Queue Stability Constrained Robust Secure Beamforming for Low-Altitude UAV-ISAC Systems
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摘要: 针对低空无人机通感一体化(UAV-ISAC)系统中的数据到达量随机、机体抖动以及窃听威胁等问题，该文提出了一种基于队列稳定性约束的鲁棒安全波束成形算法。首先，构建以最小化系统长时隙平均发射功率为目标函数，以队列稳定性、安全通信速率下限、感知性能下限和发射功率上限为约束的长时隙队列稳定性优化问题。其次，由于长时隙优化问题难以直接求解，采用Lyapunov优化框架将长时隙随机性优化问题转化为前后时隙关联的短时隙优化问题；在短时隙优化中利用二阶泰勒展开对UAV机体抖动导致的通信链路角度误差进行近似处理，并提出一种基于惩罚连续凸逼近的鲁棒安全优化算法。仿真结果表明，所提算法与多种基准方案相比，可有效保障UAV-ISAC系统在抖动场景下的数据传输稳定性与安全性。
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关键词:
- 无人机 /
- 通感一体化 /
- 队列稳定性 /
- Lyapunov优化 /
- 鲁棒安全波束成形
Abstract:Objective To address the challenges of antenna array angle errors caused by UAV jitter, transmission instability induced by random data arrivals, and secure transmission guarantee in multi-eavesdropper scenarios for low-altitude UAV-ISAC systems, this paper proposes a robust secure beamforming algorithm based on queue stability constraints. The proposed algorithms aims to minimize long-term transmit power consumption while maintaining data queue stability while enhancing beamforming robustness against UAV jitter. Methods To guarantee the stability of the wireless transmission in UAV-ISAC systems, this paper formulates an optimization problem aimed at minimizing the long-term average transmit power, subject to constraints on data queue stability, secure communication rate, sensing performance, and maximum transmit power. Since this long-term optimization problem is intractable, the Lyapunov optimization framework is employed to transform it into a sequence of short-term subproblems. To handle the antenna array angle errors caused by UAV jitter within each short slot, we jointly adopt the second-order Taylor series expansion and the S-Procedure method to approximate the short-term subproblem into a convex form. Consequently, a robust secure beamforming algorithm based on penalty successive convex approximation optimization is proposed. Results and Discussions Simulation results demonstrate the impact of the number of antennas, secrecy rate threshold, beam gain threshold, UAV jitter error, and Lyapunov weight factor on the system transmit power. As illustrated by the beam gain pattern in Fig. 3 , the communication beamformer facilitates cooperative sensing toward the sensing area, while the sensing beamformer enhances system security by directing interference toward potential eavesdroppers. This validates the effectiveness of the proposed algorithm in simultaneously improving sensing and secure communication performance. Furthermore, leveraging the dual-function characteristics of the communication and sensing beamformers, the proposed integrated sensing and communication scheme achieves significantly higher resource utilization efficiency than the communication-only and sensing-only schemes, as shown inFig. 5 . Additionally,Fig. 6 indicates that, compared with the non-robust scheme, the proposed robust scheme strictly satisfies security requirements under various angle errors. Finally,Fig. 8 shows that the proposed queue-aware scheme can effectively suppress the transmit power fluctuations caused by random data arrivals, exhibiting superior stability compared to the queue-free baseline.Conclusions This paper investigates a robust secure beamforming method for UAV-ISAC systems subject to queue stability constraints. First, based on the Lyapunov optimization framework, the long-term stochastic optimization problem is transformed into a sequence of short-term subproblems. Second, to address the issue of UAV jitter, the second-order Taylor series expansion and the S-Procedure method are jointly employed to approximate the non-convex constraints into tractable convex forms. Finally, a robust secure BF optimization algorithm based on penalty successive convex approximation is proposed to efficiently solve the deterministic short-term subproblems. Simulation results demonstrate that the proposed scheme can effectively tackle the challenges posed by random data arrivals, UAV jitter, and eavesdropping threats, thereby ensuring the stability and security of downlink data transmission in low-altitude UAV-ISAC systems. -
Key words:
- UAV /
- ISAC /
- Queue stability /
- Lyapunov optimization /
- Robust secure beamforming
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表 1 鲁棒安全波束成形算法
(1) 初始化队列积压量$ Q(0) $和可行初始点$ ({\boldsymbol{W}}_{\text{c}}(0),{\boldsymbol{W}}_{\text{s}}(0)) $。 (2) 根据$ {\boldsymbol{W}}_{\text{c}}(0) $和$ {\boldsymbol{W}}_{\text{s}}(0) $计算$ {R}_{\text{G}}(0) $，并设置$ t=1 $。 (3) While $ t\leq T $: (4) $ t=t+1 $； (5) 获取$ A(t-1) $，并依据公式(9)更新$ Q(t) $； (6) 设置时隙$ t $的初始点$(\mathbf{\overline{\boldsymbol{W}}}_{\text{c}}^{0},\mathbf{\overline{\boldsymbol{W}}}_{\text{s}}^{0})=({\boldsymbol{W}}_{\text{c}}(t-1) $,
$ {\boldsymbol{W}}_{\text{s}}(t-1)) $和$ i=0 $；(7) do： (8) $ i=i+1 $； (9) 求解优化问题(P5)，获得最优解$ (\mathbf{\overline{\boldsymbol{W}}}_{\text{c}}^{i},\mathbf{\overline{\boldsymbol{W}}}_{\text{s}}^{i}) $； (10) While$ \left|\left|\mathbf{\overline{\boldsymbol{W}}}_{\text{c}}^{i}-\mathbf{\overline{\boldsymbol{W}}}_{\text{c}}^{i-1}\right|\right|+\left|\left|\mathbf{\overline{\boldsymbol{W}}}_{\text{s}}^{i}-\mathbf{\overline{\boldsymbol{W}}}_{\text{s}}^{i-1}\right|\right|\rightarrow 0 $ (11) 更新$ ({\boldsymbol{W}}_{\text{c}}(t),{\boldsymbol{W}}_{\text{s}}(t))=(\mathbf{\overline{\boldsymbol{W}}}_{\text{c}}^{i},\mathbf{\overline{\boldsymbol{W}}}_{\text{s}}^{i}) $； (12) 根据$ {\boldsymbol{W}}_{\text{c}}(t) $和$ {\boldsymbol{W}}_{\text{s}}(t) $计算$ {R}_{\text{G}}(t) $； (13) end 
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表 2 仿真参数
参数名称 符号 数值 参数名称 符号 数值 天线数量 $ N $ 3×3 平均数据到达量 $ \lambda $ 10 无人机高度 $ H $ 100 m[13] 安全速率阈值 $ R_{\text{sec}}^{\text{th}} $ 3 bps/Hz 噪声功率 $ {\sigma }^{2} $ –110 dBm[12] 感知波束增益阈值 $ {\varGamma } $ –30 dBm[12] 载波频率 $ {f}_{\text{c}} $ 20 GHz[20] 发射功率上限 $ P_{\text{T}}^{\max } $ 30 dBm 感知区域采样点数 $ K $ 9 总时隙 $ T $ 2000 抖动误差界限 $ \varepsilon $ 3°[15] Lyapunov权重参数 $ V $ 20
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