Low-intercept Waveform Sequence Design Based on Iterative Quadratic Optimization Algorithm

LIU Qiang; ZHANG Min; GUO FuCheng; YIN JiaPeng; HU WeiDong

doi:10.11999/JEIT231333

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LIU Qiang, ZHANG Min, GUO FuCheng, YIN JiaPeng, HU WeiDong. Low-intercept Waveform Sequence Design Based on Iterative Quadratic Optimization Algorithm[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT231333

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LIU Qiang, ZHANG Min, GUO FuCheng, YIN JiaPeng, HU WeiDong. Low-intercept Waveform Sequence Design Based on Iterative Quadratic Optimization Algorithm[J]. Journal of Electronics & Information Technology. doi: 10.11999/JEIT231333

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Low-intercept Waveform Sequence Design Based on Iterative Quadratic Optimization Algorithm

doi: 10.11999/JEIT231333

College of Electronic Science, National University of Defense Technology, Changsha 410073, China

Received Date: 2023-12-04
Rev Recd Date: 2024-02-07

Available Online: 2024-03-08

Abstract

Abstract

In modern radar technology, a key research area is the design of special waveforms to prevent non-cooperative electronic reconnaissance systems from intercepting and detecting radar signals. This paper focuses on reducing the power interception probability of electronic reconnaissance systems while maintaining the radiation energy. Specifically, waveform design techniques are explored for passive countermeasures, considering the time-frequency distribution of energy and the characteristics of Short-Time Fourier Transform (STFT) wideband digital reconnaissance receivers. To address this, a low-intercept model for STFT wideband digital reconnaissance receiver is established, and then the low-intercept problem is converted into a constant envelope sequence iterative optimization problem using a quadratic optimization model. To improve autocorrelation performance, an auxiliary scalar is employed to transform the optimization model into a quadratic form and a sequence of low-interception waveforms are generated through an iterative algorithm. Furthermore, the computational complexity of our proposed method is discussed. The simulation results, demonstrate that our sequence exhibits superior low-interception capability compared to commonly used phase-coded signals at the same receive Signal-to-Noise Ratio (SNR). Additionally, we introduce Pareto weights are introduced to control the autocorrelation characteristics of the proposed sequence, thereby enhancing the design flexibility.
- Low intercept radar,
- Waveform design,
- Iterative quadratic optimization

