## 2 Related Works
The LoS holding distance, which is a random variable, represents how far LoS conditions persist, depending on varying clutter densities and the satellite elevation angle. In reference [27], the channel performance of a terrestrial FSO communication system is investigated and, in order to model the situation in which fading causes correlated frame loss, a two-state Markov chain that is similar to the cases considered is used. This model is defined as a Gilbert-Erasure channel model. The credibility of the proposed model is experimentally validated with measured frame loss statistics from typical scenarios. Several mathematical models that describe the cumulative distribution functions (CDFs), \(\mathcal{G}(z)\), or probability density functions of the received signal power, \(z\), have been used for terrestrial atmospheric optical communications [27] and hybrid FSO/RF communications [28; 29; 30]. This approach is employed to evaluate the probability of communication system failure, defined as an event in which the instantaneous signal-to-noise ratio (SNR) falls below a predefined threshold. Specifically, the system operates as follows: communication between the signal source and the relay node is maintained via FSO links if the instantaneous SNR at the receiver exceeds the FSO threshold \(\gamma_{th}^{f}\). If the SNR drops below \(\gamma_{th}^{f}\), the system switches to millimeter-wave RF channels, provided that the instantaneous SNR meets the threshold for RF links. However, if the SNR for both FSO and RF links is below their respective thresholds, the system experiences a shutdown. This ignores the possibility of improving the SNR at the receiver by increasing the power of the outgoing signal or changing the network topology. Therefore, the system model can be described by a three-state stochastic process [29; 30]. The refusal to use the FSO is calculated using the CDF as follows: \(\mathcal{G}(\gamma_{th}^{f})\). The derived mathematical expressions for the CDF-based performance metrics are formulated in terms of [PERSON]'s G-function [31], which is less practical for analysis. The CDF expressions involve numerous parameters that characterize the environment, such as the effective number of small- and large-scale eddies in the scattering medium [28]. The stochastic nature or uncertain variability of these parameters further complicates the models. Hence, it is preferable to utilize channel models with simplified closed-form expressions for their description, where parameters are clearly defined and directly measurable [27; 32]. In recent papers [33; 34] on FSO/RF hybrid communication systems, a hard-switchingapproach is employed, wherein the system transitions to the RF mode based on a direct comparison of the FSO link's SNR with a predefined threshold. However, these works do not account for the dynamics of state transitions or the temporal evolution of the communication process between modes. In [35], users transmit signals to a repeater over RF channels affected by Rayleigh fading, after which the repeater forwards the decoded signal to the destination via an FSO channel with turbulence. However, the possibility of switching between FSO and RF based on environmental conditions is not considered. This influenced the direction of our subsequent research. To the best of our knowledge, no prior work has extended the Gilbert-Elliott model to the context of hybrid RF/FSO communication systems, nor has any study derived analytical expressions for the state probabilities of such a system.