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

作　　者：张钰婉 张志超 

机构地区：[1]南京信息工程大学数学与统计学院,江苏 南京

出　　处：《理论数学》2023年第3期493-515,共23页Pure Mathematics

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。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.

关 键 词：线性正则变换 线性调频信号 瞬时互相关函数型Wigner分布 τ-Wigner分布 

分 类 号：G63[文化科学—教育学]