基于分数阶Gabor变换的LFM回波信号压缩采样方法

doi:10.12305/j.issn.1001-506X.2022.04.05

摘要/Abstract

摘要：

针对现有的压缩采样系统在线性调频(linear frequency modulated, LFM)回波信号压缩采样重构过程中存在的重构效果不佳的问题, 提出一种基于分数阶Gabor变换的回波信号压缩采样方法。首先, 利用不同目标回波信号在时延上的差异性, 给出基于分数阶Gabor变换的LFM回波信号稀疏表示方法, 并分析了分数阶Gabor变换的完备性条件。然后, 根据分数阶Gabor变换低通滤波的实现方式, 设计了LFM回波信号压缩采样系统, 建立了信号重构模型。最后, 通过仿真实验与应用实例分析, 验证了所提压缩采样系统的有效性。实验结果表明, 与现有压缩采样系统相比, 所提压缩采样系统的重构误差更低、重构效果更好。

关键词: 分数阶Gabor变换, 线性调频, 回波信号, 压缩采样

Abstract:

In order to overcome the poor reconstruction performance of current compressive sampling methods, a novel compressive sampling method based on the fractional Gabor transform is proposed for linear frequency modulated (LFM) echo signals. Firstly, utilizing the difference in time delay of different echoes, the fractional Gabor transform is introduced to achieve the sparse representation for LFM echo signals, and the corresponding completeness condition is analyzed. Then, according to the low-pass filter implementation of fractional Gabor transform, compressive sampling system is designed for LFM echo signals. And the signal reconstruction model is also established. Finally, the effectiveness of the proposed method is verified by simulation and application examples. Experimental results show that compared with the existing compressive sampling methods, the proposed method has lower reconstruction error and better reconstruction performance.

Key words: fractional Gabor transform, linear frequency modulated (LFM), echo signal, compressive sampling

中图分类号:

TN911

王强, 孟晨, 王成, 张瑞. 基于分数阶Gabor变换的LFM回波信号压缩采样方法[J]. 系统工程与电子技术, 2022, 44(4): 1103-1112.

Qiang WANG, Chen MENG, Cheng WANG, Rui ZHANG. Compressive sampling method based on fractional Gabor transform for LFM echo signals[J]. Systems Engineering and Electronics, 2022, 44(4): 1103-1112.

