Holographic MIMO communication was proposed to sufficiently exploit the propagation characteristics of electromagnetic channels and boost the channel capacity. Unfortunately, the application of the electromagnetic theory to the electromagnetically large (compared to the wave-length) antenna arrays leads to a non-separable correlation structure for the small-scale fading due to the coupling effect between the transmit and receive antennas. Such a non-separable correlation structure poses challenging issues for characterizing the fundamental limits of holographic MIMO channels, which has not been tackled in the literature. In this paper, we investigate the distribution for the mutual information (MI) of holographic MIMO systems with the non-separable channel correlation, where both the line-of-sight and non-line-of-sight components are considered. We set up a central limit theorem for the MI by random matrix theory (RMT) and give the closed-form expressions for the mean and variance. The derived results are used to approximate the outage probability and reveal interesting physical insights regarding the impact of antenna spacing. It is shown that reducing antenna spacing will improve the ergodic MI and decrease the outage probability of holographic MIMO systems. The scaling law of the ergodic MI with respect to the antenna spacing is also derived. Numerical simulations validate the accuracy of the evaluation results.

翻译：全息MIMO通信旨在充分利用电磁信道的传播特性以提升信道容量。然而，当电磁理论应用于电大尺寸（相对于波长）天线阵列时，由于发射天线与接收天线间的耦合效应，小尺度衰落呈现不可分离的相关结构。这种不可分离的相关结构对表征全息MIMO信道的基本极限提出了严峻挑战，这在现有文献中尚未得到解决。本文针对具有不可分离信道相关性的全息MIMO系统，研究了互信息（MI）的分布特性，同时考虑视距与非视距分量。通过随机矩阵理论（RMT）建立了MI的中心极限定理，并给出了均值和方差的闭式表达式。推导结果用于近似中断概率，并揭示了关于天线间距影响的物理规律。研究表明，减小天线间距将提升全息MIMO系统的遍历MI并降低中断概率，同时推导了遍历MI随天线间距变化的标度律。数值仿真验证了评估结果的准确性。