Modeling alpha-stable interference in the presence of Gaussian noise and its applications to communication systems

It is well known that the performance of communication systems is limited by the presence of unwanted energy. These are typically classified based on their sources and characteristics as either noise or interference. Noise is generally modeled as additive white Gaussian noise which is especially attractive from a practical point of view due to the existence of a corresponding closed form probability density function (pdf). However, wireless communication systems are also subject to interference from other users. In a homogeneous Poisson distributed network of users, this interference may be modeled as following a symmetric alpha-stable (SS) distribution. However, this model does not lend itself easily to practical implementations due to a lack of a closed form pdf either in the univariate or bivariate case except in very few special cases. This problem is further accentuated when both forms of the unwanted energy are present. In this dissertation, we propose to approximate the pdf of the combination of these two forms of noise by a simple, parametric closed form expression which lends itself very easily to real time implementations, both for the univariate and the bivariate cases.;We first consider the univariate case. Using the properties of the Gaussian and SS distributions, we propose a parametric form of the combined noise pdf. We show the excellent agreement of the proposed result with the numerically computed exact pdf and also show the application of this model in design of detectors in communication systems. The bit error rate results show that the proposed model is nearly optimal (difference of less than 0.1dB) for a wide range of noise parameters at a fraction of the computational complexity of the numerical approach. We further show that these results may be generalized to the spherically symmetric bivariate case and, as a byproduct, to the corresponding amplitude probability densities.