基于矩阵低秩分解的PEPC-MIMO雷达主瓣压制干扰抑制方法

张翔; 兰岚; 马楠; 钟垒; 廖桂生

doi:10.12000/JR25227

基于矩阵低秩分解的PEPC-MIMO雷达主瓣压制干扰抑制方法

DOI: 10.12000/JR25227 CSTR: 32380.14.JR25227

张翔¹,
兰岚^1, ,,
马楠²,
钟垒²,
廖桂生¹

1.
西安电子科技大学雷达信号处理全国重点实验室西安 710071
2.
中国电子科技集团公司第二十九研究所成都 610000

基金项目: 国家自然科学基金(62522120, 62471348)，中央高校基本科研业务费专项资金资助(QTZX23068, YJSJ25008)

详细信息

作者简介:
张　翔，博士生，主要研究方向为新体制阵列雷达抗干扰、智能化抗干扰等

兰　岚，博士，教授，主要研究方向为新体制阵列雷达信号处理、智能化抗干扰、目标检测与参数估计等

马　楠，硕士，高级工程师，主要研究方向为综合射频系统设计、电子对抗技术等

钟　垒，博士，高级工程师，主要研究方向为机载电子进攻系统技术、电磁场与微波技术

廖桂生，博士，教授，主要研究方向为雷达系统技术与阵列处理、雷达稀疏成像处理等

通讯作者:
兰岚 lanlan@xidian.edu.cn

责任主编：崔国龙 Corresponding Editor: CUI Guolong

中图分类号: TN957
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出版历程
- 收稿日期: 2025-11-05
- 修回日期: 2025-12-23

Mainlobe Blanket Interference Suppression with PEPC-MIMO Radar via Low-rank Matrix Decomposition

1.
National Key Laboratory of Radar Signal Processing, Xidian University, Xi’an 710071, China
2.
Southwest China Research Institute of Electronic Equipment, Chengdu 610000, China

Funds: The National Natural Science Foundation of China (62522120, 62471348), The Fundamental Research Funds for the Central Universities (QTZX23068, YJSJ25008)

More Information

Corresponding author: LAN Lan, lanlan@xidian.edu.cn

摘要

摘要: 阵元-脉冲编码( EPC-MIMO)雷达通过在发射阵元和脉冲间引入相位编码，可实现主瓣欺骗干扰抑制，但仍然无法应对主瓣压制干扰的威胁。对此，该文在EPC-MIMO雷达中加入极化调制，研究了极化阵元-脉冲编码(PEPC-MIMO)雷达体制下的主瓣压制干扰抑制方法。具体而言，基于主值成分追踪(SPCP)分解框架，利用压制干扰在空间-极化联合域的低秩特性，将主瓣压制干扰抑制问题转化为一个“低秩+稀疏”模型的优化问题。随后，利用L-BFGS-AO算法进行迭代求解，实现目标回波和主瓣压制干扰的精准分离。进一步地，提出了一种基于稀疏重构的PEPC-MIMO雷达参数估计方法用于估计目标回波信号的发射角度、接收角度以及目标距离模糊区，从而构造最优的波束形成权矢量对各通道信号进行加权求和。仿真实验验证了所提方法在无先验知识前提下抑制主瓣压制干扰方面的有效性。
- 极化阵元-脉冲编码雷达 /
- 主瓣压制干扰抑制 /
- 低秩分解 /
- 稀疏重构 /
- 参数估计
Abstract: By applying phase coding in transmit elements and pulses, the Element-Pulse Coding Multiple-Input Multiple-Output (EPC-MIMO) radar can effectively suppress mainlobe deceptive interference. However, this approach remains ineffective against mainlobe blanket interference. To address this drawback, this paper investigates the mainlobe blanket interference suppression using a Polarization Element–Pulse Coding Multiple-Input Multiple-Output (PEPC-MIMO) radar system. Specifically, within the framework of stable principal component pursuit decomposition, the interference suppression problem is formulated as a “low-rank + sparse” optimization model by exploiting the low-rank structure of the received signal in the joint time-space-polarization domain. The resulting optimization problem is solved iteratively using a Limited-memory Broyden-Fletcher-Goldfarb-Shanno-based alternating optimization (L-BFGS-AO) algorithm, thereby enabling accurate separation of target echoes from mainlobe blanket interference. Furthermore, a sparse reconstruction–based parameter estimation method is proposed to estimate the target’s transmit angle, receive angle, and range ambiguity region. These estimates are then used to construct optimal receive weight vectors for the weighted summation of signals across channels. Simulation results demonstrate the effectiveness of the proposed approach in suppressing mainlobe blanket interference without requiring prior knowledge of the interference.
- PEPC-MIMO radar /
- Mainlobe blanket interferences suppression /
- Matrix low-rank decomposition /
- Sparse reconstruction /
- Parameter estimation

