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Research on the Method of Composing Very Low Frequency Signals Based on the Staggered Array
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摘要: 10 kHz量级甚低频电磁波信号具有较强的地物穿透能力，可用于地质勘探。由于其天线尺寸在10 km量级，其应用场合受到限制，研究基于适当尺寸高频雷达天线的甚低频电磁波信号产生方法具有重要意义。该文提出基于高频阵列天线产生甚低频信号的概念，利用阵列天线合成产生近光速远离运动雷达多普勒信号，实现信号频率的大幅降低。给出了发射波形、交错阵列设计和阵列参数选择方法。将周期脉冲串信号作为辐射单元信号，增大合成信号脉宽。利用阵列产生的脉宽展宽量填补脉冲信号的休止期，在目标区合成时间连续的甚低频信号。采用峰值旁瓣比(PSLR)、积分旁瓣比(ISLR)、阵列发射信号与合成信号的频谱对比评价合成低频信号的性能和发射信号的能量利用率。该文仿真了百米量级阵列100 MHz辐射单元信号在目标区合成10 kHz甚低频信号的情况：9行阵列构成交错阵列、辐射单元信号脉宽设置为0.115 μs时，合成信号频谱的峰值旁瓣比和积分旁瓣比分别为–13.34 dB和–9.44 dB, 10 kHz低频信号在合成信号中的能量占比为89.79%。该文分析了辐射单元间距误差、辐射单元信号时间、相位与幅度误差以及目标偏离预定位置的影响。仿真结果表明了该文方法的有效性。Abstract: The Very Low Frequency (VLF) signal of 10 kHz has strong penetrability of ground objects. Because of the antenna size, its application is limited. Therefore, it is important to study the VLF signal generation method based on appropriately sized high frequency radar antennas. The concept of generating VLF signal with high frequency array antenna is proposed in this paper. The waveform of the emission signal, staggered array structure design, and array parameter selection methods are presented and discussed. The pulse width of the composite signal is increased by using periodic pulse signals as radiation element signals. The resting period of the pulse signals is filled with the pulse width expansion generated by the array and the VLF signal with continuous time is composed in the target area. The performance of the composite VLF signal and the energy utilization of the emission signal are evaluated using Peak SideLobe Ratio (PSLR), Integrated SideLobe Ratio (ISLR) and through the spectrum comparison between the emission signal and the composite signal. With the 10 kHz VLF signal composed by 100 MHz radiant element signals, the hundred meter array is simulated. When the staggered array is constituted by nine arrays and the pulse width of the radiation element is set to 0.115 μs, PSLR and ISLR of the composite signal spectrum are –13.34 dB and –9.44 dB respectively, and the energy proportion of 10 kHz low-frequency signal in the composite signal is 89.79%. The effects of radiation element spacing error, time error, phase error and amplitude error of the radiation element signal and the target’s deviation are analyzed. It is found that the proposed method is an effective one and the simulation results have illustrated the effectiveness.
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图 2 多普勒效应中的发射/接收信号波形与频谱
Figure 2. The emission/received signal waveform and spectrum of Doppler effect
图 3 运动雷达发射信号过程分解和天线阵列等效雷达运动示意图
Figure 3. Schematic diagram of the decomposed process of radar transmitting signals and the equivalent radar motion generated by the antenna array
图 6 辐射单元信号周期为
${{{T_0}} / 2}$ 时合成信号的波形、频谱与频谱对比图Figure 6. Waveform, spectrum and spectral contrast diagram of the composite signal when the radiation unit signal period being
${{{T_0}} / 2}$ 
图 7 辐射单元信号周期为
${{{T_0}} / 6}$ 时合成信号的波形、频谱与频谱对比图Figure 7. Waveform, spectrum and spectral contrast diagram of the composite signal when the radiation unit signal period being
${{{T_0}} / 6}$ 
图 8 辐射单元信号周期为
${{{T_0}} / 6}$ 时9行阵列构成的交错阵列在目标区合成信号的波形、频谱与频谱对比图Figure 8. Waveform, spectrum and spectral contrast diagram of the composite signal generated by the 9-row staggered array when the radiation unit signal period being
${{{T_0}} / 6}$ 
图 10 辐射单元间距误差分布、目标区合成信号的波形与频谱图
Figure 10. The distribution of spacing error, waveform and spectrum of the composite signal in target area
图 11 辐射单元信号时间误差分布、目标区合成信号的波形与频谱图
Figure 11. The distribution of radiation unit signal time error, waveform and spectrum of the composite signal in target area
图 12 辐射单元信号相位误差分布、目标区合成信号的波形与频谱图
Figure 12. The distribution of radiation unit signal phase error, waveform and spectrum of the composite signal in target area
图 13 辐射单元信号幅度误差分布、目标区合成信号的波形与频谱图
Figure 13. The distribution of radiation unit signal amplitude error, waveform and spectrum of the composite signal in target area
图 14 目标在xoy平面内45°扫描角方向距离阵列近端20 km时目标区合成信号的波形与频谱
Figure 14. Waveform and spectrum of the composite signal in the target area when the target is 20 km away from the near end of the array at 45° scanning angle in xoy plane
图 15 目标在xoy平面内45°扫描角方向距离阵列近端40 km时目标区合成信号的波形与频谱
Figure 15. Waveform and spectrum of the composite signal in the target area when the target is 40 km away from the near end of the array at 45° scanning angle in xoy plane
图 16 目标沿
$z$ 轴偏离1 km时目标区合成信号的波形与频谱Figure 16. Waveform and spectrum of the composite signal in the target area when the target deviates 1 km along the z-axis
图 17 受综合误差影响时目标区合成信号的波形与频谱
Figure 17. Waveform and spectrum of the composite signal in the target area influenced by synthetical error
表 1 辐射单元信号周期取
${{{{{T_0}}}} / {{2}}}$ 和${{{{{T_0}}}} / {{6}}}$ 时的仿真参数与结果Table 1. Simulation parameters and results when the radiation unit signal period being
${{{{{T_0}}}} / {{2}}}$ and${{{{{T_0}} / 6}}}$ respectively参数 辐射单元信号周期取${{{T_0}} / 2}$ 辐射单元信号周期取${{{T_0}} / 6}$ 最大辐射单元信号周期${T_0}$(μs) 1.38 1.38 辐射单元信号周期数(个) 200 600 辐射单元信号脉宽(μs) 0.345 0.115 辐射单元信号脉宽展宽(μs) 0.345 0.115 辐射单元信号周期(μs) 0.69 0.23 辐射单元信号休止期(μs) 0.345 0.115 合成信号脉宽(μs) 138.36 138.59 峰值旁瓣比(dB) –11.45 –13.34 积分旁瓣比(dB) –4.33 –8.77 低频信号能量占比(%) 73.05 88.29 频谱对比图中的10 kHz分量(dB) –14.610 –5.081 发射信号能量利用率(%) 18.60 55.71 
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表 2 不同误差影响下合成信号频谱参数(dB)
Table 2. Spectrum parameters of the composite signal influenced by different errors (dB)
误差 峰值旁瓣比 积分旁瓣比 辐射单元间距误差 –13.31 –8.95 辐射单元信号时间误差 –13.34 –7.64 辐射单元信号相位误差 –13.34 –9.07 辐射单元信号幅度误差 –13.34 –9.33 目标在xoy平面内距离阵列近端20 km –13.34 –9.44 目标在xoy平面内距离阵列近端40 km –13.34 –9.44 目标在z轴偏离1 km –13.34 –8.97 综合误差 –13.28 –6.63
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