基于线性正则域τ-Wigner分布输出信噪比不等式建模的雷达信号检测研究
Research on Radar Signal Detection Based on Output Signal-to-Noise Ratio Inequality Modeling of τ-Wigner Distribution in Linear Regular Domain
摘要: 为提升瞬时互相关函数型Wigner分布(Instantaneous Cross-correlation Function Wigner Distribu-tion, ICFWD)检测性能，本文采用τ-Wigner分布与其结合，提出瞬时互相关函数型τ-Wigner分布(Instantaneous Cross-correlation Function τ-Wigner Distribution, ICFτWD)，通过构建其输出信噪比不等式模型克服优化模型无法针对双分量线性调频(Linear Frequency-Modulated, LFM)信号进行求解的困难，得出有关线性正则变换(Linear Canonical Transform, LCT)自由参数与参数τ的不等式约束，据此实现白噪声干扰的单、双分量LFM信号高性能检测。数值仿真实验验证了理论分析的正确性，以及ICFτWD在检测性能方面的优势。
Abstract: To improve the detection performance of the instantaneous cross-correlation function Wigner distribution (ICFWD), this paper combines the τ-Wigner distribution with the ICFWD to propose the instantaneous cross-correlation function τ-Wigner distribution (ICFτWD). In this study, we overcome the difficulty that the optimization model fails to solve for the two-component linear frequency-modulated (LFM) signal by constructing the output signal-to-noise ratio (SNR) inequality model of the ICFτWD, and obtain the inequality constraints on the LCT free parameter and the parameter τ. Accordingly, we achieve the high-performance detection of the white noise jamming single component and two-component LFM signals. Numerical simulation experiments verify the correctness of the theoretical analysis and the advantages of the ICFτWD in the detection perfor-mance.
文章引用：张钰婉, 张志超. 基于线性正则域τ-Wigner分布输出信噪比不等式建模的雷达信号检测研究[J]. 理论数学, 2023, 13(3): 493-515. https://doi.org/10.12677/PM.2023.133054

