基于非最优阶次FrFT的间歇采样转发干扰抑制方法

doi:10.12305/j.issn.1001-506X.2025.11.12

摘要/Abstract

摘要：

间歇采样转发干扰作为典型有源欺骗干扰，利用雷达相干特性可实现单个或多个假目标群效果，常规信号处理手段难以对其实现有效抑制。为解决该问题，分析间歇采样转发干扰特征和线性调频（linear frequency modulation，LFM）信号的分数阶傅里叶变换（fractional Fourier transform，FrFT）特性，得出受间歇采样转发干扰的LFM信号经p?1阶FrFT处理后、输出结果为多个具有频率差异的正弦信号的结论。利用这一结论将目标回波与间歇采样转发干扰转化为不同频率的正弦信号，并变换至时频域，对代表干扰分量的频率向量进行检测、标记、遮盖，最终完成干扰抑制。仿真实验结果表明，所提算法对3种类型间歇采样转发干扰均可起到抑制作用，且在处理可生成多个假目标群的间歇采样直接转发干扰（interrupted-sampling direct forwarding jamming，ISDJ）和间歇采样循环转发干扰（interrupted-sampling loop forwarding jamming，ISLJ）时更具优势。

关键词: 间歇采样转发干扰, 分数阶傅里叶变换, 正弦信号, 频率差异

Abstract:

Interrupted-sampling repeater jamming, as a typical active spoofing jamming, can achieve the effect of single or multiple false target group by using radar coherence characteristics, which is difficult to be effectively suppressed by conventional signal processing means. In order to solve the above problem, the characteristics of interrupted-sampling repeater jamming and the fractional Fourier transform （FrFT） characteristics of linear frequency modulation （LFM） signal are analyzed. It is concluded that LFM signal affected by interrupted-sampling repeater jamming is processed by p?1 order FrFT, and the output is multiple sinusoidal signals with frequency difference. Based on this conclusion, the target echo and interrupted-sampling repeater jamming are transformed into sinusoidal signals of different frequencies, and then transformed into time-frequency domain to detect, mark and cover the frequency vector representing the jamming component to complete jamming suppression. Simulation results show that the proposed algorithm can suppress three types of interrupted-sampling repeater jamming, and is more advantageous when dealing with interrupted-sampling direct forwarding jamming （ISDJ） and interrupted-sampling loop forwarding jamming （ISLJ）, which can generate multiple false target groups.

Key words: interrupted-sampling repeater jamming, fractional Fourier transform （FrFT）, sinusoidal signal, frequency difference

中图分类号:

TN 947

温镇铭, 王国宏, 张亮, 于洪波. 基于非最优阶次FrFT的间歇采样转发干扰抑制方法[J]. 系统工程与电子技术, 2025, 47(11): 3635-3643.

Zhenming WEN, Guohong WANG, Liang ZHANG, Hongbo YU. Interrupted-sampling repeater jamming suppression method based on non-optimal order FrFT[J]. Systems Engineering and Electronics, 2025, 47(11): 3635-3643.

