An Extended Kalman Filtering Based Secure Transmission Scheme for Intelligent Reflecting Surfaces-assisted Integrated Sensing and Communication System
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摘要: 为了解决智能反射面(IRS)辅助的通感一体化系统(ISAC)的安全通信问题，该文提出一种基于扩展卡尔曼滤波(EKF)目标追踪的安全传输方案。首先，针对作为潜在窃听者的移动感知目标，利用ISAC基站的感知功能从雷达回波中获取其状态参数，并采用EKF技术对其运动轨迹进行实时跟踪和预测。然后，利用感知目标的实时位置和信道状态信息调整基站发射波束成形和IRS反射波束成形。在此基础上，通过联合优化基站的发射波束成形、接收波束成形、上行链路用户的发射功率以及IRS的反射波束成形，最大化系统的保密速率。利用交替优化的思想将该非凸优化问题解耦为3个独立的子问题，并分别基于连续凸近似、丁克尔巴赫变换和优化最小化求解子问题。仿真结果表明，该方案可以对移动的感知目标进行有效的轨迹追踪，以提供更高的保密速率。同时证实了与没有IRS的方案相比，IRS的辅助能够实现更好的安全通信性能。Abstract:
Objective With the rapid increase in wireless devices and the growing demand for sensing services, Integrated Sensing And Communication (ISAC) has become a key technology to address spectrum scarcity. ISAC systems enable joint communication and sensing by sharing spectrum and hardware resources, thereby improving both spectral and energy efficiency. They also exploit the complementary properties of sensing and communication to enhance system performance. However, due to spectrum sharing and the broadcast nature of wireless signals, ISAC systems face major security risks. Physical Layer Security (PLS) has emerged as an effective approach for enhancing ISAC security. PLS designs transmission strategies based on the randomness and diversity of wireless channels to reduce eavesdropping risks and enhance security. Intelligent Reflecting Surfaces (IRS), a core technology for next-generation wireless networks, can manipulate the propagation environment of wireless signals by adjusting reflection phases. IRS enables more stable communication and sensing links, extends coverage, increases accuracy, and strengthens the overall security of ISAC systems. It thus offers a promising solution to PLS challenges in ISAC. However, when eavesdroppers are highly mobile, rapid changes in location and Channel State Information (CSI) hinder the acquisition of accurate channel data and real-time secure transmission. Leveraging ISAC’s sensing capabilities to track mobile eavesdroppers is therefore critical for ensuring security. This paper proposes an IRS-assisted ISAC system that enhances secure transmission by integrating PLS strategies in scenarios where rapidly moving aerial sensing targets act as potential eavesdroppers. Methods This study establishes an IRS-assisted ISAC system model comprising an ISAC base station, a rapidly moving aerial sensing target, a legitimate user, and an IRS equipped with multiple reflective elements. The system utilizes the base station’s sensing capability to estimate the location and dynamic state of the sensing target via radar echoes. An Extended Kalman Filtering (EKF) is used to track and predict the target’s trajectory in real time. Based on the predicted trajectory, a joint optimization problem is formulated to maximize the system’s secrecy rate. The formulation accounts for the tracking performance constraints of EKF, the transmission power budgets of both the base station and the legitimate user, and the IRS phase shift constraints. The optimization variables include the base station’s beamforming vector, the IRS reflective beamforming configuration, and the transmission power of the legitimate user. To improve real-time performance and security, the problem is designed as a non-convex optimization. This is decomposed into three sub-problems using an alternating optimization framework. The sub-problems are then solved using Successive Convex Approximation (SCA), Dinkelbach’s algorithm, and Majorization–Minimization (MM) methods. Results and Discussions Simulation results confirm the effectiveness of the proposed method in target tracking, system security, and performance enhancement. The trajectory prediction error of the proposed approach is substantially lower than that of radar echo-based estimation methods. Additionally, the EKF-based tracking algorithm achieves accuracy comparable to Particle Filtering (PF), while reducing computational complexity and conserving system resources. The convergence of the proposed algorithm is also verified. Under three different settings for the number of IRS reflection elements, the algorithm converges within five iterations, indicating stable and efficient convergence behavior. The results further show that the system’s secrecy rate increases with the number of transmit antennas. This improvement arises from the additional spatial degrees of freedom provided by the antennas, which enable the base station to generate more focused beams toward the sensing target. These beams enhance interference directed at the target during