基于分数阶傅里叶变换的低信噪比线性调频信号参数快速估计算法

刘利民; 李豪欣; 李琦; 韩壮志; 高振斌

doi:10.11999/JEIT200973

基于分数阶傅里叶变换的低信噪比线性调频信号参数快速估计算法

doi: 10.11999/JEIT200973

1.
陆军工程大学石家庄校区电子与光学工程系石家庄 050003
2.
河北工业大学电子信息工程学院天津 300401

基金项目: 国家自然科学基金(61601496)，河北省自然科学基金(F2019506037)

详细信息

作者简介:
刘利民：男，1971年生，教授，博士生导师，研究方向为雷达对抗、雷达信号处理

李豪欣：女，1997年生，硕士，研究方向为雷达信号处理

李琦：男，1974年生，教授，硕士生导师，研究方向为雷达信号处理、信息与编码理论

韩壮志：男，1972年生，副教授，硕士生导师，研究方向为雷达信号处理、武器系统性能评估

高振斌：男，1973年生，教授，硕士生导师，研究方向为雷达信号处理

通讯作者:
李琦　liqi@hebut.edu.cn

中图分类号: TN957.51
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- 被引次数: 0
出版历程
- 收稿日期: 2020-11-12
- 修回日期: 2021-08-16
- 网络出版日期: 2021-08-27
- 刊出日期: 2021-10-18

A Fast Signal Parameter Estimation Algorithm for Linear Frequency Modulation Signal under Low Signal-to-Noise Ratio Based on Fractional Fourier Transform

1.
Department of Electronic and Optical Engineering, Army Engineering University, Shijiazhuang 050003, China
2.
School of Electronics Information Engineering, Hebei University of Technology, Tianjin 300401, China

Funds: The National Natural Science Foundation of China (61601496), The Nature Science Foundation of Hebei Province (F2019506037)

摘要

摘要: 针对低信噪比线性调频信号参数估计精度低且运算量大的问题，该文提出一种基于高效分数阶傅里叶变换(FRFT)和分数阶频谱4阶原点矩的快速估计算法。该算法通过判断调频斜率的正负，以确定旋转阶次所在初始区间；进而应用高效FRFT获得初始旋转阶次；最终利用分数阶频谱4阶原点矩，进一步确定搜索区间和步长，实现精准搜索，从而满足参数精度的要求。实验结果表明，该算法尤其适合用于低信噪比情况下的线性调频(LFM)信号检测与参数的准确估计，而且运算量较低。
- 线性调频信号 /
- 高效分数阶傅里叶变换 /
- 分数阶频谱4阶原点矩 /
- 低信噪比
Abstract: An algorithm based on high-efficiency FRactional Fourier Transform (FRFT) and fourth-order origin moments in the fractional-domain spectrum is proposed to estimate quickly the chirp signal at low signal-to-noise ratio. Firstly, the initial interval of the rotation order is determined by the sign of the FM slope. Then, the rotation order is estimated roughly by the efficient FRFT algorithm. Finally, the search interval and step size are determined according to the fourth-order origin moments of the spectrum in the fractional-domain. The simulation results show that the Linear Frequency Modulation (LFM) signal can be detected under low signal-to-noise ratio and the parameters of the signal can be estimated accurately using this algorithm, and the signal can be detected with a small amount of calculation.

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图 1 FRFT频谱幅度与阶次关系图

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图 2 归一化幅度对比图

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图 3 FRFT与W-V分布关系图

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图 4 LFM信号时频分布

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图 5 改进算法流程图

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图 6 算法检测性能曲线

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图 7 两种算法对比

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表 1 3种算法对比仿真结果

估计方法	允许阶次误差	$\hat k\left({\rm{Hz /t}} \right)$	$\hat f\left( {{\rm{Hz}}} \right)$	${k_{{{\rm{error}}}}}\left( \% \right)$	${f_{{{\rm{error}}}}}\left( \% \right)$	FRFT运算次数
高效FRFT算法	–	1537.2000	1580.3	53.7244	5.3565	3
FRFT 2维搜索	<0.0100	1104.0000	1511.1	10.4010	0.7417	201
FRFT 2维搜索	<0.0010	1024.6000	1501.8	2.4580	0.1214	2001
FRFT 2维搜索	<0.0001	1003.9000	1501.5	0.3950	0.1007	20001
改进搜索算法	<0.0100	940.2061	1510.2	5.9794	0.6800	7
改进搜索算法	<0.0010	993.1624	1501.1	0.6838	0.0754	20
改进搜索算法	<0.0001	1002.3000	1500.8	0.2281	0.0531	43

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参考文献(16)

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