基于深度学习的FDA-MIMO雷达协方差矩阵缺失数据恢复方法

丁梓航; 谢军伟; 王博

doi:10.12000/JR23002

基于深度学习的FDA-MIMO雷达协方差矩阵缺失数据恢复方法

DOI: 10.12000/JR23002

丁梓航^1, ,,
谢军伟^1, ,,
王博²

1.
空军工程大学防空反导学院西安 710051
2.
空军工程大学空管领航学院西安 710051

基金项目: 国家自然科学基金(62001506)

详细信息

作者简介:
丁梓航，博士生，主要研究方向包括频控阵雷达抗干扰技术、波束优化理论、智能信号处理等

谢军伟，博士，教授，主要研究方向包括雷达干扰与抗干扰技术、新体制雷达系统等

王　博，博士，讲师，主要研究方向包括频控阵雷达波束设计、抗干扰应用等

通讯作者:
丁梓航 dingzihang0831@163.com

谢军伟 xjw_xjw_123@163.com

责任主编：朱圣棋 Corresponding Editor: ZHU Shengqi
中图分类号: TN958
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- 被引次数: 6
出版历程
- 收稿日期: 2023-01-04
- 修回日期: 2023-03-17
- 网络出版日期: 2023-04-04
- 刊出日期: 2023-10-28

Missing Covariance Matrix Recovery with the FDA-MIMO Radar Using Deep Learning Method

DING Zihang^{1
, ,},
XIE Junwei^{1
, ,},
WANG Bo²

1.
Air and Missile Defense College, Air Force Engineering University, Xi’an 710051, China
2.
Air Traffic Control and Navigation College, Air Force Engineering University, Xi’an 710051, China

Funds: The National Natural Science Foundation of China (62001506)

More Information

Corresponding author: DING Zihang, dingzihang0831@163.com; XIE Junwei, xjw_xjw_123@163.com

摘要

摘要: 频控阵-多输入多输出(FDA-MIMO)雷达通过波束形成技术实现抗干扰的研究已经十分丰富。然而，在实际工作中，受元器件老化和存储设备容量等硬件因素的影响，计算得到的信号协方差矩阵可能会出现数据缺失的情况。为了克服协方差矩阵数据缺失对波束形成算法性能的影响，该文提出了一种基于深度学习的FDA-MIMO雷达协方差矩阵数据恢复方法，并建立了协方差矩阵恢复-自适应波束形成的两阶段处理框架；提出了一种双通道生成对抗网络(GAN)来解决矩阵数据恢复问题，该网络主要由鉴别器(D)和生成器(G)两部分组成：生成器主要功能是输出完整的矩阵数据，鉴别器则是判别数据为真实数据还是填补数据。整个网络通过鉴别器和生成器之间相互对抗使生成器生成样本接近于真实数据的分布，从而实现对协方差矩阵缺失数据的恢复。此外，考虑到协方差矩阵数据为复数，分别构造两个独立的GAN网络以满足矩阵数据实部和虚部的训练。最后，数值实验结果表明，协方差矩阵真实数据与恢复后的数据平均均方根误差仅为0.01量级，验证了所提方法能够有效恢复协方差矩阵的缺失数据。
- 数据恢复 /
- 生成对抗网络 /
- FDA-MIMO雷达 /
- 深度学习 /
- 波束形成
Abstract: The realization of anti-jamming technologies via beamforming for applications in Frequency-Diverse Arrays and Multiple-Input and Multiple-Output (FDA-MIMO) radar is a field that is undergoing intensive research. However, because of limitations in hardware systems, such as component aging and storage device capacity, the signal covariance matrix data computed by the receiver system may be missing. To mitigate the impact of the missing covariance matrix data on the performance of the beamforming algorithm, we have proposed a covariance matrix data recovery method for FDA-MIMO radar based on deep learning and constructed a two-stage framework based on missing covariance matrix recovery-adaptive beamforming. Furthermore, a learning framework based on this two-stage framework and the Generative Adversarial Network (GAN) is constructed, which is mainly composed of a discriminator (D) and a generator (G). G is primarily used to output complete matrix data, while D is used to judge whether this data is real or filled. The entire network closes the gap between the samples generated by G and the distribution of the real data via a confrontation between D and G, consequently leading to the missing data of the covariance matrix being recovered. In addition, considering that the covariance matrix data is complex, two independent networks are constructed to train the real and imaginary parts of the matrix data. Finally, the numerical experiment results reveal that the difference in the root square mean error levels between the real and recovery data is 0.01 in magnitude.
- Matrix recovery /
- Generative Adversarial Network (GAN) /
- Frequency-Diverse Arrays and Multiple-Input and Multiple-Output (FDA-MIMO) radar /
- Deep learning /
- Beamforming

HTML全文

图 1 双通道GAN网络的框架

Figure 1. The framework of dual channel GAN network

下载: 全尺寸图片幻灯片

图 2 鉴别器和生成器网络结构

Figure 2. The structure of D and G network

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图 3 协方差矩阵实部灰度图(单干扰源)

Figure 3. The grayscale image of the real part of covariance matrix (single interference)

