Sensing Matrix Optimization for Random Stepped-Frequency Signal Based on Two-Dimensional Ambiguity Function

LYU Mingjiu; CHEN Hao; YANG Jun; WU Xia; ZHOU Ming; MA Xiaoyan

doi:10.23919/cje.2022.00.046

Volume 33 Issue 1

Jan. 2024

Turn off MathJax

Article Contents

Article Navigation > Chinese Journal of Electronics > 2024 > 33(1): 161-174

Mingjiu LYU, Hao CHEN, Jun YANG, et al., “Sensing Matrix Optimization for Random Stepped-Frequency Signal Based on Two-Dimensional Ambiguity Function,” Chinese Journal of Electronics, vol. 33, no. 1, pp. 161–174, 2024 doi: 10.23919/cje.2022.00.046

Citation:

Mingjiu LYU, Hao CHEN, Jun YANG, et al., “Sensing Matrix Optimization for Random Stepped-Frequency Signal Based on Two-Dimensional Ambiguity Function,” Chinese Journal of Electronics, vol. 33, no. 1, pp. 161–174, 2024 doi: 10.23919/cje.2022.00.046

Citation:

PDF( 3554 KB)

Sensing Matrix Optimization for Random Stepped-Frequency Signal Based on Two-Dimensional Ambiguity Function

doi: 10.23919/cje.2022.00.046

LYU Mingjiu^{1
,
,},
CHEN Hao^2
,,
YANG Jun^2
,,
WU Xia¹,
ZHOU Ming²,
MA Xiaoyan^1
,

1.
Radar NCO School, Air Force Early Warning Academy, Wuhan 430019, China
2.
Department of Early Warning Technology, Air Force Early Warning Academy, Wuhan 430019, China

More Information

Author Bio:
Mingjiu LYU received the B.S., M.S. and Ph.D. degree in information and communication engineering from Air Force Early Warning Academy, China, in 2008, 2010 and 2018, respectively. Currently, he is a Lecturer in Air Force Early Warning Academy. His research interests include compressed sensing, sparse signal recovery and their applications in ISAR imaging. (Email: lv_mingjiu@163.com)

Hao CHEN received the B.S., M.S. degrees from Air Force Early Warning Academy in 2016 and 2018. He works as a Lecturer in Air Force Early Warning Academy. His research interests include array signal processing, radar signal processing and network radar. (Email: ch19930922@163.com)

Jun YANG received the B.S. and the M.S. degree in information and communication engineering from Air Force Early Warning Academy, Wuhan, China, in 1996 and 1999, respectively. He received the Ph. D. degree from Air Force Engineering University, Xi’an, China, in 2003. Now, he is a Full Professor at the Air Force Early Warning Academy. His research interest covers radar system, radar imaging, and compressed sensing. (Email: yangjem@163.com)

Xiaoyan MA received the B.S. degree from Nanjing University of Science and Technology, China, in 1982, the M.S. degree from National University of Defense Technology, China in 1988, the Ph.D. degree from Tsinghua University, Beijing, China in 2002. He is currently a Full Professor at the Air Force Early Warning Academy. His research interests include radar system, target detection and imaging, and ISAR signal processing. (Email: ma_x_yan@163.com)
Corresponding author: Email: lv_mingjiu@163.com
Received Date: 2022-03-15
Accepted Date: 2022-09-15

Available Online: 2022-12-27

Publish Date: 2024-01-05

Abstract

Abstract

Compressive sensing technique has been widely applied to achieve range-Doppler reconstruction of high frequency radar by utilizing sparse random stepped-frequency (SRSF) signal, which can suppress the complex electromagnetic interference and greatly reduce the coherent processing interval. An important way to improve the performance of sparse signal reconstruction is to optimize the sensing matrix (SM). However, the existing research on the SM optimization needs to design a measurement matrix with superior performance, which needs a large amount of computation and does not consider the influence of the waveform parameters design. In order to improve the superior reconstruction performance, a novel SM optimization approach for SRSF signal is proposed by using two-dimensional ambiguity function (TDAF) in this paper. Firstly, based on the two-dimensional sparse reconstruction model of the SRSFs, the internal relationship between the waveform parameters and the SM was derived. Secondly, the SM optimization problem was directly transformed into the waveform design of SRSFs. Furthermore, on the basis of analyzing the relationship between the mutual coherence matrix of SM and the TDAF matrix of SRSFs, the purpose of optimizing the SM can be achieved by designing the TDAF of the SRSFs. Based on this analysis, a sparse waveform optimization method with joint constraints of maximum and mean sidelobes of the TDAF by using the genetic algorithm was derived. Compared with the traditional SM optimization method, our method not only avoids generating a new measurement matrix, but also further reduces the complexity of the waveform optimization. Simulation experiments verified the effectiveness of the proposed method.
- Sparse random stepped-frequency signal,
- Two-dimensional ambiguity function,
- Waveform design,
- Compressed sensing,
- Sensing matrix optimization