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参考文献 31

1	安涛, 杨祎綪, 刘金鹏. 基于间歇采样的雷达自卫干扰技术研究[J]. 舰船电子工程, 2020, 40 (4): 79- 82. doi: 10.3969/j.issn.1672-9730.2020.04.020
	AN T , YANG Y Q , LIU J P . Research on self-defense jamming technology of radar based on intermittent sampling[J]. Ship Electronic Engineering, 2020, 40 (4): 79- 82. doi: 10.3969/j.issn.1672-9730.2020.04.020
2	FAN H Y , REN L X , MAO E , et al. A high-precision phase-derived velocity measurement method for high-speed targets based on wideband direct sampling LFM radar[J]. IEEE Trans.on Geoence and Remote Sensing, 2019, 57 (12): 10147- 10163. doi: 10.1109/TGRS.2019.2931633
3	ARAB H , DUFOUR S , MOLDOVAN E , et al. Accurate and robust CW-LFM radar sensor: transceiver front-end design and implementation[J]. IEEE Sensors Journal, 2018, 19 (5): 1943- 1950.
4	GAO L , ZENG Y H , WANG L D , et al. Data compression method based on information preservation for wideband radar LFM signal echo[J]. The Journal of Engineering, 2019, 2019 (21): 7568- 7572. doi: 10.1049/joe.2019.0624
5	ZHOU Y W , ZHANG F Z , PAN S L . Instantaneous frequency analysis of broadband LFM signals by photonics-assisted equivalent frequency sampling[J]. Chinese Optics Letters, 2021, 19 (1): 0139011.
6	刘方正, 韩振中, 曾瑞琪. 基于变分模态分解和压缩感知的弱观测条件下雷达信号重构方法[J]. 电子与信息学报, 2021, 43 (6): 1- 9.
	LIU F Z , HAN Z Z , ZENG R Q . Damaged radar signal reconstruction method based on variational mode decomposition and compressed sensing[J]. Journal of Electronics and Information Technology, 2021, 43 (6): 1- 9.
7	PELISSIER M , STUDER C . Non-uniform wavelet sampling for RF analog-to-information conversion[J]. IEEE Trans.on Circuits & Systems Ⅰ: Regular Papers, 2018, 65 (2): 471- 484.
8	ARIE R , BRAND A , ENGELBERG S . Compressive sensing and sub-Nyquist sampling[J]. IEEE Instrumentation and Mea-surement Magazine, 2020, 23 (2): 94- 101. doi: 10.1109/MIM.2020.9062696
9	DONG N F , WANG J X . Sub-Nyquist sampling and parameters estimation of wideband LFM signals based on FRFT[J]. Radioelectronics and Communications Systems, 2018, 61 (8): 333- 341. doi: 10.3103/S0735272718080010
10	BERUJON S , COJOCARU R , PIAULT P E , et al. X-ray optics and beam characterization using random modulation: theory[J]. Journal of Synchrotron Radiation, 2020, 27 (2): 284- 292. doi: 10.1107/S1600577520000491
11	TROPP J A , LASKA J N , DUARTE M F , et al. Beyond Nyquist: efficient sampling of sparse bandlimited signals[J]. IEEE Trans.on Information Theory, 2010, 56 (1): 520- 543. doi: 10.1109/TIT.2009.2034811
12	MISHALI M , ELDAR Y C . From theory to practice: sub-Nyquist sampling of sparse wideband analog signals[J]. IEEE Journal of Selected Topics in Signal Processing, 2010, 4 (2): 375- 391. doi: 10.1109/JSTSP.2010.2042414
13	GAI J X, DU H C, LIU Q. Support recovery for MWC based on random reduction and null space[C]//Proc. of the IEEE International Conference on Cognitive Informatics & Cognitive Computing, 2018: 501-506.
14	LI A , HAO H , TAO R , et al. Implementation of mixing sequence optimized modulated wideband converter for ultra-wideband frequency hopping signals detection[J]. IEEE Trans.on Aerospace and Electronic Systems, 2020, 56 (6): 4698- 4710. doi: 10.1109/TAES.2020.2999997
15	LI X M , WANG H L , LUO H C . A compressed sampling receiver based on modulated wideband converter and a parameter estimation algorithm for fractional bandlimited LFM signals[J]. Circuits, Systems, and Signal Processing, 2021, 40 (2): 918- 957. doi: 10.1007/s00034-020-01507-6
16	方标, 黄高明, 高俊, 等. FRFT域LFM雷达回波信号的压缩采样模型[J]. 西安电子科技大学学报, 2015, 42 (1): 200- 206. doi: 10.3969/j.issn.1001-2400.2015.01.032
	FANG B , HUANG G M , GAO J , et al. Compressive sensing of linear frequency modulated echo signals in fractional Fourier domains[J]. Journal of Xidian University, 2015, 42 (1): 200- 206. doi: 10.3969/j.issn.1001-2400.2015.01.032
17	ZHAO H R , QIAO L Y , ZHANG J C , et al. Generalized random demodulator associated with fractional Fourier transform[J]. Circuits, Systems & Signal Processing, 2018, 37 (11): 5161- 5173.
18	ZHAO H R , ZHANG J C , QIAO L Y , et al. A multichannel compressed sampling method for fractional bandlimited signals[J]. Signal Processing, 2017, 134, 139- 148. doi: 10.1016/j.sigpro.2016.11.023
19	张武才, 潘明海, 陈诗弘. 基于LFM子脉冲的宽带雷达目标回波模拟方法[J]. 系统工程与电子技术, 2017, 39 (4): 768- 774.
	ZHANG W C , PAN M H , CHEN S H . Method of wide-band radar target echo signal simulation based on LFM subpulse[J]. Systems Engineering and Electronics, 2017, 39 (4): 768- 774.
20	邓兵, 王旭, 陶然, 等. 基于分数阶傅里叶变换的线性调频脉冲时延估计特性分析[J]. 兵工学报, 2012, 33 (6): 764- 768.
	DENG B , WANG X , TAO R , et al. Performance analysis of time delay estimation for linear frequency-modulated pulse based on fractional Fourier transform[J]. Acta Armamentarii, 2012, 33 (6): 764- 768.
21	WU X , TAO R , HONG D F , et al. The FrFT convolutional face: toward robust face recognition using the fractional Fourier transform and convolutional neural networks[J]. Science China: Information Sciences, 2020, 63 (1): 235- 237.
22	ZHAO Z C , TAO R , LI G , et al. Clustered fractional Gabor transform[J]. Signal Processing, 2019, 166, 107240.
23	SHI J , ZHENG J B , LIU X P , et al. Novel short-time fractional Fourier transform: theory, implementation, and applications[J]. IEEE Trans.on Signal Processing, 2020, 68, 3280- 3295. doi: 10.1109/TSP.2020.2992865
24	MALLAT S , ZHANG Z F . Matching persuits with time-frequency dictionaries[J]. IEEE Trans.on Signal Processing, 1993, 41 (12): 3397- 3415. doi: 10.1109/78.258082
25	YOU Y , ZHANG L . Bayesian matching pursuit-based channel estimation for millimeter wave communication[J]. IEEE Communications Letters, 2020, 24 (2): 344- 348. doi: 10.1109/LCOMM.2019.2953706
26	WIPF D P , RAO B D . An empirical Bayesian strategy for solving the simultaneous sparse approximation problem[J]. IEEE Trans.on Signal Processing, 2007, 55 (7): 3704- 3716. doi: 10.1109/TSP.2007.894265
27	QU M W , CHEN T T , LU S Q , et al. Inverse solution of steady-state responses based on sparse Bayesian learning[J]. IEEE Access, 2021, 9, 15133- 15148. doi: 10.1109/ACCESS.2021.3051644
28	DONOHO D L . Compressed sensing[J]. IEEE Trans.on Information Theory, 2006, 52 (4): 1289- 1306. doi: 10.1109/TIT.2006.871582
29	CUMMING I G , WONG F H . Digital processing of synthetic aperture radar data: algorithms and implementation[M]. Boston: Artech House Publishers, 2005.
30	YANG L , XING M , ZHANG L , et al. Entropy-based motion error correction for high-resolution spotlight SAR imagery[J]. IET Radar, Sonar & Navigation, 2012, 6 (7): 627- 637.
31	MARTORELLA M , BERIZZI F , HAYWOOD B . Contrast maximisation based technique for 2-D ISAR autofocusing[J]. IEE Proceedings—Radar, Sonar & Navigation, 2005, 152 (4): 253- 262.

