On Second-Order Statistics of the Composite Channel Models for UAV-to-Ground Communications with UAV Selection

Unmanned-aerial-vehicles (UAVs) are intended to be a vital part of beyond 5G (B5G) and 6G communication networks. UAV-to-ground communications in urban and populated areas are usually exposed to highly variable propagation conditions that can be often characterized by composite fading channels. This paper provides mathematical framework for the performance evaluation of UAV-to-ground communications over double-scattered single-shadowed (DS-SS), and double scattered double shadowed (DS-DS) fading channels. To analyse in details we provide probability density function (PDF), cumulative distribution function (CDF), average fade duration (AFD) and level crossing rate (LCR) of the product of double Nakagami-m (DN) and single inverse Gamma (SIG) random processes (RPs), as well as the product of DN and double inverse Gamma (DIG) RPs. Furthermore, the derived integral-form formulas for the second order (SO) statistical measures are approximated by Laplace integration (LI) and exponential LI in order to provide closed-form expressions. The impact of DS-SS and DS-DS fading types on the SO statistics of UAV-to-ground propagation scenario are thoroughly examined. Moreover, the impact of different values of DS-SS and DS-DS fading severities on the SO statistics are also taken into investigation. Lastly, the proposed UAV-to-ground model is extended to include the SO performance analysis of L-number of UAVs. All the analytical results for the SO statistics are confirmed by Monte-Carlo simulations.