Circuits, Systems, and Signal Processing

, Volume 38, Issue 7, pp 3170–3186 | Cite as

A Robust Parameter Estimation of LFM Signal Based on Sigmoid Transform Under the Alpha Stable Distribution Noise

  • Li LiEmail author
  • Tianshuang Qiu


In this paper, a novel method, which employs the fractional Fourier transform and the Sigmoid transform, is proposed to estimate parameters of the linear frequency modulation (LFM) signal under the alpha stable distribution noise environment. Two novel functions, Sigmoid fractional correlation function and Sigmoid fractional power spectrum density (Sigmoid-FPSD), are defined. Basing on these two definitions, a novel method based on Sigmoid-FPSD under alpha stable distribution noise is proposed to estimate parameters of the LFM signal. Moreover, boundedness of Sigmoid-FPSD to the \( S\alpha S \) noise and the feasibility analysis of the Sigmoid-FPSD are presented to evaluate the performance of the proposed method. Both theoretical analysis and simulations demonstrate the superior performances of the proposed approach over other existing methods. Furthermore, the proposed method does not need a priori knowledge of noise with higher estimation accuracy in alpha stable distribution noise environment.


Alpha stable distribution noise Sigmoid transform Fractional power spectrum density LFM signal Parameter estimation 



This work was partly supported by the National Natural Science Foundation of China under Grants 61401055 and 61671105, the Ph.D. Programs Foundation of Liaoning Province of China 20170520421 and the China Scholarship Fund.


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.College of Information EngineeringDalian UniversityDalianPeople’s Republic of China
  2. 2.Department of Electrical and Computer EngineeringMississippi State UniversityMississippi StateUSA
  3. 3.Faculty of Electronic Information and Electrical EngineeringDalian University of TechnologyDalianPeople’s Republic of China

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