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Weak Harmonic Signal Detecting in Chaotic Noise Based on Empirical Likelihood Ratio

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Abstract

Aiming at the problem of insufficient detection ability of weak harmonic signals under the background of chaotic noise, a method for detecting weak harmonic signals using empirical likelihood ratio (ELR) is proposed. First, the problem of detecting weak harmonic signals in a chaotic background is transformed into a test of heteroscedasticity hypothesis in a chaotic background. Then, based on the sensitivity of chaotic signal to initial value and short-term predictability, the phase space of observation signal is reconstructed, and the chaotic linear prediction model (CLP model) is established. The mean square error, mean absolute error, and root mean square error are used as the evaluation criteria for the chaotic linear prediction model. Then, an estimation equation is established according to the CLP model, and the existence of harmonic signals is tested by the ELR method. The method of sequential quadratic programming is used to optimize the model parameters, and the chi-square distribution is used to judge whether there are harmonic signals, so as to detect the weak harmonic signals submerged in the background of chaotic noise. Finally, Lorenz system was used as the background of chaotic noise for simulation experiments. The experimental results showed that the weak harmonic signals in the chaotic background could still be detected when the SNR was − 72.801 dB, which was more effective than the traditional method.

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No data were used to support this study.

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Acknowledgements

This paper was supported by was funded by the Natural Science Project of CQ CSTC of China (Grant No. cstc2018jcyjAX0464).

Funding

Natural Science Foundation Project of Chongqing,Chongqing Science and Technology Commission (CN), Grant No. (cstc2018jcyjAX0464).

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Authors and Affiliations

  1. School of Science, Chongqing University of Technology, Chongqing, 400054, China

    Liyun Su, Wanlin Zhu, Xiu Ling & Shengli Zhao

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  1. Liyun Su
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  2. Wanlin Zhu
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  4. Shengli Zhao
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Correspondence to Liyun Su.

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Su, L., Zhu, W., Ling, X. et al. Weak Harmonic Signal Detecting in Chaotic Noise Based on Empirical Likelihood Ratio. Wireless Pers Commun 126, 335–350 (2022). https://doi.org/10.1007/s11277-022-09747-2

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