Reconfigurable intelligent surface (RIS) becomes an increasingly important technology in sixth-generation (6G). The key aspect of RIS is smartly configuring the wireless propagation environment and providing supplementary links to enhance the signal transmission between the BS and the UE. In recent years, there has been a surge of interest in RISs in joint active and passive beamforming design to improve the system performance of RIS-assisted systems with the assumption of uncorrelated environments. To date, far too little attention has been paid to the situations that consider the correlations among the antennas and RIS reflecting elements. In this article, we focus on an RIS-assisted multiple-input multiple-output (MIMO) system under spatial fading correlations, with the statistical channel state information (CSI) known at the transmitter and the RIS. We aim to maximize the ergodic spectral efficiency (SE) of this system. At first, we derive a tight upper bound on the ergodic SE. Concise upper bounds are also shown in special cases of independent and identically distributed (i.i.d.) Rician and Rayleigh, correlated Rayleigh as well as extreme Rician MIMO channels. Next, we propose a benchmark algorithm based on the semidefinite relaxation (SDR) technique to jointly optimize the beamforming vector at the transmitter and phase shift matrix of the RIS. Alternative manner is utilised until both arrive at convergence. Furthermore, we apply the dominant eigen direction transmission scheme to do beamforming in order to reduce the complexity of the algorithm, and consider the column control of the RIS to facilitate practical hardware implementation. Numerical results show the tightness of the upper bounds and the effectiveness of our proposed algorithm for improving the ergodic SE as well as the effects of freedom degrees on performances.

中文翻译：

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可重构智能表面辅助 MIMO 系统的联合发射波束成形和相移设计

可重构智能表面（RIS）成为第六代（6G）中越来越重要的技术。RIS 的关键在于智能配置无线传播环境并提供补充链路以增强BS 和UE 之间的信号传输。近年来，人们对 RIS 在联合主动和被动波束成形设计中的兴趣激增，以在不相关环境的假设下提高 RIS 辅助系统的系统性能。迄今为止，对考虑天线和RIS反射元件之间相关性的情况关注太少。在本文中，我们关注空间衰落相关下的 RIS 辅助多输入多输出 (MIMO) 系统，使用在发射机和 RIS 处已知的统计信道状态信息 (CSI)。我们的目标是最大化该系统的遍历谱效率 (SE)。首先，我们推导出遍历 SE 的严格上限。在独立同分布 (iid) Rician 和 Rayleigh、相关 Rayleigh 以及极端 Rician MIMO 信道的特殊情况下，也显示了简洁的上限。接下来，我们提出了一种基于半定松弛 (SDR) 技术的基准算法，以联合优化发送端的波束形成向量和 RIS 的相移矩阵。使用替代方式直到两者达到收敛。此外，我们应用主导本征方向传输方案进行波束成形，以降低算法的复杂度，并考虑 RIS 的列控制，以方便实际的硬件实现。数值结果显示了上界的紧缩性和我们提出的改进遍历 SE 算法的有效性以及自由度对性能的影响。