基于混沌振子与小波的低信噪比信号检测研究与应用
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摘要
低信噪比信号广泛存在于保密通信，信号侦察，探地信号处理，深海声纳探测，机电系统状态监测，医学信号处理等领域中，低信噪比信号检测成为这些信号处理中首先需要解决的问题。
利用Duffing振子系统从混沌进入外周期轨道运动的非平衡相变条件具有对小信号的敏感性以及对噪声的免疫性，可从强噪声背景中检测低信噪比周期信号，并输出提高信噪比后的信号。本文重点研究了低信噪比条件下，Duffing振子系统对周期信号、线性调频信号的检测。
含噪信号的小波变换系数中，信号和噪声产生的系数具有不同性态。通过采用线性或非线性处理方法，可以减去噪声小波系数，最大限度地保留信号小波系数，从而得到提高了信噪比的输出信号。本文针对低信噪比信号检测，提出了对小波去噪算法的改进。
本文的主要成果和创新之处体现在：
1．研究了高斯白噪声条件下Duffing振子系统用于周期信号检测时输出统计特性，提出了利用周期平均输出信噪比改善率衡量混沌振子系统的检测能力。通过理论论证和仿真实验，验证了该比率的准确性和有效性，并得到不同输入信噪比条件下的周期平均改善率。
2．研究了Duffing振子系统对低信噪比线性调频(LFM)信号的检测，发现了系统具有在一定条件下对LFM信号的直接检测能力，及线性调频信号的调制参数对系统可检测最低信噪比的影响。
3．研究了基于最小均方误差条件的软阈值去噪，获得了针对不同统计特性噪声的最佳软阈值去噪修正值，推导并验证了高斯白噪声条件下的小波系数最佳收缩量。
4．研究了基于SURE无偏估计的自适应小波软阈值去噪算法，提出一种新的阈值函数族，是一种可微阈值函数的统一表达式。该函数族具有可调参数，可更接近于Donoho提出的最优软阈值函数，连续并具有无穷阶导数，便于自适应寻求最优阈值。
5．研究了最优小波基的选取，通过计算周期信号与db小波基的相关系数，发现了小波基紧支区间内信号周期数与小波基函数的波动性的关系，得到了针对LFM信号和正弦信号进行分析的最优小波基。
6．研究综合利用混沌振子、小波去噪和相关分析等技术进行低信噪比信号的检测，并应用于雷达信号的双(多)基地接收和处理中，增强了系统的低信噪比信号检测能力。
Low signal-to-noise ratio (SNR) signals exist widely in secure communication, signal reconnaissance, ground penetrating signal processing, deep sea sonar exploration, electricity & machine system appearance monitor, medical signal processing etc. Thus, the detection of low SNR signals becomes the first issues to be addressed in these tasks.
Duffing oscillator is sensitive to weak signals yet immune to noise when system changes from chaotic to outer periodic orbits. Using this character the weak periodic signal in strong noise can then be detected and the improved SNR signal will be output. In this dissertation, the detections of periodic signal and linear frequency modulated (LFM) signal at low SNR by Duffing oscillator are investigated.
The wavelet coefficients of signal and noise after wavelet have the different natures. Using the linear or nonlinear denoising methods, the most signal coefficients will be preserved while the noise coefficients are reduced. Therefore the output signal with the improved SNR is achieved. In this dissertation, some wavelet denoising methods are improved in low SNR signal detection.
The main research works and contributions of this dissertation are as follows:
1. The output Statistics natures in detection of periodic signal by Duffing oscillator under the Gauss white noise are researched. And then we presented an evaluation index for detection ability of chaotic oscillator system using periodic mean of output SNR improvement ratio (pmoSNRir). The validity of pmoSNRir is demonstrated through theory analysis and simulation experiments. We also give pmoSNRirs in different SNRs.
2. The detection ability of Duffing oscillator system on low SNR LFM signal is investigated, and then influence of modulating parameters to detectable minimum input SNR of LFM signal is acquired.
3. The soft threshold denoising method based on minimum mean square error (MMSE) is investigated. The optimal shrinkage of wavelet coefficients under the Gauss white noise is deduced and verified.
4. The adaptive wavelet threshold denoising method based on SURE estimation is investigated and a novel set of threshold functions, which is a uniform expression of differentiable threshold functions, is presented. The function family with the adjustable parameters is close to Donoho soft threshold function and has continuous derivative. The advantages of the new threshold function family make it possible to construct an adaptive algorithm to look for the best threshold.
5. The selection of optimal wavelet basis function is investigated. The cross correlation coefficients between periodic signals and db wavelets are calculated and the optimal wavelet to analysis LFM and sine signal is found.
