ADPM-Based Secure Beamforming Design Method for Low-Altitude Integrated Sensing and Communication

WANG Zhiwei; WANG Jingjing; SI Zhichun; CHEN Jianrui; WU Guangyu; JIANG Chunxiao

doi:10.12263/DZXB.20260165

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ADPM-Based Secure Beamforming Design Method for Low-Altitude Integrated Sensing and Communication

Integrated Sensing and Communications Towards Low\-Altitude Economy | 更新时间：2026-10-16

- ADPM-Based Secure Beamforming Design Method for Low-Altitude Integrated Sensing and Communication
- ACTA ELECTRONICA SINICA Vol. 54, Issue 6, Pages: 2637-2648(2026)
- 作者机构：
  
  1.北京航空航天大学网络空间安全学院，北京 100191
  2.鹏城实验室，广东深圳 518100
  3.北京大学计算机学院，北京 100871
  4.清华大学信息国家研究中心，北京 100084
- 作者简介：
- 基金信息：
  
  National Natural Science Foundation of China(U24A20213;62571011;72542016;625B2015;625B2010;62325108;62341131);Beijing Natural Science Foundation(QY24126)
- DOI：10.12263/DZXB.20260165
  CLC： TN911.7;TN929.5
- Received：25 March 2026，
  
  Accepted：16 April 2026，
  
  Published：25 June 2026
- 稿件说明：
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王智伟, 王景璟, 司智淳, 等. 基于ADPM的低空通感一体化安全波束赋形设计方法[J]. 电子学报, 2026, 54(06): 2637-2648.

WANG Zhiwei, WANG Jingjing, SI Zhichun, et al. ADPM-Based Secure Beamforming Design Method for Low-Altitude Integrated Sensing and Communication[J]. Acta Electronica Sinica, 2026, 54(06): 2637-2648.
王智伟, 王景璟, 司智淳, 等. 基于ADPM的低空通感一体化安全波束赋形设计方法[J]. 电子学报, 2026, 54(06): 2637-2648. DOI：10.12263/DZXB.20260165

WANG Zhiwei, WANG Jingjing, SI Zhichun, et al. ADPM-Based Secure Beamforming Design Method for Low-Altitude Integrated Sensing and Communication[J]. Acta Electronica Sinica, 2026, 54(06): 2637-2648. DOI：10.12263/DZXB.20260165

摘要

随着低空经济的快速发展，无人机在物流、安防等领域的应用日益广泛，低空空域的安全监管成为迫切需求。通信感知一体化（Integrated Sensing And Communication，ISAC）技术能够协同实现高可靠通信与高精度目标感知，已成为保障低空安全的重要技术手段。然而，低空无线信道的极度开放性使得ISAC系统在执行通感任务时，极易遭受物理层的窃听威胁。现有基于高精度感知的波束赋形设计往往忽略了安全传输需求，难以实现感知与安全的协同。针对这一问题，本文研究了低空场景下兼顾感知精度与抗窃听性能的安全波束赋形方案。为从理论下界提升感知性能，本文首先推导了关于低空感知目标角度估计的渐近克拉美罗界（Cramér-Rao Bound，CRB），进而建立了一个以最小化CRB为目标函数的非凸优化模型。其次，为在复杂的低空环境中同时兼顾通信服务质量与高度的隐蔽性需求，本文进一步对该模型施加了多重严格的系统约束。具体而言，模型引入了通信波形相似度约束，以灵活且高效地抑制多用户间的信号干扰。同时，为确保通信链路的可靠传输，模型引入了用户接收能量约束，以严格保障接收机正常工作所需的解调门限。再次，针对安全传输的核心要求，模型引入了窃听方向能量泄漏约束，意在通过波束能量的空间零陷，从物理层面上消除潜在的窃听威胁。最后，模型还需严格满足系统的总功率约束，以符合实际硬件的能耗限制。为了高效求解上述模型，本文利用增广拉格朗日函数与变量分裂技术，提出了一种基于交替方向惩罚法（Alternating Direction Penalty Method，ADPM）的迭代求解算法，将带有复杂约束的原始优化问题分解为多个存在闭式解或高精度数值解的子问题。仿真结果表明：相较于传统交替方向乘子法（Alternating Direction Method of Multipliers，ADMM），本文所提算法不仅具有更快的收敛速度，还能够稳定收敛至更低的目标函数值，表现出较强的数值稳定性与鲁棒性，成功实现了低空高精度感知与物理层安全传输的协同优化。

Abstract

With the rapid development of the low-altitude economy

the application of unmanned aerial vehicles in logistics

security and other fields is becoming increasingly widespread

and the safety supervision of low-altitude airspace has become an urgent need. Integrated sensing and communication (ISAC) technology has become an important technical means for ensuring low-altitude security due to its ability to cooperatively achieve high-reliability communication and high-precision target sensing. However

the extreme openness of low-altitude wireless channels makes ISAC systems highly vulnerable to physical layer eavesdropping threats when performing sensing and communication tasks. Existing beamforming designs based on high-precision sensing often ignore secure transmission requirements

making it difficult to achieve the coordination of sensing and security. To address this issue

this paper investigates a secure beamforming scheme in low-altitude scenarios that considers both sensing accuracy and anti-eavesdropping performance. To improve sensing performance from the theoretical lower bound

this paper first derives the asymptotic Cramér-Rao bound (CRB) regarding the angle estimation of low-altitude sensing targets

and further establishes a non-convex optimization model with the minimization of the CRB as the objective function. In order to simultaneously balance communication quality of service and high stealth requirements in complex low-altitude environments

this paper further imposes multiple strict system constraints on the model. Specifically

the model introduces a communication waveform similarity constraint to flexibly and efficiently suppress signal interference among multiple users. Meanwhile

to ensure the reliable transmission of communication links

the model introduces a user received energy constraint to strictly guarantee the demodulation threshold required for the normal operation of the receiver. Additionally

in response to the core requirements of secure transmission

the model introduces an eavesdropping direction energy leakage constraint

aiming to eliminate potential eavesdropping threats from the physical layer through spatial nulling of beam energy. Finally

the model must strictly satisfy the total system power constraint to comply with the energy consumption limits of actual hardware. To efficiently solve the aforementioned model

this paper utilizes the augmented Lagrangian function and variable splitting technique to propose an iterative solving algorithm based on the alternating direction penalty method (ADPM)

which decomposes the original optimization problem with complex constraints into multiple sub-problems that possess closed-form solutions or high-precision numerical solutions. Simulation results show that

compared with the traditional alternating direction method of multipliers (ADMM)

the proposed algorithm not only has a faster convergence speed but is also able to stably converge to a lower objective function value

exhibiting strong numerical stability and robustness

and successfully achieving the collaborative optimization of high-precision low-altitude sensing and physical layer secure transmission.

关键词

Keywords

references

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