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图 1 PEPC-MIMO雷达信号收发示意图

Figure 1. Illustration of signal transmission and reception for PEPC-MIMO radar

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图 2 信号分解示意图

Figure 2. Illustration of signal decomposition

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图 3 信号处理流程示意图

Figure 3. The flowchart of signal processing

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图 4 干扰抑制前后发射-接收二维空间谱及收敛曲线

Figure 4. Transmit-receive 2D spatial spectra and convergence curves

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图 5 噪声卷积干扰抑制结果

Figure 5. Suppression of Noise convolution interference

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图 6 噪声调幅干扰抑制结果

Figure 6. Suppression of noise amplitude-modulated interference

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图 7 噪声调频干扰抑制结果

Figure 7. Suppression of noise frequency-modulated interference

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图 8 稀疏矩阵估计结果

Figure 8. Estimation of sparse coefficient matrix

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图 9 干扰抑制结果

Figure 9. Results of interference suppression

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1 基于L-BFGS-AO的主瓣压制干扰分离算法

1. Separation of blanket interference suppression based on L-BFGS-AO algorithm

输入：第k个脉冲接收信号$ {\boldsymbol{S}}_{k} $, $ {c}_{1} $, $ {c}_{2} $, $ \delta $
初始化：$ i=1 $, $ \boldsymbol{R}_{k}^{(i)} $, $ \boldsymbol{V}_{k}^{(i)} $, $ \boldsymbol{S}_{0,k}^{(i)} $,U，最大迭代次数I
while $ i\text{ < }I $
1. 计算梯度$ \nabla \boldsymbol{R}_{k}^{(i)} $, $ \nabla \boldsymbol{V}_{k}^{(i)} $；
2. 将变量和梯度分别矢量化，得到$ \boldsymbol{r}_{k}^{(i)} $和$ \nabla \boldsymbol{f}_{k}^{(i)} $，并计算变量　　增量$ \boldsymbol{c}_{k}^{(i-1)} $和梯度增量$ \boldsymbol{y}_{k}^{(i-1)} $；
3. 初始化$ {\boldsymbol{a}}^{(i-1)}=\nabla \boldsymbol{f}_{k}^{(i)} $，若$ i\leq \text{U} $，令$ {U}_{0}=i $，否则令　　$ {U}_{0}=U $;
4. for $ u=(i-1)\colon (i-{U}_{0}) $
5. 　$ {\eta }_{u}={\left(\boldsymbol{c}_{k}^{(u)}\right)}^{\text{T}}{\boldsymbol{a}}^{(u)}/{\left(\boldsymbol{y}_{k}^{(u)}\right)}^{\text{T}}\boldsymbol{c}_{k}^{(u)} $;
6. 　$ {\boldsymbol{a}}^{(u-1)}={\boldsymbol{a}}^{(u)}-{\eta }_{u}\boldsymbol{y}_{k}^{(u)} $;
7. end
8. 　$ {\boldsymbol{b}}^{(i-{{U}_{0}})}={\boldsymbol{a}}^{(u-1)} $
9. for $ u=(i-{U}_{0})\colon (i-1) $
10. $ {\beta }_{u}={\left(\boldsymbol{y}_{k}^{(u)}\right)}^{\text{T}}{\boldsymbol{b}}^{(u)}/{\left(\boldsymbol{y}_{k}^{(u)}\right)}^{\text{T}}\boldsymbol{c}_{k}^{(u)} $;
11. $ {\boldsymbol{b}}^{(u+1)}={\boldsymbol{b}}^{(u)}+\boldsymbol{c}_{k}^{(u)}\left({\eta }_{u}-{\beta }_{u}\right) $;
12. end
13. $ \boldsymbol{d}_{k}^{(i)}=-{\boldsymbol{b}}^{(u+1)} $；
14. 更新$ \boldsymbol{r}_{k}^{(i+1)} = \boldsymbol{r}_{k}^{(i)} + \alpha _{k}^{(i)}\boldsymbol{d}_{k}^{(i)} $，计算得到$ \boldsymbol{R}_{k}^{(i+1)} $和$ \boldsymbol{V}_{k}^{(i+1)} $;
15. 计算$ \boldsymbol{S}_{0,k}^{(i+1)}=\text{sign}\left(\boldsymbol{Z}_{k}^{(i+1)}\right)\odot \max \left(\left\| \boldsymbol{Z}_{k}^{(i+1)}\right\| -\dfrac{{\lambda }_{\text{s}}}{2},0\right) $;
16. if $ \left\| f\left(\boldsymbol{R}_{k}^{(i+1)},\boldsymbol{V}_{k}^{(i+1)},\boldsymbol{S}_{0,k}^{(i+1)}\right)-\right. $ 　　$ \left. f\left(\boldsymbol{R}_{k}^{(i)},\boldsymbol{V}_{k}^{(i)},\boldsymbol{S}_{0,k}^{(i)}\right)\right\| \leq \delta $ then
17. 令$ \boldsymbol{S}_{0,k}^{(\ast )}=\boldsymbol{S}_{0,k}^{(i)} $，停止迭代；
18. end
19.$ i=i+1 $；
end while
输出：$ \boldsymbol{S}_{0,k}^{(\ast )} $

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表 1 PEPC-MIMO雷达系统仿真参数

Table 1. System parameters of PEPC-MIMO radar

参数	数值	参数	数值
发射阵元数M	8	接收阵元数N	8
载频$ {f}_{0} $	8 GHz	脉冲重复频率$ {f}_{r} $	10 kHz
脉冲数K	64	发射编码系数$ \gamma $	0.125
采样率	50 MHz	脉宽$ {T}_{p} $	10 μs

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表 2 目标干扰仿真参数

Table 2. Parameters of true and false targets

参数	目标	主瓣压制干扰
发射角度	13°	\
接收角度	10°	10°
SNR/JNR(dB)	5	40
目标速度(m/s)	20	\
主值距离(km)	5.5	\
脉冲延迟数	3	\
极化参数$ \left(\vartheta ,{\gamma }_{s}\right) $	(60°, 45°)	(45°,0)

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