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摘要: 针对多目标突防组网雷达系统(NRS)场景，该文提出一种面向组网雷达干扰任务的多干扰机资源联合优化分配方法。首先，采用组网雷达在干扰环境中对目标的检测概率作为干扰性能指标；然后，结合不同突防目标的检测性能需求，建立了包含干扰波束和发射功率2个优化变量的资源优化模型，并利用粒子群算法对资源优化问题进行求解；最后，考虑到组网雷达系统参数不确定性带来的检测概率泛化误差，建立了干扰资源稳健优化分配模型。仿真结果表明，该文提出的优化方法能有效压制组网雷达，降低组网雷达对突防目标的检测概率；相比传统方法，稳健方法提升了多干扰机对组网雷达的协同干扰性能，且具有鲁棒性。Abstract: An optimal joint allocation of multijammer resources is proposed for jamming a Netted Radar System (NRS) in the case of multitarget penetration. First, the multitarget detection probabilities of NRS in the suppressive jamming environment are used as an interference performance metric. Then, the resource optimization model is established, including two optimization variables, namely, jamming beam and transmitting power, considering the detection performance requirements of different targets. Particle swarm optimization is used to solve the resource-optimization problem. Finally, considering the generalization error of the detection probability caused by the parameter uncertainty of the NRS, the robust resource-optimization model is established. The simulation results show that the proposed optimization model is effective in suppressing the NRS and reducing the probability of the penetrating targets detected by the NRS. Compared with the traditional method, the robust algorithm improves the cooperative interference performance of multiple jammers against NRS and is robust.
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图 2 干扰机、雷达和目标的空间位置关系
Figure 2. Relative geometry position of the jammer, radar and target
图 5 优化算法资源分配结果
Figure 5. The results of resource allocation achieved by the proposed optimization strategy
图 6 稳健算法资源分配结果
Figure 6. The results of resource allocation achieved by the proposed robust strategy
图 9
$k = 15$ 时代价函数适应度值收敛曲线Figure 9. The convergence curve of the cost function fitness value at
$k = 15$ 表 1 不同融合准则下的组网雷达检测概率
Table 1. The detection probability of the NRS with different fusion rules
融合准则 检测概率 AND准则($K = N$) ${\rm{Pd} }_k^q = {\displaystyle\prod\limits_{i = 1}^N } {\rm{Pd} }_{i,k}^q$ OR准则($K = 1$) ${\rm{Pd} }_k^q = 1 - \displaystyle\prod \limits^N_{i = 1} (1 - {\rm{Pd} }_{i,k}^q)$ 秩K准则 ${\rm{Pd} }_k^q = \displaystyle\sum\limits_{j = K}^N {\left\{ {\sum\limits_{\forall \left\{ {\sum {v_{i,k}^q = j} } \right\} } {\mathop \prod \limits_i { {({\rm{Pd} }_{i,k}^q)}^{v_{i,k}^q} }{ {(1 - {\rm{Pd} }_{i,k}^q)}^{1 - v_{i,k}^q} } } } \right\} }$ 
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表 2 基于PSO的波束指向
$\boldsymbol{u}_k^{{\rm{opt}}}$ 求解方法Table 2. The solution algorithm of the beam selection
$\boldsymbol{u}_k^{{\rm{opt}}}$ based on PSO步骤1 初始化$\boldsymbol{P}_k^{{\rm{uni}}}$, $\boldsymbol{u}_k^{{\rm{opt}}}{\rm{ = }}{{\bf{0}}_{M \times N}}$, $\boldsymbol{u}_k^{{\rm{con}}} \in [0,1]$； 步骤2 PSO求解式(32)，得到松弛结果$\boldsymbol{u}_{k,{\rm{opt}}}^{{\rm{con}}}$； 步骤3 循环$l = 1, 2,··· ,L \times M$
寻找最大值$[{m_l},{i_l}] = \arg \;\max \{ \boldsymbol{u}_{k,{\rm{opt}}}^{{\rm{con}}}\} $;
更新$\boldsymbol{u}_k^{{\rm{opt}}}({m_l},{i_l}) = 1$，且$\boldsymbol{u}_{k,{\rm{opt}}}^{{\rm{con}}}({m_l},{i_l}) = 0$;
判断$\boldsymbol{u}_k^{{\rm{opt}}}$是否满足式(2)—式(4)的约束条件，若不满足则
$\boldsymbol{u}_k^{{\rm{opt}}}({m_l},{i_l}) = 0$;
循环结束步骤4 输出波束指向结果$\boldsymbol{u}_k^{{\rm{opt}}}$。
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表 3 干扰机工作参数
Table 3. The working parameters of the jammer
参数 数值 干扰机总功率$P_m^{{\rm{total}}}$ 130 W 波束个数L 2 天线增益$G_m^{\rm{J}}$ 10 dB 极化失配损失${\gamma ^{\rm{J}}}$ 0.5 工作波长${\lambda _{\rm{f}}}$ 0.1 m 天线波瓣宽度${\theta _{0.5}}$ 3°
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表 4 雷达工作参数
Table 4. The working parameters of the radar node
参数 数值 发射功率$P_i^{\rm{t}}$ 200 MW 最多被干扰波束个数$S$ 1 发射天线增益$G_i^{\rm{t}}$ 40 dB 虚警概率 10–6 工作波长${\lambda _{\rm{f}}}$ 0.1 m
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