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摘要: 传统的组网雷达功率分配一般在干扰模型给定的情况下进行优化，而干扰机资源优化是在雷达功率分配方式给定情况下，这样的研究缺乏博弈和交互。考虑到日益严重的雷达和干扰机相互博弈的作战场景，该文提出了伴随压制干扰下组网雷达功率分配深度博弈问题，其中智能化的目标压制干扰采用深度强化学习(DRL)训练。首先在该问题中干扰机和组网雷达被映射为两个智能体，根据干扰模型和雷达检测模型建立了压制干扰下组网雷达的目标检测模型和最大化目标检测概率优化目标函数。在组网雷达智能体方面，由近端策略优化(PPO)策略网络生成雷达功率分配向量；在干扰机智能体方面，设计了混合策略网络来同时生成波束选择动作和功率分配动作；引入领域知识构建更加有效的奖励函数，目标检测模型、等功率分配策略和贪婪干扰功率分配策略3种领域知识分别用于生成组网雷达智能体和干扰机智能体的导向奖励，从而提高智能体的学习效率和性能。最后采用交替训练方法来学习两个智能体的策略网络参数。实验结果表明；当干扰机采用基于DRL的资源分配策略时，采用基于DRL的组网雷达功率分配在目标检测概率和运行速度两种指标上明显优于基于粒子群的组网雷达功率分配和基于人工鱼群的组网雷达功率分配。Abstract: The traditional networked radar power allocation is typically optimized with a given jamming model, while the jammer resource allocation is optimized with a given radar power allocation method; such research lack gaming and interaction. Given the rising seriousness of combat scenarios in which radars and jammers compete, this study suggests a deep game problem of networked radar power allocation under escort suppression jamming, in which intelligent target jamming is trained using Deep Reinforcement Learning (DRL). First, the jammer and the networked radar are mapped as two agents in this problem. Based on the jamming model and the radar detection model, the target detection model of the networked radar under suppressed jamming and the optimized objective function for maximizing the target detection probability are established. In terms of the networked radar agent, the radar power allocation vector is generated by the Proximal Policy Optimization (PPO) policy network. In terms of the jammer agent, a hybrid policy network is designed to simultaneously create beam selection and power allocation actions. Domain knowledge is introduced to construct more effective reward functions. Three kinds of domain knowledge, namely target detection model, equal power allocation strategy, and greedy interference power allocation strategy, are employed to produce guided rewards for the networked radar agent and the jammer agent, respectively. Consequently, the learning efficiency and performance of the agent are improved. Lastly, alternating training is used to learn the policy network parameters of both agents. The experimental results show that when the jammer adopts the DRL-based resource allocation strategy, the DRL-based networked radar power allocation is significantly better than the particle swarm-based and the artificial fish swarm-based networked radar power allocation in both target detection probability and run time metrics.
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图 1 压制干扰机掩护目标穿越组网雷达防区的示例
Figure 1. An example of a suppression jammer protecting a target through the networked radar defense area
图 2 干扰机智能体和组网雷达智能体的博弈流程图
Figure 2. The game closed-loop process of the jammer agent and the networked radar agent
图 3 干扰机、雷达和目标的相对空间位置
Figure 3. The relative spatial position of the jammer, radar and target
图 4 组网雷达智能体与环境交互图
Figure 4. The networked radar agent and environment interaction diagram
图 5 知识辅助的组网雷达智能体奖励模块
Figure 5. The knowledge-assisted reward module for the networked radar agent
图 8 知识辅助的干扰机智能体奖励函数模块
Figure 8. The knowledge-assisted reward function module for the jammer agent
图 10 组网雷达部署和目标编队轨迹
Figure 10. The deployment of the networked radar and the trajectory of the target formation
图 13 3种组网雷达功率分配策略的目标检测概率
Figure 13. The target detection probability of three networked radar power allocation strategies
图 14 不同干扰模式下基于DRL组网雷达功率分配策略的目标检测概率
Figure 14. The target detection probability of the DRL-based networked radar power allocation strategy under different interference models
图 17 干扰机和组网雷达的距离变化
Figure 17. The distance variation of the jammer and the networked radar
表 1 雷达工作参数
Table 1. The working parameters of the radars
参数 数值 参数 数值 发射总功率$P_{\text{r}}^{{\text{total}}}$ 10 mW 工作频率 100 GHz 最小发射功率$P_{\text{r}}^{\min }$ 0 最大发射功率$P_{\text{r}}^{\max }$ 2 mW 天线增益${G_{\text{r} } }$ 45 dB 虚警概率${P_{\text{f}}}$ 10–6 
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表 2 干扰机工作参数
Table 2. The working parameters of the jammer
参数 数值 参数 数值 干扰总功率$ P_{\text{j}}^{{\text{total}}} $ 60 W 干扰天线增益${G_{\text{j}}}$ 10 dB 最小发射功率$ P_{\text{j}}^{\min } $ 0 最大发射功率$ P_{\text{j}}^{\max } $ 60 W 干扰波束个数L 3 天线波瓣宽度$ {\theta _{0.5}} $ 3° 工作频率 100 GHz 极化失配损失$ {\gamma _{\text{j}}} $ 0.5
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表 3 算法参数设置
Table 3. The algorithm parameters setting
参数 取值 参数 取值 离散Actor的NN层数/节点数 3/128 离散Actor网络学习率 3e–3 连续Actor的NN层数/节点数 3/128 连续Actor网络学习率 3e–3 批量训练样本大小 128 经验回放区大小 1024 Critic网络学习率 3e–3 执行性奖励权重 0.15 PPO裁剪参数 0.2 检测概率奖励权重 0.85 折扣因子 0.998 优化器 Adam 衰减因子$\beta $ 0.9999 导向奖励参数${b_1},{b_2}$ 0.5, 0.1
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表 4 各策略的资源调度运行时间
Table 4. The resource scheduling running time of each strategy
调度策略 资源调度运行时间(s) 基于DRL的分配策略 0.009237 基于PSO的分配策略 5.227107 基于AFSA的分配策略 67.365983
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