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Generating low-frequency electromagnetic waves based on high-frequency antenna and illuminating targets with multi-band signals can be an effect way that can not only reduce the physical dimension of a low frequency antenna, but also improve the performance of radar detection. Combining the electromagnetic wave doppler effect principle and the array antenna architecture, a method of generating a low-frequency signal around the illuminated target is proposed based on the controlling of array antenna parameters, including array radiation element signal timing, phase and element spacing. The principles of array parameter design are described. Composite signals are simulated respectively under two typical geometric relationships between targets and array antenna, target located along the array direction and in the direction of 45° scanning angle. The peak sidelobe ratio (PSLR) and integral sidelobe ratio (ISLR) are used to evaluate the quality of the composite signals. Aiming at practical applications, the effects of array element spacing error, phase error and target location error on the composite signal are simulated and analyzed. Under the condition of sparse uniform array, the influence of the radiation element spacing on the composite signal is analyzed. The simulation results show that the harmonic components of the composite signal increase with the radiating element spacing error and phase error growing.
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Keywords:
- frequency transformation /
- array antenna /
- doppler effect /
- thinned array
[1] 许道明, 张宏伟 2018 现代防御技术 46 148
Google Scholar
Xu D M, Zhang H W 2018 Modern Defence Technology 46 148
Google Scholar
[2] 代红, 何丹 2016 电子信息对抗技术 31 40
Google Scholar
Dai H, He D 2016 Electronic Information Warfare Technology 31 40
Google Scholar
[3] 周建卫, 李道京, 胡烜 2017 中国科学院大学学报 34 411
Google Scholar
Zhou J W, Li D J, Hu X 2017 J. Un. Chin. Ac. Sci. 34 411
Google Scholar
[4] 周建卫, 李道京, 田鹤, 潘洁, 胡烜 2017 电子与信息学报 39 1058
Google Scholar
Zhou J W, Li D J, Tian H, Pan J, Hu X 2017 J. El. Inf. Tech. 39 1058
Google Scholar
[5] 张仁李, 胡丽红, 盛卫星, 马晓峰, 韩玉兵 2016 电波科学学报 31 284
Google Scholar
Zhang R L, Hu L H, Sheng W X, Ma X F, Han Y B 2016 Chin. J. Rad. Sci. 31 284
Google Scholar
[6] Arazm F, Benson F A 1980 IEEE Trans. Electromag. Compat. EMC 22 142
Google Scholar
[7] 顾继慧, 陈如山 2001 现代雷达 1 24
Google Scholar
Gu J H, Chen R S 2001 Mod. Radar. 1 24
Google Scholar
[8] 张元仲 2016 物理与工程 26 3
Google Scholar
Zhang Y Z 2016 Physics and Engineering 26 3
Google Scholar
[9] Jearl Walker, David Halliday, Robert Resnick 2014 Fundamentals of Physics (United States of America: John Wiley) pp1135–1137
[10] 别业广 2003 物理与工程 4 62
Google Scholar
Bie Y G 2003 Physics and Engineering 4 62
Google Scholar
[11] 高炳坤, 王凤林 2003 大学物理 8 15
Google Scholar
Gao B K, Wang F L 2003 College Physics 8 15
Google Scholar
[12] 严欣达, 程先卿 1987 大学物理 11 25
Google Scholar
Yan X D, Cheng X Q 1987 College Physics 11 25
Google Scholar
[13] 王景雪, 汤正新, 陈庆东, 尤景汉 2009 大学物理 28 24
Google Scholar
Wang J X, Tang Z X, Chen Q D, You J H 2009 College Physics 28 24
Google Scholar
[14] 吴翊, 朱炬波, 易东云, 王正明 1997 中国空间科学技术 6 47
Wu Y, Zhu J B, Yi D Y, Wang Z M 1997 Chin. Space. Sci. Technol. 6 47
[15] 房鹏 2009 硕士学位论文 (北京: 清华大学)
