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RF Stealth-Oriented Joint Optimization Algorithm for the Detection Window and Beam-Position Energy in Space-Based Radar Regional Search
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摘要: 针对天基雷达区域搜索场景下时序耦合带来的射频隐身能量管控难题，该文提出面向射频隐身的天基雷达区域搜索探测窗口与波位能量联合优化算法。首先，将搜索区域离散为波位集合，根据天基雷达运动特性与波位串行驻留时序，建立考虑探测窗口、波位能量及时变几何链路的波位检测概率模型；结合波位先验威胁权重，对各波位检测概率进行加权融合，推导包含波位先验威胁、探测窗口起始时刻、时变几何链路系数与波位能量等参数的区域加权检测概率解析表达式，并将其作为区域搜索任务性能的衡量指标。在此基础上，构建面向射频隐身的天基雷达区域搜索探测窗口与波位能量联合优化模型，即以最小化天基雷达总辐射能量为优化目标，以满足预先设定的区域加权检测概率阈值、单波位能量上/下界和区域可见窗口要求为约束条件，对探测窗口起始时刻与波位能量进行联合优化设计。针对上述优化问题，设计外层探测窗口起始时刻搜索与内层波位能量迭代优化相结合的双层联合求解框架：外层以总辐射能量最小化为准则确定探测窗口起始时刻，内层迭代更新波位照射时刻和时变几何链路系数，并基于Karush-Kuhn-Tucker (KKT) 条件求解约束能量分配。仿真结果表明，与现有方法相比，所提算法能够进一步降低天基雷达在区域搜索任务中的总辐射能量，从而提升其射频隐身效能。Abstract: To address the challenge of radio frequency (RF) stealth energy management induced by temporal coupling in space-based radar regional search scenarios, this paper proposes an RF stealth-oriented joint optimization algorithm for the detection window and beam-position energy in space-based radar regional search. First, based on the motion characteristics of the space-based radar and by jointly considering the detection window, beam-position energy, and time-varying geometric link, the algorithm derives the beam-position detection probability. Next, the prior threat weight of each beam position is incorporated into a regional composite detection metric for characterizing the regional search performance. The optimization aims to minimize the total radiated energy of the space-based radar subject to multiple constraints: the prescribed weighted-detection probability threshold, the upper and lower bounds of single-beam-position energy, and the visible-window time. Accordingly, the start time of the detection window is optimized jointly with the beam-position energy. Finally, a two-layer joint solution framework is designed to address the coupling among the detection window, beam-position energy, and time-varying geometric link. The outer layer optimizes the start time of the detection window using minimal total radiated energy as the criterion. The inner layer iteratively updates the beam-position illumination time and geometric link coefficient and solves the constrained energy allocation under the Karush–Kuhn–Tucker conditions. Simulation results show that compared with existing methods, the proposed algorithm can further reduce the total radiated energy of the space-based radar while satisfying the specified regional search performance requirement, thereby enhancing its RF stealth performance.
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Key words:
- RF stealth /
- Space-based radar /
- Detection window /
- Energy management /
- Regional search
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图 3 探测窗口起始时刻对所需辐射能量与探测窗口时长的影响
Figure 3. Impact of detection-window initiation time on the required radiated energy and detection window duration
图 4 优化探测窗口起始时刻下的波位检测概率与能量分配结果
Figure 4. Beam-position detection probability and energy allocation results at the optimized detection start time
图 5 不同算法能量消耗与检测性能对比
Figure 5. Comparison of energy consumption and detection performance under different algorithms
1 面向射频隐身的天基雷达区域搜索探测窗口与波位能量联合优化算法
1. RF stealth-oriented joint optimization algorithm of detection window and beam-position energy for space-based radar regional search
输入：区域可见窗口、波位集合及固定执行序列、先验威胁权重、
轨道与几何链路模型、雷达系统参数、检测概率门限、单波位能
量上/下界、候选起始时刻间隔、最大迭代次数、收敛阈值。输出：探测窗口起始时刻、探测结束时刻、波位能量分配结果、
区域加权检测概率、总辐射能量、探测窗口时长。步骤1 根据区域可见窗口和候选起始时刻间隔，生成候选探测
窗口起始时刻集合，并初始化；对每一个候选探测窗口起始时刻，
按照固定执行序列初始化各波位照射时刻和几何链路系数；步骤2 在当前几何链路系数下，构造满足检测概率门限和单波
位能量上/下界约束的波位能量分配子问题；基于KKT条件求解
当前子问题，得到该次迭代下的波位能量分配结果；步骤3 根据当前波位能量分配结果更新各波位驻留时间，并按
串行执行序列递推更新各波位实际照射时刻；步骤4 根据更新后的照射时刻重新计算各波位几何链路系数，
判断能量分配结果是否收敛；若未收敛，则返回步骤2继续迭
代；若收敛，更新结果；步骤5 输出探测窗口起始时刻、探测结束时刻、波位能量分配
结果、区域加权检测概率、总辐射能量和探测窗口时长；
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表 1 天基雷达仿真参数设置
Table 1. Simulation parameters of the space-based radar
参数 数值 参数 数值 $ {G}_{\text{t}} $ 46 dB $ {L}_{\text{s}} $ 3 dB $ \lambda $ 0.03 m $ {k}_{\text{B}} $ $ 1.38\times {10}^{-23}\;\text{J/K} $ $ {T}_{\text{e}} $ 290 K $ \sigma $ $ 1\;{\text{m}}^{2} $ $ {A}_{\text{e}} $ 4 m2 $ {P}_{\text{fa}} $ $ 1\text{e}-6 $
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表 2 不同策略下的能量消耗与探测窗口对比
Table 2. Comparison of energy consumption and detection window under different algorithms
算法策略 窗口起始时刻/s 窗口时长/s 总辐射能量/ (kJ) 能量节约比 均匀资源分配基线 171.44 25.52 63.79 27.62% 先验加权分配基线 161.80 21.82 54.55 15.36% 几何加权分配基线 171.44 25.10 62.74 26.41% 本文所提算法 168.23 18.47 46.17 -
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