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 which 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 probability of such a zero-detection solution. We prove that this probability converge to 1 as the number of IRS tends to infinity. We provide an iterative algorithm to find a perfectly covert scheme 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：隐蔽通信专注于通过物理层隐藏通信行为本身的存在性。本文研究了无线网络中完美隐蔽通信问题。具体而言，通过利用智能反射面（IRS），我们聚焦于使发射机能够完全隐藏通信的方案，使得非预期监听者（威利）处的能量为零，从而检测概率为零。此类方案的应用价值不仅限于隐蔽性——即使威利已知码本、时序及信道特征，我们仍能阻止其实现检测或解码。换言之，完美隐蔽性还能确保即便假设通信已发生且码本已知，威利仍无法解码。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，并定义了优化问题。针对N=2个IRS单元，我们分析了存在可行解的概率并推导出闭式解。随后通过分析零检测解的存在概率，研究了N>2个IRS单元的问题。我们证明了当IRS数量趋于无穷时，该概率收敛于1。我们提出了一种迭代算法以寻找完美隐蔽方案，并证明了其收敛性。仿真结果进一步表明，即使仅用少量IRS单元，合法用户即可获得正速率，同时非预期监听者的检测概率为零。