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A Novel Joint Radar-communication Waveform Design Method Based on Distributed Aperture
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摘要: 雷达通信一体化波形设计是近年来的研究热点。基于紧凑式阵列的一体化波形支持多方向目标探测和多用户通信，但面对主瓣内同方向不同距离的干扰和窃听行为时，存在抗主瓣干扰能力差、通信信息泄露等问题。因此，该文提出了一种基于分布式孔径的雷达通信一体化波形设计方法以操控波形在三维空间的分布。首先，根据近场信号传播模型建立波形合成约束，在指定位置合成所需的雷达和通信波形。然后，对各个子孔径增加恒模约束，构建以最小化发射功率为准则的一体化波形优化模型。由于模型的非凸性，采用交替投影算法进行迭代求解。仿真结果表明，该文所提方法在雷达目标和通信目标位置同时合成了期望波形，实现了三维空间波形操控。Abstract: Joint radar-communication waveform design has been the focus of intensive research in recent years. The integrated waveform based on a collocated antenna can simultaneously detect targets and communicate with multiple users in different directions. However, integrated waveforms possess poor anti-jamming properties and lack secure communication abilities, which limits their capacity to address the jamming and eavesdropping behaviors that generate at various ranges in the same beam direction. In this study, a novel joint radar-communication waveform design method based on a distributed aperture is proposed to control waveform distributions in the three-dimensional space. First, the waveform synthesis constraint is established to synthesize the desired radar and communication waveforms in designated directions. Second, the constant modulus constraint is added to each sub-aperture, following which an integrated waveform optimization model is established based on the minimum transmission power. Finally, the alternating projection algorithm is used to iteratively solve the nonconvex optimization problem. Simulation results demonstrate that the proposed method synthesizes desired waveforms at target positions and realizes three-dimensional spatial waveform manipulation.
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图 2 基于紧凑式阵列的一体化波形空间能量和波形分布示意图
Figure 2. Space energy and waveform distribution of the integrated waveform based on collocated antenna
图 4 分布式孔径与波胞的几何关系
Figure 4. Geometric relationship between distributed aperture and wave cell
图 8 场景1中雷达合成波形的空间分布情况
Figure 8. Spatial distribution of radar synthetic waveform in the first scenario
图 9 场景1中雷达目标周围合成波形的时域表现
Figure 9. Time domain representation of synthetic waveforms around radar target in the first scenario
图 10 场景1中通信合成波形的空间分布情况
Figure 10. Spatial distribution of communication synthetic waveform in the first scenario
图 11 场景1中通信目标周围合成波形表现
Figure 11. Performance of synthetic waveforms around communication user in the first scenario
图 14 场景2中雷达合成波形的空间分布情况
Figure 14. Spatial distribution of radar synthetic waveforms in the second scenario
图 15 场景2中雷达目标周围合成波形的时域表现
Figure 15. Time domain representation of synthetic waveforms around radar target in the second scenario
图 16 场景2中通信合成波形的空间分布情况
Figure 16. Spatial distribution of radar synthetic waveform in the second scenario
图 17 场景2中通信目标周围合成波形表现
Figure 17. Performance of synthetic waveforms around communication user in the second scenario
图 20 场景3中雷达合成波形的空间分布情况
Figure 20. Spatial distribution of radar synthetic waveforms in the third scenario
图 21 场景3中雷达目标周围合成波形的时域表现
Figure 21. Time domain representation of synthetic waveforms around radar target in the third scenario
图 22 场景3中通信合成波形的空间分布情况
Figure 22. Spatial distribution of radar synthetic waveform in the third scenario
图 23 场景3中通信目标周围合成波形表现
