基于波形优化和天线位置选择的MIMO雷达波束扫描算法研究

范文 蔚保国 陈镜 张航 李淳泽

范文, 蔚保国, 陈镜, 等. 基于波形优化和天线位置选择的MIMO雷达波束扫描算法研究[J]. 雷达学报, 2022, 11(4): 530–542. doi: 10.12000/JR22135
引用本文: 范文, 蔚保国, 陈镜, 等. 基于波形优化和天线位置选择的MIMO雷达波束扫描算法研究[J]. 雷达学报, 2022, 11(4): 530–542. doi: 10.12000/JR22135
FAN Wen, YU Baoguo, CHEN Jing, et al. Joint waveform optimization and antenna position selection for MIMO radar beam scanning[J]. Journal of Radars, 2022, 11(4): 530–542. doi: 10.12000/JR22135
Citation: FAN Wen, YU Baoguo, CHEN Jing, et al. Joint waveform optimization and antenna position selection for MIMO radar beam scanning[J]. Journal of Radars, 2022, 11(4): 530–542. doi: 10.12000/JR22135

基于波形优化和天线位置选择的MIMO雷达波束扫描算法研究

doi: 10.12000/JR22135
基金项目: 国家重点研发计划(2021YFB3900801)
详细信息
    作者简介:

    范 文(1986-),男,陕西安康人,博士,工程师。主要研究方向为波形设计、MIMO雷达、最优化理论算法以及阵列信号处理等

    蔚保国(1966-),男,内蒙古凉城人,研究员,博士生导师。主要研究方向为综合时空体系设计与通导遥一体化系统

    陈 镜(1977-),男,山西临县人,硕士,高级工程师。主要研究方向为雷达系统设计

    张 航(1983-),男,河北保定人,博士生,高级工程师。主要研究方向为自组织网络、一体化电子系统

    李淳泽(1996-),男,河北邢台人,硕士。主要研究方向为无线通信、数字信号处理

    通讯作者:

    范文 fanwen@mail.nwpu.edu.cn

  • 责任主编:梁军利 Corresponding Editor: LIANG Junli
  • 1 雷达天线单元间间距不同,且有可能大于半波长。
  • 中图分类号: TN958

Joint Waveform Optimization and Antenna Position Selection for MIMO Radar Beam Scanning

Funds: The National Key Research and Development Program (2021YFB3900801)
More Information
  • 摘要: 为实现集中式多输入多输出(MIMO)雷达波束扫描,本文在峰值平均功率比(PAPR)、能量以及布尔(天线位置选择)约束下,基于min-max波束图匹配准则,首次提出MIMO雷达天线位置和多组探测波形(一组波形对应一个独立的波束图)的联合优方法。由于非凸PAPR约束、布尔约束以及min-max目标函数的非凸非光滑性导致了优化问题成为典型的大规模NP-难问题。为求解该NP-难优化问题,该文首先利用Lawson算法将min-max问题转化为迭代加权最小二乘(ILS)问题,然后根据上界函数最小化(MM)准则简化ILS优化问题,最后用交替方向乘子法(ADMM)求解简化后的上界优化问题。数值仿真结果检验了所提算法的有效性。

     

  • 图  1  仿真样例1

    Figure  1.  Simulation example 1

    图  2  收敛性分析

    Figure  2.  Convergence performance analysis

    图  3  仿真样例2($L = 20$, $\hat L = 12$)

    Figure  3.  Simulation example 2 ($L = 20$, $\hat L = 12$)

    图  4  仿真样例2($L = 17$, $\hat L = 12$)

    Figure  4.  Simulation example 2 ($L = 17$, $\hat L = 12$)

    图  5  仿真样例2($L = 20$, $\hat L = 15$)

    Figure  5.  Simulation example 2 ($L = 20$, $\hat L = 15$)

