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Cooperative Multi-constraint of a Sparse Array in Multiple-Input Multiple-Output Radar for Near-field Imaging
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摘要: 在多输入多输出(MIMO)雷达近场成像中，二维MIMO阵列通过扩展阵列规模可有效提升空间分辨率。该文系统基于时分多址(TDMA)波形体制，利用MIMO阵列进行近场孔径合成成像，通过在波数域对多通道原始回波进行相干累加，实现对近场区域的高分辨率三维覆盖。该体制相较于传统机械扫描，更适用于民航安检等对实时性要求高的场景。然而，毫米波波长较短，为满足奈奎斯特采样准则设计的MIMO雷达阵列会导致收发阵元数量显著增加，造成较大的成本开销。针对以上问题，该文提出一种多约束协同稀疏阵列(CMC-SA)MIMO雷达近场成像算法，该算法在阵列方向图主瓣增益不变、旁瓣电平压低的约束条件下，以权向量$ {\ell}_{P} $范数正则化为目标函数，构造近场MIMO雷达阵列优化模型。通过引入辅助变量，求解阵列权向量闭合解，实现对均匀布置MIMO阵列的稀疏化处理，解决最小化非零激励值的阵列配置问题，同时满足高分辨成像需求。为降低多约束间的传播误差以及目标函数与复杂约束的耦合难度，算法将原优化问题中的耦合变量拆分为多个独立变量，并通过等式约束使其保持一致性，基于“分解-调和”思想，实现多约束条件下的权向量求解。在近场二维MIMO雷达中，该协同稀疏设计方法在保障成像性能的前提下，有效降低了系统复杂度。仿真实验结果显示，相比单约束、贝叶斯等稀疏算法，所提CMC-SA算法在满足MIMO雷达近场聚焦条件下，能以72.6%的阵元稀疏率获得更低的旁瓣电平和更优的聚焦性能。此外，基于设计的稀疏阵列采集实测回波数据后，利用距离徙动算法(RMA)与特征恢复算法实现稀疏MIMO雷达高分辨成像。结果验证了所提CMC-SA-MIMO雷达近场成像算法在保证成像结果的同时降低了系统复杂性的优势。Abstract: In near-field imaging with multiple-input multiple-output (MIMO) radar, spatial resolution is effectively enhanced by extending the aperture of a two-dimensional MIMO array. The proposed system is based on a time-division multiple-access waveform and performs near-field aperture synthesis imaging using the MIMO array. High-resolution three-dimensional coverage of the near-field region is achieved by coherently accumulating multichannel raw echo data in the wavenumber domain. Compared with traditional mechanical scanning, this system is considered more suitable for scenarios with extremely high real-time requirements, such as civil aviation security inspection. However, millimeter waves have a short wavelength, so numerous transmit/receive elements must be placed in MIMO arrays to satisfy the Nyquist sampling criterion. This necessity leads to a substantial resource overhead. Thus, the cooperative multi-constraint of sparse array (CMC-SA) algorithm is proposed for MIMO radar near-field imaging. Under the constraints of maintaining constant main lobe gain and suppressing sidelobe levels in the array pattern, an optimization model for near-field MIMO radar array configurations is constructed, with the weight $ {\ell}_{P} $ norm regularization of the weight vector serving as the objective function. By introducing auxiliary variables, a closed-form solution for the array weight vector is derived. The sparse processing of uniformly configured MIMO arrays is achieved, and the array configuration problem of minimizing the number of nonzero excitations is solved while meeting the high-resolution imaging requirements. To reduce the propagation error among multiple constraints and alleviate the difficulty of coupling the objective function with complex constraints, the coupled variables in the original optimization problem are decomposed into multiple independent variables, with their consistency enforced through equality constraints. The “decomposition–coordination” concept is employed to determine weight vectors under multi-constraint conditions. In near-field 2D MIMO radar, this collaborative sparse design method is implemented to effectively reduce system complexity while ensuring imaging performance. The simulation results demonstrate that, compared with sparse algorithms such as the single-constraint and Bayesian methods, the CMC-SA algorithm achieves lower sidelobe levels and superior focusing performance under near-field MIMO radar focusing conditions, with an element sparsity rate of 72.6%. Furthermore, high-resolution imaging of the sparse MIMO radar is realized using measured echo data acquired with the designed sparse array, processed via the range migration algorithm (RMA) and a feature recovery algorithm. The results confirm that the proposed CMC-SA-MIMO near-field imaging algorithm considerably reduces system complexity while maintaining imaging quality.