Figure 23. Performance of synthetic waveforms around communication user in the third scenario
1 基于“波胞形成”的一体化波形优化模型求解算法流程
1. Integrated waveform optimization model solving algorithm based on “wave cell”
1. 输入：A, S, I, $ {\boldsymbol{\varepsilon }}$ 2. 初始化：计算${{\boldsymbol{X}}^{\left( 0 \right)}}$(根据式(12)) 3. for $i = 1,2, \cdots ,I$执行 4. 计算$ {{\boldsymbol{\tilde X}}^{\left( i \right)}} $(根据式(18)) 5. for $ {m_{\text{N}}} = 1,2, \cdots ,{M_{\text{N}}} $ 6. 计算$ {\sigma _{{m_{\text{N}}}}} $(根据式(21)) 7. 计算${ {\boldsymbol{X} }^{\left( i \right)} }\left( {\left( { {m_{\text{N} } } - 1} \right){M_{\text{M} } } + 1:{m_{\text{N} } }{M_{\text{M} } },}: \right)$(根据
式(22))8. end for(当$ {m_{\text{N}}} = {M_{\text{N}}} $时) 9. 计算迭代误差$ \Delta {\boldsymbol{X}} = {{{{{\left\| {{{\boldsymbol{X}}^{\left( i \right)}} - {{\boldsymbol{X}}^{\left( {i - 1} \right)}}} \right\|}_{\text{F}}}} \mathord{\left/ {\vphantom {{{{\left\| {{{\boldsymbol{X}}^{\left( i \right)}} - {{\boldsymbol{X}}^{\left( {i - 1} \right)}}} \right\|}_{\text{F}}}} {\left\| {{{\boldsymbol{X}}^{\left( {i - 1} \right)}}} \right\|}}} \right. } {\left\| {{{\boldsymbol{X}}^{\left( {i - 1} \right)}}} \right\|}}_{\text{F}}} $ 10. end for(当$\Delta {\boldsymbol{X} } \le {{\varepsilon} }$或$i = I$时) 11. 输出：${{\boldsymbol{X}}^{\left( i \right)}}$ 
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表 1 仿真参数
Table 1. Simulation parameters
参数名称 参数符号 数值 分布式孔径总阵元个数 M 512 子孔径个数 ${M_{\text{N}}}$ 16 子孔径内阵元个数 ${M_{\text{M}}}$ 32 子孔径内阵元间距(m) d 0.05 子孔径间距(m) ${D_d}$ 50 采样点数 N 1024 波形载频(GHz) ${f_0}$ 3 波形时宽(μs) T 2.048 雷达波形带宽(MHz) B 300 符号个数 ${N_{{\text{sym}}}}$ 64 期望波形间功率差(dB) $ \Delta {P_{{\text{rc}}}} $ 3 最大迭代次数 I 300
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表 2 场景1中波胞尺寸分析
Table 2. Wave cell size analysis in the first scenario
类别 理论值(m) 测量值(m) 误差(%) 宽度 高度 宽度 高度 宽度 高度 雷达波胞 59.098 160.380 59.068 160.380 0.05 0 通信波胞 46.835 123.191 46.797 123.136 0.08 0.04
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表 3 场景1中空间合成波形雷达性能表现
Table 3. Radar performance of spatial synthetic waveform in the first scenario
空间坐标(m) 是否位于雷达波胞内 脉压峰值(dB) 峰值旁瓣比(dB) 积分旁瓣比(dB) (0,1000) 是 60.21 –13.30 –9.73 (0,970) 是 53.94 –13.30 –9.72 (–26,940) 否 18.38 –13.22 –3.39
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表 4 场景2中波胞尺寸分析
Table 4. Wave cell size analysis in the second scenario
类别 理论值(m) 测量值(m) 误差(%) 宽度 高度 宽度 高度 宽度 高度 雷达波胞 53.597 139.095 53.570 139.097 0.05 0.001 通信波胞 32.495 74.472 32.500 74.470 0.02 0.003
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表 5 场景2中空间合成波形雷达性能表现
Table 5. Radar performance of spatial synthetic waveform in the second scenario
空间坐标(m) 是否位于
雷达波胞内脉压峰值(dB) 峰值旁瓣比(dB) 积分旁瓣比(dB) (0,900) 是 60.21 –13.30 –9.73 (3,904) 是 56.87 –13.30 –9.72 (–30,840) 否 27.82 –12.02 0.15
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表 6 场景3中波胞尺寸分析
Table 6. Wave cell size analysis in the third scenario
类别 理论值(m) 测量值(m) 误差(%) 宽度 高度 宽度 高度 宽度 高度 雷达波胞 45.355 119.372 45.354 119.372 0.002 0 通信波胞 36.607 72.135 34.607 72.134 0 0.001
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表 7 场景3中空间合成波形雷达性能表现
Table 7. Radar performance of spatial synthetic waveform in the third scenario
空间坐标(m) 是否位于雷达波胞内 脉压峰值(dB) 峰值旁瓣比(dB) 积分旁瓣比(dB) $\left( {600,800} \right)$ 是 60.21 –13.30 –9.73 $\left( {580,800} \right)$ 是 44.59 –13.30 –9.67 $\left( {560,800} \right)$ 否 22.96 –12.87 0.16
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