Abstract
The probability density function (PDF) of the symmetric alpha-stable distribution is investigated using the inverse Fourier transform of its characteristic function. For general values of the stable parameter alpha, it is shown that the PDF and the cumulative distribution function of the symmetric stable distribution can be expressed in terms of the Fox H function as closed-form. As an application, the probability of error of single input single output communication systems using different modulation schemes with an alpha-stable perturbation is studied. In more details, a generic formula is derived for generalized fading distribution, such as the extended generalized-K distribution. Later, simpler expressions of these error rates are deduced for some selected special cases and compact approximations are derived using asymptotic expansions.