一种空域线性调频加权的空时联合频控阵雷达波形

兰宇; 周剑雄

doi:10.11999/JEIT250561

一种空域线性调频加权的空时联合频控阵雷达波形

doi: 10.11999/JEIT250561 cstr: 32379.14.JEIT250561

兰宇,
周剑雄^,

国防科技大学电子科学学院长沙 410073

基金项目: 国家自然科学基金(62231026)

详细信息

作者简介:
兰宇：女，博士生，研究方向为阵列雷达波形设计

周剑雄：女，教授，博士，研究方向为高分辨雷达成像、特性分析及识别

通讯作者:
周剑雄　zjxjanet@sina.com

中图分类号: TN957
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- 被引次数: 0
出版历程
- 收稿日期: 2025-06-18
- 修回日期: 2025-10-28
- 网络出版日期: 2025-10-31

A Space–Time Joint Waveform for Frequency Diverse Array Radar with Spatial Linear Frequency Modulation Weighting

LAN Yu,
ZHOU Jianxiong^,

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

Funds: The National Natural Science Foundation of China(62231026)

摘要

摘要: 频控阵(FDA)具有随快时间变化的发射方向图和空时耦合导向矢量，在多目标跟踪、宽覆盖探测、抗主瓣干扰等应用中有潜在优势。空域调制方法和基带波形设计是决定FDA模糊函数性能的两个互相关联的重要因素。针对目前FDA波形难以兼顾高距离分辨率及低旁瓣水平的问题，该文提出一种空域线性调频加权与时域相位编码结合的空时联合FDA波形，该波形通过空时联合调制抑制条带样高增益旁瓣，通过空域线性调频加权降低多普勒敏感性，具有距离分辨力高、旁瓣水平低、多普勒容限高等特点。仿真实验表明，该波形在距离分辨、旁瓣水平及多普勒容限性等方面存在优势。
- 频控阵 /
- 空域线性调频加权方法 /
- 旁瓣水平
Abstract: Objective Frequency Diverse Array (FDA) radar exhibits a fast time-varying beampattern and a space-time coupled steering vector, offering potential advantages for multi-target tracking, wide-area surveillance, and mainlobe interference suppression. However, the beampattern of conventional coherent FDA radar is narrow, resulting in a shorter beam dwell time than that of phased arrays. This limitation prevents the ambiguity function of conventional coherent FDA from achieving both high range resolution and low sidelobe level simultaneously. When the baseband signal is modulated with a Linear Frequency Modulation (LFM) waveform, the ambiguity function presents low range resolution and low sidelobe level. Conversely, when the baseband signal is modulated with a phase-coded waveform, it achieves high range resolution but exhibits high sidelobe levels with strip-like high-gain sidelobes. The degradation in range resolution or sidelobe performance significantly constrains detection capability. To address this problem, this study proposes a novel space-time joint FDA waveform with spatial LFM weighting, which simultaneously achieves high range resolution, low sidelobe level, and reduced Doppler sensitivity. Methods The spatial-domain modulation scheme and the time-domain baseband waveform are two interdependent factors that determine the ambiguity function performance of FDA radar. Selecting a time-domain baseband waveform with a thumbtack-shaped ambiguity function enables the range resolution to remain independent of space-time coupling. By modulating the spatial weighting phase, the beampattern shape of the FDA can be adjusted to extend beam dwell time, suppress strip-like high-gain sidelobes, and smooth sidelobe energy distribution. The proposed space-time joint waveform thus achieves both high range resolution and low sidelobe level. Doppler tolerance is another key metric for evaluating ambiguity function performance. A space-time joint waveform with spatial phase-coded weighting exhibits high Doppler sensitivity, leading to significantly elevated sidelobe levels and sharp reductions in transmit beamforming gain. In contrast, the spatial LFM weighting method proposed in this study enhances Doppler tolerance while maintaining desirable range and sidelobe characteristics. Results and Discussions By combining the spatial LFM weighting method with a time-domain baseband waveform exhibiting a thumbtack-shaped ambiguity function (e.g., a phase-coded waveform), this study addresses the limitation of conventional coherent FDA waveforms, which cannot simultaneously achieve high range resolution and low sidelobe level. The proposed waveform demonstrates robust pulse compression performance, even under target motion. Simulation experiments were conducted to analyze the ambiguity functions under both stationary and motion conditions, and the results are summarized as follows: (1) The average sidelobe levels near the target peak for the space-time joint FDA waveform with spatial LFM weighting and spatial phase-coded weighting are both approximately –30 dB (Fig.3(a)–(b)). In comparison, the average sidelobe level near the target peak for the spatial phase-coded weighting FDA using a time-domain LFM baseband waveform is about –20 dB (Fig.3(c)), while that of the coherent FDA with a time-domain phase-coded waveform is about –12 dB (Fig.3(d)). Thus, the two space-time joint FDA waveforms achieve the lowest average sidelobe levels. (2) The imaging results of both space-time joint FDA waveforms show no strip-like high-gain sidelobes (Fig.4(a)–(b)). By contrast, the spatial phase-coded weighting FDA and the coherent FDA with a time-domain phase-coded waveform both display prominent high-gain sidelobes (Fig.4(c)–(d)). These sidelobes from high Signal-to-Noise Ratio (SNR) targets can obscure nearby low-SNR targets. (3) All four FDA waveforms achieve a range resolution of 0.75 m (Fig. 5), corresponding to a bandwidth of 200 MHz. (4) Under motion conditions, the space-time joint FDA waveform with spatial phase-coded weighting exhibits a notable increase in peak sidelobe level compared with stationary conditions (Fig. 6(a)). In contrast, the space-time joint FDA waveform with spatial LFM weighting maintains the lowest peak sidelobe level among all four FDA configurations (Fig. 6(b)). Conclusions This study proposes a space-time joint FDA waveform with spatial LFM weighting. The proposed waveform effectively resolves the issue of degraded range resolution in conventional coherent FDA systems, ensuring that range resolution depends solely on bandwidth. It also eliminates the strip-like high-gain sidelobes commonly observed in conventional FDA waveforms. Under simulation conditions, the average sidelobe level near the target peak is reduced by approximately 10 dB and 18 dB compared with those of the spatial phase-coded weighting FDA and the coherent FDA with a time-domain phase-coded waveform, respectively. This reduction substantially mitigates the masking of low-SNR targets by sidelobes from high-SNR targets and demonstrates strong Doppler tolerance. However, under relative motion conditions, the proposed waveform exhibits Doppler-angle coupling, which will be addressed in future research through the development of coupling mitigation strategies.
- Frequency Diverse Array (FDA) /
- Spatial Linear Frequency Modulation (LFM) weighting /
- Sidelobe level

