非理想信道条件下面向信息年龄最小化的短包隐蔽通信设计

朱开基; 马瑞谦; 林志; 马越; 王勇; 管新荣; 蔡跃明

doi:10.11999/JEIT250836

非理想信道条件下面向信息年龄最小化的短包隐蔽通信设计

doi: 10.11999/JEIT250836 cstr: 32379.14.JEIT250836

1.
国防科技大学电子对抗学院合肥 230037
2.
南京理工大学近程射频感知芯片与微系统教育部重点实验室南京 210094
3.
陆军工程大学通信工程学院南京 210007

基金项目: 国家自然科学基金(62471477和62301254)，江苏省基础研究计划自然科学基金(BK20230916)，中央高校基本科研业务费专项资金资助(30925010602)

详细信息

作者简介:
朱开基：男，硕士生，研究方向为隐蔽通信

马瑞谦：男，副教授，研究方向为协同通信、短包通信、隐蔽通信

林志：男，副教授，研究方向为天地一体化信息网络、物理层安全、智能反射面

马越：男，副教授，研究方向为隐蔽通信、阵列信号处理

王勇：男，教授，研究方向为卫星网络安全

管新荣：男，副教授，研究方向为研究方向为智能超表面、短包通信

蔡跃明：男，教授，研究方向为移动通信、协同通信、无线物理层安全

通讯作者:
马瑞谦　ruiqian1996@163.com

中图分类号: TN918
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出版历程
- 收稿日期: 2025-09-01
- 修回日期: 2026-01-04
- 录用日期: 2026-01-04
- 网络出版日期: 2026-01-12

Short-packet Covert Communication Design for Minimizing Age of Information under Non-ideal Channel Conditions

1.
College of Electronic Engineering, National University of Defense Technology, Hefei 230037, China
2.
Key Laboratory of Near-Range RF Sensing ICs & Microsystems, Ministry of Education, Nanjing University of Science and Technology, Nanjing 210094, China
3.
College of Communications Engineering, Army Engineering University of PLA, Nanjing 210007, China

Funds: The National Natural Science Foundation of China (62471477 and 62301254), The Natural Science Foundation of Jiangsu Province (BK20230916), The Fundamental Research Funds for the Central Universities (30925010602)

摘要

摘要: 该文针对短包隐蔽通信场景，考虑信道估计误差导致的非理想信道条件，研究了最小化平均隐蔽信息年龄(CAoI)的通信参数优化问题。具体地，首先推导了非理想信道条件下的隐蔽约束和平均CAoI的闭式表达式；其次，推导了最小化平均CAoI的发送功率表达式。在此基础上，进一步基于黄金分割法对导频信号包长和数据信号包长进行优化，以最小化平均CAoI，从而实现通信隐蔽性和时效性之间的最优折中。此外，该文还分析了平均CAoI与收发距离、隐蔽容忍度等参数的变化关系。仿真结果表明，存在最优包长和最优导频信号包长，使得平均CAoI最小，并且与固定包长分配比例的情况相比，所提优化方法可以获得更好的性能。并且当隐蔽性约束更严格时，由于发送功率的降低，最优的导频信号包长随之增大。
- 隐蔽通信 /
- 短包通信 /
- 非理想信道 /
- 隐蔽信息年龄
Abstract: Objective With the rapid development of mobile communication technologies and the widespread adoption of smart devices, the security and timeliness of information transmission are critical. Most existing studies on covert communication assume ideal channel conditions and long packet lengths, which are impractical for delay-sensitive applications. This paper addresses the problem of minimizing the average Covert Age of Information (CAoI) under non-ideal channel conditions caused by limited pilot symbols. The objective is to improve both timeliness and security in short-packet covert communication systems. Methods A system model is considered in which a transmitter sends short packets to a legitimate receiver under the surveillance of a warden. The effects of pilot length and transmit power on channel estimation error are characterized. Based on this analysis, closed-form expressions for the detection error probability and the average CAoI are derived. A joint optimization problem is then formulated to determine the optimal transmit power, total blocklength, and pilot-to-data ratio. This problem is solved using a golden-section search algorithm. Results and Discussions Numerical results show that an optimal total packet length and an optimal pilot-to-data ratio exist for minimizing the average CAoI (Fig. 3). The proposed joint optimization strategy significantly outperforms fixed-ratio schemes (Fig. 4). As the covertness constraint becomes stricter, the transmit power decreases, which requires longer pilot sequences to preserve channel estimation accuracy (Fig. 6(a)). The optimal total packet length is also shown to decrease as the covertness constraint is relaxed (Fig. 6(b)). Additionally, increasing the distance between Alice and Bob degrades the average CAoI performance due to poorer channel conditions (Fig. 5). Conclusions This study optimizes the average CAoI in short-packet covert communication systems with imperfect channel estimation. Closed-form expressions for covertness and CAoI are obtained, and a golden-section search method is applied to dynamically adjust the packet structure to minimize the average CAoI. Numerical results confirm that the optimized design outperforms fixed-allocation methods. The results further show that stricter covertness constraints require longer pilot sequences to compensate for reduced transmit power, providing useful design guidance for latency-sensitive covert wireless systems.
- Covert communication /
- Short-packet communication /
- Non-ideal channel /
- Covert age of information

