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Three-Dimensional Target Parameter Estimation Method Based on Limited-Mode Vortex Electromagnetic Wave Radar
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摘要: 与传统雷达系统相比，基于轨道角动量(OAM)的涡旋电磁波(VEMW)雷达为目标探测提供了额外的自由度。然而，现有大多数VEMW雷达成像与目标参数估计方法依赖大量的OAM模态，显著增加了系统的硬件成本与复杂度，同时，高阶模态的引入还会导致涡旋电磁波主瓣偏离感兴趣区域并导致系统噪声鲁棒性下降，严重限制了其在实际工程中的应用。针对上述局限性，该文提出了一种基于有限OAM模态的三维目标参数估计方法。首先，构建了VEMW雷达前视成像几何模型，利用脉冲压缩技术提取目标的距离信息。随后，构造对偶OAM模态的和差波束回波比值，利用贝塞尔函数的对称性，实现方位角信息的估计。最后，构造相邻OAM模态的回波信号比值，利用贝塞尔函数的递推性质，实现俯仰角信息的估计。进一步地，针对同一距离门内双目标场景，构造相邻OAM模态回波比值，并利用其相位差异特性，实现了同一距离门内双目标参数估计。此外，该文推导了方位角与俯仰角估计的克拉美-罗下界，并将所提闭式三维估计方法的均方根误差与理论下界进行了对比分析。数值仿真与微波暗室实验均表明，所提方法在多目标及噪声环境下能够实现可靠的三维参数估计，展现出良好的抗噪性与工程应用潜力。Abstract: Compared with traditional radar systems, the vortex electromagnetic wave (VEMW) radar based on orbital angular momentum (OAM) provides additional degrees of freedom for target detection. However, most existing VEMW radar imaging and parameter estimation methods rely on a large number of OAM modes, which significantly increases the hardware cost and complexity of the system. Moreover, the introduction of high-order modes causes the main lobe of the VEMW to deviate from the region of interest while reducing the system’s robustness to noise, severely limiting its practical engineering applications. To address these limitations, this study proposes a three-dimensional target parameter estimation method based on limited OAM modes. First, a forward-looking imaging geometric model of the VEMW radar is constructed, and pulse compression technology is used to extract the target’s range information. Subsequently, the echo ratio between the sum and difference beams of dual OAM modes is constructed, and the symmetry of the Bessel function is utilized to estimate the target’s azimuth angle information. Finally, the echo signal ratio of adjacent OAM modes is constructed, and the recurrence property of the Bessel function is used to estimate the target’s elevation angle information. Furthermore, for a dual-target scenario within the same range bin, the echo signal ratio of adjacent OAM modes is constructed, and the target parameters are estimated by exploiting the phase difference characteristics of the echoes. In addition, this paper derives the Cramér–Rao lower bound for azimuth and elevation angle estimation and compares the root mean square error of the proposed closed-form three-dimensional estimation method with the theoretical lower bound. Numerical simulations and microwave anechoic chamber experiments show that the proposed method achieves reliable three-dimensional parameter estimation in multitarget and noisy environments, thereby verifying its effectiveness and engineering feasibility.
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图 2 不同OAM模态CRLB随目标俯仰角变化分析
(c) Variation of azimuth angle CRLB with target elevation angle when OAM mode $ l=\pm 3 $ (d) OAM模态$ l=\{4,5,6\} $时俯仰角CRLB
Figure 2. Analysis of CRLB variation with target pitch angle in different OAM mode
图 3 不同对偶OAM模态组合下的候选残差解分布示意图
Figure 3. Schematic diagram of the candidate residual solution distribution under different dual OAM mode combinations
图 4 同一距离门内单目标参数估计方法流程图
Figure 4. Flowchart of the parameter estimation method for a single target within the same range bin
图 5 同一距离门内双目标俯仰角估计误差
Figure 5. Elevation angle estimation error for dual targets within the same range bin
图 6 同一距离门双目标方位角信息估计流程图
Figure 6. Flowchart of azimuth angle information estimation for dual targets within the same range bin
图 7 理论方差随方位角差值变化图
Figure 7. Variation of theoretical variance with azimuth angle difference
图 8 同一距离门内双目标俯仰角估计误差随方位角差值变化图
Figure 8. Variation of elevation angle estimation error with azimuth angle difference for dual targets within the same range bin
图 9 跨距离门多目标在不同信噪比下的RMSE
Figure 9. RMSE of multiple targets across range bins under different SNR
图 10 单目标场景下所提算法与现有算法的测角性能对比
Figure 10. Comparison of angle measurement performance between the proposed algorithm and existing algorithms in a single-target scene
图 11 随机目标在不同信噪比下的仿真结果
Figure 11. Simulation results of random targets under different SNR
图 12 随机目标的空间位置在不同信噪比下的误差
Figure 12. Spatial position errors of random targets under different SNR
表 1 本文所提参数估计方法的仿真和实测参数
Table 1. Simulation and measured parameters of the parameter estimation method proposed in this paper
参数 数值 载频$ {\text{f}}_{c} $ 36 GHz 带宽$ {B}_{r} $ 6 GHz 波长$ \lambda $ 0.0083 m半径a 6.52$ \lambda $ 发射阵元数量 16 接收阵元数量 1 OAM模态l [−2, −1, 1, 2, 3] 
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表 2 实验测量结果
Table 2. Experimental measurement results
目标 真实位置 场景1实验结果 场景2实验结果 1 (10.24 m, 4.2°, 117°) (10.24 m, 4.05°, 115.5°) (10.24 m, 4.9°, 119.7°) 2 (9.86 m, 7.0°, −20°) / (9.87 m, 7.6°, −20.7°)
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