Abstract
In many communication channels the impulsive noise is usually assumed to be of a symmetric alpha stable (SαS) distribution. Unfortunately, except for the Gaussian, Cauchy, and Lévy laws, the analytical expressions for the probability density functions (PDF) of alpha stable distributions are unknown, resulting in very limited application of this distribution. In a practical system, the bi-parameter Cauchy–Gaussian mixture (BCGM) distribution is used to approximate the PDF of the SαS distribution to tackle this difficulty. In this paper, we derive the optimal mixture ratio of the BCGM model based on the minimum square error criterion and furthermore propose a simplified and robust version of BCGM for the SαS distribution. Numerical simulations show that our proposed model achieves better performance and is more robust than the conventional models, without incurring additional complexity.
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Acknowledgements
The authors would like to thank Miss Shui-Qin Chu, Dr. Ke-Lin Du, and Professor Gang Li for their valuable and helpful comments which have improved the presentation. This material is based upon work funded by Zhejiang Provincial Natural Science Foundation of China under Grant No. Y1101077, Zhejiang Provincial Key Science and Technology Innovative Team (2010R5011), and Zhejiang Provincial Education Department Research Project (Y201010060).
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Xu, ZJ., Wang, K., Wu, Y. et al. Minimum-Error-Based Approximation Model for Symmetric Alpha Stable Distribution. Circuits Syst Signal Process 31, 2195–2204 (2012). https://doi.org/10.1007/s00034-012-9423-0
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DOI: https://doi.org/10.1007/s00034-012-9423-0