Signal processing for discontinuous-spectrum high-frequency radar based on sparse iterative approach
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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.
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关键词:
- 高频雷达 /
- 非连续谱 /
- 调频连续波（FMCW） /
- 距离-多普勒处理 /
- 稀疏迭代算法
Abstract: In congested spectral environments, transmitting signals in several discontinuous frequency segments and coherent synthesizing at the receiver side is a method for obtaining signals with large equivalent bandwidth. This paper investigates the discontinuous spectrum-frequency modulated continuous wave (DS-FMCW) and its application in high frequency radar specially. Firstly, a sampling point displacement method is proposed, and a spectral analysis model of non-uniformly sampled sequences for the fast-time processing of DS-FMCW is established. Secondly, two-dimensional range-Doppler spectral estimation model is developed, and processing schemes for handling range migration are proposed for DS-FMCW. Finally, to solve the problem of high range sidelobes, range and range-Doppler spectral estimation methods for DS-FMCW are proposed based on an iterative sparse recovery algorithm which is applicable in the single-snapshot scenario. Fast implementations of these spectral estimation methods are also presented. Simulation experiments show that the proposed range-Doppler processing schemes of DS-FMCW are able to compensate the range migration effectively, and when the utilization rate of the frequency band is above 20%, the proposed spectral estimation method can steadily resolve two targets which are separated by one third of the intrinsic radar range resolution in the range domain, and its range estimation accuracy is better than the classical least-squares algorithm and the orthogonal matching pursuit algorithm. Finally, the proposed fast implementation algorithm is verified to have a low computational complexity in a single iteration, which makes it suitable for real-time systems. -
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 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 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$\gamma _{p,q}^{''},p = 1, \cdots ,P,q = 1, \cdots ,Q$ 
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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${\boldsymbol{\hat \gamma }} = {\boldsymbol{\gamma }}(i + 1)$
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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${\boldsymbol{\hat \gamma }} = {\boldsymbol{\gamma }}(i + 1)$
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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 - $\begin{array}{l} O(QMN) + O(QP{\log _2}P) + \\ O(Q{n_{ {\rm{CG} } } }{N^2}) \\ \end{array}$
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