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

姚誉, 李泽清, 范文, 等. 基于ABSUM的MIMO雷达频谱兼容波形设计[J]. 雷达学报, 2022, 11(4): 543–556. doi: 10.12000/JR22138
引用本文: 姚誉, 李泽清, 范文, 等. 基于ABSUM的MIMO雷达频谱兼容波形设计[J]. 雷达学报, 2022, 11(4): 543–556. doi: 10.12000/JR22138
YAO Yu, LI Zeqing, FAN Wen, et al. Spectrally compatible waveform design for MIMO radar based on ABSUM method[J]. Journal of Radars, 2022, 11(4): 543–556. doi: 10.12000/JR22138
Citation: YAO Yu, LI Zeqing, FAN Wen, et al. Spectrally compatible waveform design for MIMO radar based on ABSUM method[J]. Journal of Radars, 2022, 11(4): 543–556. doi: 10.12000/JR22138

基于ABSUM的MIMO雷达频谱兼容波形设计

doi: 10.12000/JR22138
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

Spectrally Compatible Waveform Design for MIMO Radar Based on ABSUM Method

Funds: The National Natural Science Foundation of China (61761019)
More Information
  • 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。

     

  • 图  1  已优化波形特征

    Figure  1.  The feature of the optimized waveforms

    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

    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}} $

    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 ${\varepsilon }{{'}}=\text{0}\text{.5},\text{1}\text{.0},\text{2}\text{.0}$

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

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

    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

    图  7  波形功率谱图(${\varepsilon '} = 1.0$)

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

    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 ${E_I} = {10^{ - 4}}$

    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 (${E_I} = {10^{ - 4}}$)

    图  10  MIMO模糊度函数的距离-角度切割

    Figure  10.  Range-azimuth plane of MIMO CAF

    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

    ${\varepsilon'}$ABSUMGFASOA
    SINRTimeSINRTimeSINRTime
    0.517.215.315.4135.813.6637.9
    1.018.819.116.5141.514.8853.1
    1.319.221.517.5154.416.5963.1
    2.019.319.819.3169.319.3812.1
    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

    ${E_I}$ABSUMSOAMMGFA
    SINRtimeSINRtimeSINRtimeSINRtime
    ${10^{ - 2}}$19.214.316.745.319.110.216.8120.8
    ${10^{ - 3}}$19.016.216.855.218.913.416.7134.5
    ${10^{ - 4}}$18.819.116.866.818.615.716.5141.5
    下载: 导出CSV
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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

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