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Deep Learning-based Integrated Search-imaging Waveform Design for Coherent Frequency Diverse Array Radar
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摘要: 相参频率分集阵列(FDA)雷达具有系统结构简单、波束扫描灵活和发射自由度高等优点，在宽覆盖对空探测任务中展现出巨大潜力，但固有的波束扫描机制导致其在特定方向的驻留时间缩短，从而限制了传统宽带波形成像时的距离分辨率。为解决广域搜索与高分辨率成像之间的内在矛盾，该文提出了一种基于深度学习的相参FDA搜索成像一体化波形设计方法。该方法利用相参FDA多自由度灵活发射的优势，在保证宽覆盖搜索能力的同时，为多个感兴趣区域(ROI)定制化地设计波形、带宽、发射增益等多维发射资源。为了解决基带波形设计中恒模与相关性双重约束的非凸优化问题，该文构建了以残差自编码网络为核心优化器，旨在直接学习并建立从初始相位空间到满足预设性能准则的最优相位空间的高维非线性映射关系。该网络能够高效地生成一组在多个ROI方向上同时具备低自相关旁瓣和低互相关电平的相位编码子波形。仿真结果验证了所提方法的有效性，表明其设计的波形在同步执行搜索与多目标成像任务时，(相比于窄带搜索模式)能够在指定ROI方向同时获得发射增益和距离分辨率提升，且自相关与互相关性能相较于传统方法具有显著优势，为提高现代雷达系统的同时多任务探测能力提供了一种有效途径。Abstract: Coherent Frequency Diverse Array (FDA) radar demonstrates significant potential for wide-area search tasks due to its simple system architecture, flexible beam scanning, and high transmit Degrees of Freedom (DOF). However, its inherent beam-scanning mechanism reduces dwell time in specific directions, thereby limiting the imaging range resolution when a conventional wideband waveform is used. To resolve the intrinsic contradiction between wide-area search and high-resolution imaging, this paper proposes a deep learning–based integrated search-imaging waveform design method. By leveraging the multi-DoF flexible transmission capability of coherent FDA, the proposed method customizes multidimensional transmit resources, including waveform, bandwidth, and transmit gain, for multiple regions of interest (ROIs) while preserving wide-coverage search performance. To address the nonconvex optimization problem with dual constraints of constant modulus and low correlation in baseband waveform design, a residual autoencoder-based optimizer is developed. This network directly learns and establishes a high-dimensional nonlinear mapping from the initial phase space to the optimized phase space that satisfies predefined performance criteria. The network efficiently generates a set of phase-coded subwaveforms exhibiting low autocorrelation sidelobes and low cross-correlation levels for multiple ROIs. Simulation results validate the effectiveness of this method, demonstrating that the designed waveforms achieve higher processing gain (compared with the narrowband searching mode) and improved imaging resolution in the designated ROIs during simultaneous search and multitarget imaging. Moreover, the autocorrelation and cross-correlation performance of the proposed method significantly outperforms that of conventional approaches, indicating that it provides an effective solution for enhancing the multitask capabilities of modern radar systems.
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图 2 相参FDA波束扫描的“空-时”滑窗效应示意图
Figure 2. Space-time windowing effect induced by coherent FDA radar beamscanning
图 4 相参FDA雷达窄带宽覆盖搜索模式
Figure 4. Searching mode of coherent FDA radar with narrowband and wide coverage
图 5 相参FDA雷达宽带多目标成像模式
Figure 5. Multi-targets imaging mode of coherent FDA radar with wideband and ROI coverage
图 6 多目标成像模式下的相参FDA雷达探测效果示意图
Figure 6. Visualization of multi-targets imaging mode based on coherent FDA radar
图 8 第1个发射通道的设计波形时频图
Figure 8. Spectrogram of the designed waveform at the first transmit element
