Covert communication is focused on hiding the mere existence of communication from unwanted listeners via the physical layer. In this work, we consider the problem of perfect covert communication in wireless networks. Specifically, harnessing an Intelligent Reflecting Surface (IRS), we turn our attention to schemes that allow the transmitter to completely hide the communication, with zero energy at the unwanted listener (Willie) and hence zero probability of detection. Applications of such schemes go beyond simple covertness, as we prevent detectability or decoding even when the codebook, timings, and channel characteristics are known to Willie. That is, perfect covertness also ensures Willie is unable to decode, even assuming communication took place and knowing the codebook. We define perfect covertness, give a necessary and sufficient condition for it in IRS-assisted communication, and define the optimization problem. For $N=2$ IRS elements, we analyze the probability of finding a solution and derive its closed form. We then investigate the problem of $N>2$ IRS elements by analyzing the probability of such a zero-detection solution. We prove that this probability converges to $1$ as the number of IRS tends to infinity. We provide an iterative algorithm to find a perfectly covert solution and prove its convergence. The results are also supported by simulations, showing that a small amount of IRS elements allows for a positive rate at the legitimate user yet with zero probability of detection at an unwanted listener.

翻译：隐蔽通信聚焦于通过物理层隐藏通信本身的存在，使其不被非预期监听者察觉。本文研究了无线网络中的完美隐蔽通信问题。具体而言，借助智能反射面（IRS），我们关注能够使发射机完全隐藏通信的方案，使得非预期监听者（Willie）处的能量为零，从而检测概率为零。此类方案的应用不仅限于简单隐蔽性，即使Willie已知码本、时序和信道特性，我们也阻止其可检测性或解码能力。换言之，完美隐蔽性还确保Willie即便假设通信已发生且知道码本，也无法进行解码。我们定义了完美隐蔽性，给出了其在IRS辅助通信中的充要条件，并提出了优化问题。对于$N=2$个IRS单元，我们分析了存在解的概率，并推导出其闭式解。随后，我们通过分析零检测解的概率，研究了$N>2$个IRS单元的问题。我们证明，随着IRS单元数量趋于无穷，该概率收敛于$1$。我们提出了一种迭代算法以找到完美隐蔽解，并证明了其收敛性。仿真结果也支持了上述结论，表明少量IRS单元即可在合法用户处实现正速率，同时使得非预期监听者的检测概率为零。