Collaborative Interference Resource Allocation Method Based on Improved Secretary Bird Algorithm
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摘要: 在战场环境中，针对多波束干扰系统突防组网雷达场景下干扰资源分配的问题，该文提出一种引入柯西变异和全局协同控制策略的改进秘书鸟算法(ISBOA)对战场上的干扰资源进行优化分配。首先，建立突防场景下的多波束干扰系统模型，并将组网雷达检测融合概率作为多干扰机协同压制干扰组网雷达的性能评估指标；其次，以最小化检测概率为目标函数，对多干扰机干扰样式、干扰波束和功率资源进行联合优化分配；最后，利用ISBOA进行求解。实验结果经过对比表明，ISBOA算法搜索能力更强，收敛精度更高，具有更强的稳定性，能够更加合理地分配战场上的干扰资源。Abstract:
Objective In the complex electromagnetic environment of Networked Radars (NR), efficiently utilizing limited interference resources to reduce enemy detection capabilities and support successful penetration remains a critical challenge. Existing heuristic algorithms, while partially effective, do not jointly optimize interference patterns, beams, and power resources in multi-beam systems, limiting their applicability in penetration scenarios. To address this limitation, this study proposes an interference resource allocation strategy based on the Improved Secretary Bird Optimization Algorithm (ISBOA). The proposed strategy minimizes detection probability by integrating Cauchy mutation and global collaborative control, enabling the joint optimization of interference patterns, beams, and power across multiple jammers. This approach ensures rational resource allocation, enhances search capability, and improves convergence accuracy, thereby meeting the demands of penetration scenarios. The findings provide a novel solution for interference resource allocation in multi-beam systems against NR. Methods This study models the complex interference resource allocation problem as a multi-constrained nonlinear mixed-integer programming problem and addresses it using an improved intelligent optimization algorithm. A mixed-integer programming model incorporating interference patterns, beams, and power resources is established, with the detection and fusion probability of networked radar as the performance evaluation metric. The model accounts for the dynamic interactions between radars and jammers, as well as the pulse compression gains of various interference patterns. To overcome the limitations of the traditional Secretary Bird Optimization Algorithm (SBOA) in handling discrete variables and complex constraints, the study integrates Cauchy mutation and global collaborative control strategies. Cauchy mutation leverages its long-tail characteristics to enhance the algorithm’s global search capability, reducing the risk of convergence to local optima. The global collaborative control strategy incorporates penalty factors to ensure compliance with multi-variable constraints, enabling the simultaneous optimization of discrete and continuous variables. Results and Discussions This study presents an innovative interference resource allocation method for multi-beam jamming systems targeting networked radar, leveraging the ISBOA. By integrating Cauchy mutation and global cooperative control strategies, ISBOA significantly enhances optimization performance. Simulation results indicate that ISBOA outperforms other algorithms, including the original SBOA, Harris Hawks Optimizer (HHO), and Sparrow Search Algorithm (SSA). In a scenario with six jammers and eight radars, ISBOA achieved an optimal function value of 0.6095 , which is notably lower than0.8158 (SBOA),1.2666 (HHO), and1.3679 (SSA) (Fig. 4 ). Moreover, ISBOA demonstrated faster convergence and greater stability across 50 independent experiments, yielding an average optimal function value of0.6892 (Fig. 5 ) and a convergence error of0.1449 (Fig. 6 ). ISBOA’s joint optimization of interference patterns, beams, and power resources enables more efficient allocation of jamming resources and reduces the detection probability of networked radar. This advantage is further validated across various scenarios, where ISBOA consistently outperformed other algorithms in solution quality and computational efficiency (Fig. 8 ). The experimental results highlight ISBOA’s robustness and adaptability, demonstrating its potential for application in complex battlefield environments.Conclusions This study proposes an optimization method for interference resource allocation in multi-beam jamming systems targeting networked radar scenarios, utilizing ISBOA. A mixed-integer programming model integrating interference patterns, beams, and power resources is developed. ISBOA incorporates Cauchy mutation and global cooperative control strategies to enhance global search capability and stability. Simulation results demonstrate that ISBOA outperforms the original SBOA, HHO, and SSA in terms of convergence speed and search efficiency. ISBOA exhibits superior stability and enables more rational allocation of interference resources, effectively reducing the detection probability of networked radar. Moreover, ISBOA demonstrates strong adaptability and robustness across various scenarios, providing an effective solution for interference resource allocation in complex battlefield environments. -
表 1 干扰信号脉压增益
干扰样式 脉压增益 参数说明 随机移频干扰 ${\left(1 - \dfrac{{|\zeta |}}{B}\right)^2}B\tau $ $\zeta $为移频宽度
$B$为信号宽度
$\tau $为信号时宽卷积灵巧噪声干扰 $\dfrac{{\tau + {\tau _n}}}{{1/B + {\tau _n}}}$ ${\tau _n}$为噪声时宽 间歇采样重复转发干扰 $\left( {\begin{array}{*{20}{c}} {{\eta ^2} + 2\dfrac{{{{\sin }^2}\left( {\pi \eta } \right)}}{{{\pi ^2}}}} \end{array}} \right)B\tau $ $\eta $为间隙采样占空比 
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表 2 不同融合准则对应的检测概率
融合准则 检测概率 AND准则(K=N) $ {\rm{P d}}_{q}^{t}=\displaystyle\prod_{n=1}^{N} {\rm{P d}}_{n, A}^{t} $ OR准则(K=1) ${\mathrm{Pb}}_q^t=1-\displaystyle\prod_{n=1}^N(1-{\mathrm{Pd}}_{n,q}^t) $ 秩K准则 ${\mathrm{Pd}}_q^t = \displaystyle\sum\limits_{f = K}^N {\left\{ {\displaystyle\sum\limits_{\forall \left\{ {\displaystyle\sum {{h_n}} = f} \right\}} {\left( {\displaystyle\prod\limits_n {{{\left( {{\mathrm{Pd}}_{n,q}^t} \right)}^{{h_n}}}} {{\left( {1 - {\mathrm{Pd}}_{n,q}^t} \right)}^{1 - {h_n}}}} \right)} } \right\}} $
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表 3 雷达的仿真参数设置
参数名称 参数值 雷达功率(kW) 200 天线增益(dB) 45 脉冲宽度(μs) 1 工作波长(m) 0.1 虚警概率 ${10^{ - 6}}$ 目标雷达散射截面(m2) 1 有效噪声温度(K) 290 噪声系数(dB) 3
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表 4 干扰机及干扰信号参数设置
参数名称 参数值 干扰总功率(W) 600 单机最小发射功率(W) 0 单机最大发射功率(W) 100 天线增益(dB) 10 极化失配损失 0.5 间歇转发占空比 0.5 移频最大带宽(MHz) 2.5 卷积视频噪声宽度(μs) 0.2
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表 6 算法总体性能对比
算法名称 最优目标函数平均值 收敛误差平均值 ISBOA 0.6892 0.1449 SBOA 0.6936 0.1647 HHO 0.9409 0.1911 SSA 0.9924 0.2384
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