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摘要: 摘要：经典的直方图方法易受反侦察参数的欺骗干扰。针对此问题，该文提出一种对抗反侦察欺骗干扰的分选方法。通过理论推导建立兼容0～50%脉冲丢失率的骨架周期检测机制；进而联合自相关与交叠率实现骨架周期的精准识别，有效区分伪装成固定脉冲重复间隔(PRI)的干扰项，避免分选被误导；同时引入相干鉴别机制以有效应对参数相似场景，并且实现同一框架内兼容固定、参差、滑变及正弦4种PRI调制。实验表明，面对反侦察参数，直方图方法性能骤降，最大降至0，而所提方法性能最低为96.5%；同时，参数相似场景下该方法性能最低为95.31%。该方法无论反侦察参数存在与否，均可有效应对4种调制，显著提升了复杂电磁环境下的分选可靠性，对电子战系统的发展具有重要意义。Abstract: Radar signal deinterleaving is a critical technology in electronic intelligence and electronic support measures systems. The classical histogram-based method, although valued for its simplicity, is susceptible to deceptive jamming under counter-reconnaissance parameter design. This study proposes a deinterleaving method that is resistant to such deception. The main contributions are as follows: a frame period detection mechanism compatible with pulse missing rates from 0% to 50% is established through theoretical derivation; by integrating autocorrelation and the overlap rate, accurate frame period identification is achieved, which effectively distinguishes interference disguised as fixed Pulse Repetition Intervals (PRI) and prevents interference with the deinterleaving process; moreover, a coherent discrimination mechanism is introduced to handle scenarios with similar parameters and to accommodate fixed, staggered, sliding, and wobulated PRI modulation—within a unified framework. Experimental results show that the performance of histogram-based methods degrades severely in the presence of counterreconnaissance parameters, with maximum performance dropping to 0, while the proposed method maintains a minimum performance of 96.5%. Meanwhile, the proposed method reaches a minimum performance of 95.31% in parameter-similar scenarios. The proposed method remains effective against the four modulation types, whether counterreconnaissance parameters are present or not. It demonstrates antideception capability against counterreconnaissance design, strong generalization across modulation types, and reliable performance in parameter-similar scenarios, thereby greatly improving the deinterleaving reliability in complex electromagnetic environments and offering important implications for the development of electronic warfare systems.
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图 3 相干分解示意图($ \text{p}\_\text{law}=\{{p}_{1},{p}_{2},{p}_{3}\} $)
Figure 3. Diagram of coherent decomposition ($ \text{p}\_\text{law}=\{{p}_{1},{p}_{2},{p}_{3}\} $)
图 4 干扰项作用下的脉冲序列提取结果(非相干分解)
Figure 4. Sequence extraction results under the intervention of interference items (not coherent decomposition)
图 7 不同脉冲丢失率下的自相关及交叠率与自相关的差值(公式计算)
Figure 7. Autocorrelation and the difference between overlap rate and autocorrelation under different missing pulse rates (formula calculation)
图 9 不同阶数条件下对参差信号的分选性能
Figure 9. Performance under different orders in deinteleaving stagered sequences
图 10 不同阶数条件下对滑变信号的分选性能
Figure 10. Performance under different orders in deinteleaving sliding sequences
图 11 不同阶数条件下对正弦信号的分选性能
Figure 11. Performance under different orders in deinteleaving wobulated sequences
表 1 PRI调制类型
Table 1. PRI modulation types
