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Joint Design of Doppler-tolerant Complementary Sequences and Receiving Filters Against Interrupted Sampling Repeater Jamming
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摘要: 作为一种典型的相干干扰，间歇采样转发干扰利用欠采样原理，能够在雷达接收机产生多个高逼真假目标，使雷达对真实目标的检测失效。针对这一问题，该文提出了一种基于多普勒容忍的多脉冲互补序列和接收滤波器联合设计的抗间歇采样转发干扰方法。首先，考虑设计序列的多普勒容限，以最小化发射序列和接收滤波器模糊函数旁瓣能量以及干扰信号和接收滤波器模糊函数能量为优化指标，同时考虑了发射波形的恒模约束以及非匹配滤波体制的信噪比损失约束等。然后，提出了基于优化最小化方法的交替迭代优化算法解决所提出的非凸优化问题。最后，仿真实验表明，相比于传统方法，该文方法设计的收发序列具有更好的脉压旁瓣性能和抗间歇采样转发干扰性能，能够显著提升雷达在干扰场景下对运动目标的检测能力。Abstract: As a typical coherent jamming method, Interrupted Sampling Repeater Jamming (ISRJ) can generate multiple false targets with high fidelity at the radar receiver using under-sampling, which causes real targets detection to become invalid. To solve this problem, an anti-ISRJ method based on the joint design of Doppler-tolerant complementary sequences and receiving filters is proposed in this paper. First, by considering the Doppler tolerance of sequences, the sum of the energy of the ambiguity function of transmitted sequences and receiving filters and energy of the ambiguity function of ISRJ signals and receiving filters is chosen as the objective function. Meanwhile, the constant modulus constraint on sequences and signal-to-noise ratio constraint are considered. Then, an alternately iterative algorithm based on the Majorization-Minimization (MM) method is proposed to solve the non-convex optimization problem. Finally, numerical results are presented as a way to compare with conventional methods, and the sequences and receiving filters designed by the proposed method show better pulse compression correlation and anti-ISRJ performance. These procedures can substantially improve the radar detection ability to move targets in the jamming scene.
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图 2 设计序列的模糊函数性能
Figure 2. Ambiguity functions of designed sequences by the proposed method
图 4 不同信干比和信噪比条件下下本文方法脉压输出干扰峰值
Figure 4. The jamming peak of the pulse compression output of the proposed method with different SJRs and SNRs
图 5 不同干扰参数下ISRJ信号脉压输出峰值
Figure 5. The peak of the pulse compression output of the ISRJ signals under different jamming parameters
表 1 抗ISRJ的多普勒容忍互补序列和接收滤波器集联合设计流程
Table 1. Joint design of Doppler tolerant complementary sequences and receiving filters for anti-ISRJ
1：令$i = 0$，利用随机相位序列初始化${{\boldsymbol{x}}^{\left( 0 \right)} }$和${{\boldsymbol{h}}^{\left( 0 \right)} }$ 2：重复 3：对于固定的${{\boldsymbol{x}}^{\left( i \right)} }$，根据式(23)和式(24)计算矩阵${\boldsymbol{P}}_{}^{\left( i \right)}$和矢量${{\boldsymbol{p}}^{\left( i \right)} }$ 4：利用SQUAREM加速框架和式(26)更新计算${{\boldsymbol{h}}^{\left( {i + 1} \right)} }$ 5：对于固定的${{\boldsymbol{h}}^{\left( {i + 1} \right)} }$，根据式(31)和式(32)计算矩阵${{\boldsymbol{Q}}^{\left( {i + 1} \right)} }$和
矢量${{\boldsymbol{q}}^{\left( {i + 1} \right)} }$6：利用SQUAREM加速框架和式(34)更新计算${{\boldsymbol{x}}^{\left( {i + 1} \right)} }$ 7：令$i = i + 1$ 8：直到满足收敛准则。输出${{\boldsymbol{x}}^{\left( i \right)} }$和${{\boldsymbol{h}}^{\left( i \right)} }$ 
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表 2 互补序列和接收滤波器模糊函数旁瓣峰值和实际信噪比损失(dB)
Table 2. Peak sidelobe levels and actual SNR losses of the ambiguity functions of complementary sequences and receiving filters (dB)
信噪比损失约束 脉冲数 K = 2 K = 4 K = 6 $\mu = 1.0{\text{ dB}}$ $ - 38.78\left( {1.017} \right)$ $ - 46.26\left( {1.007} \right)$ $ - 53.52\left( {1.007} \right)$ $\mu = 1.5{\text{ dB}}$ $ - 39.28\left( {1.512} \right)$ $ - 51.95\left( {1.503} \right)$ $ - 56.71\left( {1.501} \right)$ $\mu = 2.0{\text{ dB}}$ $ - 39.61\left( {2.016} \right)$ $ - 52.71\left( {2.003} \right)$ $ - 62.83\left( {2.001} \right)$
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表 3 ISRJ信号和接收滤波器模糊函数峰值(dB)
Table 3. Peak levels of the ambiguity functions of ISRJ signals and receiving filters (dB)
信噪比损失约束 脉冲数 K = 2 K = 4 K = 6 $\mu = 1.0{\text{ dB}}$ $ - 39.41$ $ - 48.93$ $ - 53.51$ $\mu = 1.5{\text{ dB}}$ $ - 39.55$ $ - 51.64$ $ - 56.39$ $\mu = 2.0{\text{ dB}}$ $ - 40.01$ $ - 52.16$ $ - 60.82$
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表 4 干扰场景仿真参数
Table 4. Simulation parameters of the jamming scene
参数 数值 雷达载频 ${f_0} = 2{\text{ GHz}}$ 脉冲重复频率 ${\text{PRF} } = 5{\text{ kHz} }$ 目标距离 ${d_1} = 7400{\text{ m}},{d_2} = 8000{\text{ m}}$ 目标速度 ${v_1} = 30{\text{ } }{ {\text{m} }/ {\rm{s}}},{v_2} = 40{\text{ } }{ {\text{m} } / {\rm{s}}}$ 目标雷达散射截面积 ${\text{RCS}}_1^2{\text{ = }}0{\text{ dB}},{\text{RCS}}_2^2{\text{ = }} - 10{\text{ dB }}$ ISRJ干扰机距离 ${\bar d_1} = 9000{\text{ m}},{\bar d_2} = 9500{\text{ m}}$ ISRJ干扰机速度 ${\bar v_1} = 0{\text{ } }{ {\text{m} } /{\rm{s}}},{\bar v_2} = 0{\text{ } }{ {\text{m} }/{\rm{s}}}$ ISRJ干扰机时延 0.5 μs 信干比 $- 15{\text{ dB} }$ 信噪比 $15{\text{ dB} }$
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