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

In this paper, we derive the exact statistical characteristics of the maximum and the minimum of two modified 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 1) a dual-branch free-space optical selection combining (FSO SC) diversity and 2) a dual-hop (DH) FSO 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 (BER) of the two systems at a high signal-to-noise ratio (SNR) regime. Computer-based Monte Carlo simulations verify our new analytical results.