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基于有限新息率的正交偶极子阵列信号参数估计算法

陈涛 赵立鹏 史林 申梦雨

陈涛, 赵立鹏, 史林, 申梦雨. 基于有限新息率的正交偶极子阵列信号参数估计算法[J]. 电子与信息学报, 2022, 44(7): 2469-2477. doi: 10.11999/JEIT210357
引用本文: 陈涛, 赵立鹏, 史林, 申梦雨. 基于有限新息率的正交偶极子阵列信号参数估计算法[J]. 电子与信息学报, 2022, 44(7): 2469-2477. doi: 10.11999/JEIT210357
CHEN Tao, ZHAO Lipeng, SHI Lin, SHEN Mengyu. Signal Parameter Estimation Algorithm for Orthogonal Dipole Array Based on Finite Rate of Innovation[J]. Journal of Electronics & Information Technology, 2022, 44(7): 2469-2477. doi: 10.11999/JEIT210357
Citation: CHEN Tao, ZHAO Lipeng, SHI Lin, SHEN Mengyu. Signal Parameter Estimation Algorithm for Orthogonal Dipole Array Based on Finite Rate of Innovation[J]. Journal of Electronics & Information Technology, 2022, 44(7): 2469-2477. doi: 10.11999/JEIT210357

基于有限新息率的正交偶极子阵列信号参数估计算法

doi: 10.11999/JEIT210357
基金项目: 国家自然科学基金(62071137),国防科技基础加强计划(2019-JCJQ-ZD-067-00)
详细信息
    作者简介:

    陈涛:男,1974年生,教授,博士,研究方向为宽带信号处理、检测与识别

    赵立鹏:男,1997年生,硕士生,研究方向为极化敏感阵列信号处理

    史林:男,1990年生,博士生,研究方向为阵列信号处理、波达方向估计

    申梦雨:女,1997年生,硕士生,研究方向为阵列信号处理、波达方向估计

    通讯作者:

    赵立鹏 zlp2014@hrbeu.edu.cn

  • 中图分类号: TN911.7

Signal Parameter Estimation Algorithm for Orthogonal Dipole Array Based on Finite Rate of Innovation

Funds: The National Natural Science Foundation of China (62071137), The National Defense Science and Technology Foundation Strengthening Program (2019-JCJQ-ZD-067-00)
  • 摘要: 为解决极化敏感阵列波达方向(DOA)估计中压缩感知类算法的网格失配问题,该文提出一种基于有限新息率(FRI)的正交偶极子阵列无网格信号参数估计算法。首先,利用均匀正交偶极子线阵中不同极化指向天线的两个子阵,求取其自相关矩阵之和,并通过协方差拟合准则恢复出满足Toeplitz结构的协方差矩阵。然后,利用该协方差矩阵构建FRI信号重构模型,求解以重构结果为系数的多项式的零点,就可以得到入射信号DOA参数的估计结果。最后,根据已估计出的DOA参数以及两个子阵的自相关矩阵和互相关矩阵,利用最小二乘法计算得到入射信号的极化参数估计结果。仿真实验表明,该算法与子空间类和压缩感知类算法相比,具有更高的估计精度及更好的角度分辨力。
  • 图  1  阵列空间结构及电磁波传播示意图

    图  2  DOA估计归一化空间谱图

    图  3  极化参数估计结果

    图  4  均方根误差随信噪比的变化

    图  5  多入射信号随角度间隔变化的分辨成功率

    图  6  多入射信号随信噪比差变化的分辨成功率

    图  7  算法运行时间

    表  1  算法流程

    输入:子阵1及子阵2接收的多快拍入射信号${{\boldsymbol{x}}_1}(t)$和${{\boldsymbol{x}}_2}(t)$;
    初始化:内部最大迭代次数${N_{{\rm{in}}} }$,外部最大迭代次数${N_{{\rm{out}}} }$,内部迭代次数$n = 1$,外部迭代次数$z = 1$,噪声容限$ \varepsilon $;
    输出:入射信源的DOA估计结果$ {\tilde \varphi _k} $及极化参数估计结果$ {\tilde \gamma _k} $和$ {\tilde \eta _k} $。
    步骤1计算${{\boldsymbol{x}}_1}(t)$和${{\boldsymbol{x}}_2}(t)$的自相关矩阵${{\boldsymbol{R}}_{11}}$, ${{\boldsymbol{R}}_{22}}$和互相关矩阵${{\boldsymbol{R}}_{12}}$,${{\boldsymbol{R}}_{21}}$,并计算${\boldsymbol{R}} = {{\boldsymbol{R}}_{11}} + {{\boldsymbol{R}}_{22}}$;
    步骤2求解式(13)中的半正定规划问题,得到优化变量$ {\boldsymbol{b}} $的结果$ {\boldsymbol{\tilde b}} $;
    步骤3根据式(16)和式(21)构造矩阵${\boldsymbol{\bar T}}({\boldsymbol{\tilde b}})$;
    步骤4随机初始化$ {{\boldsymbol{\bar c}}_0} \ne {\boldsymbol{0}} $;
    步骤5根据式(17)和式(21)构造矩阵$ {\boldsymbol{\bar R}}({{\boldsymbol{\bar c}}^{(n{{\rm{ - }}}1)}}) $;
    步骤6求解式(19)的非齐次线性方程组,得到$ {{\boldsymbol{\bar c}}^{(n)}} $并构造矩阵$ {\boldsymbol{\bar R}}({{\boldsymbol{\bar c}}^{(n)}}) $;
    步骤7求解式(20)的非齐次线性方程组,得到$ {{\boldsymbol{\bar b}}^{(n)}} $;
    步骤8判断$\left\| {{\boldsymbol{\bar {\tilde b}}} - {\boldsymbol{\bar b}}} \right\|_2^2 \le \varepsilon $是否成立,若成立,则进入步骤11,否则$n = n + 1$;
    步骤9判断$n \le {N_{{\rm{in}}} }$是否成立,若成立,则返回步骤5,否则$z = z + 1$;
    步骤10判断$z \le {N_{{\rm{out}}} }$是否成立,若成立,则返回步骤4,否则继续下一步骤;
    步骤11根据式将${{\boldsymbol{\bar c}}^{(n)}}$转换回复数形式${\boldsymbol{\tilde c}}$,并以${\boldsymbol{\tilde c}}$为系数,建立如式(14)的多项式,根据式(22)计算DOA参数$ {\tilde \varphi _k} $;
    步骤12将估计出的$ {\tilde \varphi _k} $代回$ {\boldsymbol{\tilde U}} = ({\boldsymbol{A}}_u^* \odot {{\boldsymbol{A}}_u}) $,并将${{\boldsymbol{R}}_{ij}}$向量化得到${{\boldsymbol{r}}_{ij}}$;
    步骤13根据式(23)计算$ {{\boldsymbol{\tilde p}}_{ij}} $;
    步骤14根据式(24)和式(25)计算得到极化参数估计结果$ {\tilde \gamma _k} $和$ {\tilde \eta _k} $。
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-04-25
  • 修回日期:  2021-08-24
  • 网络出版日期:  2021-09-15
  • 刊出日期:  2022-07-25

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