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References

[1]	SCHLEHER D C. LPI radar: Fact or fiction[J]. IEEE Aerospace and Electronic Systems Magazine, 2006, 21(5): 3–6. doi: 10.1109/MAES.2006.1635166.
[2]	SHAPERO S. Introduction to modern EW systems, 2nd edition (de Martino, A. ) [Book review][J]. IEEE Aerospace and Electronic Systems Magazine, 2019, 34(8): 62–63. doi: 10.1109/MAES.2019.2921175.
[3]	WANG Yuanhang, ZHANG Tianxian, KONG Lingjiang, et al. A stochastic simulation optimization-based range gate pull-off jamming method[J]. IEEE Transactions on Evolutionary Computation, 2023, 27(3): 580–594. doi: 10.1109/TEVC.2022.3175517.
[4]	DING Xiaojin, SONG Tiecheng, ZOU Yulong, et al. Security-reliability tradeoff analysis of artificial noise aided two-way opportunistic relay selection[J]. IEEE Transactions on Vehicular Technology, 2017, 66(5): 3930–3941. doi: 10.1109/TVT.2016.2601112.
[5]	SHI Chenguang, WANG Fei, SELLATHURAI M, et al. Power minimization-based robust OFDM Radar waveform design for Radar and communication systems in coexistence[J]. IEEE Transactions on Signal Processing, 2018, 66(5): 1316–1330. doi: 10.1109/TSP.2017.2770086.
[6]	LAWRENCE D E. Low probability of intercept antenna array beamforming[J]. IEEE Transactions on Antennas and Propagation, 2010, 58(9): 2858–2865. doi: 10.1109/TAP.2010.2052573.
[7]	巩朋成, 王兆彬, 谭海明, 等. 杂波背景下基于交替方向乘子法的低截获频控阵MIMO雷达收发联合优化方法[J]. 电子与信息学报, 2021, 43(5): 1267–1274. doi: 10.11999/JEIT200445. GONG Pengcheng, WANG Zhaobin, TAN Haiming, et al. Joint design of the transmit and receive beamforming via alternating direction method of multipliers for LPI of frequency diverse array MIMO Radar in the presence of clutter[J]. Journal of Electronics & Information Technology, 2021, 43(5): 1267–1274. doi: 10.11999/JEIT200445.
[8]	GLENN A. Low probability of intercept[J]. IEEE Communications Magazine, 1983, 21(4): 26–33. doi: 10.1109/MCOM.1983.1091402.
[9]	LIU Xinyu, ZHANG Tianxian, YU Xianxiang, et al. LPI waveform design for radar system against cyclostationary analysis intercept processing[J]. Signal Processing, 2022, 201: 108681. doi: 10.1016/j.sigpro.2022.108681.
[10]	GRIFFITHS H D. Detecting and classifying low probability of intercept radar – Second edition. P. E. Pace Artech House, 16 Sussex Street, London, SW1V 4RW, UK. 2009. 857pp. + diskette Illustrated. £100, ISBN 978-1-59693-234-0[J]. The Aeronautical Journal, 2011, 115(1168): 389. doi: 10.1017/S0001924000005960.
[11]	CHEN Jun, WANG Jie, ZHANG Yidong, et al. Spatial information-theoretic optimal LPI radar waveform design[J]. Entropy, 2022, 24(11): 1515. doi: 10.3390/e24111515.
[12]	CHEN Jun, WANG Fei, and ZHOU Jianjiang. Information-theoretic optimal radar waveform selection with multi-sensor cooperation for LPI purpose[J]. IEEE Access, 2022, 10: 113649–113661. doi: 10.1109/ACCESS.2022.3217554.
[13]	HIZAL A and DEMIR Ş. Pulsed FMCW waveform design for LPI radars based on stretch processing[C]. The 9th European Radar Conference, Amsterdam, Netherlands, 2012: 306–309.
[14]	GOVONI M A, LI Hongbin, and KOSINSKI J A. Low probability of interception of an advanced noise radar waveform with linear-FM[J]. IEEE Transactions on Aerospace and Electronic Systems, 2013, 49(2): 1351–1356. doi: 10.1109/TAES.2013.6494419.
[15]	WAN Tao, JIANG Kaili, LIAO Jingyi, et al. Research on LPI radar signal detection and parameter estimation technology[J]. Journal of Systems Engineering and Electronics, 2021, 32(3): 566–572. doi: 10.23919/JSEE.2021.000048.
[16]	GODRICH H, PETROPULU A P, and POOR H V. Power allocation strategies for target localization in distributed multiple-radar architectures[J]. IEEE Transactions on Signal Processing, 2011, 59(7): 3226–3240. doi: 10.1109/TSP.2011.2144976.
[17]	SHI Yuxin, AN Kang, and LI Yusheng. Index modulation based frequency hopping: Anti-Jamming design and analysis[J]. IEEE Transactions on Vehicular Technology, 2021, 70(7): 6930–6942. doi: 10.1109/TVT.2021.3087640.
