矩阵，并利用可达速率与MSE之间的关系优化有源波束成形矩阵。数值结果表明：1）所提波束训练方案能在显著降低训练开销的同时实现接近最优的性能；2）与仅考虑角度的远场信道模型相比，在进行近场通信波束设计时考虑额外的距离信息将有效提升可达速率。