下载: 全尺寸图片幻灯片

图 4 协方差矩阵虚部灰度图(单干扰源)

Figure 4. The grayscale image of the imaginary part of covariance matrix (single interference)

下载: 全尺寸图片幻灯片

图 5 矩阵恢复数据的RMSE在训练过程中的变化情况(不同损失率 $\varepsilon$ )

Figure 5. RMSE performance versus training process (different $\varepsilon$ )

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图 6 矩阵恢复数据的RMSE在训练过程中的变化情况(不同网络层数k)

Figure 6. RMSE performance versus training process (different k)

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图 7 基于不同协方差矩阵的FDA-MIMO雷达波束方向图(多干扰源)

Figure 7. FDA-MIMO radar beampattern based on different covariance matrices (single interference)

下载: 全尺寸图片幻灯片

图 8 协方差矩阵实部灰度图(多干扰源)

Figure 8. The grayscale image of the real part of covariance matrix (multiple interferences)

下载: 全尺寸图片幻灯片

图 9 协方差矩阵虚部灰度图(多干扰源)

Figure 9. The grayscale image of the imaginary part of covariance matrix (multiple interferences)

下载: 全尺寸图片幻灯片

图 10 基于不同协方差矩阵的FDA-MIMO雷达波束方向图(多干扰源)

Figure 10. FDA-MIMO radar beampattern based on different covariance matrices (multiple interferences)