    图  6  仿真样例3

    Figure  6.  Simulation example 3

    图  7  不同方法获得的波束图结果

    Figure  7.  Beampattern results obtained by using different method

    表  1  基于波形优化和天线位置选择的MIMO雷达波束扫描算法

    Table  1.   Algorithm for joint waveform optimization and antenna position selection for MIMO radar beam scanning

     输入参数:I, ${\boldsymbol{\varTheta }}_m^i$, ${\boldsymbol{\varTheta }}_s^i$, ${\boldsymbol{\varTheta }}_n^i$, ${\boldsymbol{\varTheta }}_t^i$, ${{\boldsymbol{W}}^i},\forall i$, ${\zeta _l},\forall l$, $\gamma $, $\hat L$, L, $\rho $, ${\delta _{{\rm{out}}} } = {10^{ - 8} }$, ${\delta _{{\rm{inner}}} } = {10^{ - 8} }$,
          $\{ \{ {{\boldsymbol{X}}^i}(0),{{\boldsymbol{Z}}^i}(0),{{\boldsymbol{\varPsi }}^i}(0)\} _{i = 1}^I,{\boldsymbol{\alpha }}(0),{\boldsymbol{\bar s}}(0)\} $, $\tilde R_{m,q}^i(0) = W_{m,q}^i\left[ {{{\boldsymbol{W}}^i}; \cdots ;{{\boldsymbol{W}}^I}} \right]$, $\forall i,\forall m,\forall q$, ${K_{{\rm{max}}} }$, $k = 0$
      1 WHILE {$|{\rm{obj}}(k) - {\rm{obj}}(k - 1)| > {\sigma _{{\rm{out}}} }$ & $k \le {K_{ {\rm{max} } } }$}(Lawson迭代)
      2 $t = 0$;
      3 WHILE $\left\{ {\dfrac{1}{I}\displaystyle\sum\limits_{i = 1}^I {\left\| { { {\boldsymbol{Z} }^i}(t) - { {\boldsymbol{Z} }^i}(t - 1)} \right\|_{\rm F}^2} > {\sigma _{{\rm{inner}}} } } \right\}$(M-ADMM迭代)
      4   $ \bullet $ 更新${\boldsymbol{d}}_m^i(t + 1)$
      5   $ \bullet $ 顺序更新$\{ {\boldsymbol{\bar s}}(t + 1),{\boldsymbol{\alpha }}(t + 1),\{ {{\boldsymbol{X}}^i}(t + 1)\} _{i = 1}^I\} $
      6   $ \bullet $ 更新$\{ {{\boldsymbol{Z}}^i}(t + 1)\} _{i = 1}^I$
      7   $ \bullet $ 更新$\{ {{\boldsymbol{\varPsi }}^i}(t + 1)\} _{i = 1}^I$
      8   $t: = t + 1$;
      9 ENDWHILE(M-ADMM迭代结束)
      10 ${{\boldsymbol{Z}}^i}(k + 1) = {{\boldsymbol{Z}}^i}(t - 1),\forall i,{\beta ^i}(k + 1) = {\bar h^i}({{\boldsymbol{Z}}^i}(k + 1)),\forall i$;
      11 更新Lawson权值$w_m^i(k)$;
      12 ${\rm{obj}}(k) = {\max _{m,i} }\{ G_m^i({ {\boldsymbol{Z} }^i}(k + 1),{\beta ^i}(k + 1))\}$;
      13 $k: = k + 1$;
      14 ENDWHILE(Lawson迭代结束)
     输出:探测波形${{\boldsymbol{Z}}^i}( \star ) = {{\boldsymbol{Z}}^i}(t),i = 1,2,\cdots,I$,天线位置${\boldsymbol{\bar s}}( \star ) = {\boldsymbol{\bar s}}(t)$。
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  • 收稿日期:  2022-07-06
  • 修回日期:  2022-08-12
  • 网络出版日期:  2022-08-25
  • 刊出日期:  2022-08-28

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