Proof of Proposition 2.

<div><p>This paper investigates the performance of hybrid radio frequency/free space optical (RF/FSO) systems combined with non-orthogonal multiple access communications technology. We examine a scenario where the source and destination are separated by a large distance, with no direct link between them. The relay, denoted R, operates using the decode-and-forward (DF) protocol. Under the DF relaying scheme, the relay employs successive interference cancellation (SIC). In this setup, the FSO link from the source to the relay follows a Gamma-Gamma distribution, while the RF link from the relay to multiple users follow a Nakagami-<i>m</i> distribution. Based on this system model, we analyze the outage probability (OP). Our findings indicate a direct relationship between SIC and OP performance: the higher the SIC capability, the more effective the system. In addition, the system’s performance is dependent on the parameters of the FSO channel. Finally, Monte Carlo simulations are presented to further validate our framework and findings.</p></div>