Linear Canonical Wigner Distribution Based Noisy LFM Signals Detection Through the Output SNR Improvement Analysis
Linear Canonical Wigner Distribution Based Noisy LFM Signals Detection Through the Output SNR Improvement Analysis
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DOI：
10.1109/tsp.2019.2941071
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发表时间：
2019-11
影响因子：
5.4
通讯作者：
Zhichao Zhang
中科院分区：
文献类型：
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作者：
Zhichao Zhang
在我们以前的工作中，我们通过引入一种封闭形式的瞬时互相关函数型Wigner分布（CICFWD），解决了Wigner分布在线性正则变换（LCT）域上的统一表示问题，该函数型可以看作Wigner分布在线性正则变换域上的封闭形式表示。然后通过数值仿真分析方法讨论了CICFWD在线性调频（LFM）信号检测中的应用，发现LCT自由参数与检测性能之间存在因果关系。本文的主要贡献是提供了一个数学模型，这种因果关系，以揭示非平稳信号检测性能的内在机制触发LCT自由参数的改善。本文首先回顾了CICFWD的定义，建立了CICFWD的基本性质和离散化等相关理论。在此基础上，建立了输出信噪比改善的数学理论基础，给出了一般含噪信号情况下传统WD与CICFWD输出信噪比的不等式关系，并讨论了如何求解该不等式得到无LCT参数。在已建立的输出信噪比改善分析框架内，我们还探讨了添加白色噪声的LFM信号的无LCT参数选择结果。最后通过数值实验验证了LCT自由参数确定策略的正确性和输出信噪比改善分析方法的可行性。
In our previous work, we addressed a unified representation problem on Wigner distribution (WD) in linear canonical transform (LCT) domains by introducing a kind of closed-form instantaneous cross-correlation function type of Wigner distribution (CICFWD) that can be regarded as the WD's closed-form representation in the linear canonical domain. We then discussed the application of CICFWD in the detection of linear frequency-modulated (LFM) signals through the numerical simulation analysis approach, and it turns out that there is a causation between LCT free parameters and the detection performance. The main contribution of this paper is to provide a mathematical model for this causality in order to disclose the intrinsic mechanism of non-stationary signal detection performance improvement triggered by LCT free parameters. We first revisit the definition of CICFWD, and establish some related theories including its essential properties and discretization. We then formulate a mathematical theory foundation of the output signal-to-noise ratio (SNR) improvement, an output SNR inequality relation between the traditional WD and the CICFWD for a general noisy signal, and discuss how to solve this inequality to come out LCT free parameters. Within the well-established output SNR improvement analysis framework, we also explore LCT free parameters selection results on LFM signals added with white noise. Finally, numerical experiments are carried out to validate the correctness of strategies on determination LCT free parameters and the feasibility of output SNR improvement analysis approach.