Fang P 2009 M. S. Thesis (Beijing: Tsinghua University) (in Chinese)
[16] 保铮, 邢孟道, 王彤 2005 雷达成像技术 (北京: 电子工业出版社) 第125−132页
Bao Z, Xing M D, Wang T 2005 Radar Imaging Technology (Beijing: Publishing House of Electronics Industry) pp125−132 (in Chinese)
[17] 魏钟铨 2001 合成孔径雷达卫星 (北京: 科学出版社) 第204−206页
Wei Z Q 2001 Synthetic Aperture Radar Satellite (Beijing: Science Press) pp204−206 (in Chinese)
[18] 王建 2015 阵列天线理论与工程应用 (北京: 电子工业出版社) 第8页
Wang J 2015 Theory and Engineering Application of Array Antenna (Beijing: Publishing House of Electronics Industry) p8 (in Chinese)
[19] 左群声, 徐国良, 马林, 王等纯 等 译) 2006 雷达系统导论(北京: 电子工业出版社) 第429−452页
Merrill I. Skolnik (translated by Zuo Q S, Xu G L, Ma L, Wang D C) 2006 Introduction to Radar System (Beijing: Publishing House of Electronics Industry) pp429−452 (in Chinese)[Merrill I. Skolnik
[20] 李道京, 侯颖妮, 滕秀敏, 李烈辰 2014 稀疏阵列天线雷达技术及其应用 (北京: 科学出版社) 第6−15页
Li D J, Hou Y N, Teng X M, Li L C 2014 Sparse Array Antenna Radar Technology and Its Application (Beijing: Science Press) pp6−15 (in Chinese)
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图 1 雷达运动示意图
Figure 1. Schematic diagram of the radar’s movement
图 2 多普勒效应中的发射/接收信号波形与频谱 (a) 发射信号波形; (b) 接收信号波形; (c) 发射信号与接收信号频谱
Figure 2. The emission/received signal waveform and spectrum of doppler effect: (a) The emission signal waveform; (b) the received signal waveform; (c) spectrum of the emission/received signal.
图 3 空时坐标系中对运动雷达发射信号过程分解的示意图
Figure 3. Schematic diagram of decomposition of moving radar in space-time coordinate system.
图 4 阵列天线结构等效运动雷达的示意图
Figure 4. Schematic diagram of the array antenna structure equivalent to the moving radar.
图 5 目标在阵列方向时的阵列天线结构
Figure 5. Array antenna structure when the target being in the array direction.
图 6 辐射单元信号首尾相接时合成信号的波形与频谱 (a) 合成信号波形; (b)合成信号频谱
Figure 6. Waveform and spectrum of the composite signal when signals of radiating elements being connected end to end: (a) Waveform of the composite signal; (b) spectrum of the composite signal.
图 7 辐射单元发射信号相位调制频率81 MHz时合成信号的包络移动情况、波形与频谱 (a) 合成信号的包络移动情况; (b) 合成信号的波形; (c) 合成信号的频谱
Figure 7. Envelope movement, waveform and spectrum of the composite signal when the phase modulation frequency of the radiating element signal being 81 MHz: (a) Envelope movement of the composite signal; (b) waveform of the composite signal; (c) spectrum of the composite signal.
图 8 相位调制频率为81 MHz和39 MHz时辐射单元信号的频谱 (a) 相位调制频率为81 MHz时辐射单元信号的频谱; (b) 相位调制频率为39 MHz时辐射单元信号的频谱
Figure 8. Spectrums of the radiating element signal when the phase modulation frequency being 81 MHz and 39 MHz: (a) Spectrum of the radiating element signal when the phase modulation frequency being 81 MHz; (b) spectrums of the radiating element signal when the phase modulation frequency being 39 MHz
图 9 辐射单元发射信号相位调制频率39 MHz时合成信号的波形、频谱以及阵列发射信号与合成信号的频谱对比图 (a) 合成信号的波形; (b) 合成信号的频谱; (c) 阵列发射信号与合成信号的频谱对比
Figure 9. Waveform, spectrum of the composite signal and the spectrum comparison between the signal transmitted by the array and the composite signal when the phase modulation frequency of radiating element signals being 39 MHz: (a) Waveform of the composite signal; (b) spectrum of the composite signal; (c) spectrum comparison between the signal transmitted by the array and the composite signal.
图 10 波束扫描角为45°时的阵列结构
Figure 10. Array structure when the beam scanning angle being 45°.
