Communications and Signal Processing Lab (ComSP)

Title	Analysis of Gaussian Quadratic Forms with Application to Statistical Channel Modeling
State	Finished
Author	Pablo Ramírez Espinosa
Director/s	Eduardo Martos Naya ,  José Antonio Cortés Arrabal
University	Universidad de Málaga
Center	Escuela Técnica Superior de Ingeniería de Telecomunicación
Department	Departamento de Ingeniería de Comunicaciones
Reading date	24/01/2020
File	PDF

This thesis provides novel and tight approximations to the distribution of both real

and complex non-central Gaussian quadratic forms (GQFs). To that end, a new method

to analyze random variables is proposed, which is based on the analysis of a suitably defined

sequence of auxiliary random variables that converges in distribution to the target

one. Consequently, the major advantage of this proposal is that the resulting expressions

always represent a valid distribution, in contrast to classical approximation methods

based on series expansions.

By leveraging such convergence, simple and recursive approximations for the probability

density function (PDF) and the cumulative distribution function (CDF) of positive

definite real GQFs are given. In the context of indefinite complex GQFs, the application

of the proposed technique leads to very tractable approximants for their first order statistics

in terms of elementary functions, i.e., exponentials and powers. Thus, the obtained

expressions are more useful for further analytical purposes than other solutions available

in the literature. This tractability is exemplified through the performance analysis of

maximal ratio combining systems over correlated Rice channels, providing closed-form

approximations for the outage probability and the bit error.

Moreover, in the context of channel modeling, the proposed methodology of analysis

of variables gives raise to two generalizations of the well-know k-u shadowed fading

model. These new models, namely the fluctuating Beckmann and the correlated k-u

shadowed models, include as particular cases the vast majority of fading distributions,

ranging from the classical ones such as Rayleigh and Rice models to more refined extensions

as the Beckmann distribution or the n-u model. The statistical characterization

of both distributions is provided, giving closed-form expressions for their moment generating

function (MGF), PDF and CDF; along with the formulation of the second order

statistics of the fluctuating Beckmann model.