HTML全文

图 1 隐蔽通信场景

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图 2 AoI随时间变化示意图

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图 3 不同总包长下平均CAoI随导频信号包长的变化示意图

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图 4 联合优化前后最小平均CAoI随总包长的变化示意图

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图 5 最小平均CAoI与$ \varepsilon $的关系图

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图 6 (a)最优导频包长$ n\mathrm{_p} $和最优总包长$ N $与$ \varepsilon $的关系图

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1 黄金分割包长分配优化算法

1：输入：总包长$ N $，先验传输概率$ {\rho }_{1} $，隐蔽约束容忍度$ \varepsilon $，整数搜索容差$ {\mathrm{tol}} $等；
2：计算该总包长对应的最优发送功率$ P $；
3：初始化搜索区间：分别用$ n_{\mathrm{v}} $(整数)和$ n\mathrm{_u} $(整数)表示搜索区间的下限和上限，初始化$ n\mathrm{_v}=n_{\min} $, $ n_{\mathrm{u}}=n_{\max} $。定义两个中间变量$ {x}_{1} $和　$ {x}_{2} $，表示两个分割点，$ x_1=n\mathrm{_v}+0.382\left(n_{\mathrm{u}}-n\mathrm{_v}\right) $, $ x_2=n_{\mathrm{v}}+0.618\left(n\mathrm{_u}-n\mathrm{_v}\right) $，并进行取整；
4：将连续分割点映射到邻近整数，导频信号包长$ n\mathrm{_p} $看作变量，则数据信号包长$ n_{\mathrm{d}}=N-n\mathrm{_p} $。分别代入$ n_{\mathrm{p}}=x_1 $和$ n\mathrm{_p}=x_2 $求解对应的　信息年龄$ {f}_{{\mathrm{CAOI}}}\left({x}_{1}\right) $和$ {f}_{{\mathrm{CAOI}}}\left({x}_{2}\right) $。
5：重复进行
6：如果$ {f}_{{\mathrm{CAOI}}}\left({x}_{1}\right) \gt {f}_{{\mathrm{CAOI}}}\left({x}_{2}\right) $，则下一次搜索的搜索区间更新为$ \left[x_1,n_{\mathrm{u}}\right] $，然后令$ n_{\mathrm{v}}=x_1 $, $ {x}_{1}={x}_{2} $, $ x_2=n_{\mathrm{v}}+0.618\left(n_{\mathrm{u}}-n\mathrm{_v}\right) $，　并且更新$ {f}_{{\mathrm{CAOI}}}\left({x}_{1}\right) $和$ {f}_{{\mathrm{CAOI}}}\left({x}_{2}\right) $；
7：否则，下一次搜索的搜索区间更新为$ \left[n_{\mathrm{v}},x_2\right] $，然后令$ n_{\mathrm{u}}=x_2 $, $ {x}_{2}={x}_{1} $, $ x_1=n_{\mathrm{v}}+0.382\left(n_{\mathrm{u}}-n\mathrm{_v}\right) $，并且更新$ {f}_{{\mathrm{CAOI}}}\left({x}_{1}\right) $和　$ {f}_{{\mathrm{CAOI}}}\left({x}_{2}\right) $；
8：直到$ n_{\mathrm{u}}-n\mathrm{_v} < \mathrm{tol} $(即区间内整数点数量足够少)；
9：对最后约束区间$ \left[n_{\mathit{v}},n_{\mathrm{u}}\right] $内的所有整数进行枚举并比较，找到使得信息年龄更小的包长值作为最优解$ n\mathrm{_p^*} $；
10：输出：$ n_{\mathrm{p}}=n_{\mathrm{p}}^* $(整数)，$ n\mathrm{_d}=n_{\mathrm{d}}^=N-n_{\mathrm{p}}^ $(整数)，$ \min \_ {\mathrm{CAoI}} $。

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