FullText(HTML)

References(30)

References

[1]	S. R. J. Axelsson, “Analysis of random step frequency radar and comparison with experiments,” IEEE Transactions on Geoscience and Remote Sensing, vol. 45, no. 4, pp. 890–904, 2007. doi: 10.1109/TGRS.2006.888865
[2]	D. L. Donoho, “Compressed sensing,” IEEE Transactions on Information Theory, vol. 52, no. 4, pp. 1289–1306, 2006. doi: 10.1109/TIT.2006.871582
[3]	T. Chen, J. Yang, and M. R. Guo, “A MIMO radar-based DOA estimation structure using compressive measurements,” Sensors, vol. 19, no. 21, article no. 4706, 2019. doi: 10.3390/s19214706
[4]	E. J. Candes and M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Processing Magazine, vol. 25, no. 2, pp. 21–30, 2008. doi: 10.1109/MSP.2007.914731
[5]	A. Flinth and S. Keiper, “Recovery of binary sparse signals with biased measurement matrices,” IEEE Transactions on Information Theory, vol. 65, no. 12, pp. 8084–8094, 2019. doi: 10.1109/TIT.2019.2929192
[6]	X. Q. Wang, G. Li, C. Quan, et al., “Distributed detection of sparse stochastic signals with quantized measurements: the generalized Gaussian case,” IEEE Transactions on Signal Processing, vol. 67, no. 18, pp. 4886–4898, 2019. doi: 10.1109/TSP.2019.2932884
[7]	J. C. Chen and Y. L. Liu, “Stable recovery of structured signals from corrupted sub-Gaussian measurements,” IEEE Transactions on Information Theory, vol. 65, no. 5, pp. 2976–2994, 2019. doi: 10.1109/TIT.2018.2890194
[8]	S. H. Yao, Z. G. Zheng, T. Wang, et al., “An efficient joint compression and sparsity estimation matching pursuit algorithm for artificial intelligence application,” Future Generation Computer Systems, vol. 86, pp. 603–613, 2018. doi: 10.1016/j.future.2018.04.039
[9]	J. M. Wang, S. P. Ye, Z. Y. Xu, et al., “Low storage space of random measurement matrix for compressed sensing with semi-tensor product,” Acta Electronica Sinica, vol. 46, no. 4, pp. 797–804, 2018. (in Chinese) doi: 10.3969/j.issn.0372-2112.2018.04.005
[10]	J. A. Tropp and A. C. Gilbert, “Signal recovery from random measurements via orthogonal matching pursuit,” IEEE Transactions on Information Theory, vol. 53, no. 12, pp. 4655–4666, 2007. doi: 10.1109/TIT.2007.909108
[11]	M. Elad, “Optimized projections for compressed sensing,” IEEE Transactions on Signal Processing, vol. 55, no. 12, pp. 5695–5702, 2007. doi: 10.1109/TSP.2007.900760
[12]	V. Abolghasemi, S. Ferdowsi, and S. Sanei, “A gradient-based alternating minimization approach for optimization of the measurement matrix in compressive sensing,” Signal Processing, vol. 92, no. 4, pp. 999–1009, 2012. doi: 10.1016/j.sigpro.2011.10.012
[13]	Y. H. Quan, Y. J. Wu, Y. C. Li, et al., “Range-Doppler reconstruction for frequency agile and PRF-jittering radar,” IET Radar, Sonar & Navigation, vol. 12, no. 3, pp. 348–352, 2018. doi: 10.1049/iet-rsn.2017.0421
[14]	S. Y. Du, Y. H. Quan, M. H. Sha, et al., “Waveform optimization for SFA radar based on evolutionary particle swarm optimization,” Systems Engineering and Electronics, vol. 44, no. 3, pp. 834–840, 2022. (in Chinese) doi: 10.12305/j.issn.1001-506X.2022.03.16
[15]	G. M. Shi, J. Lin, X. Y. Chen, et al., “UWB echo signal detection with ultra-low rate sampling based on compressed sensing,” IEEE Transactions on Circuits and Systems II:Express Briefs, vol. 55, no. 4, pp. 379–383, 2008. doi: 10.1109/TCSII.2008.918988
