互耦条件下基于稀疏重构的MIMO雷达角度估计

肖炯; 唐波; 王海

doi:10.12000/JR24061

互耦条件下基于稀疏重构的MIMO雷达角度估计

doi: 10.12000/JR24061

国防科技大学电子对抗学院合肥 230037

基金项目: 国家自然科学基金(62171450)，安徽省杰出青年科学基金(2108085J30)，国防科技大学自主创新科学基金(23-ZZCX-JDZ-42)

详细信息

作者简介:
肖　炯，硕士生，主要研究方向为雷达信号处理

唐　波，博士，教授。主要研究方向为雷达信号处理、通信信号处理和阵列信号处理等

王　海，博士，教授。主要研究方向为雷达与雷达对抗等

通讯作者:
唐波 tangbo06@gmail.com

责任主编：张弓 Corresponding Editor: ZHANG Gong
中图分类号: TN959.1
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出版历程
- 收稿日期: 2024-04-03
- 修回日期: 2023-12-06

Sparse Reconstruction–Based Direction of Arrival Estimation for MIMO Radar in the Presence of Unknown Mutual Coupling

College of Electronic Engineering, National University of Defense Technology, Hefei 230037, China

Funds: The National Natural Science Foundation of China (62171450), The Anhui Provincial Natural Science Foundation (2108085J30), Research Plan of National University of Defense Technology (23-ZZCX-JDZ-42)

More Information

Corresponding author: Tang Bo, tangbo06@gmail.com

摘要

摘要: 为了降低阵列互耦对多输入多输出(MIMO)雷达波达角度(DOA)估计性能的影响，实现少量快拍条件下的目标角度估计，本文提出了基于迭代最小化稀疏学习算法(SLIM)的互耦校正和目标角度估计算法。所提算法利用目标回波信号的空域稀疏性，通过迭代优化算法估计了MIMO雷达发射和接收阵列的阵元互耦系数，以及目标稀疏空间谱。该算法无需设置超参数，且具有良好的收敛特性。仿真结果表明，当MIMO雷达发射和接收阵列存在互耦时，如果目标角度间隔较小，所提算法能够在较高信噪比条件下基于少量快拍高精度地估计目标角度；如果目标角度间隔较大，则在较低信噪比和少量快拍条件下仍有较高的角度估计精度。
- MIMO雷达 /
- 波达角度(DOA)估计 /
- 阵列互耦 /
- SLIM算法 /
- 少量快拍
Abstract: To improve the accuracy of Direction Of Arrival (DOA) estimation Multiple-Input–Multiple-Output (MIMO) radar systems under unknown mutual coupling, we propose a mutual coupling calibration and DOA estimation algorithm based on sparse learning via iterative minimization. The proposed algorithm utilizes the spatial sparsity of target signals and estimates the spatial pseudo-spectra and the mutual coupling matrices of MIMO arrays through cyclic optimization. Moreover, it is hyperparameter-free and guarantees convergence. Numerical examples demonstrate that for MIMO radar under unknown mutual coupling conditions, the proposed algorithm can accurately estimate the DOA of targets with small angle separations and relatively high Signal-to-Noise Ratios (SNRs), even with a limited number of samples. In addition, low DOA estimation errors are achieved for targets with large angle separations and small sample sizes, even under low-SNR conditions.
- MIMO radar /
- DOA estimation /
- mutual coupling /
- Sparse Learning via Iterative Minimization /
- small sample size

HTML全文

图 1 集中式MIMO雷达示意图

Figure 1. Colocated MIMO radar

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图 2 算法流程图

Figure 2. Flow chart of the proposed algorithm

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图 3 算法收敛曲线

Figure 3. Convergence analysis of the proposed algorithm

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图 4 SLIMMC与SLIMMC-RELAX算法RMSE随快拍数变化图(SNR=10 dB)

Figure 4. RMSEs of the SLIMMC and SLIMMC-RELAX algorithms versus the number of snapshots (SNR=10 dB)

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图 5 SLIMMC与SLIMMC-RELAX算法RMSE随SNR变化图(L=10)

Figure 5. RMSEs of the SLIMMC and SLIMMC-RELAX algorithms versus SNR (L=10)

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图 6 不同非零互耦系数时算法RMSE随SNR变化图

Figure 6. RMSEs of the proposed algorithm versus SNR for different numbers of nonzero mutual coupling coefficients

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图 7 不同互耦效应下的算法RMSE随快拍数变化图(SNR=10 dB)

Figure 7. RMSEs of the proposed algorithm versus the number of snapshots for different mutual coupling coefficients (SNR=10 dB)

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图 8 不同互耦效应下的算法RMSE随SNR变化图(L=10)

Figure 8. RMSEs of the proposed algorithm versus SNR for different mutual coupling coefficients (L=10)

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图 9 目标角度间隔较小时算法空间谱图(SNR=10dB)

Figure 9. Spectrum for targets with small angle separation (SNR=10dB)

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图 12 目标角度间隔较大时算法空间谱图(SNR=10dB)

Figure 12. Spectrum for targets with large angle separation (SNR=10dB)

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图 10 目标角度间隔较小时算法RMSE随SNR变化图

Figure 10. RMSEs versus SNR for targets with small angle separation.

