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Range–Azimuth Two-Dimensional Imaging Method with Single-Mode Vortex Electromagnetic Wave Radar
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摘要: 由于携带轨道角动量(OAM)，涡旋电磁波的波前相位结构呈螺旋状，其回波包含受贝塞尔函数调制的幅度项和受目标方位角调制的相位项，基于不同OAM模态可使目标散射点在方位角向得以差异性度量，从而实现目标方位角向高分辨成像。然而，现有方法需使用较多OAM模态对目标进行观测，且不同模态的涡旋回波贝塞尔函数项不一致会导致方位角成像分辨率下降。此外，贝塞尔函数项受目标散射点俯仰角调制，使回波俯仰角-方位角信息强耦合，当目标各散射点俯仰角存在差异时难以对其进行补偿，导致方位角分辨性能进一步急剧下降。因此，该文采用单模态涡旋电磁波观测目标，通过对回波信号进行补偿，将目标散射点方位角信息从回波相位提取至振幅中获得单模态期望信号，弱化俯仰角差异对信号幅度项的影响，从而降低俯仰角差异对方位角成像的影响。同时，利用其振幅时延分辨散射点方位角，从而基于单模态期望信号实现目标距离-方位角二维成像。仿真实验表明，所提方法的方位角分辨率在俯仰角存在差异时仍能接近衍射极限，且具有较好的鲁棒性。Abstract: Owing to their inherent Orbital Angular Momentum (OAM), vortex electromagnetic waves display a helical wavefront phase structure. Their echoes include an amplitude component modulated by Bessel functions and a phase component modulated by the azimuth angle of the target. By utilizing different OAM modes, the azimuthal scattering points of targets can be measured differentially, enabling high-resolution azimuth imaging. However, current methods require observing targets with multiple OAM modes. The inconsistency of Bessel function terms across modes causes azimuth imaging resolution to degrade. Additionally, the Bessel function term is influenced by the elevation angle of the scattering points, resulting in strong coupling between elevation and azimuth information. When the elevation angles change, compensation becomes challenging, further reducing azimuth resolution. To overcome these issues, this paper uses single-mode vortex electromagnetic waves to observe targets. By compensating the echo signals, the azimuth information of the scattering points is shifted from the phase to the amplitude, producing the desired single-mode signal. This method diminishes the effect of elevation angle variations on the amplitude component, thereby lessening their impact on azimuth imaging. At the same time, the amplitude time-delay is employed to locate the azimuth positions of the scattering points, enabling two-dimensional range–azimuth imaging based on the single-mode signal. Simulation experiments show that the proposed method achieves azimuth resolution close to the diffraction limit even with changing elevation angles, while maintaining strong imaging performance.
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图 2 俯仰角差异对现有涡旋电磁波雷达成像模型的影响
Figure 2. Effect of elevation angle difference on existing VEMW radar imaging model
图 3 俯仰角差异对所提涡旋电磁波雷达成像方法的影响
Figure 3. Effect of elevation angle difference on proposed VEMW radar imaging method
图 6 所提方法的方位角分辨率随$ ka\sin {\theta }_{\text{P}} $变化曲线
Figure 6. Azimuth angle resolution of the proposed method as a function of $ ka\sin {\theta }_{\text{P}} $
图 7 字典俯仰角无偏时的目标方位角重构结果
Figure 7. Reconstruction results of target azimuth angle when dictionary elevation angle is unbiased
图 8 字典俯仰角偏差为0.01 rad时的目标方位角重构结果
Figure 8. Reconstruction results of target azimuth angle when dictionary elevation angle deviation is 0.01 rad
图 9 不同方位角间距时的目标方位角重构结果(两散射点俯仰角间距0.015 rad，字典俯仰角偏差0.01 rad)
Figure 9. Reconstruction results of target azimuth angle with different azimuth angle spacing
(scattering point elevation angle spacing 0.015 rad, dictionary elevation angle deviation 0.01 rad)
图 10 所提方法方位角重构结果随散射点俯仰角间距变化
Figure 10. Reconstruction results of target azimuth angle by proposed method varying with elevation angle spacing
图 11 所提方法的实际方位角分辨率随雷达波束角$ \theta _{\text{T}}^{0} $的变化
Figure 11. The variation of the actual azimuth resolution of the proposed method with the radar beam angle $ \theta _{\text{T}}^{0} $
图 13 不同OAM模态下的方位角重构结果
Figure 13. Reconstruction results of target azimuth angle under different OAM modes
图 14 二维成像结果(散射点俯仰角间距0.015 rad，字典俯仰角偏差0.01 rad)
Figure 14. 2-D imaging results (scattering point elevation angle spacing 0.015 rad, dictionary elevation angle deviation 0.01 rad)
图 15 二维成像结果(①散射点俯仰角一致，字典俯仰角无偏；②散射点俯仰角间距0.015 rad，字典俯仰角偏差0.01 rad)
Figure 15. 2-D imaging results (① Scattering point elevation angles are consistent, dictionary elevation angle is unbiased; ② Scattering point elevation angle spacing 0.015 rad, dictionary elevation angle deviation 0.01 rad)
图 16 所提方法二维成像结果RMSE随信噪比变化
Figure 16. RMSE of 2-D imaging result by proposed method varying with SNR
图 17 二维成像结果(字典俯仰角偏差0.01 rad)
Figure 17. 2-D imaging results (dictionary elevation angle deviation 0.01 rad)
图 18 二维成像结果(散射点俯仰角一致，字典俯仰角无偏)
Figure 18. 2-D imaging results (scattering point elevation angles are consistent; dictionary elevation angle is unbiased)
图 19 不同信噪比下所提方法的二维成像结果
Figure 19. 2-D imaging results by proposed method with different SNR
A1 不同$ {\theta }_{e} $下字典$ {\boldsymbol{d}}_{e} $中各列向量的相关系数
A1. The correlation coefficients of the vectors in different dictionary $ {\boldsymbol{d}}_{e} $ with different $ {\theta }_{e} $
表 1 涡旋电磁波雷达参数
Table 1. Parameters of VEMW Radar
参数 值 载频$ {f}_{\text{c}} $ 9 GHz 脉冲持续时间$ {T}_{\text{p}} $ 1 μs 带宽B 300 MHz 雷达波束角$ \theta _{\text{T}}^{0} $ 0.1 rad 阵列半径a 0.5 m 阵元数目N 60 OAM模态$ \alpha $ 1 
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