On the Double-Generalized Gamma Statistics and Their Application to the Performance Analysis of V2V Communications

Important statistical properties of the double-generalized Gamma (dGG) distribution are studied in this paper. The dGG distribution is suitable for modeling non-homogeneous double-scattering radio propagation fading conditions, which can be frequently observed in vehicle-to-vehicle (V2V) communications. In this context, important statistical metrics for the bivariate dGG distribution, such as the joint probability density function, cumulative distribution function, and the moments, are derived for the first time, while simplified expressions for the corresponding marginal statistical metrics are presented. Moreover, the second-order statistics of this distribution are also analytically studied. The derived analytical framework has been employed to analyze the performance of a transmit antenna selection system operating in V2V communication channels modeled by the dGG distribution. In this scenario, the impact of outdated channel state information (CSI) to the system's performance is investigated in terms of various metrics, including the level crossing rate and the average fade duration. Furthermore, simplified asymptotic closed-form expressions for the outage probability have been derived to examine the achievable diversity and coding gains. Based on our analysis, insightful discussions are provided. It is shown that the diversity gain is independent from the number of transmit antennas when the available CSI becomes outdated.