1-bit采样下雷达脉压性能分析

doi:10.12305/j.issn.1001-506X.2022.10.10

摘要/Abstract

摘要：

1-bit采样因其低成本、低功耗等优势引起了广泛关注, 本文主要讨论1-bit采样下雷达的脉压性能。首先, 推导了1-bit采样造成的信噪比损失, 分析了1-bit采样的适用条件, 进而发现1-bit采样适合于单次回波信噪比较低的应用场景。接着, 通过理论分析可知相对于高精度脉压系数, 1-bit脉压系数会带来额外的脉压信噪比损失, 但实现方式更为简单。此外, 分析了在高信噪比下, 发射信号为线性调频(linear frequency modulation, LFM)信号时周期性假目标出现的原因, 并且指出相位编码可有效避免假目标出现。仿真实验验证了以上理论推导的正确性。最后, 结合某高频(high frequency, HF) 地波雷达的实测数据验证了1-bit采样的可行性。

关键词: 1-bit采样, 脉冲压缩, 高频地波雷达

Abstract:

1-bit sampling has attracted extensive attention because of its advantages of low cost and low power consumption. This paper mainly discusses the pulse compression performance of radar under 1-bit sampling. Firstly, the loss of signal to noise ratio caused by 1-bit sampling is deduced, the applicable conditions of 1-bit sampling are analyzed, and it is found that 1-bit sampling is suitable for the application scenario with low signal to noise ratio of single echo. Then, through theoretical analysis, compared with high-precision pulse compression coefficient, 1-bit pulse compression coefficient will bring additional loss of pulse compression signal to noise ratio, but the implementation method is simpler. In addition, the causes of periodic false targets when the transmitted signal is linear frequency modulation (LFM) signal under high signal to noise ratio are analyzed, and it is pointed out that phase coding can effectively avoid false targets. Simulation experiments verify the correctness of the above theoretical derivation. Finally, combined with the measured data of a high frequency (HF) ground wave radar, the feasibility of 1-bit sampling is verified.

Key words: 1-bit sampling, pulse compression, high frequency (HF) ground wave radar

中图分类号:

TP957

刘冰凡, 陈伯孝, 杨明磊. 1-bit采样下雷达脉压性能分析[J]. 系统工程与电子技术, 2022, 44(10): 3072-3082.

Bingfan LIU, Boxiao CHEN, Minglei YANG. Analysis of radar pulse compression performance under 1-bit sampling[J]. Systems Engineering and Electronics, 2022, 44(10): 3072-3082.

图/表 20

图1

图2

${\bar g}$ m(t)随SNR的变换情况"

图2

图3

图4

图5

表1

理论脉压峰值"

仿真	脉压系数	回波信号		理论峰值
仿真	脉压系数	SNR≪0 dB	SNR≫0 dB	SNR≪0 dB	SNR≫0 dB
H₁	a	Aa	Aa	$\frac{\left\|A \boldsymbol{a}^{\mathrm{H}} \boldsymbol{a}\right\|}{\\|\boldsymbol{a}\\|^2}=A$	$\frac{\left\|A \boldsymbol{a}^{\mathrm{H}} \boldsymbol{a}\right\|}{\\|\boldsymbol{a}\\|^2}={A}$
H₂	a	a≈γAa	$\bar{\boldsymbol{a}} \approx \frac{4}{\pi} \boldsymbol{a}$	$\frac{\left\|\gamma A \boldsymbol{a}^{\mathrm{H}} \boldsymbol{a}\right\|}{\\|\boldsymbol{a}\\|^2}=\gamma {A}$	$\frac{4}{{\rm{ \mathsf{ π} }}} \frac{\\|\boldsymbol{a}\\|^2}{\\|\boldsymbol{a}\\|^2}=\frac{4}{{\rm{ \mathsf{ π} }}}$
H₃	γa	a≈γAa	$\bar{\boldsymbol{a}} \approx \frac{4}{\pi} \boldsymbol{a}$	$\frac{{\left\| {\gamma A{\boldsymbol{a}^{\rm{H}}} \cdot \gamma \boldsymbol{a}} \right\|}}{{{{\left\\| {\gamma \boldsymbol{a}} \right\\|}^2}}} = A$	$\frac{4}{{\rm{ \mathsf{ π} }}} \frac{\left\|\boldsymbol{a}^{\mathrm{H}} \cdot \gamma \boldsymbol{a}\right\|}{\\|\gamma \boldsymbol{a}\\|^2}=\frac{4}{{\rm{ \mathsf{ π} }} \gamma}$
H₄	a	a≈γAa	$\bar{\boldsymbol{a}} \approx \frac{4}{\pi} \boldsymbol{a}$	$\frac{\left\|\gamma A \boldsymbol{a}^{\mathrm{H}} \cdot \overline{\boldsymbol{a}}\right\|}{\\|\bar{\boldsymbol{a}}\\|^2} \approx \frac{\left\|\gamma A \boldsymbol{a}^{\mathrm{H}} \cdot \frac{4}{{\rm{ \mathsf{ π} }}} \boldsymbol{a}\right\|}{\\|\overline{\boldsymbol{a}}\\|^2}=\frac{2}{{\rm{ \mathsf{ π} }}} \gamma A$	$\frac{\left\|\overline{\boldsymbol{a}}^{\mathrm{H}} \cdot \overline{\boldsymbol{a}}\right\|}{\\|\overline{\boldsymbol{a}}\\|^2}=1$

