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基于稀疏迭代的非连续谱高频雷达信号处理方法

潘孟冠 刘鹏 刘升恒 陈伯孝

潘孟冠,刘鹏,刘升恒,等. 基于稀疏迭代的非连续谱高频雷达信号处理方法[J]. 电波科学学报,2022,37(2):262-273. DOI: 10.12265/j.cjors.2021032
引用本文: 潘孟冠,刘鹏,刘升恒,等. 基于稀疏迭代的非连续谱高频雷达信号处理方法[J]. 电波科学学报,2022,37(2):262-273. DOI: 10.12265/j.cjors.2021032
PAN M G, LIU P, LIU S H, et al. Signal processing for discontinuous-spectrum high-frequency radar based on sparse iterative approach[J]. Chinese journal of radio science,2022,37(2):262-273. (in Chinese). DOI: 10.12265/j.cjors.2021032
Citation: PAN M G, LIU P, LIU S H, et al. Signal processing for discontinuous-spectrum high-frequency radar based on sparse iterative approach[J]. Chinese journal of radio science,2022,37(2):262-273. (in Chinese). DOI: 10.12265/j.cjors.2021032

基于稀疏迭代的非连续谱高频雷达信号处理方法

doi: 10.12265/j.cjors.2021032
基金项目: 国家自然科学基金重点项目(U1936201)
详细信息
    作者简介:

    潘孟冠:(1992—),男,安徽人,博士,研究方向为参数估计理论、通信与雷达信号处理技术

    刘鹏:(1981—),男,山东人,博士,副教授,研究方向为无线网络与无线定位、5G网络定位技术

    刘升恒:(1987—),男,湖北人,博士,副教授,研究方向为智能无线通信及传感探测技术

    陈伯孝:(1966—),男,安徽人,博士,教授,研究方向为新体制雷达系统设计与实现、雷达信号处理、目标精确制导与跟踪等

    通讯作者:

    潘孟冠 E-mail: pmengguan@163.com

  • 中图分类号: TN957.51

Signal processing for discontinuous-spectrum high-frequency radar based on sparse iterative approach

  • 摘要: 在拥挤频谱环境中,雷达系统在多个非连续频段发射信号并在接收端进行综合相干处理,是一种获得等效大带宽的方式. 本文专门就非连续谱调频连续波(discontinuous spectrum-frequency modulated continuous wave, DS-FMCW)及其在高频雷达中的应用展开研究. 首先提出采样点平移方法,建立DS-FMCW快时间维的非均匀采样序列谱估计模型;随后,进一步建立DS-FMCW距离-多普勒二维谱估计模型,提出解决距离徙动的方案;最后为解决距离高旁瓣问题,基于一种适用于单次快拍的迭代式稀疏重构算法提出DS-FMCW的距离与距离-多普勒谱估计方法,并提出相应的快速谱求解方法. 仿真试验表明:所提DS-FMCW距离-多普勒处理方案能有效补偿距离徙动;当频带利用率大于20%时,所提谱估计方法能够稳定地分辨距离维间隔为雷达固有距离分辨率的1/3的两个目标,且距离估计精度优于经典最小二乘算法以及正交匹配追踪算法;所提快速算法单次迭代运算量低,适用于实时系统.
  • 图  1  DS-FMCW信号频率-时间关系示意图

    Fig.  1  Illustration of frequency-time relationship of DS-FMCW signals

    图  2  采样点平移方法示意图

    Fig.  2  Illustration of sampling points displacement method

    图  3  LS、OMP以及SLIM算法的距离估计RMSE

    Fig.  3  Range estimation RMSE of LS, OMP and SLIM algorithms

    图  4  算法运行时间对比

    Fig.  4  Comparison of running time

    图  5  所设计的DS-FMCW信号时-频关系

    Fig.  5  Time-frequency relationship of the designed DS-FMCW signal

    图  6  LS方法的谱分析结果(联合与级联处理方案)

    Fig.  6  Spectral analysis results of LS method (joint and cascading schemes)

    图  7  SLIM算法的谱分析结果(距离-多普勒联合处理方案)

    Fig.  7  Spectral analysis results of SLIM algorithm (range-Doppler joint processing schemes)

    图  8  SLIM算法的谱分析结果(距离-多普勒级联处理方案)

    Fig.  8  Spectral analysis results of SLIM algorithm (range-Doppler cascading processing schemes)

