  In this paper, the performance of two-way relaying in mixed RF/FSO
communication system with a backup RF link is investigated. Uplink RF channels
are used to send data of $K$ users to a two-way relay, $R$, whereas FSO link is
mainly used to exchange data between a base station $S$ and $R$. We propose to
have a backup RF link between the relay $R$ and the node $S$ to improve
reliability under certain conditions. All uplink RF channels follow Rayleigh
fading model while $\alpha$-$\mu$ is adopted to model both backup RF and FSO
links. We approximate the widely used Gamma-Gamma fading model using the
$\alpha$-$\mu$ distribution based on moments-based estimator technique assuming
perfect alignment between transmitter and receiver antennas. This approximation
shows good agreement under certain atmospheric turbulence conditions. Then, we
derive exact closed-form expressions for the outage and average symbol error
probabilities and derive approximations at high signal-to-noise ratio (SNR). We
corroborate our analytical expressions with extensive Monte-Carlo simulations
and demonstrate exact match. Furthermore, we analyze the effect of number of
nodes, opportunistic scheduling among $K$ nodes, and $\alpha$-$\mu$ parameters
on the overall performance of mixed RF/FSO and backup RF systems. Our numerical
results illustrate an achievable coding gain when increasing $K$; however,
performance degradation occurs as the relay applies selection that favors the
domination of specific links in the system.