图/表 15

图1

图2

图3

图4

表1

图5

图6

图7

图8

图9

图10

图11

图12

图13

图14

参考文献 30

1	GRECO M, GINI F, FARINA A. Radar detection and classification of jamming signals belonging to a cone class[J]. IEEE Trans.on Signal Processing, 2008, 56 (5): 1984- 1993. doi: 10.1109/TSP.2007.909326
2	SUN Q Y, SHU T, YU K B, et al. A novel deceptive jamming method against two-channel SAR-GMTI based on two jammers[J]. IEEE Sensors Journal, 2019, 19 (14): 5600- 5610. doi: 10.1109/JSEN.2019.2908030
3	BERGER S D. Digital radio frequency memory linear range gate stealer spectrum[J]. IEEE Trans.on Aerospace and Electronic Systems, 2003, 39 (2): 725- 735. doi: 10.1109/TAES.2003.1207279
4	ZHANG J D, ZHU D Y, ZHANG G. New antivelocity deception jamming technique using pulses with adaptive initial phases[J]. IEEE Trans.on Aerospace and Electronic Systems, 2013, 49 (2): 1290- 1300. doi: 10.1109/TAES.2013.6494414
5	LIU Z, SU W M, MA C, et al. Improved interrupted sampling repeater jamming based on DRFM[C]//Proc.of the IEEE International Conference on Signal Processing, Communications and Computing, 2014: 254−257.
6	ZHOU C, LIU Q H, CHEN X L. Parameter estimation and supp-ression for DRFM-based interrupted sampling repeater jammer[J]. IET Radar, Sonar & Navigation, 2018, 12 (1): 56- 63.
7	YUAN H, WANG C Y, LAN X L. A method against interrupted-sampling repeater jamming based on energy function detection and band-pass filtering[J]. International Journal of Antennas and Propagation, 2017, 2017 (2): 6759169.
8	王雪松, 刘建成, 张文明, 等. 间歇采样转发干扰的数学原理[J]. 中国科学: 信息科学, 2006, 36 (8): 891- 901.
	WANG X S, LIU J C, ZHANG W M, et al. Mathematical principle of interrupted sampling and repeater jamming[J]. SCIENTIA SINICA Informationis, 2006, 36 (8): 891- 901.
9	周超, 刘泉华, 胡程. 间歇采样转发式干扰的时频域辨识与抑制[J]. 雷达学报, 2019, 8 (1): 100- 106. doi: 10.12000/JR18080
	ZHOU C, LIU Q H, HU C. Time-frequency analysis techniques for recognition and suppression of interrupted sampling repeater jamming[J]. Journal of Radars, 2019, 8 (1): 100- 106. doi: 10.12000/JR18080
10	张亮, 王国宏, 张翔宇, 等. 基于分数阶字典的间歇采样转发干扰自适应抑制算法[J]. 系统工程与电子技术, 2020, 42 (7): 1439- 1448.
	ZHANG L, WANG G H, ZHANG X Y. An interrupted-sampling repeater jamming adaptive suppression algorithm based on fractional dictionaries[J]. Systems Engineering and Electronics, 2020, 42 (7): 1439- 1448.
11	杜思予, 刘智星, 吴耀君, 等. 频率捷变波形联合时频滤波器抗间歇采样转发干扰[J]. 系统工程与电子技术, 2023, 45 (12): 3819- 3827.
	DU S Y, LIU Z X, WU Y J, et al. Frequency agility waveform combined with time-frequency filter to suppress interrupted-sampling repeater jamming[J]. Systems Engineering and Electronics, 2023, 45 (12): 3819- 3827.
12	刘智星, 杜思予, 吴耀君, 等. 脉间-脉内捷变频雷达抗间歇采样干扰方法[J]. 雷达学报, 2022, 11 (2): 301- 312.
	LIU Z X, DU S Y, WU Y J, et al. Anti-interrupted sampling repeater jamming method for interpulse and intrapulse frequency-agile radar[J]. Journal of Radars, 2022, 11 (2): 301- 312.
13	万鹏程, 白渭雄, 付孝龙. 基于FrFT的LFM间歇采样转发干扰对抗方法[J]. 火力与指挥控制, 2018, 43 (10): 35- 39. doi: 10.3969/j.issn.1002-0640.2018.10.007
	WAN P C, BAI W X, FU X L. Fractional Fourier transform-based LFM radars for countering interrupted-sampling repeater jamming[J]. Fire Control & Command Control, 2018, 43 (10): 35- 39. doi: 10.3969/j.issn.1002-0640.2018.10.007
14	盖季妤, 姜维, 张凯翔, 等. 基于差分特征的间歇采样转发干扰辨识与抑制方法[J]. 雷达学报, 2023, 12 (1): 186- 196. doi: 10.12000/JR22058
	GAI J Y, JIANG W, ZHANG K X, et al. A method for interrupted sampling repeater jamming identification and suppression based on differential features[J]. Journal of Radars, 2023, 12 (1): 186- 196. doi: 10.12000/JR22058
15	周凯, 李德鑫, 粟毅, 等. 基于雷达发射波形和非匹配滤波联合设计的间歇采样转发干扰抑制方法[J]. 电子与信息学报, 2021, 43 (7): 1939- 1946. doi: 10.11999/JEIT200299