[18]	BURGOS-GARCIA M, SANMARTIN-JARA J, PEREZ-MARTINEZ F, et al. Radar sensor using low probability of interception SS-FH signals[J]. IEEE Aerospace and Electronic Systems Magazine, 2000, 15(4): 23–28. doi: 10.1109/62.839631.
[19]	PAN Qihe and NARAYANAN R M. Delay-modulated RF tag system concept using ultrawideband noise radar waveforms[J]. International Journal of Distributed Sensor Networks, 2011, 7(1): 156582. doi: 10.1155/2011/156582.
[20]	QIONGDAN Qiongdan, LI Yong, ZENG Yaoping, et al. Design and characteristic analysis of multicarrier chaotic phase coded radar pulse train signal[J]. International Journal of Antennas and Propagation, 2014, 2014: 724294. doi: 10.1155/2014/724294.
[21]	CHOI K and LIU Huaping. Quasi-synchronous CDMA using properly scrambled Walsh codes as user-spreading sequences[J]. IEEE Transactions on Vehicular Technology, 2010, 59(7): 3609–3617. doi: 10.1109/TVT.2010.2050916.
[22]	GROSS F B and CHEN K. Comparison of detectability of traditional pulsed and spread spectrum radar waveforms in classic passive receivers[J]. IEEE Transactions on Aerospace and Electronic Systems, 2005, 41(2): 746–751. doi: 10.1109/TAES.2005.1468765.
[23]	LIU X, ZHANG T, SHI Q. LPI Radar Waveform Design With Desired Cyclic Spectrum and Pulse Compression Properties[J]. IEEE Transactions on Vehicular Technology, 2023, 72(5): 6789–6793. doi: 10.1109/TVT.2022.3233446.
[24]	SCHRICK G and WILEY R G. Interception of LPI radar signals[C]. IEEE International Conference on Radar, Arlington, USA, 1990: 108–111. doi: 10.1109/RADAR.1990.201147.
[25]	LOU Mingyue, ZHONG Taineng, LI Min, et al. Low probability of intercept waveform optimization method for Sar imaging[C]. 2021 IEEE International Geoscience and Remote Sensing Symposium IGARSS, Brussels, Belgium, 2021: 3963–3966. doi: 10.1109/IGARSS47720.2021.9554227.
[26]	LIU Shuai, CAO Yunhe, YEO T S, et al. Range sidelobe suppression for randomized stepped-frequency chirp radar[J]. IEEE Transactions on Aerospace and Electronic Systems, 2021, 57(6): 3874–3885. doi: 10.1109/TAES.2021.3082670.
[27]	LIU Shuai, CAO Yunhe, YEO T S, et al. Adaptive clutter suppression in randomized stepped-frequency radar[J]. IEEE Transactions on Aerospace and Electronic Systems, 2021, 57(2): 1317–1333. doi: 10.1109/TAES.2020.3040530.
[28]	朱勇刚, 张毅, 李玉生, 等. 一种时频码联合捷变波形及其反侦察性能[J]. 通信对抗, 2020, 39(1): 1–4,18. ZHU Yonggang, ZHANG Yi, LI Yusheng, et al. A joint time-frequency-code agile waveform and its anti-reconnaissance performance[J]. Communication Countermeasures, 2020, 39(1): 1–4,18.
[29]	WANG Liu, WANG Wenqin, GUAN Haoliang, et al. LPI property of FDA transmitted signal[J]. IEEE Transactions on Aerospace and Electronic Systems, 2021, 57(6): 3905–3915. doi: 10.1109/TAES.2021.3083402.
[30]	GONG Pengcheng, ZHANG Zhuoyu, WU Yuntao, et al. Joint design of transmit waveform and receive beamforming for LPI FDA-MIMO radar[J]. IEEE Signal Processing Letters, 2022, 29: 1938–1942. doi: 10.1109/LSP.2022.3205206.
[31]	GONG Pengcheng, XU Kaiyan, WU Yuntao, et al. Optimization of LPI-FDA-MIMO radar and MIMO communication for spectrum coexistence[J]. IEEE Wireless Communications Letters, 2023, 12(6): 1076–1080. doi: 10.1109/LWC.2023.3261419.
[32]	JIN Yan, DUAN Pengting, and JI Hongbing. Parameter estimation of LFM signals based on scaled ambiguity function[J]. Circuits, Systems, and Signal Processing, 2016, 35(12): 4445–4462. doi: 10.1007/s00034-016-0280-0.
[33]	HAMSCHIN B M, FERGUSON J D, and GRABBE M T. Interception of multiple low-power linear frequency modulated continuous wave signals[J]. IEEE Transactions on Aerospace and Electronic Systems, 2017, 53(2): 789–804. doi: 10.1109/TAES.2017.2665140.
[34]	ALPHONSE S and WILLIAMSON G A. On estimating nonlinear frequency modulated radar signals in low SNR environments[J]. IEEE Transactions on Aerospace and Electronic Systems, 2021, 57(3): 1793–1802. doi: 10.1109/TAES.2021.3050649.
[35]	符颖, 王星, 周一鹏, 等. 基于改进半监督朴素贝叶斯的LPI雷达信号识别[J]. 系统工程与电子技术, 2017, 39(11): 2463–2469. doi: 10.3969/j.issn.1001-506X.2017.11.11. FU Ying, WANG Xing, ZHOU Yipeng, et al. Recognition of LPI radar signals based on revised semi-supervised Naïve Bayes[J]. Systems Engineering and Electronics, 2017, 39(11): 2463–2469. doi: 10.3969/j.issn.1001-506X.2017.11.11.
