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RM Operator Learning-driven Non-line-of-sight 3D Imaging Method for Millimeter Wave Radar
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摘要: 非视距(NLOS)毫米波雷达三维成像利用电磁波反射、衍射、散射、穿透等传播特性，实现对隐蔽环境目标的探测、定位和成像，在无人驾驶、灾害救援、城市作战等领域具有重要应用潜力。然而，受实际非视距场景中反射面、遮挡面等不确定性引入的相位误差、孔径遮蔽、多径效应影响，雷达成像出现分辨率差、伪影增多等问题。针对上述问题，结合深度展开网络和环境先验感知，本文提出了一种基于距离徙动(RM)算子学习驱动的非视距毫米波雷达三维成像方法。首先，建立了拐角(LAC)场景下非视距毫米波雷达三维成像模型，引入RM核算子提高成像效率，降低计算复杂度；其次，构建了一种基于快速迭代收缩阈值(FISTA)框架的高精度非视距三维成像网络，利用非视距场景特性，将算法参数设计为网络权重的函数，实现非视距目标高精度、高效率三维重构；最后，搭建了近场非视距毫米波雷达成像平台，完成了理想与非理想反射面场景下金属字母“O”,“S”以及埃菲尔铁塔模型、人造卫星模型等目标的实验验证，结果表明所提方法在提升三维成像精度的同时，运行速度较传统稀疏成像算法提升了两个数量级。Abstract: Non-Line-Of-Sight (NLOS) millimeter wave radar 3D imaging leverages electromagnetic wave propagation characteristics such as reflection, diffraction, scattering, and penetration to detect, locate, and image hidden targets in occluded environments. It holds significant potential for applications in autonomous driving, disaster rescue, and urban warfare. However, uncertainties introduced by reflection surfaces and occluding objects in practical NLOS scenarios, such as phase errors, ghost targets, and aperture shadowing, lead to issues such as blurred imaging and increased artifacts. To address these challenges, this studty proposes a 3D imaging method for NLOS millimeter wave radar based on Range Migration (RM) operator learning, leveraging the adaptive optimization properties of deep unfolding networks and prior environmental perception. First, a 3D imaging model for NLOS millimeter wave radar in Looking Around Corner (LAC) scenarios is established. An RM kernel operator is introduced to enhance imaging efficiency and reduce computational complexity. Second, a high-precision NLOS 3D imaging network is constructed based on the Fast Iterative Shrinkage/Thresholding Algorithm (FISTA) framework. Utilizing features specific to NLOS scenes and designing algorithm parameters as functions of network weights, the method achieves high-precision, high-efficiency 3D reconstruction of NLOS targets. Finally, a near-field NLOS millimeter wave radar imaging platform is developed. Experimental validations are performed on targets, including metal letters “O” and “S,” an Eiffel Tower model, and an artificial satellite model, under both ideal and non-ideal reflection surface conditions. The results demonstrate that the proposed method significantly improves 3D imaging precision, achieving a two-orders-of-magnitude increase in computational speed over traditional sparse imaging algorithms.
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图 1 非视距毫米波雷达三维成像几何模型
Figure 1. 3D NLOS imaging geometry model for millimeter wave radar
图 7 基于RM核算子学习驱动的NLOS毫米波雷达三维成像框架
Figure 7. RM-operator Learning-driven framework for 3D NLOS imaging via millimeter wave radar
图 10 各算法在采样率100%时各个目标在不同反射面下的非视距三维成像结果
Figure 10. NLOS 3D imaging results of various hidden targets under different reflective surfaces at 100% sampling rate
图 11 不同反射面场景下，各算法在采样率为70%, 50%, 30%时字母“O”非视距三维成像结果
Figure 11. Under different reflective surface conditions, NLOS 3D imaging results of letter “O” by different algorithms when sampling ratio are 70%, 50% and 30%
图 12 不同反射面场景下，各算法在采样率为70%, 50%, 30%时字母“S”非视距三维成像结果
Figure 12. Under different reflective surface conditions, NLOS 3D imaging results of letter “S” by different algorithms when sampling ratio are 70%, 50% and 30%
图 13 不同反射面场景下，各算法在采样率为70%, 50%, 30%时埃菲尔铁塔模型非视距三维成像结果
Figure 13. Under different reflective surface conditions, NLOS 3D imaging results of the Eiffel Tower model by different algorithms when sampling ratio are 70%, 50% and 30%
图 14 不同反射面场景下，各算法在采样率为70%, 50%, 30%时人造卫星模型非视距三维成像结果
Figure 14. Under different reflective surface conditions, NLOS 3D imaging results of the satellite model by different algorithms when sampling ratio are 70%, 50% and 30%
