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.

中文翻译：

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具有硬件损伤的 RIS 辅助 MIMO 系统：稳健的波束成形设计和分析

可重构智能表面（RIS）被认为是一种新的具有成本效益的技术，可以提高未来无线系统的性能。在本文中，我们在存在收发器硬件损伤、RIS 相位噪声和不完善的信道状态信息 (CSI) 的情况下研究了一个实用的 RIS 辅助多输入多输出 (MIMO) 系统。特别考虑了 MIMO 收发器和 RIS 反射矩阵的联合设计，以最小化所有数据流的总平均均方误差 (MSE)。由于新考虑的实际缺陷，这个联合设计问题是非凸的并且难以解决。为了解决这个问题，我们首先通过结合上述系统缺陷的影响来分析总平均 MSE。然后，为了处理紧密耦合的优化变量和非凸NP-hard约束，提出了一种基于交替优化（AO）框架的高效迭代算法，保证收敛，其中每个子问题通过利用主要化来承认封闭形式的最优解-最小化（MM）技术。此外，通过利用单位模约束的特殊结构，我们提出了一种改进的黎曼梯度上升（RGA）算法，用于离散RIS相移优化。此外，在视距（LoS）信道条件下验证了所提算法的最优性，并且在高信噪比（SNR ) 制度。