表1

表2

图6

表3

图7

图8

表4

图9

图10

图11

图12

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图15

图16

参考文献 29

1	REN J Y, LI J. One-bit digital radar[C]//Proc. of the Asilomar Conference on Signals, 2017.
2	FRANCESCHETTI G , PASCAZIO V , SCHIRINZI G . Processing of Signum coded SAR signal: theory and experiments[J]. Radar & Signal Processing IEE Proceedings F, 1991, 138 (3): 192- 198.
3	CAPPUCCINO G, COCORULLO G, CORSONELLO P, et al. Real-time processing of one-bit-coded SAR data[C]//Proc. of the IEEE Electronic Technical Conference, 1996.
4	PASCAZIO V , SCHIRINZI G . Synthetic aperture radar imaging by one bit coded signals[J]. Electronics & Communications Engineering Journal, 1998, 10 (1): 17- 28. doi: 10.3321/j.issn:1001-506X.1998.01.005
5	FRANCESCHETTI G . Time-domain convolution of one-bit coded radar signals[J]. Radar & Signal Processing IEE Proceedings F, 1991, 138 (5): 438- 444.
6	BAR-SHALOM O , WEISS A J . DOA estimation using one-bit quantized measurements[J]. IEEE Trans.on Aerospace and Electronic Systems, 2002, 38 (3): 868- 884. doi: 10.1109/TAES.2002.1039405
7	GAO Y L , HU D S , CHEN Y P , et al. Gridless one-bit DOA estimation exploiting SVM approach[J]. IEEE Communications Letters, 2017, 21 (10): 2210- 2213. doi: 10.1109/LCOMM.2017.2723359
8	JACQUES L , LASKA J N , BOUFOUNOS P T , et al. Robust 1-bit compressive sensing via binary stable embeddings of sparse vectors[J]. IEEE Trans.on Information Theory, 2013, 59 (4): 2082- 2102. doi: 10.1109/TIT.2012.2234823
9	MENG X M , ZHU J . A generalized sparse bayesian learning algorithm for 1-bit DOA estimation[J]. IEEE Communications Letters, 2018, 22 (7): 1414- 1417. doi: 10.1109/LCOMM.2018.2834904
10	HUANG X , LIAO B . One-bit MUSIC[J]. IEEE Signal Processing Letters, 2019, 26 (7): 961- 965. doi: 10.1109/LSP.2019.2913452
11	LIU C L, VAIDYANATHAN P P. One-bit sparse array DOA estimation[C]//Proc. of the IEEE International Conference on Acoustics, Speech and Signal Processing, 2017: 3126-3130.
12	LI Y Z , TAO C , SECO-GRANADOS G , et al. Channel estimation and performance analysis of one-bit massive MIMO systems[J]. IEEE Trans.on Signal Processing, 2017, 65 (15): 4075- 4089. doi: 10.1109/TSP.2017.2706179
13	WANG F Y , FANG J , LI H B , et al. One-bit quantization design and channel estimation for massive MIMO systems[J]. IEEE Trans.on Vehicular Technology, 2018, 67 (11): 10921- 10934. doi: 10.1109/TVT.2018.2870580
14	CHOI J , MO J , HEATH R W . Near maximum-likelihood detector and channel estimator for uplink multiuser massive MIMO systems with one-bit ADCs[J]. IEEE Trans.on Commu-nications, 2015, 64 (5): 2005- 2018.
15	ZHANG J Y , DAI L L , SUN S Y , et al. On the spectral efficiency of massive MIMO systems with low-resolution ADCs[J]. IEEE Communications Letters, 2015, 20 (5): 842- 845.
16	SHAO Z , LANDAU L T N , DE L R C . Dynamic oversampling for 1-bit ADCs in large-scale multiple-antenna systems[J]. IEEE Trans.on Communications, 2021, 69 (5): 3423- 3435. doi: 10.1109/TCOMM.2021.3059303
17	LI A , LIU F , MASOUROS C , et al. Interference exploitation 1-bit massive MIMO precoding: a partial branch-and-bound solution with near-optimal performance[J]. IEEE Trans.on Wireless Communications, 2020, 19 (5): 3474- 3489. doi: 10.1109/TWC.2020.2973987
18	LI C X , LI G , VARSHNEY P K . Distributed detection of sparse stochastic signals with 1-bit data in tree-structured sensor networks[J]. IEEE Trans.on Signal Processing, 2020, 68, 2963- 2976. doi: 10.1109/TSP.2020.2988598
19	GIANELLI C, XU L Z, LI J, et al. One-bit compressive sampling with time-varying thresholds for sparse parameter estimation[C]//Proc. of the IEEE Sensor Array and Multichannel Signal Processing Workshop, 2016.
20	GIANELLI C, XU L Z, LI J, et al. One-bit compressive sampling with time-varying thresholds: maximum likelihood and the Cramér-Rao bound[C]//Proc. of the IEEE 50th Asilomar Conference on Signals, Systems and Computers, 2016.
21	AMERI A , BOSE A , LI J , et al. One-bit radar processing with time-varying sampling thresholds[J]. IEEE Trans.on Signal Processing, 2019, 67 (20): 5297- 5308. doi: 10.1109/TSP.2019.2939086
22	JIN B Z , ZHU J , WU Q H , et al. One-bit LFMCW radar: spectrum analysis and target detection[J]. IEEE Trans.on Aerospace and Electronic Systems, 2020, 56 (4): 2732- 2750. doi: 10.1109/TAES.2020.2978374
23	JIN B Z , ZHANG X F , ZHAO B , et al. One-bit LFM pulse radar: harmonic analysis and target reconstruction[J]. IEEE Access, 2019, 7, 109482- 109494. doi: 10.1109/ACCESS.2019.2933640
24	吕元浩. 单比特合成孔径雷达稀疏成像技术的研究[D]. 合肥: 中国科学技术大学, 2017.
	LYV Y H. Studies on 1-bit coded synthetic aperture radar sparse imaging[D]. Heifei: University of Science and Techno-logy of China, 2017.
25	周崇彬. 单比特合成孔径雷达稀疏成像技术的研究[D]. 合肥: 中国科学技术大学, 2016.
	ZHOU C B. Studies on 1-bit coded synthetic aperture radar sparse imaging[D]. Heifei: University of Science and Techno-logy of China, 2016.
26	赵博, 黄磊, 周汉飞. 基于单频时变阈值的1-bit SAR成像方法研究[J]. 雷达学报, 2018, 7 (4): 446- 454.
	ZHAO B , HUANG L , ZHOU H F . 1-bit SAR imaging method based on single-frequency time-varying threshold[J]. Journal of Radars, 2018, 7 (4): 446- 454.
27	ABRAMOWITZ M , STEGUN I A , MCQUARRIE D A , et al. Handbook of mathematical functions[M]. American: National Bureau of Standard, 1964.
28	LIU B F , CHEN B X , YANG M L . Signal processing of coast-ship bistatic high-frequency surface-wave radar using one-bit quantized measurement[J]. IEEE Access, 2020, 8, 55578- 55591. doi: 10.1109/ACCESS.2020.2981482
29	潘孟冠. 稀疏谱高频地波雷达信号处理技术研究[D]. 西安: 西安电子科技大学, 2018.
	PAN M G. Study on signal processing technology of sparse spectrum high frequency ground wave radar[D]. Xi'an: Xidian University, 2018.

