This work proposes an On-Off Keying (OOK) coding scheme for covert communication over complex Gaussian channels. In particular, a transmitter Alice employs phase deflection to covertly transmit information to a receiver Bob, simultaneously ensuring that the communication intent is concealed from a warden Willie. The utilization of phase deflection allows Alice to improve the transmission rate by leveraging Willie’s uncertainty about the received phase, without changing the codebook construction. Considering the asymmetry of the OOK codebook’s input distribution and shape constellation, we first analyze the relationship between the input distribution and the signal amplitude, and then propose a scheme that can achieve covert transmission with the input distribution of the “on” symbol $a_{n}=\mathcal {O}\left ({{\frac {1}{\sqrt {n}}}}\right)$ and an average transmission power $\beta ^{2}=\mathcal {O}({1})$ . We quantify the improvement brought from the phase resource as phase deflection gain and derive its closed-form expression by approximating the Kullback-Leibler (KL) divergence and mutual information through Taylor expansion. Numerical results show that our scheme achieves significant phase deflection gain, and the maximum gain can be achieved by fully utilizing the phase resources through three stages.

中文翻译：

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通过相位偏转增强 OOK 方案中的隐蔽通信


这项工作提出了一种 On-Off Keying （OOK） 编码方案，用于复杂高斯通道上的隐蔽通信。特别是，发射器 Alice 采用相位偏转将信息秘密传输到接收器 Bob，同时确保对典狱长 Willie 隐藏通信意图。利用相位偏转使 Alice 能够利用 Willie 对接收相位的不确定性来提高传输速率，而无需改变码本结构。考虑到OOK码本输入分布和形状星座的不对称性，我们首先分析了输入分布与信号幅度之间的关系，然后提出了一种方案，该方案可以利用“on”符号$a_{n}=\mathcal {O}\left （{{\frac {1}{\sqrt {n}}}}\right）$和平均传输功率$\beta ^{2}=\mathcal {O}（{1}）$的输入分布来实现隐蔽传输。我们将相资源带来的改进量化为相位偏转增益，并通过泰勒展开近似 Kullback-Leibler （KL） 散度和互信息来推导出其闭式表达式。数值结果表明，该方案实现了显著的相位偏转增益，并且通过三个阶段充分利用相位资源可以实现最大增益。