Distribui??o a-k-u bivari?vel - Souza, Geordan Caldeira de (2015)
In wireless communications, the multipath fading in modeled by several distributions including Hoyt, Rayleigh, Weibull, Nakagami-m e Rice. In this dissertation, new, exact expressions for the bivariate a-k-u e k-u correlated in a non-stationary environment are derived. More specifically, the following are obtained: joint probability density function, joint cumulative distribution function, the envelope correlation coefficient, and some statistics related to the signal-to-noise ratio at the output of the selection combiner, namely, outage probability and probability density function. The envelope correlation coefficient is analyzed in terms of typical physical parameters in wireless communications: Doppler, separation between reception points, frequency and the delay spread. The expressions derived are mathematically tractable and have sufficient flexibility to accommodate a large number of correlation sets useful in examination of a more general fading environment. Recently, the fading model a-k-u, and your particular case k-u has been proposed. This model takes into accounts for the non-linearity of the propagation medium as well as for the multipath clustering of the radio waves. The distribution a-k-u is general, flexible, and mathematically easily tractable. It includes important distributions such as a-u, k-u, Gamma (and its discrete versions Erlang and Center Chi-Square), Nakagami-m (and its discrete version Chi), Exponential, Weibull, One-Side Gaussian, and Rayleigh. In this dissertation, a formulation through infinite series for the bivariate a-k-u joint probability density function and non-identically distributed variates is derived. The expression is exact and general and includes all of the results previously published in the literature concerning the distributions comprised by the a-k-u distribution. As an important contribution of this work, all the theoretical results are validated by way of simulation using the Cholesky method, in order to produce correlation between Gaussian variables that make up the process a-k-u and consequently produce the correlation between the variables a-k-u. Additionally, we analyzed the performance of the combiner for maximum ratio and gain equal using the numerical solution of integral and simulations.