图 9 根据ROI设计波形的空间覆盖能力分析
Figure 9. Spatial coverage analysis of the designed waveform according to ROIs
图 10 3个ROI方向上的“距离-角度”模糊函数
Figure 10. Range-angle ambiguity functions in three different ROIs
图 11 3个ROI方向上距离角度模糊函数的一维距离向剖面
Figure 11. The range profile of range-angle ambiguity functions in three different ROIs
图 12 全脉冲匹配与子脉冲匹配在3个ROI方向上的一维距离向剖面对比
Figure 12. Comparisons between full-pulse compression and subpulse compression in three different ROIs
图 13 $ \Delta \theta $分别取0.5°和1°时，3个ROI方向上一维距离像剖面的对比
Figure 13. Comparisons of range profiles in three different ROIs when $ \Delta \theta \text{=0}{\text{.5}}^{\circ } $ and $ {\text{1}}^{\circ } $
图 14 APSL、峰值增益损失随角度偏差$ \Delta \theta $变化的统计曲线
Figure 14. Statistical variations of APSL and peak gain loss induced by angle bias $ \Delta \theta $
图 15 所提RAE算法与CON算法、Multi-CAN算法在3个ROI方向上的一维距离向剖面对比
Figure 15. Comparisons of range profiles between the RAE, CON and Multi-CAN in three different ROI directions
图 16 非ROI区间$ {\theta }_{0}=-{10}^{\circ },{15}^{\circ } $对应的“距离-角度”模糊函数及距离向剖面
Figure 16. Range-angle ambiguity functions and range profiles when $ {\theta }_{0}=-{10}^{\circ },{15}^{\circ } $ (outside of ROI)
表 1 多目标成像模式的相参FDA雷达系统参数设计方法
Table 1. System design of multi-targets imaging mode based on coherent FDA radar
输入：相参FDA发射/接收阵元数$ \text{M} $、$ \text{N} $，阵元间距d，参考载频$ {f}_{\rm c} $，脉冲宽度$ {T}_{p} $，搜索阶段确定的L个ROI方向$ \boldsymbol{{\varTheta }}=\left[{{\varTheta }}_{\text{1}},{{\varTheta }}_{2},\cdots,{{\varTheta }}_{L}\right] $。 初始化：阵元间载频差$ \Delta {f}^{0} $，L个方向上的波束驻留时间序列$ \left[T_{s,1}^{\text{0}},T_{s,\text{2}}^{\text{0}},\cdots,T_{s,L}^{\text{0}}\right] $，目标方向上的设计发射增益$ \left[{G}_{1},{G}_{2},\cdots,{G}_{L}\right] $，迭代步
长$ {\Delta }_{T} $和发射增益设计拟合误差$ {\delta }_{g} $。1 代入当前参数，通过式(5)计算L个方向上的发射增益。 2 for $ l=1,2,\cdots,L $ do 3 while $ \Delta {G}_{l} > {\delta }_{g} $ do 4 针对第l个目标方向，令$ T_{s,l}^{q}\leftarrow \left(1+i{\Delta }_{T}\right)T_{s,l}^{0} $； 5 适当调整并代入$ T_{s,l}^{i} $，通过式(12)计算第l个子脉冲内的载频差$ \Delta {f}_{l}{}^{i} $； 6 代入当前参数，通过式(5)计算第l个方向上的发射增益； 7 计算第l个方向上的实际增益与设计增益$ {G}_{l} $差的绝对值$ \Delta {G}_{l} $； 8 $ i\leftarrow i+1 $； 9 end 10 end 11 更新系统参数，通过式(15)计算K个非ROI子脉冲对应的载频差$ \Delta {f}_{K} $； 12 通过式(12)计算K个非ROI子脉冲的子脉冲宽度； 13 针对L个定制子脉冲设计低APSL, ICSL的相位编码波形； 14 针对K个非ROI子脉冲设计窄带搜索波形； 15 根据设计所得系统参数及基带波形，通过式(13)组合$ {N}_{p} $个子脉冲得到M个通道的发射波形组。 输出: 相参FDA雷达M个通道发射波形组$ \mathbf{s}\left(t\right)={\left[{s}_{1}\left(t\right),{s}_{2}\left(t\right),\cdots,{s}_{M}\left(t\right)\right]}^{\rm T} $。 
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表 2 相参FDA雷达系统参数
Table 2. System parameters of coherent FDA radar
参数 数值 参考载频$ {f}_{\rm c} $ 10 GHz 发射/接收阵元数目N/M 12 阵元间距d 0.015 m 脉冲重复周期$ {T}_{p} $ 10 μs 采样频率$ {F}_{s} $ 300 MHz 波束扫描覆盖范围$ {{\varOmega }}_{\text{FDA}} $ $ \left[-{90}^{\circ },{90}^{\circ }\right] $ 目标1位置$ {{\varTheta }}_{1} $ -30° 目标2位置$ {{\varTheta }}_{2} $ 0° 目标3位置$ {{\varTheta }}_{3} $ 30°
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表 3 RAE网络参数设计
Table 3. Parameters of residual auto-encoder network
参数 数值 编码器残差块维度 [512, 256, 128] 潜在空间维度$ {d}_{lat} $ 64 解码器残差块维度 [128, 256, 512] 损失函数权重系数 $ {\lambda }_{a}=\text{1} $, ${\lambda }_{c}=\text{0}.1 $ 学习率 0.001 批处理大小(Batch Size) 10 训练周期(Epochs) 1000
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