Minimum-Error-Based Approximation Model for Symmetric Alpha Stable Distribution

摘要

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 Levy 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 SaS distribution. Numerical simulations show that our proposed model achieves better performance and is more robust than the conventional models, without incurring additional complexity.