On the Sum of α-F and Double α-F VariatesWith Application to MRC and RIS

In this letter, a statistical framework is presented for the sum of $\alpha $ - ${\mathcal{F}}$ and double $\alpha $ - ${\mathcal{F}}$ random variates. The statistical results are applied in two scenarios: i) communication systems with maximum ratio combiner (MRC)-based receivers, in which new expressions are derived for the bit error probability (BEP), the outage probability (OP), and the area under the receiver operating characteristics (AUC) curve; and ii) reconfigurable intelligent surfaces (RIS)-aided wireless systems, in which novel expressions for the BEP and OP are deduced. In some cases, an asymptotic analysis is provided. Curves are presented and the theoretical results are corroborated by Monte-Carlo simulations.