On the Maximum and Minimum of Double Generalized Gamma Variates with Applications to the Performance of Free-space Optical Communication Systems

In this work, we derive the exact statistical characteristics of the maximum and the minimum of two modified1 double generalized gamma variates in closed-form in terms of Meijer’s G-function, Fox’s H-function, the extended generalized bivariate Meijer’s G-function and H-function in addition to simple closed-form asymptotic results in terms of elementary functions. Then, we rely on these new results to present the performance analysis of (i) a dual-branch free-space optical selection combining diversity and of (ii) a dual-hop free-space optical relay transmission system over double generalized gamma fading channels with the impact of pointing errors. In addition, we provide asymptotic results of the bit error rate of the two systems at high SNR regime. Computer-based Monte-Carlo simulations verify our new analytical results.