detection, thereby improving secure transmission. The secrecy rate also increases significantly with the number of IRS reflection elements. A larger number of elements allows the IRS to exploit additional spatial freedom, achieving higher beamforming gains and improving secure communication performance. In scenarios involving mobile sensing targets, the proposed method yields greater secrecy rate improvements than radar echo-based approaches. This advantage is attributed to the EKF’s ability to estimate the target’s position more accurately and in real time, enabling timely adjustment of beamforming strategies and enhancing security. Moreover, the optimized IRS configuration outperforms random phase shift designs, particularly in large-scale IRS deployments. Optimizing the IRS phase shift matrix contributes to higher secrecy rates and improved communication performance. Conclusions This paper presents a secure transmission scheme for an IRS-assisted ISAC system, targeting scenarios in which a rapidly moving sensing target serves as a potential eavesdropper. The ISAC base station leverages its sensing capability to extract the target’s state parameters from radar echoes and applies EKF to track and predict the target’s trajectory in real time. Based on this tracking, an optimization model is constructed to maximize the system’s secrecy rate by jointly optimizing the uplink user’s transmission power, the base station’s transmit and receive beamforming vectors, and the IRS phase shift matrix. To solve this problem efficiently, an alternating iterative optimization framework is adopted, which decomposes the non-convex objective into three independent sub-problems. These sub-problems are addressed using SCA, Dinkelbach transformation, and MM methods. Simulation results demonstrate that the proposed approach effectively detects the sensing target, maintains robust tracking performance, and ensures secure communication. Moreover, compared with the scenario without IRS, the IRS-assisted design achieves a substantially higher secrecy rate, highlighting both the advantages of IRS deployment in ISAC systems and the effectiveness of the proposed algorithm. -
图 5 系统保密速率与合法用户最大发射功率$ P_{{\text{max}}}^{\text{U}} $的关系，$(M,{N_x},{N_y}) = {\text{(50,4,4)}}$
图 7 系统保密速率与IRS反射单元数量$ M $的关系，$(P_{{\text{max}}}^{\text{U}},{N_x},{N_y}) = (4{\text{ dBm}},4,4)$
1 基于MM算法的IRS相移矩阵优化算法
(1)输入：$\tilde \sigma _{\text{B}}^2$, $\tilde \sigma _{\text{E}}^2$, $ {{\boldsymbol{\alpha}} _{\text{B}}} $, $ {{\boldsymbol{\alpha}} _{\text{E}}} $, ${\tilde \alpha _{\text{B}}}$, ${\tilde \alpha _{\text{E}}}$, $\varepsilon $,$L$ (2)初始化迭代次数$l = 1$, ${{\boldsymbol{v}}^{(0)}}$, ${\mu ^{(0)}} = 0$； (3)计算问题式(52)中的目标函数初始值${f_1}({{\boldsymbol{v}}^0})$； (4)重复 (5) 根据式(49)–式(51)，计算${\lambda _{\max }}({\boldsymbol{\varLambda}} )$,${\boldsymbol{d}}$； (6) 将式(53)代入目标函数式(47a)得到${\tilde \varpi ^ * }(\mu )$，利用二分搜索
法求解${\varpi ^ * }(\mu ) = 0$的根${\mu '^{(l)}}$并更新${{\boldsymbol{v}}^{(l)}}$。(8) 计算问题式(46)中的目标函数${f_1}({{\boldsymbol{v}}^l})$。 (9) 设置$l = l + 1$。 (10)直到$|{f_1}({{\boldsymbol{v}}^l}) - {f_1}({{\boldsymbol{v}}^{l - 1}})|/{f_1}({{\boldsymbol{v}}^l}) \le \varepsilon $或者$l = L$。 (11)输出${\boldsymbol{\varPhi}} = {\text{diag(}}{{\boldsymbol{v}}^ * }{\text{(}}\mu {\text{))}}$。 
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2 时隙$n$中求解问题(29)的交替迭代优化方案
(1)输入：$P_{{\text{max}}}^{\text{U}}$, $P_{{\text{max}}}^{\text{B}}$, ${\varGamma _{\text{E}}}$, $\varepsilon $, $L$ (2)根据式(24)–式(28)得到${{\boldsymbol{\hat c}}_{\text{E}}}[n + 1|n]$, ${\boldsymbol{M}}[n + 1]$； (3)初始化设置迭代次数$l = 1$, ${{\boldsymbol{F}}^{(0)}} = {\boldsymbol{f}}{{\boldsymbol{f}}^{\text{H}}}$, ${P^{(0)}} = P$,
${{\boldsymbol{W}}^{(0)}} = {\boldsymbol{w}}{{\boldsymbol{w}}^{\text{H}}}$, ${{\boldsymbol{v}}^{(0)}} = {\boldsymbol{v}}$, ${\beta ^{(0)}} = 0$；(4)重复 (5) 给定${{\boldsymbol{\varPhi}} ^{\left( {l - 1} \right)}}$, $ {{\boldsymbol{w}}^{\left( {l - 1} \right)}} $，通过求解问题式(37)计算${P^{\left( l \right)}}$,
$ {{\boldsymbol{f}}^{\left( l \right)}} $；(6) 给定${{\boldsymbol{\varPhi}} ^{\left( {l - 1} \right)}}$, ${P^{\left( l \right)}}$, $ {{\boldsymbol{f}}^{\left( l \right)}} $，通过求解问题式(39)计算$ {{\boldsymbol{w}}^{\left( l \right)}} $； (7) 给定${P^{\left( l \right)}}$, $ {{\boldsymbol{f}}^{\left( l \right)}} $, $ {{\boldsymbol{w}}^{\left( l \right)}} $，通过求解问题式(52)计算${{\boldsymbol{\varPhi}} ^{\left( l \right)}}$； (8) 计算问题式(29)中的目标函数$R_{\sec }^{(l)}$。 (9) 设置$l = l + 1$。 (10)直到$(R_{\sec }^{(l)} - R_{\sec }^{(l - 1)})/R_{\sec }^{(l)} \lt \varepsilon $或者$l = L$。 (11)输出$P$, $ {\boldsymbol{f}} $, $ {\boldsymbol{w}} $, ${\boldsymbol{\varPhi}} $
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