6. A low SNR signal detection system is founded by synthesizing Duffing oscillator, wavelet denoising and correlation technique, which is applied to signal receiving and processing in radar bistatic-based system. The ability of detection low SNR signal of corresponding system is improved.
利用Duffing振子系统从混沌进入外周期轨道运动的非平衡相变条件具有对小信号的敏感性以及对噪声的免疫性，可从强噪声背景中检测低信噪比周期信号，并输出提高信噪比后的信号。本文重点研究了低信噪比条件下，Duffing振子系统对周期信号、线性调频信号的检测。
含噪信号的小波变换系数中，信号和噪声产生的系数具有不同性态。通过采用线性或非线性处理方法，可以减去噪声小波系数，最大限度地保留信号小波系数，从而得到提高了信噪比的输出信号。本文针对低信噪比信号检测，提出了对小波去噪算法的改进。
本文的主要成果和创新之处体现在：
1．研究了高斯白噪声条件下Duffing振子系统用于周期信号检测时输出统计特性，提出了利用周期平均输出信噪比改善率衡量混沌振子系统的检测能力。通过理论论证和仿真实验，验证了该比率的准确性和有效性，并得到不同输入信噪比条件下的周期平均改善率。
2．研究了Duffing振子系统对低信噪比线性调频(LFM)信号的检测，发现了系统具有在一定条件下对LFM信号的直接检测能力，及线性调频信号的调制参数对系统可检测最低信噪比的影响。
3．研究了基于最小均方误差条件的软阈值去噪，获得了针对不同统计特性噪声的最佳软阈值去噪修正值，推导并验证了高斯白噪声条件下的小波系数最佳收缩量。
4．研究了基于SURE无偏估计的自适应小波软阈值去噪算法，提出一种新的阈值函数族，是一种可微阈值函数的统一表达式。该函数族具有可调参数，可更接近于Donoho提出的最优软阈值函数，连续并具有无穷阶导数，便于自适应寻求最优阈值。
5．研究了最优小波基的选取，通过计算周期信号与db小波基的相关系数，发现了小波基紧支区间内信号周期数与小波基函数的波动性的关系，得到了针对LFM信号和正弦信号进行分析的最优小波基。
6．研究综合利用混沌振子、小波去噪和相关分析等技术进行低信噪比信号的检测，并应用于雷达信号的双(多)基地接收和处理中，增强了系统的低信噪比信号检测能力。
Low signal-to-noise ratio (SNR) signals exist widely in secure communication, signal reconnaissance, ground penetrating signal processing, deep sea sonar exploration, electricity & machine system appearance monitor, medical signal processing etc. Thus, the detection of low SNR signals becomes the first issues to be addressed in these tasks.
Duffing oscillator is sensitive to weak signals yet immune to noise when system changes from chaotic to outer periodic orbits. Using this character the weak periodic signal in strong noise can then be detected and the improved SNR signal will be output. In this dissertation, the detections of periodic signal and linear frequency modulated (LFM) signal at low SNR by Duffing oscillator are investigated.
The wavelet coefficients of signal and noise after wavelet have the different natures. Using the linear or nonlinear denoising methods, the most signal coefficients will be preserved while the noise coefficients are reduced. Therefore the output signal with the improved SNR is achieved. In this dissertation, some wavelet denoising methods are improved in low SNR signal detection.
The main research works and contributions of this dissertation are as follows:
1. The output Statistics natures in detection of periodic signal by Duffing oscillator under the Gauss white noise are researched. And then we presented an evaluation index for detection ability of chaotic oscillator system using periodic mean of output SNR improvement ratio (pmoSNRir). The validity of pmoSNRir is demonstrated through theory analysis and simulation experiments. We also give pmoSNRirs in different SNRs.
2. The detection ability of Duffing oscillator system on low SNR LFM signal is investigated, and then influence of modulating parameters to detectable minimum input SNR of LFM signal is acquired.
3. The soft threshold denoising method based on minimum mean square error (MMSE) is investigated. The optimal shrinkage of wavelet coefficients under the Gauss white noise is deduced and verified.
4. The adaptive wavelet threshold denoising method based on SURE estimation is investigated and a novel set of threshold functions, which is a uniform expression of differentiable threshold functions, is presented. The function family with the adjustable parameters is close to Donoho soft threshold function and has continuous derivative. The advantages of the new threshold function family make it possible to construct an adaptive algorithm to look for the best threshold.
5. The selection of optimal wavelet basis function is investigated. The cross correlation coefficients between periodic signals and db wavelets are calculated and the optimal wavelet to analysis LFM and sine signal is found.
6. A low SNR signal detection system is founded by synthesizing Duffing oscillator, wavelet denoising and correlation technique, which is applied to signal receiving and processing in radar bistatic-based system. The ability of detection low SNR signal of corresponding system is improved.
引文
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