下载: 全尺寸图片幻灯片

算法1 双通道GAN伪代码
Alg. 1 Pseudocode of dual channels GAN network
while 训练损失值未达到收敛条件 or 未达到预设的迭代次数 do
1 鉴别器训练( ${ {\rm{D} }_1}$ 和 ${ {\rm{D} }_2}$ 分别为实部和虚部网络的鉴别器)
从训练数据集取出 ${J_{\text{D}}}$ 个样本作为一批量的数据 $\left\{ {\left( { {\text{Re} }\left( {\tilde {\boldsymbol{x}}\left( j \right)} \right),{\boldsymbol{m} }\left( j \right)} \right)} \right\}_{j = 1}^{ {J_{\text{D} } } }$ , $\left\{ {\left( { {\text{Im} }\left( {\tilde {\boldsymbol{x}}\left( j \right)} \right),{\boldsymbol{m} }\left( j \right)} \right)} \right\}_{j = 1}^{ {J_{\text{D} } } }$ ，并分别归一化处理。
随机采样 ${J_{\text{D}}}$ 个样本 $\left\{ {{\boldsymbol{z}}\left( j \right)} \right\}_{j = 1}^{ {J_{\text{D} } } }$ , $\left\{ {{\boldsymbol{b}}\left( j \right)} \right\}_{j = 1}^{ {J_{\text{D} } } }$ ，并分别归一化处理。
for $j = 1,2,\cdots,{J_{\text{D} } }$ do
${ {\rm{Re} } } \left( {\bar {\boldsymbol{x}}\left( j \right)} \right) \leftarrow {\text{G} }\left( { { {\rm{Re} } } \left( {\tilde {\boldsymbol{x}}\left( j \right)} \right),{\boldsymbol{m} }\left( j \right),{\boldsymbol{z} }\left( j \right)} \right)$ , ${ {\rm{Im} } } \left( {\bar {\boldsymbol{x}}\left( j \right)} \right) \leftarrow {\text{G} }\left( { { {\rm{Im} } } \left( {\tilde {\boldsymbol{x}}\left( j \right)} \right),{\boldsymbol{m} }\left( j \right),{\boldsymbol{z} }\left( j \right)} \right)$
${ {\rm{Re} } } \left( {\hat {\boldsymbol{x}}\left( j \right)} \right) \leftarrow {\boldsymbol{m} }\left( j \right) \odot { {\rm{Re} } } \left( {\tilde {\boldsymbol{x} } \left( j \right)} \right) + \left( {1 - {\boldsymbol{m} }\left( j \right)} \right) \odot { {\rm{Re} } } \left( {\bar {\boldsymbol{x}}\left( j \right)} \right)$ , ${ {\rm{Im} } } \left( {\hat {\boldsymbol{x}}\left( j \right)} \right) \leftarrow {\boldsymbol{m} }\left( j \right) \odot { {\rm{Im} } } \left( {\tilde {\boldsymbol{x} }\left( j \right)} \right) + \left( {1 - {\boldsymbol{m} }\left( j \right)} \right) \odot { {\rm{Im} } } \left( {\bar {\boldsymbol{x}}\left( j \right)} \right)$
${\boldsymbol{h} }\left( j \right) = {\boldsymbol{b} }\left( j \right) \odot {\boldsymbol{m} }\left( j \right) + 0.5\left( {1 - {\boldsymbol{b}}\left( j \right)} \right)$
end for
使用随机梯度下降(Stochastic Gradient Descent, SGD)算法, 分别更新 ${{\text{D}}_1}$ 和 ${{\text{D}}_2}$ 网络参数(固定 ${{\text{G}}_1}$ 和 ${{\text{G}}_2}$ 网络的参数) 　　　 ${{\text{∇}} _{ { {\text{D} }_1} } } - \displaystyle\sum\limits_{j = 1}^{ {J_{\text{D} } } } { {\mathcal{L}_{\text{D} } }\left( { {\boldsymbol{m} }\left( j \right),{ {\text{D} }_1}\left( { {\text{Re} }\left( {\hat {\boldsymbol{x} }\left( j \right)} \right),{\boldsymbol{h} }\left( j \right)} \right),{\boldsymbol{b} }\left( j \right)} \right)}$
${{\text{∇}} _{ { {\text{D} }_2} } } - \displaystyle\sum\limits_{j = 1}^{ {J_{\text{D} } } } { {\mathcal{L}_{\text{D} } }\left( { {\boldsymbol{m} }\left( j \right),{ {\text{D} }_2}\left( { {\text{Im} }\left( {\hat {\boldsymbol{x} }\left( j \right)} \right),{\boldsymbol{h} }\left( j \right)} \right),{\boldsymbol{b} }\left( j \right)} \right)}$
2 生成器训练( ${ {\rm{G} }_1}$ 和 ${ {\rm{G} }_2}$ 分别为实部和虚部网络的生成器)
从训练数据集取出 ${J_{\text{G}}}$ 个样本作为一批量的数据 $\left\{ {\left( { {\text{Re} }\left( {\tilde {\boldsymbol{x}}\left( j \right)} \right),{\boldsymbol{m}}\left( j \right)} \right)} \right\}_{j = 1}^{ {J_{\text{G} } } }$ , $\left\{ {\left( { {\text{Im} }\left( {\tilde {\boldsymbol{x}}\left( j \right)} \right),{\boldsymbol{m} }\left( j \right)} \right)} \right\}_{j = 1}^{ {J_{\text{G} } } }$
随机采样 ${J_{\text{G}}}$ 个样本 $\left\{ {{\boldsymbol{z}}\left( j \right)} \right\}_{j = 1}^{ {J_{\text{G} } } }$ , $\left\{ {{\boldsymbol{b}}\left( j \right)} \right\}_{j = 1}^{ {J_{\text{G} } } }$
for $j = 1,2,\cdots,{J_{\rm{D}}}$ do
${\boldsymbol{h} }\left( j \right) = {\boldsymbol{b} }\left( j \right) \odot {\boldsymbol{m} }\left( j \right) + 0.5\left( {1 - {\boldsymbol{b}}\left( j \right)} \right)$
end for
使用SGD算法更新 ${{\text{G}}_1}$ 和 ${{\text{G}}_2}$ 网络(固定 ${{\text{D}}_1}$ 和 ${{\text{D}}_2}$ 网络参数) 　　 ${{\text{∇}} _{ { {\text{G} }_1} } } - \displaystyle\sum\limits_{j = 1}^{ {J_{\text{G} } } } { {\mathcal{L}_{\text{G} } }\left( { {\boldsymbol{m} }\left( j \right),\hat {\boldsymbol{m} }\left( j \right),{\boldsymbol{b} }\left( j \right)} \right)} + \beta {\mathcal{L}_{\text{M} } }\left( { {\text{Re} }\left( {\hat {\boldsymbol{x} }\left( j \right)} \right),{\text{Re} }\left( {\tilde {\boldsymbol{x} }\left( j \right)} \right)} \right)$
${{\text{∇}} _{ { {\text{G} }_2} } } - \displaystyle\sum\limits_{j = 1}^{ {J_{\text{G} } } } { {\mathcal{L}_{\text{G} } }\left( { {\boldsymbol{m} }\left( j \right),\hat {\boldsymbol{m} }\left( j \right),{\boldsymbol{b} }\left( j \right)} \right)} + \beta {\mathcal{L}_{\text{M} } }\left( { {\text{Im} }\left( {\hat {\boldsymbol{x} }\left( j \right)} \right),{\text{Im} }\left( {\tilde {\boldsymbol{x} }\left( j \right)} \right)} \right)$
end while

下载: 导出CSV

表 1 测试集矩阵恢复数据的平均RMSE(不同损失率 ${\boldsymbol{\varepsilon}}$ )

Table 1. Average RMSE of the missing data recovery (different ${\boldsymbol{\varepsilon}}$ )

损失率	平均RMSE	损失率	平均RMSE
$\varepsilon = 0.2$	1.43E–02	$\varepsilon = 0.4$	2.20E–02
$\varepsilon = 0.3$	1.59E–02	$\varepsilon = 0.5$	2.33E–02

下载: 导出CSV

表 2 测试集矩阵恢复数据的平均RMSE(不同网络层数k)

Table 2. Average RMSE of the missing data recovery (different k)

网络层数	平均RMSE
3	1.92E–02
6	1.59E–02
9	1.63E–02

下载: 导出CSV

表 3 测试集矩阵恢复数据的平均RMSE(不同方法)

Table 3. Average RMSE of the missing data recovery (different methods)

矩阵缺失数据恢复方法	平均RMSE
EM	3.66E–02
随机森林	2.87E–02
降噪自编码器	3.08E–02
本文所提算法	1.59E–02

下载: 导出CSV

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