[36]	WILLIAMS E C, BRIDGES C P, and BOWYER M D J. Nowhere to hide? Passive, non-cooperative maritime surveillance from a nanosat[C]. 2018 IEEE Aerospace Conference, Big Sky, USA, 2018: 1–10. doi: 10.1109/AERO.2018.8396548.
[37]	ELLIS P, RHEEDEN D V, and DOWLA F. Use of Doppler and Doppler rate for RF geolocation using a single LEO satellite[J]. IEEE Access, 2020, 8: 12907–12920. doi: 10.1109/ACCESS.2020.2965931.
[38]	LEMIEUX J A and INGELS F M. Analysis of FSK/PSK modulated radar signals using Costas arrays and complementary Welti codes[C]. IEEE International Conference on Radar, Arlington, USA, 1990: 589–594. doi: 10.1109/RADAR.1990.201115.
[39]	KIM I, PARK K H, SONG M K, et al. Design of LPI signals using optimal families of perfect polyphase sequences[C]. Proceedings of 2016 International Symposium on Information Theory and Its Applications (ISITA), Monterey, USA, 2016: 261–264.
[40]	WARNKE L, CORRELL B, and SWANSON C N. The density of Costas arrays decays exponentially[J]. IEEE Transactions on Information Theory, 2023, 69(1): 575–581. doi: 10.1109/TIT.2022.3202507.
[41]	李正杰, 谢军伟, 张浩为, 等. 一种低截获背景下的集中式MIMO雷达快速功率分配算法[J]. 雷达学报, 2023, 12(3): 602–615. doi: 10.12000/JR22203. LI Zhengjie, XIE Junwei, ZHANG Haowei, et al. A fast power allocation algorithm in a collocated MIMO Radar under low interception backgrounds[J]. Journal of Radars, 2023, 12(3): 602–615. doi: 10.12000/JR22203.
[42]	巩朋成, 吴云韬. 基于ADMM改进的低截获FDA-MIMO雷达发射波束设计[J]. 通信学报, 2022, 43(4): 133–142. doi: 10.11959/j.issn.1000-436x.2022065. GONG Pengcheng and WU Yuntao. Improved transmit beamforming design based on ADMM for low probability of intercept of FDA-MIMO radar[J]. Journal on Communications, 2022, 43(4): 133–142. doi: 10.11959/j.issn.1000-436x.2022065.
[43]	王宏伟, 赵国庆, 王玉军, 等. 一种宽带数字信道化接收机[J]. 西安电子科技大学学报:自然科学版, 2010, 37(3): 487–491, 553. doi: 10.3969/j.issn.1001-2400.2010.03.018. WANG Hongwei, ZHAO Guoqing, WANG Yunjun, et al. Wideband digital channelized receiver design[J]. Journal of Xidian University, 2010, 37(3): 487–491, 553. doi: 10.3969/j.issn.1001-2400.2010.03.018.
[44]	周一宇, 安玮, 郭福成, 等. 电子对抗原理与技术[M]. 北京: 电子工业出版社, 2014: 24–63. ZHOU Yiyu, AN Wei, GUO Fucheng, et al. Principles and Technologies of Electronic Warfare System[M]. Beijing: Publishing House of Electronics Industry, 2014: 24–63.
[45]	HUANG Xiangao, HUANG Wei, WANG Chao, et al. Blind reconnaissance of the pseudo-random sequence in DS/SS signal with negative SNR[J]. Science in China Series F:Information Sciences, 2007, 50(3): 510–520. doi: 10.1007/s11432-007-0039-0.
[46]	STOICA P, HE Hao, and LI Jian. New algorithms for designing unimodular sequences with good correlation properties[J]. IEEE Transactions on Signal Processing, 2009, 57(4): 1415–1425. doi: 10.1109/TSP.2009.2012562.
[47]	STOICA P, HE Hao, and LI Jian. On designing sequences with impulse-like periodic correlation[J]. IEEE Signal Processing Letters, 2009, 16(8): 703–706. doi: 10.1109/LSP.2009.2021378.
[48]	JOSE S and VIJAYALAKSHMI C. Design and analysis of multi-objective optimization problem using evolutionary algorithms[J]. Procedia Computer Science, 2020, 172: 896–899. doi: 10.1016/j.procs.2020.05.129.
[49]	TROPP J A, DHILLON I S, HEATH R W, et al. Designing structured tight frames via an alternating projection method[J]. IEEE Transactions on Information Theory, 2005, 51(1): 188–209. doi: 10.1109/TIT.2004.839492.
[50]	GOLAY M. A class of finite binary sequences with alternate auto-correlation values equal to zero (Corresp. )[J]. IEEE Transactions on Information Theory, 1972, 18(3): 449–450. doi: 10.1109/TIT.1972.1054797.
[51]	ZHANG N and GOLOMB S W. Polyphase sequence with low autocorrelations[J]. IEEE Transactions on Information Theory, 1993, 39(3): 1085–1089. doi: 10.1109/18.256535.
[52]	HE H. Waveform design for active sensing systems — a computational approach[D]. [Ph. D. dissertation], University of Florida, 2011.