参考文献

[1] Xu, T.Z. and Li, B.Z. (2013) Linear Canonical Transforms and Its Applications. Science Press, Beijing.
[2] Bai, R.-F., Li, B.-Z. and Cheng, Q.-Y. (2012) Wigner-Ville Distribution Associated with the Linear Canonical Transform. Journal of Applied Mathematics, 2012, Article ID: 740161. [Google Scholar] [CrossRef] 
[3] Zhang, Z.-C. (2016) New Wigner Distribution and Ambiguity Function Based on the Generalized Translation in the Linear Canonical Transform Domain. Signal Processing, 118, 51-61. [Google Scholar] [CrossRef] 
[4] Zhang, Z.-C. (2015) Unified Wigner-Ville Distribution and Ambiguity Function in the Linear Canonical Transform Domain. Signal Processing, 114, 45-60. [Google Scholar] [CrossRef] 
[5] Zhao, H., Ran, Q.-W., Ma, J. and Tan, L.-Y. (2011) Linear Canonical Ambiguity Function and Linear Canonical Transform Moments. Optik, 122, 540-543. [Google Scholar] [CrossRef] 
[6] Che, T.-W., Li, B.-Z. and Xu, T.-Z. (2012) The Ambiguity Func-tion Associated with the Linear Canonical Transform. EURASIP Journal on Advances in Signal Processing, 2012, Article No. 138. [Google Scholar] [CrossRef] 
[7] 李炳照, 陶然, 王越. 线性正则变换域的框架理论研究[J]. 电子学报, 2007, 35(7): 1387-1390.
[8] 许天周, 李炳照. 线性正则变换及其应用[M]. 北京: 科学出版社, 2013.
[9] 陶然, 邓兵, 王越. 分数阶傅里叶变换及其应用[M]. 北京: 清华大学出版社, 2009.
[10] 史军. 分数傅里叶变换理论及其在信号处理中的应用[D]: [博士学位论文]. 哈尔滨: 哈尔滨工业大学, 2013.
[11] 马金铭, 苗红霞, 苏新华, 高畅, 康学净, 陶然. 分数傅里叶变换理论及其应用研究进展[J]. 光电工程, 2018, 45(6): 1-24.
[12] 张贤达. 现代信号处理[M]. 第2版. 北京: 清华大学出版社, 2013.
[13] 张贤达, 保铮. 非平稳信号分析与处理[M]. 北京: 国防工业出版社, 1998.
[14] Moshinsky, M. and Quesne, C. (1971) Linear Canonical Transformations and Their Unitary Representations. Journal of Mathematical Physics, 12, 1772-1783. [Google Scholar] [CrossRef] 
[15] Pei, S.-C. and Ding, J.-J. (2001) Relations between Fractional Operations and Time-Frequency Distributions and Their Applications. IEEE Transactions on Signal Processing, 49, 1638-1655. [Google Scholar] [CrossRef] 
[16] Zhang, Z.C. (2019) Linear Canonical Wigner Distribution Based Noisy LFM Signals Detection through the Output SNR Improvement Analysis. IEEE Transactions on Signal Processing, 67, 5527-5542. [Google Scholar] [CrossRef] 
[17] Zhang, Z.-C., Qiang, S.-Z., Jiang, X., Han, P.-Y., Shi, X.-Y. and Wu, A.-Y. (2021) Linear Canonical Wigner Distribution of Noisy LFM Signals via Variance-SNR Based Inequalities System Analysis. Optik, 237, Article ID: 166712 [Google Scholar] [CrossRef] 
[18] Zhang, Z.C., Li, D., Chen, Y.J. and Zhang, J.W. (2021) Linear Canonical Wigner Distribution of Noisy LFM Signals via Multiobjective Optimization Analysis Involving Variance-SNR. IEEE Communications Letters, 25, 546-550. [Google Scholar] [CrossRef] 
[19] Zhang, Z.C. (2019) The Optimal Linear Canonical Wigner Distribution of Noisy Linear Frequency-Modulated Signals. IEEE Signal Processing Letters, 26, 1127-1131. [Google Scholar] [CrossRef] 
[20] Qiang, S.-Z., Jiang, X., Qiang, S.-Z., Han, P.-Y., Shi, X.-Y., Wu, A.-Y., Sun, Y., Chen, Y.-J. and Zhang, Z.-C. (2021) Instantaneous Cross-Correlation Function Type of WD Based LFM Signals Analysis via Output SNR Inequality Modeling. EURASIP Journal on Advances in Signal Processing, 2021, Article No. 122. [Google Scholar] [CrossRef] 
[21] Wu, A.-Y., Shi, X.-Y., Sun, Y., Jiang, X., Qiang, S.-Z., Han, P.-Y. and Zhang, Z.C. (2022) A Computationally Efficient Optimal Wigner Distribution in LCT Domains for Detecting Noisy LFM Signals. Mathematical Problems in Engineering, 2022, Article ID: 2036285. [Google Scholar] [CrossRef] 
[22] Shi, X.Y., Wu, A.Y., Sun, Y., Qiang, S.Z., Jiang, X., Han, P.Y., Chen, Y.J. and Zhang, Z.C. (2022) Unique Parameters Selection Strategy of Linear Canonical Wigner Distribution via Multiobjective Optimization Modeling. Chinese Journal of Electronics.
[23] Boggiatto, P., De Donno, G. and Oliaro, A. (2010) Time-Frequency Representations of Wigner Type and Pseudo-Differential Operators. Transactions of the American Mathematical Society, 362, 4955-4981. [Google Scholar] [CrossRef] 
[24] Boggiatto, P., Carypis, E. and Oliaro, A. (2013) Win-dowed-Wigner Representations in the Cohen Class and Uncertainty Principles. Journal of Geometric Analysis, 23, 1753-1779. [Google Scholar] [CrossRef] 
[25] Healy, J.J., Kutay, M.A., Ozaktas, H.M. and Sheridan, J.T. (2016) Linear Canonical Transforms: Theory and Applications. Springer, New York. [Google Scholar] [CrossRef] 
[26] Collins, S.A. (1970) Lens-System Diffraction Integral Written in Terms of Matrix Optics. Journal of the Optical Society of America, 60, 1168-1177. [Google Scholar] [CrossRef] 
[27] Leung, Y.-W. and Wang, Y.P. (2000) Multiobjective Programming Using Uniform Design and Genetic Algorithm IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applica-tions and Reviews), 30, 293-304. [Google Scholar] [CrossRef] 
[28] Chen, X.L., Guan, J., Huang, Y., Liu, N.B. and He, Y. (2015) Ra-don-Linear Canonical Ambiguity Function-Based Detection and Estimation Method for Marine Target with Micromotion. IEEE Transactions on Geoscience and Remote Sensing, 53, 2225-2240. [Google Scholar] [CrossRef] 

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