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图 13 目标角度间隔较大时算法RMSE随SNR变化图

Figure 13. RMSEs versus SNR for targets with large angle separation

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图 11 目标角度间隔较小时算法RMSE随快拍数变化图(SNR=10dB)

Figure 11. RMSEs versus snapshots for targets with small angle separation (SNR=10dB)

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图 14 目标角度间隔较大时算法RMSE随快拍数变化图(SNR=10dB)

Figure 14. RMSEs versus snapshots for targets with large angle separation (SNR=10dB)

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1 RELAX算法

1. RELAX algorithm

初始化：$\hat K$, ${\text{\{ }}{\hat \theta _k}{\text{\} }}_{k = 1}^{\hat K}$, ${\text{\{ }}{\hat x_{k,l}}{\text{\} }}_{k = 1,l = 1}^{\hat K,L}$
$\hat K$：SLIMMC算法得到的目标个数
${\text{\{ }}{\hat \theta _k}{\text{\} }}_{k = 1}^{\hat K}$：SLIMMC算法得到的目标角度
${\text{\{ }}{\hat x_{k,l}}{\text{\} }}_{k = 1,l = 1}^{\hat K,L}$：SLIMMC算法得到的目标回波
重复：
for k = 1, ···, $\hat K$
$ {{\boldsymbol{\tilde y}}_{k,l}} = {{\boldsymbol{y}}_l} - \displaystyle\sum\limits_{i = 1,i \ne k}^{\hat K} {{\boldsymbol{a}}{\text{(}}{{\hat \theta }_i}{\text{)}}} {\hat x_{i,l}}\;,\;\;\;\;l = 1,2, \cdots ,L $
$ {\hat \theta _k} = \mathop {{\text{argmax}}}\limits_{{\theta _k}} \displaystyle\sum\limits_{l = 1}^L {\|{\boldsymbol{a}}_{}^{\text{H}}{\text{(}}{\theta _k}{\text{)}}{{{\boldsymbol{\tilde y}}}_{k,l}}{\|^2}} $
$ {\hat x_{i,l}} = \dfrac{{{\boldsymbol{a}}_{}^{\text{H}}{\text{(}}{{\hat \theta }_k}{\text{)}}{{{\boldsymbol{\tilde y}}}_{k,l}}}}{{\|\|{\boldsymbol{a}}_{}^{\text{H}}{\text{(}}{{\hat \theta }_k}{\text{)}}\|{\|^2}}}\;,\;\;\;\;l = 1,2, \cdots ,L $
end
直到收敛
输出：${\text{\{ }}{\hat \theta _k}{\text{\} }}$

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表 1 非零互耦系数取值

Table 1. Nonzero mutual coupling coefficients setting

非零互耦系数个数	发射阵列非零互耦系数	接收阵列非零互耦系数
K_t=K_r=2	[1, -0.40+0.002j]	[1, 0.4+0.1121j]
K_t=K_r=3	[1, -0.40+0.002j, -0.1046-0.0566j]	[1, 0.4+0.1121j, 0.1383+0.0708j]

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表 2 不同互耦效应下的非零互耦系数

Table 2. Different mutual coupling coefficients

参数组	发射阵列非零互耦系数	接收阵列非零互耦系数
1	[1, -0.1346-0.0566j]	[1, 0.1683+0.0708j]
2	[1, 0.1552+0.2875j]	[1, -0.2637-0.1667j]
3	[1, -0.45+0.002j]	[1, 0.4+0.1121j]
4	[1, 0.3742+0.5918j]	[1, -0.6262-0.3679j]

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表 3 SBLMC算法超参数

Table 3. Hyperparameters for the SBLMC algorithm

SBLMC(1)	a=b=c=d=e₁=f₁=e₂=f₂=10^–2
SBLMC(2)	a=b=c=d=e₁=f₁=e₂=f₂=1

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表 4 算法计算复杂度和运行时间

Table 4. Computational complexity and running time for the three algorithms

算法	计算复杂度	运行时间(s)
算法	计算复杂度	[-2°, 2°]	[-10°, 10°]
所提算法	$ O{\text{(}}{J^3} + {N_{\text{t}}}{N_{\text{r}}}{J^2} + N_{\text{t}}^{\text{2}}N_{\text{r}}^{\text{2}}J + L{N_{\text{t}}}{N_{\text{r}}}J{\text{)}} $	1.3744	1.2526
SBLMC(1)	$ O{\text{(}}{J^3} + L{N_{\text{t}}}{N_{\text{r}}}{J^2} + N_{\text{t}}^{\text{2}}N_{\text{r}}^{\text{2}}J{\text{)}} $	105.1702	123.9081
SBLMC(2)		37.1674	37.4897
ESPRIT-Like	$ \begin{gathered} O{\text{((}}N'_{\text{t}} N'_{\text{r}} + {N_{\text{t}}}{N_{\text{r}}}{\text{)}}N'_{\text{t}} N'_{\text{r}} L + {{\text{(}}N'_{\text{t}} N'_{\text{r}} {\text{)}}^3} \\ + 2{P^2}{\text{[(}}N'_{\text{t}} - 1{\text{)}}N'_{\text{r}} + {\text{(}}N'_{\text{r}}- 1{\text{)}}N'_{\text{t}} {\text{]}} + 12{P^3}{\text{)}} \\ \end{gathered} $	0.0551	0.0629

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