    表  1  DS-FMCW信号距离-多普勒级联处理方案

    Tab.  1  Range-Doppler cascading processing scheme of DS-FMCW signals

    输入:式(17)表示的一个CPI的数据矩阵Y
    步骤1:按照式(26)对每个快时间采样点n进行慢时间速度匹配滤波
    步骤2:按照式(30)补偿快时间多普勒项
    步骤3:使用谱估计算法,按照式(31)对每个速度通道依次进行距离谱
    估计
    输出:距离-速度谱$\gamma _{p,q}^{''},p = 1, \cdots ,P,q = 1, \cdots ,Q$
    下载: 导出CSV

    表  2  SLIM谱估计算法

    Tab.  2  SLIM algorithm for spectral estimation

    输入:数据向量y
    步骤1:初始化γ(0), η(0)
    步骤2:迭代,重复以下过程直至收敛
    ${\boldsymbol{R}}(i) = {\boldsymbol{AP}}(i){{\boldsymbol{A}}^{\rm{H}}} + \eta (i){\boldsymbol{I}}$
    ${\boldsymbol{\gamma }}(i + 1) = {\rm{diag}}({\boldsymbol{P}}(i)) \odot \left( {{{\boldsymbol{A}}^{\rm{H}}}{{\boldsymbol{R}}^{ - 1}}(i){\boldsymbol{y}}} \right)$
    $\eta (i + 1) = \dfrac{1}{J}\left\| { {\boldsymbol{y} } - {\boldsymbol{A\gamma } }(i + 1)} \right\|_2^2$
    $i \leftarrow i + 1$
    输出:谱估计值${\boldsymbol{\hat \gamma }} = {\boldsymbol{\gamma }}(i + 1)$
    下载: 导出CSV

    表  3  FFT-SLIM谱估计算法

    Tab.  3  FFT-SLIM algorithm for spectral estimation

    输入:数据向量y
    步骤1:初始,γ(0), η(0)
    步骤2:迭代,重复以下过程直至收敛
    步骤2.1:计算协方差矩阵R(i)
      步骤2.1.1:根据式(45)计算${\boldsymbol{r}}$
      步骤2.1.2:根据式(43)计算${ {\boldsymbol{R} }_{\rm{c} } }(i)$
      步骤2.1.3:根据式(40)计算R(i)
    步骤2.2:计算谱值${\boldsymbol{\gamma }}(i + 1)$
      步骤2.2.1:使用CG算法计算${\boldsymbol{\hat u}} = {{\boldsymbol{R}}^{ - 1}}(i){\boldsymbol{y}}$
      步骤2.2.2:使用式(47)将${\boldsymbol{\hat u}}$扩展为${ {\boldsymbol{\hat u} }_{\rm{c} } }$
      步骤2.2.3:使用式(48)计算b
      步骤2.2.4:计算${\boldsymbol{\gamma }}(i + 1) = {\rm{diag}}({\boldsymbol{P}}(i)) \odot {\boldsymbol{b}}$
    步骤2.3:计算噪声功率估计η(i+1)
      步骤2.3.1:根据式(49)计算d
      步骤2.3.2:计算:$\eta (i + 1) = \dfrac{1}{J}{\left\| { {\boldsymbol{y} } - {\boldsymbol{Jd} } } \right\|^2}$
    步骤2.4:$i \leftarrow i + 1$
    输出:谱估计值${\boldsymbol{\hat \gamma }} = {\boldsymbol{\gamma }}(i + 1)$
    下载: 导出CSV

    表  4  基于SLIM算法的DS-FMCW距离-多普勒处理计算复杂度

    Tab.  4  Computational complexity of DS-FMCW range-Doppler processing based on SLIM algorithms

    算法联合处理方案级联处理方案
    SLIM$O(PQ{(MN)^2})$$O(QMN) + O(QP{N^2})$
    CGLS-SLIM$O({n_{ {\rm{CGLS} } } }PQMN)$$O(QMN) + O(Q{n_{ {\rm{CGLS} } } }PN)$
    FFT-SLIM-$\begin{array}{l} O(QMN) + O(QP{\log _2}P) + \\ O(Q{n_{ {\rm{CG} } } }{N^2}) \\ \end{array}$
    下载: 导出CSV
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  • 收稿日期:  2021-02-02
  • 网络出版日期:  2021-07-08

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