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首页> 外文期刊>IEEE Transactions on Signal Processing >Linear Canonical Wigner Distribution Based Noisy LFM Signals Detection Through the Output SNR Improvement Analysis
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Linear Canonical Wigner Distribution Based Noisy LFM Signals Detection Through the Output SNR Improvement Analysis

机译：通过输出SNR改进分析的基于线性规范Wigner分布的噪声LFM信号检测

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摘要

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 & x0027;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.
机译：在我们以前的工作中，我们通过引入一种可以被认为是Wigner分布（CICFWD）的闭合形式瞬时互相关函数类型，解决了线性规范变换（LCT）域中Wigner分布（WD）的统一表示问题。线性规范域中的WD＆x0027; s闭式表示形式。然后，我们通过数值模拟分析方法讨论了CICFWD在线性调频（LFM）信号检测中的应用，结果证明，无LCT参数与检测性能之间存在因果关系。本文的主要贡献是为这种因果关系提供一个数学模型，以揭示由LCT自由参数触发的非平稳信号检测性能改善的内在机理。我们首先回顾一下CICFWD的定义，并建立一些相关的理论，包括其基本性质和离散化。然后，我们为提高输出信噪比（SNR），传统WD和CICFWD之间的输出SNR不等式之间的关系奠定了数学理论基础，并讨论了如何解决该不等式以得出LCT免费参数。在完善的输出SNR改善分析框架内，我们还探索了添加了白噪声的LFM信号的无LCT参数选择结果。最后，通过数值实验验证了确定LCT自由参数策略的正确性以及输出信噪比改进分析方法的可行性。

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