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图 1 空时发射方向图及其时间轴切片

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图 2 主旁瓣平均功率增益比随发射阵元数量N的变化规律

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图 3 四种FDA波形的平均旁瓣水平随时间(距离)的变化规律(理论值参照表1)

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图 4 4种FDA波形静止条件下的多维模糊函数

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图 5 距离分辨率验证

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图 6 多普勒容限性分析

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表 1 静止条件下各FDA波形的多维模糊函数性能

FDA波形	条带样高增益旁瓣区域	平均旁瓣水平 (dB)	距离分辨率 (m)
基于空域线性调频加权的空时联合波形	无	$ 10\lg ({N_{\text{c}}} - {N_{\hat t}}) - 20\lg {N_{\text{c}}} $	$ c/(2B) $
基于空域相位编码加权的空时联合波形	无	$ 10\lg ({N_{\text{c}}} - {N_{\hat t}}) - 20\lg {N_{\text{c}}} $	$ c/(2B) $
空域相位编码加权FDA	$ \hat t = \tau - k/B $	$ 10\lg (N - \left\| k \right\|) - 20\lg N $	$ c/(2B) $
相参FDA时域相位编码	$ \hat t = \tau + \dfrac{{d(\sin {\theta _0} - \sin \theta )}}{{\Delta f\lambda }} $	$ 10\lg \displaystyle\sum\limits_{k = 1 - N}^{N - 1} {\dfrac{{{{\left( {N - \left\| k \right\|} \right)}^2}}}{{{N^2}{N_{\text{c}}}}}} $	$ c/(2B) $

