Approximation algorithm to symmetric alpha stable distribution with bi-region curve model

Abstract

The symmetric alpha stable (S S) was used to model a non-Gaussian,heavy tail and impulsive noise of com-α munication channels.However,explicit expressions for the probability density functions (PDF) in terms of elementary functions are still unknown except for some special cases,which limits the application of the SαS distribution in practice,which the bi-region separated by the triple divergence was proposed Specially,within the triple divergence,a simple exponential function with two special parameters was constructed,the two parameters were determined by using Taylor serial expansion.Compared with conventional algorithms using the series expansion,the proposed algorithm avoids the selecting the number of the series items and the risk of series expansion divergence.Moreover,numerical results verify that the proposed approximation is closer to the actual SαS PDF than the conventional Cauchy-Gaussian mixture approximation.

Keywords

• piecewise approximation;series expansion;probability density function;symmetric stableα