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Information Technology Journal

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

Kang Wang

Zhi-Jiang Xu

Yuan Wu

Jing-Yu Hua

Keywords

Research Article

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

Kang Wang, Zhi-Jiang Xu, Yuan Wu and Jing-Yu Hua
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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