基于ABSUM的MIMO雷达频谱兼容波形设计

姚誉; 李泽清; 范文; 杜晓林; 吴乐南

doi:10.12000/JR22138

基于ABSUM的MIMO雷达频谱兼容波形设计

doi: 10.12000/JR22138

姚誉^1, ,,
李泽清¹,
范文²,
杜晓林³,
吴乐南⁴

1.
华东交通大学信息工程学院南昌 330031
2.
中国电子科技集团公司第五十四研究所石家庄 050081
3.
烟台大学计算机与控制工程学院烟台 264000
4.
东南大学信息科学与工程学院南京 210096

基金项目: 国家自然科学基金(61761019)

详细信息

作者简介:
姚　誉(1986-)，男，江西宜春人，博士，华东交通大学副教授。主要研究方向为雷达波形设计与处理、雷达通信一体化、最优化理论算法以及阵列信号处理等

李泽清(1997–)，男，广东人，华东交通大学硕士研究生。主要研究方向为雷达通信一体化、波形设计与处理、机器学习等

范　文(1986–)，男，陕西人，博士。主要研究方向为雷达波形设计与处理、雷达通信一体化、最优化理论算法以及阵列信号处理等

杜晓林(1985-)，男，山东肥城人，博士，烟台大学副教授。主要研究方向为优化理论算法及其应用、波形设计、人工智能、机器学习、凸优化、协方差矩阵估计、雷达信号处理

吴乐南(1952-)，男，安徽安庆人，东南大学教授。主要研究方向为物联网技术、车联网、多媒体信息处理、信号检测与估计等

通讯作者:
姚誉 yaoyu@ecjtu.edu.cn

责任主编：梁军利 Corresponding Editor: LIANG Junli
中图分类号: TN958
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出版历程
- 收稿日期: 2022-07-07
- 修回日期: 2022-08-15
- 网络出版日期: 2022-08-26
- 刊出日期: 2022-08-28

Spectrally Compatible Waveform Design for MIMO Radar Based on ABSUM Method

YAO Yu^{1
, ,},
LI Zeqing¹,
FAN Wen²,
DU Xiaolin³,
WU Lenan⁴

1.
School of Information Engineering, East China Jiaotong University, Nanchang 330031, China
2.
The 54th Research Institute of CETC, Shijiazhuang 050081, China
3.
School of Computer and Control Engineering, Yantai University, Yantai 264000, China
4.
School of Information Science and Engineering, Southeast University, Nanjing 210096, China

Funds: The National Natural Science Foundation of China (61761019)

More Information

Corresponding author: YAO Yu, yaoyu@ecjtu.edu.cn

摘要

摘要: 该文讨论了多输入多输出(MIMO)雷达发射波形和接收滤波器的联合优化问题，以确保与叠加的授权通信网络频谱兼容。考虑信号相关杂波的干扰，在发射能量、相似性和频谱兼容约束下，所提出的信干噪比(SINR)最大化的优化问题是NP-hard问题。为此，首先引入辅助变量对原问题进行修正，然后提出了一种基于乘子块连续上界极小化的原对偶(ABSUM)算法求解该问题。此外，利用内点法求解在ABSUM算法每个更新过程中涉及的二次规划问题。最后，仿真结果表明，ABSUM算法在输出SINR、波束图、频谱特性等方面优于现有方法。
- 频谱兼容 /
- 多输入多输出雷达 /
- 收发联合设计 /
- 迭代分块连续上界最小化方法 /
- 基于交替方向乘子法
Abstract: This paper proposes a joint design method to optimize the transmit waveforms and receive filter bank in Multiple-Input Multiple-Output (MIMO) structure ensuring spectral compatibility with the surrounding communication service network. Considering the signal-dependent clutter interference, under the constraints of transmission energy, waveform similarity and spectrum compatibility, the formulated optimization problem of the output Signal-to-Interference-plus-Noise Ratio (SINR) maximization is NP-hard. Toward this end, an auxiliary variable is first introduced to modify the original problem, and then a primal-dual algorithm based on the Alternating Block Successive Upper-bound Minimization (ABSUM) method is developed to deal with the resulting problem. Furthermore, an interior point method is used to handle the quadratic programming problem involved in each update procedure of the devised ABSUM method. Finally, numerical simulations are performed to demonstrate the superiority of the proposed method over state-of-the-art methods in terms of the optimized SINR, beampattern, computational complexity and ambiguity properties.