方法	通道个数	单通道采样频率/MHz	总采样频率/MHz	单通道采样点数	总采样点数	RE		LRE
方法	通道个数	单通道采样频率/MHz	总采样频率/MHz	单通道采样点数	总采样点数	无噪声	SNR=20 dB	无噪声	SNR=20 dB
1	1	1 040	1 040	624	624	1.44×10^-1	1.60×10^-1	2.43×10^-3	6.90×10^-3
2	26	40	1 040	24	624	4.49×10^-1	8.03×10^-1	5.30×10^-3	2.05×10^-1
3	26	40	1 040	24	624	1.96×10^-2	4.45×10^-2	2.29×10^-4	4.50×10^-4

参数	数值
雷达采样频率/MHz	32.317
方位向采样频率/Hz	1 256.98
雷达中心频率/GHz	5.3
光速/(m/s)	2.997 9×10⁸
雷达脉冲调频率/(MHz/s)	721.35
方位向调频率/Hz	1 733

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[2]	裴家正, 黄勇, 陈宝欣, 关键, 陈小龙. 基于线性约束最小方差原则的稳健快速自适应脉冲压缩方法[J]. 系统工程与电子技术, 2022, 44(12): 3621-3630.
[3]	李海, 呼延泽, 毛志杰. 强杂波下基于压缩感知的低空风切变速度解模糊[J]. 系统工程与电子技术, 2022, 44(10): 3029-3036.
[4]	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.
[5]	鲍雨婷, 曹菲, 张鹍鹏, 占必超, 李君宜, 占建伟. 基于OFDM-LFM的弹载广域SAR成像距离模糊抑制[J]. 系统工程与电子技术, 2021, 43(2): 369-375.
[6]	李海, 宋迪, 呼延泽, 冯青, 庄子波. LFMCW体制下基于TDPC-JDL的低空风切变风速估计方法[J]. 系统工程与电子技术, 2020, 42(7): 1504-1509.
[7]	毛开, 杨志强, 陆智俊, 朱秋明, 宋茂忠. 基于几何统计的无人机信道模型及硬件模拟[J]. 系统工程与电子技术, 2019, 41(12): 2872-2878.
[8]	王卓, 郑学合, 常晓兰. 基于旋转降维的高速隐身目标检测算法[J]. 系统工程与电子技术, 2019, 41(1): 14-20.
[9]	姜孟超, 廖桂生, 杨志伟, 王诏丰. 一种NLFM-CPM雷达通信一体化信号设计[J]. 系统工程与电子技术, 2019, 41(1): 35-42.
[10]	马晓宇, 赵季中, 卢锦, 郭航. 基于小波变换的雷达目标回波信号提取算法[J]. 系统工程与电子技术, 2019, 41(1): 50-57.
[11]	孟庆松, 王彬, 邵高平. α稳定分布噪声下水声线性调频信号的识别[J]. 系统工程与电子技术, 2018, 40(7): 1449-1456.
[12]	孙玉雪, 罗迎, 张群, 胡健. 基于线性调频步进信号的空间自旋目标时变三维成像方法[J]. 系统工程与电子技术, 2018, 40(1): 23-31.
[13]	张素玲, 陈胜垚, 席峰, 刘中. 多带正交压缩采样雷达回波信号的快速重构[J]. 系统工程与电子技术, 2017, 39(9): 1971-1978.
[14]	崔开博, 陈曦, 黄敬健, 袁乃昌. 基于均匀圆阵时频干涉仪的LFM信号二维测向算法[J]. 系统工程与电子技术, 2017, 39(8): 1669-1676.
[15]	赵翔, 张伟, 何子述. 正交波形虚拟孔径MIMO雷达原理与性能讨论[J]. 系统工程与电子技术, 2017, 39(6): 1244-1249.