AI 中文总结
研究标量高斯隐蔽叠加模型中隐蔽通信问题，通过相对熵约束对残差施加隐蔽性，得出最大可靠传输隐蔽有效载荷遵循平方根定律，低功率高斯信号可实现该定律，还推导了已知时变条件残差方差下的一阶分配。
AI 中文摘要
隐蔽通信使爱丽丝能够向鲍勃传输信息，同时让威利难以检测到传输。我们研究了一个标量高斯隐蔽叠加模型，其中爱丽丝的低功率隐蔽信号叠加在由爱丽丝或其他可追踪源生成的聚合公共分量上。威利拥有所有物理上可获得的边信息，包括协议细节、时间、导频、信道估计和校准信息，并在测试前减去他对公共分量的最佳估计。通过基于威利边信息的预算为\(\delta\)的相对熵约束，对所得残差施加隐蔽性。在平稳情况下，无隐蔽传输时的残差方差为\(\sigma_0^2=\sigma_W^2+\sigma_e^2\)，其中\(\sigma_W^2\)是威利的接收噪声方差,\(\sigma_e^2\)是不可约抵消误差。在\(n\)次信道使用中，最大可靠传输的隐蔽有效载荷为\(R_C^\star\sqrt{n}(1+o(1))\)比特，其中\(R_C^\star=\frac{\sigma_0^2}{\sigma_B^2\ln 2}\sqrt{\delta}\)，\(\sigma_B^2\)是鲍勃的接收噪声方差。因此，平方根定律（SRL）常数由威利实际检测器输入处的方差决定，而不仅仅由接收噪声决定。低功率高斯信号实现了这个常数，并且一个匹配的逆命题在条件加性高斯创新模型中建立了一阶最优性。对于已知时变条件残差方差，我们还推导了一阶分配，它将更多的隐蔽功率分配给更大的残差方差。结果要求具有已知条件方差的高斯抵消后零残差；非高斯残差和固定的非零方差不确定性不在本文范围内。
英文摘要
Covert communication enables Alice to transmit to Bob while making the transmission difficult for Willie to detect. We study a scalar Gaussian covert-overlay model in which Alice's low-power covert signal is superimposed on an aggregate public component generated by Alice or other trackable sources. Willie is given all physically obtainable side information, including protocol details, timing, pilots, channel estimates, and calibration information, and subtracts his best estimate of the public component before testing. Covertness is imposed on the resulting residual through a relative-entropy constraint with budget $δ$ conditioned on Willie's side information. In the stationary case, the residual under no covert transmission has variance $σ_0^2=σ_W^2+σ_e^2$, where $σ_W^2$ is Willie's receiver-noise variance and $σ_e^2$ is the irreducible cancellation error. Over $n$ channel uses, the maximal reliably transmissible covert payload is $R_C^\star\sqrt{n}(1+o(1))$ bits, where $R_C^\star=\frac{σ_0^2}{σ_B^2\ln 2}\sqrtδ$, and $σ_B^2$ is Bob's receiver-noise variance. Thus, the square-root-law (SRL) constant is governed by the variance at Willie's actual detector input, not by receiver noise alone. Low-power Gaussian signaling achieves this constant, and a matching converse establishes first-order optimality within the conditioned additive Gaussian innovation model. For known time-varying conditioned residual variances, we also derive the first-order allocation, which assigns more covert power to larger residual variances. The results require a Gaussian post-cancellation null residual with known conditioned variance; non-Gaussian residuals and fixed non-vanishing variance uncertainty are outside the scope of this paper.
Comments13 pages, 6 figures. Submitted to IEEE Transactions on Communications
