基于Gabor框架的线性调频信号压缩采样与重构

doi:10.12305/j.issn.1001-506X.2021.04.04

摘要/Abstract

摘要：

针对线性调频信号在传统采集过程中存在的高采样频率问题, 提出了一种基于Gabor框架的线性调频信号压缩采样与重构方法。首先, 利用线性调频信号在Gabor变换下所具有的时频稀疏特性, 提出了基于Gabor框架的线性调频信号压缩采样系统。基于该采样系统, 分析了压缩采样系统工作过程, 建立了该系统压缩观测过程数学模型。随后, 分析了压缩采样系统重构模型, 将压缩采样重构问题转化为多观测向量重构问题。最后, 基于多维扩展的稀疏贝叶斯学习算法, 提出利用优化分类的方法来保证线性调频信号的精确重构。仿真实验结果表明, Gabor框架压缩采样系统有效降低了线性调频信号采样频率与采样点数, 在重构过程中, 本文提出的重构方法能够有效降低重构误差, 提高重构概率。

关键词: 线性调频信号, Gabor框架, 压缩采样, 重构

Abstract:

A Gabor frame based compressive sampling and reconstruction method is proposed for linear frequency modulation (LFM) signal to deal with the problem of high sampling frequency in traditional sampling method. Firstly, using the time-frequency sparsity of LFM signal in Gabor transform, the Gabor frame based compressive sampling system is proposed to achieve the sampling for LFM signal. Based on the frame theory, the working process and mathematical model of Gabor frame compressive sampling system is analyzed. Then, the reconstruction model of compressive sampling system is analyzed, and the compressive sampling reconstruction is converted into the problem of multiple measurement vectors reconstruction. Finally, based on the multiple response extension of sparse Bayesian learning algorithm, an optimized classification method is proposed to ensure the accurate reconstruction of LFM signals. The simulation results show that the proposed Gabor frame compressive sampling system decreases the sampling rate and sampling number effectively. And in reconstruction, the proposed method reduces the reconstruction error and increases the accurate reconstruction probability.

Key words: linear frequency modulation (LFM) signal, Gabor frame, compressive sampling, reconstruction

中图分类号:

TN911

孟晨, 王强, 王成, 李一宁. 基于Gabor框架的线性调频信号压缩采样与重构[J]. 系统工程与电子技术, 2021, 43(4): 883-893.

Chen MENG, Qiang WANG, Cheng WANG, Yining LI. Compressive sampling and reconstruction of linear frequency modulation signal based on Gabor frame[J]. Systems Engineering and Electronics, 2021, 43(4): 883-893.

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信号	f₀/MHz	k/(MHz/μs)	本质带宽/MHz	时域支撑/μs
1	-190	380	[-420, 420]	[0, 1]
2	-450	900	[-620, 620]	[0, 1]

信号	M的取值	未分类			分类
信号	M的取值	SOMP	SCoSaMP	M-SBL	SOMP	SCoSaMP	M-SBL
1	M=27	5.20×10^-1	5.56×10^-1	5.62×10^-1	1.59×10^-1	3.24×10^-1	1.56×10^-5
	M=32	4.54×10^-1	4.22×10^-1	4.00×10^-1	1.24×10^-3	1.99×10^-1	3.37×10^-7
	M=37	1.63×10^-1	2.36×10^-1	2.08×10^-1	6.32×10^-6	1.37×10^-3	4.05×10^-7
2	M=17	8.01×10^-1	8.72×10^-1	9.26×10^-1	3.47×10^-1	3.31×10^-1	2.56×10^-3
	M=22	7.92×10^-1	8.03×10^-1	7.99×10^-1	2.38×10^-3	2.74×10^-2	3.21×10^-6
	M=27	5.61×10^-1	6.30×10^-1	6.79×10^-1	1.21×10^-3	1.00×10^-3	9.81×10^-7

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