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表 2 雷达信号参数

雷达信号参数	数值	雷达信号参数	数值
载频	30 GHz	采样率	200 MHz
信号带宽	200 MHz	阵元间距	0.005 m
脉宽	5 μs	发射阵元数量	100
单个脉冲码元数量	1 000	接收阵元数量	1
脉冲重复时间	10 μs	空域调频系数	0.01

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参考文献(23)

[1]	王文钦, 张顺生. 频控阵雷达技术研究进展综述[J]. 雷达学报, 2022, 11(5): 830–849. doi: 10.12000/JR22141. WANG Wenqin and ZHANG Shunsheng. Recent advances in frequency diverse array radar techniques[J]. Journal of Radars, 2022, 11(5): 830–849. doi: 10.12000/JR22141.
[2]	ANTONIK P, WICKS M C, GRIFFITHS H D, et al. Frequency diverse array radars[C]. 2006 IEEE Conference on Radar, Verona, NY, USA, 2006: 215–217. doi: 10.1109/RADAR.2006.1631800.
[3]	ANTONIK P, WICKS M C, GRIFFITHS H D, et al. Multi-mission multi-mode waveform diversity[C]. 2006 IEEE Conference on Radar, Verona, NY, USA, 2006: 580–582. doi: 10.1109/RADAR.2006.1631858.
[4]	QIU Zizhou, LIAO Zhipeng, XU Jingwei, et al. Range-ambiguous clutter suppression for space-based early warning radar using vertical FDA and horizontal EPC[J]. IEEE Geoscience and Remote Sensing Letters, 2023, 20: 3502905. doi: 10.1109/LGRS.2023.3260996.
[5]	WANG Yuzhuo and ZHU Shengqi. Range ambiguous clutter suppression for FDA-MIMO forward looking airborne radar based on main lobe correction[J]. IEEE Transactions on Vehicular Technology, 2021, 70(3): 2032–2046. doi: 10.1109/TVT.2021.3057436.
[6]	SHAO Shuai, WANG Wenqin, SUN Yan, et al. Effects of spatial position on mainlobe interference suppression performance of FDA-MIMO radar[J]. IEEE Transactions on Aerospace and Electronic Systems, 2024, 60(6): 9437–9443. doi: 10.1109/TAES.2024.3443778.
[7]	TAN Ming, GONG Jian, and WANG Chunyang. Range dimensional monopulse approach with FDA-MIMO radar for mainlobe deceptive jamming suppression[J]. IEEE Antennas and Wireless Propagation Letters, 2024, 23(2): 643–647. doi: 10.1109/LAWP.2023.3331573.
[8]	丁梓航, 谢军伟, 齐铖. 基于强化学习的频控阵-多输入多输出雷达发射功率分配方法[J]. 电子与信息学报, 2023, 45(2): 550–557. doi: 10.11999/JEIT211555. DING Zihang, XIE Junwei, and QI Cheng. Transmit power allocation method of frequency diverse array-multi input and multi output radar based on reinforcement learning[J]. Journal of Electronics & Information Technology, 2023, 45(2): 550–557. doi: 10.11999/JEIT211555.
[9]	WANG Huake, LIAO Guisheng, XU Jingwei, et al. Transmit beampattern design for coherent FDA by piecewise LFM waveform[J]. Signal Processing, 2019, 161: 14–24. doi: 10.1016/j.sigpro.2019.03.010.
[10]	YU Lei, HE Feng, and SU Yi. Multiscale observation in wide-spatial radar surveillance based on coherent FDA design[J]. Science China (Information Sciences), 2024, 67(2): 122304. doi: 10.1007/s11432-022-3816-3.
[11]	YU Lei, HE Feng, SU Yi, et al. Transmitting strategy with high degrees of freedom for pulsed-coherent FDA radar[J]. IET Radar, Sonar & Navigation, 2022, 16(4): 659–667. doi: 10.1049/rsn2.12210.