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图 1 MIMO雷达近场成像系统几何模型
Figure 1. Geometric model of MIMO radar near-field imaging system
图 3 多约束协同稀疏阵列MIMO雷达近场成像算法流程图
Figure 3. Flowchart of cooperative multi-constraint of sparse array algorithm
图 4 MIMO雷达阵元数量及位置分布图
(a)MIMO雷达阵列实物图 (b)均匀MIMO雷达阵元数量及位置分布 (c)稀疏MIMO雷达阵元数量及位置分布
Figure 4. MIMO radar element quantity and position distribution diagram
图 6 不同算法下MIMO雷达阵列方向图的二维剖面图
Figure 6. 2D profile of MIMO radar array pattern under different algorithms
图 8 不同算法成像结果边缘点的剖面图
Figure 8. Profile of edge points of imaging results of different algorithms
图 9 均匀与稀疏阵列成像结果对比图
Figure 9. Comparison chart of imaging results between uniform and sparse arrays
表 1 不同稀疏阵列算法计算效率对比分析
Table 1. Comparative analysis of computational efficiency of different sparse array algorithms
算法类型 迭代次数 平均运行时间/秒 单约束稀疏算法 30 6.753019 贝叶斯稀疏算法 150 21.689509 本文CMC-SA算法 50 12.467809 注：加粗数值表示本文所提算法的迭代次数和平均运行时间。 
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表 2 多约束稀疏阵列成像不同位置点扩散函数定量分析
Table 2. Quantitative analysis of point spread functions at different positions for multi-constraint sparse array imaging
不同位置点 方位维峰
值旁瓣比方位维积
分旁瓣比3 dB宽度时
方位维分辨率高度维峰
值旁瓣比高度维积
分旁瓣比3 dB宽度时
高度维分辨率中心点 −16.12 dB −9.77 dB 9.16 mm −17.54 dB −10.83 dB 9.16 mm 边缘点 −15.84 dB −9.59 dB 9.17 mm −17.37 dB −10.47 dB 9.16 mm
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表 3 不同成像结果边缘点的剖面图定量分析
Table 3. Quantitative cross-sectional analysis of edge points with different imaging results
边缘点的
成像结果方位维峰
值旁瓣比3 dB宽度时
方位维分辨率高度维峰
值旁瓣比3 dB宽度时
高度维分辨率均匀阵列成像 −17.16 dB 9.17 mm −19.05 dB 9.16 mm 单约束稀疏阵列成像 −13.65 dB 9.20 mm −15.10 dB 9.22 mm 贝叶斯稀疏阵列成像 −14.08 dB 9.19 mm −17.35 dB 9.18 mm 本文所提算法成像 −15.84 dB 9.17 mm −17.37 dB 9.16 mm 注：加粗数值表示本文所提算法成像定量分析结果。
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表 4 MIMO雷达成像系统相关参数
Table 4. Parameters of MIMO radar imaging system
雷达参数 数值 雷达参数 数值 雷达参数 数值 工作带宽 7.68 GHz 发射阵元 480个 子阵数量 15个 工作频率 27.17 GHz 接收阵元 480个 相邻子阵
中心间距0.342 2 m 目标距离 0.85 m 阵元间距 0.005 5 m
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表 5 不同成像结果的图像熵分析
Table 5. Image entropy analysis of different imaging results
不同算法成像结果 图像熵/bit 均匀阵列成像 8.7218 单约束稀疏阵列成像 10.0215 贝叶斯稀疏阵列成像 9.1344 本文所提算法成像 8.9387 注：加粗数值表示本文所提算法成像定量分析结果。
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