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图 1 已优化波形特征

Figure 1. The feature of the optimized waveforms

下载: 全尺寸图片幻灯片

图 2 频谱兼容和相似性约束下SINR的迭代曲线

Figure 2. The SINRs with spectrum constraint and similarity constraint

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图 3 ABSUM, GFA和SOA算法的优化SINR值和${\varepsilon '}$的关系($ {E}_{I}={10}^{-2},{10}^{-\text{4}},{10}^{-\text{5}} $)

Figure 3. The optimal SINR values of ABSUM, GFA and SOA versus ${\varepsilon '}$ with $ {E}_{I}={10}^{-2},{10}^{-\text{4}},{10}^{-\text{5}} $

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图 4 不同频谱约束${E_I}$下优化SINR值与相似性约束的关系(${\varepsilon }{{'}}=\text{0}\text{.5},\text{1}\text{.0},\text{2}\text{.0}$)

Figure 4. The optimal SINR values of ABSUM, GFA and SOA versus ${E_I}$ with ${\varepsilon }{{'}}=\text{0}\text{.5},\text{1}\text{.0},\text{2}\text{.0}$

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图 5 ABSUM和GFA算法的输出SINR与${E_I}$和${\varepsilon '}$的关系

Figure 5. The output SINRs of the proposed ABSUM and GFA versus the input SNR for different ${E_I}$ and ${\varepsilon '}$

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图 6 SINR值与目标角和干扰源角度的关系图

Figure 6. The SINR versus the uncertainty of the target angle and the interference angle

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图 7 波形功率谱图(${\varepsilon '} = 1.0$)

Figure 7. ESDs of the waveform optimized via ABSUM versus normalized frequency with ${\varepsilon '} = 1.0$

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图 8 波形功率谱图(${E_I} = {10^{ - 4}}$)

Figure 8. ESDs of the waveform optimized via ABSUM versus normalized frequency with ${E_I} = {10^{ - 4}}$

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图 9 频谱和相似性约束下的波束图(频谱约束${E_I} = {10^{ - 4}}$)

Figure 9. The beampatterns of the ABSUM and GFA with spectrum and similarity constraints (${E_I} = {10^{ - 4}}$)

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图 10 MIMO模糊度函数的距离-角度切割

Figure 10. Range-azimuth plane of MIMO CAF

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算法1　基于ABSUM的发射和接收联合设计算法
Alg. 1 ABSUM algorithm for solving transmit-receive design
输入：$k = 0$，初始化${\boldsymbol{c} }_{\rm{r}}^k$, ${\boldsymbol{t} }_{\rm{r}}^k$, ${{\boldsymbol{u}}^k}$, ${v^k}$和收敛参数$ {\epsilon}^{{\rm{abs}}} $, $ {\epsilon}^{{\rm{rel}}} $
1：重复
2：$k = k + 1$
3：通过求${\boldsymbol{\varPsi } }({ {\boldsymbol{c} }^k})$和${ {\boldsymbol{\varPsi } }_{{\rm{in}}} }({ {\boldsymbol{c} }^k})$的最大广义特征值来更新${{\boldsymbol{w}}^k}$。
4：使用内点法求解问题(16)和问题(18)更新${\boldsymbol{c} }_{\rm{r}}^k$和${\boldsymbol{t} }_{\rm{r}}^k$。
5：求解问题(12)更新${{\boldsymbol{u}}^k}$和${v^k}$
6：如果满足收敛的终止条件，则算法停止迭代。

下载: 导出CSV

表 1 仿真参数

Table 1. Simulation parameter

参数	数值	参数	数值
发射天线${N_{\rm{t}}}$	4	接收天线${N_{\rm{r}}}$	8
采样个数${N_{\rm{s}}}$	64	干扰源角度${\theta _k}$	–50°, –10°, 40°
雷达目标角度${\theta _0}$	${\text{1}}{5^ \circ }$	无线网络归一化频率$f_{{\rm{lower}}}^i$, $f_{{\rm{upper}}}^i$	$[0.2,0.3]$ $[0.75,0.85]$
最大干扰量${E_I}$	${10}^{-2}, {10}^{-\text{3} }, {10}^{-\text{5} }$	相似性参数$\varepsilon $	$0.5,0.8,1.0,2.0$

下载: 导出CSV

表 2 ABSUM, GFA和SOA算法的优化SINR值(dB)和全局计算时间(s)

Table 2. SINR value (dB) and global computational times (s) for ABSUM, GFA and SOA

${\varepsilon'}$	ABSUM		GFA		SOA
${\varepsilon'}$	SINR	Time	SINR	Time	SINR	Time
0.5	17.2	15.3	15.4	135.8	13.6	637.9
1.0	18.8	19.1	16.5	141.5	14.8	853.1
1.3	19.2	21.5	17.5	154.4	16.5	963.1
2.0	19.3	19.8	19.3	169.3	19.3	812.1

下载: 导出CSV

表 3 ABSUM、BCD、MM和GFA的SINR值(dB)和全局计算时间(s)

Table 3. SINR value (dB) and global computational times (s) for ABSUM, BCD, MM and GFA

${E_I}$	ABSUM		SOA		MM		GFA
${E_I}$	SINR	time	SINR	time	SINR	time	SINR	time
${10^{ - 2}}$	19.2	14.3	16.7	45.3	19.1	10.2	16.8	120.8
${10^{ - 3}}$	19.0	16.2	16.8	55.2	18.9	13.4	16.7	134.5
${10^{ - 4}}$	18.8	19.1	16.8	66.8	18.6	15.7	16.5	141.5

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