类型 $ \text{p}\_\text{law} $ 固定 $ \{{p}_{i}=K\},N=1 $ 参差 $ \{{p}_{i}={k}_{i}|i=1,2,\cdots ,N\} $ 滑变 $ \{{p}_{i}={K}_{1}+(i-1)\Delta K|i=1,2,\cdots ,N\} $ 正弦 $ \{{p}_{i}={K}_{0}+{K}_{a}\cdot \sin (2\text{π} (i-1)/N+\phi )|i=1,2,\cdots ,N\} $ 组变 $ \{{p}_{i}|i=1,2,\cdots ,N\}=\{{n}_{1}个{s}_{1},{n}_{2}个{s}_{2},\cdots ,{n}_{m}个{s}_{m}\} $ 
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表 2 反侦察参数设计
Table 2. Design of anti-reconnaissance parameters
N 参差 滑变 正弦 3 $ {k}_{1}\colon {k}_{2}\colon {k}_{3}=2\colon 5\colon 7 $ / / 4 $ {k}_{1}\colon {k}_{2}\colon {k}_{3}\colon {k}_{4}=5\colon 7\colon 9\colon 11 $ / $ \phi =\text{3}\text{π} /4 $ 5 $ {k}_{1}\colon {k}_{2}\colon {k}_{3}\colon {k}_{4}\colon {k}_{5}=5\colon 7\colon 18\colon 11\colon 19 $ $ \Delta K={K}_{1}/4 $ 6 / $ \Delta K=2{K}_{1}/3 $ $ \phi =\text{2}\text{π} /3 $ 7 / $ \Delta K={K}_{1}/9,{K}_{1}/3,{K}_{1},3{K}_{1} $ / 8 / / $ \phi =\text{5}\text{π} /\text{8} $
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表 3 不同脉冲丢失率下积极样本剩余比例
Table 3. Remaining proportion of positive samples under various missing pulse rates
脉冲丢失率 均值 标准差 10% 0.8064 0.0246 20% 0.6381 0.0299 30% 0.4891 0.0308 40% 0.3595 0.0284 50% 0.2481 0.0249 注：加粗数值表示应用3倍标准差准则时标准差的参考基准。
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表 4 不同脉冲丢失率下的自相关及交叠率与自相关的差值(计算机仿真)
Table 4. Difference between overlap ratio and autocorrelation under different pulse missing rates in computer simulations (computer simulation)
脉冲丢失率 均值(N=1) 标准差(N=1) 均值(N=2) 标准差(N=2) 20% 0.1288 0.0100 0.2576 0.0201 30% 0.1474 0.0090 0.2948 0.0179 40% 0.1446 0.0086 0.2891 0.0171 50% 0.1258 0.0098 0.2516 0.0196 注：加粗数值表示应用3倍标准差准则时均值与标准差的参考基准。
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表 5 相干时不同交叠长度下的鉴别指标
Table 5. Discrimination indicator under different overlap lengths for the coherent case
交叠长度 均值 QF(0.98) 20 0.0020 0.0026 30 0.0020 0.0025 40 0.0020 0.0024 50 0.0020 0.0024 60 0.0020 0.0023 注：加粗数值表示相干鉴别阈值设置基准。
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表 6 不相干时不同交叠长度下的鉴别指标
Table 6. Discrimination indicator under different overlap lengths for the incoherent case
交叠长度 均值 EC( 0.0026 )5 0.0069 0.1678 10 0.0096 0.0478 15 0.0116 0.0128 20 0.0133 0.0050 25 0.0150 0.0030
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表 7 PRI调制设置
Table 7. PRI modulation settings
类型 $ \text{p}\_\text{law} $ 固定 $ K\in [50,100]\;\text{μs} $ 参差 $ {k}_{i}\in [2,19]\times 10\;\text{μs},{k}_{i}/10两两互质,N\in \{3,4,5\} $ 滑变 $ {K}_{1}\in [30,50]\;\text{μs},\Delta K\in [4,8]\;\text{μs},N\in \{5,6,7\} $ 正弦 $ {K}_{0}\in [60,80]\;\text{μs,}{K}_{a} \in [10,30]\;\text{μs,}\phi \in [-\text{π} ,\text{π} ],N \in \{4,6,8\} $
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表 8 不同脉冲丢失率下对固定信号的分选性能(%)
Table 8. Performance under different missing rate in deinteleaving fixed sequences (%)
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表 9 参数相似场景下的分选性能(%)
Table 9. Performance in scenarios with similar parameters (%)
脉冲丢失率 固定 参差 滑变 正弦 10% 99.84 98.21 99.61 97.46 20% 99.84 96.32 99.16 98.22 30% 99.82 97.77 98.23 98.42 40% 99.81 95.31 97.66 98.68
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