The white book released by the International Telecommunications Union (ITU) calls for extremely high-security and low-latency communication over fading channels. Under the low-latency requirement, the corresponding fading model is quasi-static fading while high-security can be achieved via covert communication. In response to the call of ITU, we study the finite blocklength performance of optimal codes for covert communication over quasi-static multi-antenna fading channels, under the covertness metric of Kullback-Leibler (KL) divergence. In particular, we study all four cases regarding the availability of channel state information (CSI) for legitimate transmitter and receiver, and assume that the warden knows perfect CSI for the channel from the legitimate transmitter to itself. Specifically, we show that, when the blocklength is $n$, the first-order covert rate satisfies the square root law, scaling as $Θ(n^{-\frac{1}{2}})$ with the coefficient determined by the traces of the channel matrices of the legitimate users and the warden, and the second-order rate vanishes. In contrast to the non-covert result of Yang et al. (TIT, 2014), we show that CSI availability at the legitimate users does not affect the finite blocklength performance for covert communication. Furthermore, we reveal the significant spatial diversity gain provided by multiple-antenna systems for covert communication. For the covertness analysis, we extend the quasi-$η$-neighborhood framework to fading channels and address challenges arising from the random channel matrices. For the reliability analysis, due to the vanishing power imposed by the covertness constraint, we refine the non-covert analysis by Yang et al. (TIT, 2014), by carefully controlling higher-order terms and exploiting the properties of covert outage probability.

翻译：国际电信联盟（ITU）发布的白皮书呼吁在衰落信道上实现极高安全性和低延迟通信。在低延迟要求下，相应的衰落模型为准静态衰落，而高安全性可通过隐蔽通信实现。为响应ITU的号召，我们研究了在Kullback-Leibler（KL）散度作为隐蔽性度量下，准静态多天线衰落信道上隐蔽通信的最优编码的有限块长度性能。特别地，我们研究了关于合法发射机和接收机信道状态信息（CSI）可用性的全部四种情况，并假设监视者知道从合法发射机到自身的完美CSI。具体而言，我们证明当块长度为$n$时，一阶隐蔽速率满足平方根定律，其尺度为$Θ(n^{-\frac{1}{2}})$，系数由合法用户和监视者的信道矩阵的迹决定，而二阶速率趋于零。与Yang等人（TIT, 2014）的非隐蔽结果相比，我们表明合法用户的CSI可用性不影响隐蔽通信的有限块长度性能。此外，我们揭示了多天线系统为隐蔽通信提供的显著空间分集增益。在隐蔽性分析中，我们将准$η$-邻域框架扩展到衰落信道，并应对随机信道矩阵带来的挑战。在可靠性分析中，由于隐蔽性约束导致的功率趋于零，我们通过仔细控制高阶项并利用隐蔽中断概率的性质，改进了Yang等人（TIT, 2014）的非隐蔽分析。