[12]	ZHANG Siyuan, CHEN Hui, JIA Wenkai, et al. A low probability of intercept method based on power optimization for frequency diverse array and cooperative jammer[J]. IEEE Transactions on Aerospace and Electronic Systems, 2025, 61(1): 1231–1236. doi: 10.1109/TAES.2024.3451458.
[13]	JIA Wenkai, JAKOBSSON A, and WANG Wenqin. Coherent FDA receiver and joint range–space–time processing[J]. IEEE Transactions on Antennas and Propagation, 2024, 72(1): 745–755. doi: 10.1109/TAP.2023.3321344.
[14]	LIU Zhixin, ZHU Shengqi, XU Jingwei, et al. Range-ambiguous clutter suppression for STAP-based radar with vertical coherent frequency diverse array[J]. IEEE Transactions on Geoscience and Remote Sensing, 2023, 61: 5106517. doi: 10.1109/TGRS.2023.3291738.
[15]	WANG Huake, LIAO Guisheng, XU Jingwei, et al. Subarray-based coherent pulsed-LFM frequency diverse array for range resolution enhancement[J]. IET Signal Processing, 2020, 14(4): 251–258. doi: 10.1049/iet-spr.2018.5566.
[16]	WANG Huake, LIAO Guisheng, XU Jingwei, et al. Space-time matched filter design for interference suppression in coherent frequency diverse array[J]. IET Signal Processing, 2020, 14(3): 175–181. doi: 10.1049/iet-spr.2019.0227.
[17]	于雷, 何峰, 董臻, 等. 一种基于非线性调频信号和空域编码的FDA雷达波形设计方法[J]. 雷达学报, 2021, 10(6): 822–832. doi: 10.12000/JR21008. YU Lei, HE Feng, DONG Zhen, et al. A waveform design method based on nonlinear frequency modulation and space-coding for coherent frequency diverse array radar[J]. Journal of Radars, 2021, 10(6): 822–832. doi: 10.12000/JR21008.
[18]	GUI Ronghua, HUANG Bang, WANG Wenqin, et al. Generalized ambiguity function for FDA radar joint range, angle and Doppler resolution evaluation[J]. IEEE Geoscience and Remote Sensing Letters, 2022, 19: 3502305. doi: 10.1109/LGRS.2020.3044351.
[19]	WANG Wenqin, DAI Miaomiao, and ZHENG Zhi. FDA radar ambiguity function characteristics analysis and optimization[J]. IEEE Transactions on Aerospace & Electronic Systems, 2018, 54(3): 1368–1380. doi: 10.1109/TAES.2017.2785598.
[20]	ZHOU Changlin, WANG Chunyang, GONG Jian, et al. Ambiguity function evaluation and optimization of the transmitting beamspace-based FDA radar[J]. Signal Processing, 2023, 203: 108810. doi: 10.1016/j.sigpro.2022.108810.
[21]	LIU Mingjie, WANG Chunyang, GONG Jian, et al. Ambiguity function analysis and optimization of coherent FDA radar[J]. IEEE Geoscience and Remote Sensing Letters, 2024, 21: 3507205. doi: 10.1109/LGRS.2024.3406435.
[22]	YU Lei, HE Feng, ZHANG Yongsheng, et al. Low-PSL mismatched filter design for coherent FDA radar using phase-coded waveform[J]. IEEE Geoscience and Remote Sensing Letters, 2023, 20: 3507405. doi: 10.1109/LGRS.2023.3309827.
[23]	何子述, 李军, 刘红明, 等. MIMO雷达[M]. 北京: 国防工业出版社, 2017: 199. HE Zishu, LI Jun, LIU Hongming, et al. MIMO Radar[M]. Beijing: National Defense Industry Press, 2017: 199.