1 基于RM核算子的FISTA稀疏成像算法
1. FISTA sparse imaging algorithm based on RM kernel operator
输入：稀疏降采样非视距回波$ \boldsymbol{Y} $，迭代步长$ \rho $，迭代次数T，正
则化参数$ \eta $，迭代误差$ \varepsilon $输出：非视距目标重构结果$ {\boldsymbol{X}}^{\left(T\right)}\in {\mathbb{C}}^{W\times H} $ 初始化：$ t=1 $，$ {\boldsymbol{Z}}^{\left(1\right)}={\boldsymbol{X}}^{\left(0\right)}={\text{RM}}^{\dagger }\left(\boldsymbol{Y}\right) $，$ {c}^{\left(1\right)}=1 $； 循环开始 (1) 更新动量修正量残差：$ {\boldsymbol{V}}^{\left(t\right)}=\boldsymbol{Y}-\text{RM}\left({\boldsymbol{Z}}^{\left(t\right)}\right) $； (2) 梯度下降粗估计：$ {\boldsymbol{R}}^{\left(t\right)}={\boldsymbol{Z}}^{\left(t\right)}+\rho {\text{RM}}^{\dagger }\left({\boldsymbol{V}}^{\left(t\right)}\right) $； (3) 软阈值收缩：$ {\boldsymbol{X}}^{\left(t\right)}=\text{soft}\left({\boldsymbol{R}}^{\left(t\right)},\eta \right) $； (4) 更新动量修正系数：$ {c}^{\left(t+1\right)}=\dfrac{1+\sqrt{1+4{\left({c}^{\left(t\right)}\right)}^{2}}}{2} $； (5) 更新动量修正量：
$ {\boldsymbol{Z}}^{\left(t+1\right)}={\boldsymbol{X}}^{\left(t\right)}+\left(\dfrac{{c}^{\left(t\right)}-1}{{c}^{\left(t+1\right)}}\right)\left({\boldsymbol{X}}^{\left(t\right)}-{\boldsymbol{X}}^{\left(t-1\right)}\right) $；(6) 终止准则判定：若$ \dfrac{\left|\left|{\boldsymbol{X}}^{\left(t+1\right)}-{\boldsymbol{X}}^{\left(t\right)}\right|\right|}{\left|\left|{\boldsymbol{X}}^{\left(t+1\right)}\right|\right|} > \varepsilon $则$ t=t+1 $；否
则，结束循环；(7) 迭代判定：若$ t\leq T $，则重复步骤(1)–步骤(7)；否则，结束
循环。循环结束 
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表 1 非视距毫米波雷达成像试验系统主要参数
Table 1. Main parameters of the experimental NLOS millimeter wave radar imaging system
参数 实测系统值 载频(GHz)
调频斜率(MHz/μs)79
70.295带宽(GHz) 3.998 X轴合成孔径长度(mm) 400 X轴天线阵元间距(mm) 1 Z轴合成孔径长度(mm) 400 Z轴天线阵元间距(mm) 2 脉冲发射间隔(ms) 25
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表 2 4个目标的非视距毫米波三维成像试验数据数值评估结果
Table 2. Numerical evaluation results of experimental four-target NLOS 3D imaging data using millimeter wave radar
目标 反射面 采样率 BP RMA FISTA NLFIST-Net ENT IC Time (s) ENT IC Time (s) ENT IC Time (s) ENT IC Time (s) O 金属板 70% 11.11 7.70 460.83 13.06 7.46 1.15 11.17 12.59 4.13 10.79 15.68 0.017 30% 11.73 6.49 495.48 14.13 3.77 1.14 11.02 14.59 4.67 9.86 25.09 0.016 墙面 70% 11.21 7.59 487.46 13.64 6.39 1.31 11.28 12.45 4.37 11.03 14.35 0.017 30% 11.91 6.28 494.76 14.51 3.32 2.07 11.28 13.66 4.31 10.40 20.20 0.015 S 金属板 70% 11.21 7.04 488.84 13.15 6.94 1.14 11.36 11.43 4.27 10.97 14.28 0.019 30% 11.84 5.90 495.43 14.15 3.66 1.14 11.36 12.61 3.68 10.14 21.78 0.016 墙面 70% 11.24 7.26 498.36 13.52 6.59 1.20 11.86 10.63 4.14 11.07 13.90 0.018 30% 11.92 6.00 490.90 14.42 3.42 1.21 11.39 11.50 4.62 10.53 18.77 0.016 铁塔 金属板 70% 10.68 15.91 543.18 13.93 9.90 0.74 10.90 22.83 4.03 10.08 28.24 0.016 30% 11.93 11.26 540.94 14.89 4.26 0.74 11.09 23.24 4.19 9.57 35.87 0.015 墙面 70% 12.03 10.84 458.58 15.03 3.49 0.82 12.04 16.58 4.24 10.94 23.18 0.016 30% 13.39 4.89 469.50 15.32 1.57 0.74 12.42 12.50 4.29 10.84 24.22 0.017 卫星 金属板 70% 11.00 8.47 542.64 13.22 7.44 0.84 11.32 12.95 4.31 10.79 15.95 0.018 30% 11.71 6.99 479.34 14.25 3.76 0.77 11.42 13.46 4.33 9.92 25.19 0.016 墙面 70% 11.89 6.55 479.34 14.79 3.22 0.79 11.88 11.24 4.46 11.08 14.61 0.018 30% 12.94 4.28 473.34 15.1 1.86 0.73 11.67 12.75 4.08 9.99 25.55 0.017 注：加粗数值代表数值评估最优的算法。
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表 3 各成像算法计算复杂度
Table 3. Computational complexity of different imaging algorithms
算法 FLOPs 数值实例 BP $ {N}_{x}{N}_{z}{N}_{\rm r}\times 17{N}_{l}{N}_{\rm r} $ $ 3.65\times {10}^{14} $ RMA $ {N}_{\rm r}{N}_{l}\left(10{\log }_{2}{N}_{l}+6\right) $ $ 1.56\times {10}^{9} $ FISTA $ {N}_{\text{iter}}{N}_{\rm r}{N}_{l}\left(20{\log }_{2}{N}_{l}+24\right) $ $ 4.83\times {10}^{10} $ NLFIST-Net $ T{N}_{\rm r}{N}_{l}\left(20{\log }_{2}{N}_{l}+24\right) $ $ 2.89\times {10}^{10} $
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