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Robust Frequency Estimation in Symmetric \(\alpha \)-Stable Noise

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Abstract

The symmetric \(\alpha \)-stable (S\(\alpha \)S) noise is commonly encountered in a variety of applications such as wireless communications and image processing. In this work, combining the linear prediction property and \(\ell _p\)-norm minimization, a robust frequency estimator is devised for a complex sinusoid in the presence of the S\(\alpha \)S noise. The proposed algorithm, based on the \(\ell _p\)-norm of the preprocessed linear prediction errors, can be regarded as the outlier-resistant version of the generalized weighted linear prediction frequency estimation approach. Computer simulations are conducted to contrast the performance of the proposed algorithm with three conventional frequency estimators. The results indicate that our method is robust to outliers and nearly optimal compared with Cramér–Rao lower bound.

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Acknowledgements

We would like to express our gratitude to the associate editor for handling our paper and the anonymous reviewers for their professional suggestions and criticism.

Funding

This work was supported by National Natural Science Foundation of China (Grant No. 61701021) and Fundamental Research Funds for the Central Universities (Grant No. FRF-TP-17-017A2, WUT: 2017 IVA 049).

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Authors and Affiliations

  1. School of Computer and Communication Engineering, University of Science and Technology Beijing, Xueyuan Road, Beijing, China

    Yuan Chen & Xiao Long Yang

  2. School of Information Engineering, Wuhan University of Technology, Luoshi Road, Wuhan, China

    Long-Ting Huang

  3. Department of Electronic Engineering, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong SAR, China

    Hing Cheung So

Authors
  1. Yuan Chen
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  2. Xiao Long Yang
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  3. Long-Ting Huang
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  4. Hing Cheung So
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Contributions

Yuan Chen proposed the algorithm and wrote the paper. Long-Ting Huang implemented the algorithm and performed the simulation. Xiao Long Yang and Hing Cheung So reviewed and revised the manuscript. All authors read and approved the manuscript.

Corresponding author

Correspondence to Long-Ting Huang.

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The authors declare that they have no conflicts of interest.

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Chen, Y., Yang, X.L., Huang, LT. et al. Robust Frequency Estimation in Symmetric \(\alpha \)-Stable Noise. Circuits Syst Signal Process 37, 4637–4650 (2018). https://doi.org/10.1007/s00034-018-0762-3

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  • DOI: https://doi.org/10.1007/s00034-018-0762-3

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