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Information Technology Journal

Year: 2012 | Volume: 11 | Issue: 8 | Page No.: 1121-1126
Research Article

A Robust and Simple Piecewise Approximation to SαS Distribution with Bi-Region Model

Kang Wang
Zhejiang Police College, Hangzhou, 310053, China
Zhi-Jiang Xu
College of Information Engineering, Zhejiang University of Technology, Hangzhou, 310023, China
Yuan Wu
College of Information Engineering, Zhejiang University of Technology, Hangzhou, 310023, China
Jing-Yu Hua
College of Information Engineering, Zhejiang University of Technology, Hangzhou, 310023, China
As a non-Gaussian model, the alpha stable distribution has gained much attention because of its generality to model the heavy-tail and impulsive noise which is widely observed in many communication channels. Unfortunately, there exists no analytic expression for the Probability Density Function (PDF) of Symmetric Alpha Stable (SαS) distribution. In order to approximate the PDF of SαS, we propose a bi-region curve approximation algorithm with the bi-region separated by the triple divergence. Specially, within the triple divergence, we propose a penalty function with two special parameters and adopt a very simple and effective exponential function for approximation. Different from the existing algorithms using the series expansion, our model avoids the problem of selecting the number of the series items and the risk of series expansion divergence. Compared with the conventional Cauchy-Gaussian mixture approximation, our derivation emploits the simple bi-region approximation and yields a very simple and closed-form expression. Numerical results verify that our approximation is very close to the actual PDF of SαS.
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References

  1. Brcich, R. and A. Zoubir, 1999. Estimation and detection in a mixture of symmetric α stable and Gaussian interference. Proceedings of the IEEE Signal Processing Workshop on Higher-Order Statistics, June 14-16, 1999, ISREEL, Caesarea, Israel, pp: 219-223.
  2. DuMouchel, W.H., 1973. On the Asymptotic normality of the maximum-likelihood estimate when sampling from a stable distribution. Ann. Statist., 1: 948-957.
    CrossRefDirect Link
  3. Goegebeur, Y., V. Planchon, J. Beirlant and R. Oger, 2005. Quality assessment of pedochemical data using extreme value methodology. J. Applied Sci., 5: 1092-1102.
    CrossRefDirect Link
  4. Khamnei, H.J., H. Bevrani and A.A. Haydari, 2008. Parameter estimation for the heavy tailed distributions with the empirical distribution. J. Applied Sci., 8: 1118-1121.
    CrossRefDirect Link
  5. Hong, T., T. Qiu and W. Zhang, 2005. Signal tracking with adaptive array in impulse noise environment. J. Commun., 26: 22-27.
  6. Ge, H. and W. Song, 2011. A novel adaptive regularized possibilistic linear models based median filter ARBMF for image noise suppression. Inform. Technol. J., 10: 2260-2267.
    CrossRefDirect Link
  7. Wang, K.H., C.Q. Zhang and J.L. Xu, 2010. Improved design of trellis space-time code for high spatial-and multipath diversity in MIMO-OFDM fading channels. Inform. Technol. J., 9: 1294-1305.
    CrossRefDirect Link
  8. Xutao, L., J. Lianwen and W. Shouyong, 2008. A simplified non-gaussian mixture model for signal LO detection in a-stable interference. Procedings of the Congress on Image and Signal Processing 2008. May 27-30, 2008, Sanya, China, pp: 403-407.
  9. Li, X., Z. Chen and S. Wang, 2008. An approximate representation of heavy-tailed noise: Bi-parameter Cauchy-Gaussian mixture model. Proceedings of the 9th International Conference on Signal Processing 2008, October 26-29, 2008, South China University of Technology, Beijing, China, pp:76-79.
  10. Zhaogan, L., W. Liejun, Z. Taiyi and R. Yun, 2007. A new steiner channel estimation method in MIMO OFDM systems. Inform. Technol. J., 6: 1238-1244.
    CrossRefDirect Link
  11. Nikias, C.L. and M. Shao, 1995. Signal Processing with α-Stable Distributions and Applications. John Wiley and Sons, New York, ISBN:0-471-10647-X.
  12. Nakagawa, H., D. Umehara, S. Denno and Y. Morihiro, 2005. A decoding for low density parity check codes over impulsive noise channels. Proceedings of theInternational Symposium on Power Line Communications and Its Applications, April 6-8, 2005, Kyoto University, Japan, pp: 85-89.
    CrossRef
  13. Karim, S.A.A., B.A. Karim, M.T. Ismail, M.K. Hasan and J. Sulaiman, 2011. Application of wavelet method in stock exchange problem. J. Applied Sci., 11: 1331-1335.
    CrossRef
  14. Kadry, S., 2007. Probabilistic analysis of eigenvalue of stochastic systems. J. Applied Sci., 7: 565-569.
    CrossRefDirect Link
  15. Kadry, S. and K. Smaili, 2007. An effective method for exact reliability analysis. J. Applied Sci., 7: 2333-2338.
    CrossRefDirect Link
  16. Shao, M. and C.L. Nikias, 1993. Signal processing with fractional lower order moments: Stable processes and their applications. Proc. IEEE, 81: 986-1010.
    CrossRefDirect Link
  17. Swami, A., 2000. Non-Gaussian mixture models for detection and estimation in heavy-tailed noise. IEEE Int. Conf. Acoust Speech Signal Process Proc., 6: 3802-3805.
    CrossRefDirect Link
  18. Waheed, A., 2003. Characterization of a campus network traffic. J. Applied Sci., 3: 40-46.
    CrossRefDirect Link
  19. Liejun, W., 2011. An improved water-filling power allocation method in MIMO OFDM systems. Inform. Technol. J., 10: 639-647.
    CrossRefDirect Link
  20. Shitong, W., L. Yueyang, F.L. Chung and C. Shu, 2005. Iterative self-adaptive filtering algorithm for reducing impulsive noise in color images. Inform. Technol. J., 4: 456-461.
    CrossRefDirect Link
  21. Zolotarev, V.M. and V.V. Uchaikin, 1999. Chance and Stability, Stable Distributions and Their Applications. Walter de Gruyter, Berlin, Germany, ISBN: 978-9067643016.

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