图 11 波束扫描角为45°时合成信号的波形、频谱以及阵列发射信号与合成信号的频谱对比图 (a) 合成信号波形; (b) 合成信号频谱; (c) 阵列发射信号与合成信号的频谱对比
Figure 11. Waveform and spectrum of the composite signal and the spectrum comparison between the signal transmitted by the array and the composite signal when the beam scanning angle being 45°: (a) Waveform of the composite signal; (b) spectrum of the composite signal; (c) spectrum comparison between the signal transmitted by the array and the composite signal
图 12 辐射单元间距误差和相位误差的分布直方图 (a)辐射单元间距误差的分布直方图; (b) 相位误差的分布直方图
Figure 12. Distribution histogram of radiating element spacing error and phase error: (a) Distribution histogram of radiating element spacing; (b) distribution histogram of phase error.
图 13 受到辐射单元间距误差和相位误差时合成信号的波形与频谱 (a) 合成信号的波形; (b) 合成信号的频谱
Figure 13. Waveform and spectrum of the composite signal subjected to radiating element spacing error and phase error: (a) Waveform of the composite signal; (b) spectrum of the composite signal.
图 14 实际目标距离阵列近端50 km时合成信号的波形、频谱与合成信号慢时间相位和低频信号相位的差值 (a) 合成信号的波形; (b) 合成信号的频谱; (c) 合成信号慢时间相位和低频信号相位的差值
Figure 14. Waveform, spectrum of the composite signal and slow time phase difference with that of low frequency signal when the actual target being 50 km from the near end of the array: (a) Waveform of the composite signal; (b) spectrum of the composite signal; (c) slow time phase difference with that of low frequency signal.
图 15 实际目标距离阵列近端10 km时合成信号的波形、频谱与合成信号慢时间相位和低频信号相位的差值 (a) 合成信号的波形; (b) 合成信号的频谱; (c) 合成信号慢时间相位和低频信号相位的差值
Figure 15. Waveform, spectrum of the composite signal and slow time phase difference with that of low frequency signal when the actual target being 10 km from the near end of the array: (a) Waveform of the composite signal; (b) spectrum of the composite signal; (c) slow time phase difference with that of low frequency signal.
图 16 等间隔稀疏阵列合成信号的波形与频谱 (a) 合成信号的波形; (b) 合成信号的频谱
Figure 16. Waveform and spectrum of signals composited by equally spaced sparse array: (a) Waveform of the composite signal; (b) spectrum of the composite signal.
表 1 波束扫描45°时合成信号的仿真参数
Table 1. Simulation parameters of the composite signal when beam scanning angle being 45°
参数 数据 参数 数据 阵列长度 105 m 目标与阵列距离 30 km 辐射单元信号脉宽 0.73 μs 合成信号脉宽 1.46 μs 辐射单元信号频率 1 GHz 合成信号频率 400 MHz 辐射单元间距 0.15 m 辐射单元总数 700 相位调制频率 39 MHz 相位步进 $ - \dfrac{{10}}{{13}}{\text{π}}$ 
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表 2 目标偏离预定位置时合成信号的仿真结果
Table 2. Simulation results of the composite signal when the target deviating from the predetermined position.
实际目标与阵列距离/km 峰值旁瓣比/dB 积分旁瓣比/dB 50 –23.3 –14.92 10 –17.6 –11.17
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表 3 等间隔稀疏条件下合成信号的仿真参数
Table 3. Simulation parameters of the composite signal under the condition of equispaced sparsity.
