Reconfigurable intelligent surface (RIS) has been anticipated to be a novel cost-effective technology to improve the performance of future wireless systems. In this paper, we investigate a practical RIS-aided multiple-input-multiple-output (MIMO) system in the presence of transceiver hardware impairments, RIS phase noise and imperfect channel state information (CSI). Joint design of the MIMO transceiver and RIS reflection matrix to minimize the total average mean-square-error (MSE) of all data streams is particularly considered. This joint design problem is non-convex and challenging to solve due to the newly considered practical imperfections. To tackle the issue, we first analyze the total average MSE by incorporating the impacts of the above system imperfections. Then, in order to handle the tightly coupled optimization variables and non-convex NP-hard constraints, an efficient iterative algorithm based on alternating optimization (AO) framework is proposed with guaranteed convergence, where each subproblem admits a closed-form optimal solution by leveraging the majorization-minimization (MM) technique. Moreover, via exploiting the special structure of the unit-modulus constraints, we propose a modified Riemannian gradient ascent (RGA) algorithm for the discrete RIS phase shift optimization. Furthermore, the optimality of the proposed algorithm is validated under line-of-sight (LoS) channel conditions, and the irreducible MSE floor effect induced by imperfections of both hardware and CSI is also revealed in the high signal-to-noise ratio (SNR) regime. Numerical results show the superior MSE performance of our proposed algorithm over the adopted benchmark schemes, and demonstrate that increasing the number of RIS elements is not always beneficial under the above system imperfections.

翻译：可重构智能表面（RIS）被预期为一种提升未来无线系统性能的新型低成本技术。本文研究存在收发器硬件损伤、RIS相位噪声及非完美信道状态信息（CSI）的实际RIS辅助多输入多输出（MIMO）系统。特别考虑联合设计MIMO收发器与RIS反射矩阵以最小化所有数据流的总平均均方误差（MSE）。由于新引入的实际非理想因素，该联合设计问题呈现非凸特性且求解困难。为应对该挑战，我们首先通过整合上述系统非理想因素的影响分析总平均MSE。随后，为处理紧密耦合的优化变量与非凸NP-hard约束，提出一种基于交替优化（AO）框架的高效迭代算法并保证收敛性，其中每个子问题通过利用最大最小化（MM）技术可得到闭式最优解。此外，通过利用单位模约束的特殊结构，针对离散RIS相移优化提出改进的黎曼梯度上升（RGA）算法。进一步，在视距（LoS）信道条件下验证了所提算法的最优性，并揭示了高信噪比（SNR）区域中硬件与CSI非理想性共同导致的不可消除MSE基底效应。数值结果表明，所提算法的MSE性能优于基准方案，并证明在上述系统非理想因素下增加RIS单元数并非始终有益。