Reconfigurable intelligent surface (RIS) is a novel meta-material which can form a smart radio environment by dynamically altering reflection directions of the impinging electromagnetic waves. In the prior literature, the inter-RIS links which also contribute to the performance of the whole system are usually neglected when multiple RISs are deployed. In this paper we investigate a general double-RIS assisted multiple-input multiple-output (MIMO) wireless communication system under spatially correlated non line-of-sight propagation channels, where the cooperation of the double RISs is also considered. The design objective is to maximize the achievable ergodic rate based on full statistical channel state information (CSI). Specifically, we firstly present a closed-form asymptotic expression for the achievable ergodic rate by utilizing replica method from statistical physics. Then a full statistical CSI-enabled optimal design is proposed which avoids high pilot training overhead compared to instantaneous CSI-enabled design. To further reduce the signal processing overhead and lower the complexity for practical realization, a common-phase scheme is proposed to design the double RISs. Simulation results show that the derived asymptotic ergodic rate is quite accurate even for small-sized antenna arrays. And the proposed optimization algorithm can achieve substantial gain at the expense of a low overhead and complexity. Furthermore, the cooperative double-RIS assisted MIMO framework is proven to achieve superior ergodic rate performance and high communication reliability under harsh propagation environment.

翻译：可重构智能表面(RIS)是一种新型超材料，能够通过动态改变入射电磁波的反射方向构建智能无线电环境。现有文献在部署多个RIS时通常忽略RIS间链路对系统整体性能的贡献。本文研究了一般双RIS辅助的多输入多输出(MIMO)无线通信系统，在空间相关非视距传播信道下考虑双RIS协同作用，设计目标基于完全统计信道状态信息最大化可达遍历容量。具体而言，首先利用统计物理中的复制方法给出可达遍历容量的闭式渐近表达式；其次提出基于完全统计CSI的最优设计方案，与基于瞬时CSI的方案相比避免了高导频训练开销；为进一步降低实际实现的信号处理开销与复杂度，提出双RIS协同设计的共相位方案。仿真结果表明，即使天线阵列规模较小，推导的渐近遍历容量仍具有较高精度，且所提优化算法能以较低开销和复杂度实现显著增益。此外，协同双RIS辅助MIMO框架在恶劣传播环境下展现出优越的遍历容量性能与高通信可靠性。