[16]	Y. J. Chen, K. M. Li, Q. Zhang, et al., “Adaptive measurement matrix optimization for ISAR imaging with sparse frequency-stepped chirp signals,” Journal of Electronics & Information Technology, vol. 40, no. 3, pp. 509–516, 2018. doi: 10.11999/JEIT170554
[17]	Z. N. Peng, D. Ben, G. Zhang, et al., “Sensing matrix construction for CS-MIMO radar based on sparse random array,” Acta Aeronautica et Astronautica Sinica, vol. 37, no. 3, pp. 1015–1024, 2016. doi: 10.7527/S1000-6893.2016.0020
[18]	L. Carin, D. H. Liu, and B. Guo, “Coherence, compressive sensing, and random sensor arrays,” IEEE Antennas and Propagation Magazine, vol. 53, no. 4, pp. 28–39, 2011. doi: 10.1109/MAP.2011.6097283
[19]	N. Levanon and E. Mozeson, Radar Signals. John Wiley & Sons, Inc., Hoboken, NJ, USA, pp. 34–52, 2004.
[20]	D. H. Zhao and Y. S. Wei, “Adaptive gradient search for optimal sidelobe design of hopped-frequency waveform,” IET Radar, Sonar & Navigation, vol. 8, no. 4, pp. 282–289, 2014. doi: 10.1049/iet-rsn.2013.0035
[21]	X. H. Wang, C. Y. Wang, N. Zhang, et al., “Phase-only method for designing a unimodular radar waveform with low ISL,” Journal of Radars, vol. 11, no. 2, pp. 255–263, 2022. (in Chinese) doi: 10.12000/JR21137
[22]	G. Wang and Y. Lu, “Designing single/multiple sparse frequency waveforms with sidelobe constraint,” IET Radar, Sonar & Navigation, vol. 5, no. 1, pp. 32–38, 2011. doi: 10.1049/iet-rsn.2009.0255
[23]	G. H. Wang, C. Y. Mai, J. P. Sun, et al., “Sparse frequency waveform analysis and design based on ambiguity function theory,” IET Radar, Sonar & Navigation, vol. 10, no. 4, pp. 707–717, 2016. doi: 10.1049/iet-rsn.2015.0270
[24]	C. Zhou, Z. B. Zhu, and Z. Y. Tang, “A novel waveform design method for shift-frequency jamming confirmation,” International Journal of Antennas and Propagation, vol. 2018, article no. 1569590, 2018. doi: 10.1155/2018/1569590
[25]	X. F. Song, S. L. Zhou, and P. Willett. “The role of the ambiguity function in compressed sensing radar,” in Proceedings of 2010 IEEE International Conference on Acoustics, Speech and Signal Processing, Dallas, TX, USA, pp. 2758–2761, 2010.
[26]	J. Yang, G. S. Liao, J. Li, et al., “Three dimensional MIMO radar imaging using sparse model based on waveform selection and calibration method in the presence of angle imperfections,” Journal of Electronics & Information Technology, vol. 36, no. 2, pp. 428–434, 2014. (in Chinese) doi: 10.3724/SP.J.1146.2013.00500
[27]	X. D. Zhang, Matrix Analysis and Applications, 2nd ed., Tsinghua University Press, Beijing, China, pp. 132–135, 2013. (in Chinese)
[28]	C. Y. Mai, G. H. Wang, and J. P. Sun. “Complementary codes approach to sparse frequency waveform design,” in Proceedings of the 2018 IEEE 23rd International Conference on Digital Signal Processing, Shanghai, China, pp. 1–5, 2018.
[29]	U. Maulik and S. Bandyopadhyay, “Genetic algorithm-based clustering technique,” Pattern Recognition, vol. 33, no. 9, pp. 1455–1465, 2000. doi: 10.1016/S0031-3203(99)00137-5
[30]	P. Vivekanandan, M. Rajalakshmi, and R. Nedunchezhian, “An intelligent genetic algorithm for mining classification rules in large datasets,” Computing and Informatics, vol. 32, no. 1, pp. 1–22, 2013.