SNR	仿真
SNR	H₁	H₂	H₃	H₄
-10	40.0	-9.0	40.0	-12.9
0	40.0	-1.0	38.0	-4.7
10	40.0	1.8	30.8	-1.2
20	40.0	2.04	21.0	-0.4

SNR	仿真
SNR	H₁	H₂	H₃	H₄
-10	40.0	-9.0	40.0	-9.0
0	39.9	-1.6	37.4	-1.6
10	40.0	0	29.0	0
20	40.0	0	19.0	0

仿真情况	单目标		双目标
仿真情况	LFM (图 5)	MLS (图 6)	LFM (图 7)	MLS (图 8)
H₁	29.82	29.46	30.30	29.10
H₂	27.96	27.58	28.30	27.06
H₃	27.96	27.58	28.30	27.06
H₄	26.87	27.58	27.12	27.06
H₂－H₁	-1.86	-2.21	-2.10	-2.04
H₄－H₁	-2.95	—	-3.18	—

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[12]	王秀红，毛兴鹏，张乃通. 基于CS的脉冲压缩雷达单快拍DOA估计[J]. 系统工程与电子技术, 2014, 36(9): 1737-1743.
[13]	张朝霞，周俊杰，张明江，张东泽. 利用组合脉冲解决超宽带雷达中探测盲区问题[J]. 系统工程与电子技术, 2014, 36(8): 1517-1520.
[14]	纪永刚，张杰，王祎鸣，于长军，黎明. 双频率高频地波雷达船只目标点迹关联与融合处理[J]. 系统工程与电子技术, 2014, 36(2): 266-271.
[15]	王赞, 陈伯孝. 基于压缩感知的高频地波雷达射频干扰抑制[J]. Journal of Systems Engineering and Electronics, 2012, 34(8): 1565-1570.