参数 数据 参数 数据 阵列长度 105 m 目标与阵列距离 30 km 辐射单元间距 0.3 m 辐射单元总数 350 辐射单元信号频率 1 GHz 合成信号频率 400 MHz 辐射单元信号脉宽 0.73 μs 合成信号脉宽 1.46 μs 相位调制频率 39 MHz 相位步进 $ - \dfrac{{10}}{{13}}{\text{π}}$
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[1] 许道明, 张宏伟 2018 现代防御技术 46 148
Google Scholar
Xu D M, Zhang H W 2018 Modern Defence Technology 46 148
Google Scholar
[2] 代红, 何丹 2016 电子信息对抗技术 31 40
Google Scholar
Dai H, He D 2016 Electronic Information Warfare Technology 31 40
Google Scholar
[3] 周建卫, 李道京, 胡烜 2017 中国科学院大学学报 34 411
Google Scholar
Zhou J W, Li D J, Hu X 2017 J. Un. Chin. Ac. Sci. 34 411
Google Scholar
[4] 周建卫, 李道京, 田鹤, 潘洁, 胡烜 2017 电子与信息学报 39 1058
Google Scholar
Zhou J W, Li D J, Tian H, Pan J, Hu X 2017 J. El. Inf. Tech. 39 1058
Google Scholar
[5] 张仁李, 胡丽红, 盛卫星, 马晓峰, 韩玉兵 2016 电波科学学报 31 284
Google Scholar
Zhang R L, Hu L H, Sheng W X, Ma X F, Han Y B 2016 Chin. J. Rad. Sci. 31 284
Google Scholar
[6] Arazm F, Benson F A 1980 IEEE Trans. Electromag. Compat. EMC 22 142
Google Scholar
[7] 顾继慧, 陈如山 2001 现代雷达 1 24
Google Scholar
Gu J H, Chen R S 2001 Mod. Radar. 1 24
Google Scholar
[8] 张元仲 2016 物理与工程 26 3
Google Scholar
Zhang Y Z 2016 Physics and Engineering 26 3
Google Scholar
[9] Jearl Walker, David Halliday, Robert Resnick 2014 Fundamentals of Physics (United States of America: John Wiley) pp1135–1137
[10] 别业广 2003 物理与工程 4 62
Google Scholar
Bie Y G 2003 Physics and Engineering 4 62
Google Scholar
[11] 高炳坤, 王凤林 2003 大学物理 8 15
Google Scholar
Gao B K, Wang F L 2003 College Physics 8 15
Google Scholar
[12] 严欣达, 程先卿 1987 大学物理 11 25
Google Scholar
Yan X D, Cheng X Q 1987 College Physics 11 25
Google Scholar
[13] 王景雪, 汤正新, 陈庆东, 尤景汉 2009 大学物理 28 24
Google Scholar
Wang J X, Tang Z X, Chen Q D, You J H 2009 College Physics 28 24
Google Scholar
[14] 吴翊, 朱炬波, 易东云, 王正明 1997 中国空间科学技术 6 47
Wu Y, Zhu J B, Yi D Y, Wang Z M 1997 Chin. Space. Sci. Technol. 6 47
[15] 房鹏 2009 硕士学位论文 (北京: 清华大学)
Fang P 2009 M. S. Thesis (Beijing: Tsinghua University) (in Chinese)
[16] 保铮, 邢孟道, 王彤 2005 雷达成像技术 (北京: 电子工业出版社) 第125−132页
Bao Z, Xing M D, Wang T 2005 Radar Imaging Technology (Beijing: Publishing House of Electronics Industry) pp125−132 (in Chinese)
[17] 魏钟铨 2001 合成孔径雷达卫星 (北京: 科学出版社) 第204−206页
Wei Z Q 2001 Synthetic Aperture Radar Satellite (Beijing: Science Press) pp204−206 (in Chinese)
[18] 王建 2015 阵列天线理论与工程应用 (北京: 电子工业出版社) 第8页
Wang J 2015 Theory and Engineering Application of Array Antenna (Beijing: Publishing House of Electronics Industry) p8 (in Chinese)
[19] 左群声, 徐国良, 马林, 王等纯 等 译) 2006 雷达系统导论(北京: 电子工业出版社) 第429−452页
Merrill I. Skolnik (translated by Zuo Q S, Xu G L, Ma L, Wang D C) 2006 Introduction to Radar System (Beijing: Publishing House of Electronics Industry) pp429−452 (in Chinese)[Merrill I. Skolnik
[20] 李道京, 侯颖妮, 滕秀敏, 李烈辰 2014 稀疏阵列天线雷达技术及其应用 (北京: 科学出版社) 第6−15页
Li D J, Hou Y N, Teng X M, Li L C 2014 Sparse Array Antenna Radar Technology and Its Application (Beijing: Science Press) pp6−15 (in Chinese)
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