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Fast Algorithm for Joint Waveform and Filter Design against Interrupted Sampling Repeater Jamming
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摘要: 该文研究了一种快速的抗间歇采样转发干扰波形和滤波器联合设计方法。基于罚函数和帕累托最优化原理给出了联合设计模型的优化数学模型。推导优化波形和滤波器过程中矩阵迹的解析表达式，有效降低了算法的计算复杂度。提出了一种基于平方迭代加速方法，解决了主分量最小化方法目标函数近似造成的算法收敛速度降低问题，进一步加快了算法运行速度。仿真结果表明，该文所提出的算法比传统方法具有更快的运行速度。同时，当干扰目标和真实目标在距离上不可分时，该文方法仍能够有效抑制间歇采样转发干扰。Abstract: To suppress interrupted sampling jamming, a joint waveform and filter design method was proposed in this study. A fast algorithm was also suggested to design sequences with large code lengths. The joint design problem was formulated on the basis of the penalty function and Pareto optimization method. By deriving the theoretical solution of the trace of matrices in each iteration, the computation order of the proposed algorithm was decreased significantly compared to that of the conventional algorithm. Moreover, an accelerated scheme based on the squared iterative method, which further improves the running speed of the algorithm, was proposed. Simulation results demonstrate that the proposed algorithm runs faster than traditional algorithms. Moreover, the designed waveform and filter can be applied to suppress interrupted sampling repeater jamming when the false targets are inseparable from the true targets in time-frequency domains.
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图 1 非匹配滤波性能随着权值的变化曲线
Figure 1. Curves of mismatch output performance versus Pareto weights
图 3 波形和干扰信号非匹配滤波输出(N=512)
Figure 3. Mismatch output of the waveform and jamming signal (N=512)
图 4 积分旁瓣比和积分能量比随峰值增益损耗变化
Figure 4. Integrated sidelobe levels and integrated levels versus loss of processing gain
图 7 波形和干扰信号非匹配滤波输出(N=800)
Figure 7. Mismatch output of waveform and jamming signal (N=800)
图 8 抗间歇采样转发干扰评估
Figure 8. Evaluation of interrupted sampling repeater jamming suppression
图 9 干扰机位置对抗干扰性能的影响
Figure 9. Jamming suppression performance versus location of jammer
图 10 干扰峰值随着重复周期和占空比的估计误差变化图
Figure 10. Jamming peak versus the relative error of pulse repetition period and duty ratio
表 1 快速抗间歇采样转发干扰波形和滤波器联合设计算法
Table 1. Fast algorithm for joint waveform and filter design against interrupted sampling repeater jamming
输入：波形和滤波器长度N 1：用随机相位编码序列初始化${{\boldsymbol{x}}^{\left( 0 \right)}}$ 和${{\boldsymbol{h}}^{\left( 0 \right)}}$； 2：重复 3： $ {{\boldsymbol{h}}_1} = F\left( {{{\boldsymbol{h}}^{\left( l \right)}},{{\boldsymbol{x}}^{\left( l \right)}}} \right) $ 4： $ {{\boldsymbol{h}}_2} = F\left( {{{\boldsymbol{h}}_1},{{\boldsymbol{x}}^{\left( l \right)}}} \right) $ 5： ${{\boldsymbol{r}}_1} = {{\boldsymbol{h}}_1} - {{\boldsymbol{h}}^{\left( l \right)}}$ 6： ${{\boldsymbol{v}}_1} = {{\boldsymbol{h}}_2} - {{\boldsymbol{h}}_1} - {{\boldsymbol{r}}_1}$ 7： $ {\alpha _1} = - {{{{\left\| {{{\boldsymbol{r}}_1}} \right\|}_2}} \mathord{\left/ {\vphantom {{{{\left\| {{{\boldsymbol{r}}_1}} \right\|}_2}} {{{\left\| {{{\boldsymbol{v}}_1}} \right\|}_2}}}} \right. } {{{\left\| {{{\boldsymbol{v}}_1}} \right\|}_2}}} $ 8： $ {{\boldsymbol{h}}^{\left( {l + 1} \right)}} = F\left( {{{\boldsymbol{h}}^{\left( l \right)}} - 2{\alpha _1}{{\boldsymbol{r}}_1} + \alpha _1^2{{\boldsymbol{v}}_1},{{\boldsymbol{x}}^{\left( l \right)}}} \right) $ 9： 若$ f\left( {{{\boldsymbol{x}}^{\left( l \right)}},{{\boldsymbol{h}}^{\left( {l + 1} \right)}}} \right) > f\left( {{{\boldsymbol{x}}^{\left( l \right)}},{{\boldsymbol{h}}^{\left( l \right)}}} \right) $，循环 10： $ {\alpha _1} \leftarrow {{\left( {{\alpha _1} - 1} \right)} \mathord{\left/ {\vphantom {{\left( {{\alpha _1} - 1} \right)} 2}} \right. } 2} $ 11： $ {{\boldsymbol{h}}^{\left( {l + 1} \right)}} = F\left( {{{\boldsymbol{h}}^{\left( l \right)}} - 2\alpha {{\boldsymbol{r}}_1} + {\alpha ^2}{{\boldsymbol{v}}_1},{{\boldsymbol{x}}^{\left( l \right)}}} \right) $ 12： 结束 13： $ {{\boldsymbol{x}}_1} = G\left( {{{\boldsymbol{h}}^{\left( {l + 1} \right)}},{{\boldsymbol{x}}^{\left( l \right)}}} \right) $ 14： $ {{\boldsymbol{x}}_2} = G\left( {{{\boldsymbol{h}}^{\left( {l + 1} \right)}},{{\boldsymbol{x}}_1}} \right) $ 15： ${{\boldsymbol{r}}_2} = {{\boldsymbol{x}}_1} - {{\boldsymbol{x}}^{\left( l \right)}}$ 16： ${{\boldsymbol{v}}_2} = {{\boldsymbol{x}}_2} - {{\boldsymbol{x}}_1} - {{\boldsymbol{r}}_1}$ 17： $ {\alpha _2} = - {{{{\left\| {{{\boldsymbol{r}}_2}} \right\|}_2}} \mathord{\left/ {\vphantom {{{{\left\| {{{\boldsymbol{r}}_2}} \right\|}_2}} {{{\left\| {{{\boldsymbol{v}}_2}} \right\|}_2}}}} \right. } {{{\left\| {{{\boldsymbol{v}}_2}} \right\|}_2}}} $ 18： $ {{\boldsymbol{x}}^{\left( {l + 1} \right)}} = G\left( {{{\boldsymbol{h}}^{\left( {l + 1} \right)}},{{\boldsymbol{x}}^{\left( l \right)}} - 2{\alpha _2}{{\boldsymbol{r}}_2} + \alpha _2^2{{\boldsymbol{v}}_2}} \right) $ 19： 若$ f\left( {{{{\boldsymbol{\tilde x}}}^{\left( l \right)}},{{\boldsymbol{h}}^{\left( {l + 1} \right)}}} \right) > f\left( {{{\boldsymbol{x}}^{\left( l \right)}},{{\boldsymbol{h}}^{\left( {l + 1} \right)}}} \right) $，循环 20: $ {\alpha _2} \leftarrow {{\left( {{\alpha _2} - 1} \right)} \mathord{\left/ {\vphantom {{\left( {{\alpha _2} - 1} \right)} 2}} \right. } 2} $ 21： $ {{\boldsymbol{x}}^{\left( {l + 1} \right)}} = G\left( {{{\boldsymbol{h}}^{\left( {l + 1} \right)}},{{\boldsymbol{x}}^{\left( l \right)}} - 2{\alpha _2}{{\boldsymbol{r}}_2} + \alpha _2^2{{\boldsymbol{v}}_2}} \right) $ 22： 结束 23： $l \leftarrow l + 1$ 24： 直至收敛 输出：波形和滤波器。 
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表 3 仿真参数
Table 3. Simulation parameters
参数 数值 时宽(μs) 40 带宽(MHz) 20 采样重复周期(μs) 10 采样信号时宽(μs) 2.5 雷达位置(m) (0,0,0) 干扰机位置(m) (0,2000,0) 目标位置(m) (0,3000,0) 干扰机时延(μs) 2
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