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

Abstract

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

CLC Number:

TN911

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.

Figures/Tables 16

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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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Compressive sampling and reconstruction of linear frequency modulation signal based on Gabor frame

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References 31

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信号	K₁	K₂	K	L₁	L₂	L
1	-2	39	42	-11	11	23
2	-2	39	42	-16	16	33