	ZHOU K, LI D X, SU Y. Joint transmitted waveform and mismatched filter design against interrupted-sampling repeater jamming[J]. Journal of Electronics & Information Technology, 2021, 43 (7): 1939- 1946. doi: 10.11999/JEIT200299
16	REN Z F, JIANG M, ZHANG L. Orthogonal phase-frequency coded signal in a pulse against interrupted sampling repeater jamming[J]. The Journal of Engineering, 2019, 2019 (21): 7573- 7576. doi: 10.1049/joe.2019.0500
17	ZHANG J X, ZHOU C. Interrupted sampling repeater jamming suppression method based on hybrid modulated radar signal[C]//Proc.of the IEEE International Conference on Signal, Information and Data Processing, 2019.
18	张建中, 穆贺强, 文树梁, 等. 基于脉内LFM-Costas 频率步进的抗间歇采样干扰方法[J]. 系统工程与电子技术, 2019, 41 (10): 2170- 2177. doi: 10.3969/j.issn.1001-506X.2019.10.03
	ZHANG J Z, MU H Q, WEN S L, et al. Anti-intermittent sampling jamming method based on intra-pulse LFM-Costas frequency stepping[J]. Systems Engineering and Electronics, 2019, 41 (10): 2170- 2177. doi: 10.3969/j.issn.1001-506X.2019.10.03
19	张建中, 穆贺强, 文树梁, 等. 基于 LFM 分段脉冲压缩的抗间歇采样转发干扰方法[J]. 电子与信息学报, 2019, 41 (7): 1712- 1720.
	ZHANG J Z, MU H Q, WEN S L, et al. Anti-intermittent sampling repeater jamming method based on LFM segmented pulse compression[J]. Journal of Electronics & Information Technology, 2019, 41 (7): 1712- 1720.
20	张建中, 穆贺强, 文树梁, 等. 基于脉内步进LFM时频分析的抗间歇采样干扰方法[J]. 北京理工大学学报, 2020, 40 (5): 543- 551.
	ZHANG J Z, MU H Q, WEN S L, et al. Anti-intermittent sampling repeater jamming method based on stepped LFM joint time-frequency analysis[J]. Transactions of Beijing Institute of Technology, 2020, 40 (5): 543- 551.
21	张建中, 穆贺强, 文树梁, 等. 基于脉内步进LFM波形的抗间歇采样转发干扰方法[J]. 系统工程与电子技术, 2019, 41 (5): 1013- 1020.
	ZHANG J Z, MU H Q, WEN S L, et al. Anti intermittent-sampling repeater jamming method based on stepped LFM waveform[J]. Systems Engineering and Electronics, 2019, 41 (5): 1013- 1020.
22	BULTHEEL A, MARTINEZ S H. Recent developments in the theory of the fractional Fourier transform and linear fractional transforms[J]. Bulletin of the Belgian Mathematical Society Simon Stevin, 2006, 13 (5): 971- 1005.
23	王国宏, 白杰, 张翔宇, 等. 基于FrFT域特征差异的压制干扰检测与分类算法[J]. 北京航空航天大学, 2018, 44 (6): 1125- 1130.
	WANG G H, BAI J, ZHANG X Y, et al. Detection and classification algorithm of suppression interference based on characteristic differences of FrFT domain[J]. Journal of Beijing University of Aeronautics and Astronautics, 2018, 44 (6): 1125- 1130.
24	白杰, 王国宏, 杨林. 基于FrFT域峰值特性的压制干扰检测算法[J]. 电光与控制, 2018, 25 (6): 17- 19.
	BAI J, WANG G H, YANG L. Detection algorithm of suppression interference based on peak characteristic of FrFT domain[J]. Electronics Optics & Control, 2018, 25 (6): 17- 19.
25	王国宏, 白杰, 孙殿星, 等. 基于信号-数据联合处理的压制-距离欺骗复合干扰抑制算法[J]. 电子与信息学报, 2018, 40 (10): 149- 156.
	WANG G H, BAI J, SUN D X, et al. A suppression algorithm of blanket-distance deception compound jamming based on joint signal-data processing[J]. Journal of Electronics & Information Technology, 2018, 40 (10): 149- 156.
26	OBERLIN T, MEIGNEN S, PERRIER V. The Fourier-based synchrosqueezing transform[C]//Proc.of the International Conference on Acoustics Speech and Signal Processing, 2014: 315−319.
27	BARNETT V, LEWIS T. Outliers in statistical data[M]. New York: John Wiley & Sons, 1994: 210−214.
28	OZAKTAS H M, KUTAY M A. The fractional Fourier transform with applications in optics and signal processing[M]. New York: John Wiley & Sons, 2001: 892−901.
29	HATEFFARD F, DOLATI P, HEIDARI A, et al. Assessing the performance of decision tree and neural models in mapping soil properties[J]. Journal of Mountain Science, 2019, 16 (8): 1833- 1847. doi: 10.1007/s11629-019-5409-8
30	DENG L M, HU Y, CHENG J P Y, et al. A data-driven decision support system for scoliosis[J]. IEEE Access, 2017, 5, 7874- 7884. doi: 10.1109/ACCESS.2017.2696704

参数	参数值	参数	参数值
脉宽/μs	80	干扰采样周期/μs	20
带宽/MHz	10	干扰采样脉宽/μs	5
采样频率/MHz	20	转发次数	4
脉冲数	64	目标距离/km	20
信噪比/dB	−10	干信比/dB	20

[1]	董乔龙, 刘思琪, 张伟见, 张劲东. LFM-DPC抗间歇采样转发干扰波形集设计算法[J]. 系统工程与电子技术, 2025, 47(7): 2154-2164.
[2]	周凯, 李超, 李坤, 崔新风, 姚辉伟, 陈冬冬. 抗移频间歇采样转发干扰波形与非匹配滤波器设计方法[J]. 系统工程与电子技术, 2025, 47(7): 2194-2204.
[3]	史朝鹏, 吴灏, 王万田, 朱轩, 张嘉毫, 孟进, 李强. 一种抗间歇采样转发干扰的脉内自适应凹陷LFM波形设计方法[J]. 系统工程与电子技术, 2025, 47(4): 1115-1126.
[4]	安强, 叶春茂, 鲁耀兵, 张彦. 复杂场景下间歇采样转发干扰抑制算法[J]. 系统工程与电子技术, 2025, 47(2): 463-477.
[5]	潘小义, 刘晓斌, 陈吉源, 冯学文, 顾赵宇, 肖顺平. 间歇采样转发干扰技术研究述评[J]. 系统工程与电子技术, 2024, 46(9): 2887-2901.
[6]	宁晓燕, 杨逸飞, 郭凯丰, 王震铎. 基于FrFT-FH架构LPD通信波形设计与性能分析[J]. 系统工程与电子技术, 2024, 46(8): 2857-2866.
[7]	刘茜, 戴奉周. 抗间歇采样转发干扰的发射波形与失配滤波器联合优化算法[J]. 系统工程与电子技术, 2024, 46(6): 1855-1866.
[8]	孙宗正, 刘智星, 肖国尧, 齐晗廷, 全英汇. 非均匀间歇采样转发干扰对脉内捷变雷达影响分析[J]. 系统工程与电子技术, 2024, 46(5): 1544-1554.
[9]	牛闯, 林强, 段敏, 施端阳, 谷成刚. 脉内频率-时延捷变雷达抗间歇采样转发干扰方法[J]. 系统工程与电子技术, 2024, 46(5): 1583-1598.
[10]	高一丁, 吴敏, 郝程鹏, 商志刚. 基于FrFT-Keystone运动补偿的OFDM声纳高速微弱目标相参积累检测算法[J]. 系统工程与电子技术, 2024, 46(4): 1157-1166.
[11]	赵忠凯, 孙宇晗, 高路. 对SAR的二维联合调制间歇采样转发干扰[J]. 系统工程与电子技术, 2024, 46(12): 4026-4033.
[12]	李晋杰, 曹运合, 张钰林, 王蒙. 基于STFrFT的间歇采样转发干扰抑制[J]. 系统工程与电子技术, 2024, 46(10): 3312-3324.
[13]	杜思予, 刘智星, 吴耀君, 沙明辉, 全英汇. 频率捷变波形联合时频滤波器抗间歇采样转发干扰[J]. 系统工程与电子技术, 2023, 45(12): 3819-3827.
[14]	陶臣嵩, 陈思伟, 肖顺平. 基于深度学习模型的SAR图像间歇采样转发干扰检测[J]. 系统工程与电子技术, 2023, 45(11): 3465-3473.
[15]	吕岩, 曹菲, 许剑锋, 冯晓伟. 基于FRFT的单基地MIMO雷达稳健波束形成算法[J]. 系统工程与电子技术, 2023, 45(1): 79-85.