## 1 Introduction  
Due to higher data rates and bandwidth, lower power consumption, free spectrum licensing, and ease of deployment, the FSO communication system has gained increasing attention [1; 2; 3; 4]. However, some drawbacks still exist in the FSO communication system, such as the requirement of line-of-sight (LOS) and performance loss induced by atmospheric turbulence, sensitivity to obstruction, attenuation, and misalignment [5]. Compared with the FSO communication system, RF is not sensitive to atmospheric turbulence and supplies higher mobility and better communication performance in non-line-of-sight (NLOS) conditions [6]. To merge the best features of RF and FSO link, mixed RF-FSO cooperative systems are provided in various works to reduce the impact of atmospheric turbulence and the requirement for LOS, and improve the system performance significantly [7]. As an intermediate, the cooperative relay is deployed in the RF-FSO system to transmit the signal received from the transmitter to the receiver. The relay strategies can be classified as amplify-and-forward (AF) relaying and decode-and-forward (DF) relaying protocols. AF relaying is widely used due to its simplification as compared with DF relaying, in which AF relaying simply amplifies the optical signal while DF decodes the source signal before the signal is forwarded to the optical receiver. Thus, the processing overhead is significantly higher in the case of the DF relaying technique, which increases the overall cost of the communication system. For mixed RF-FSO relaying systems, there are many fading models used in the RF channel and FSO channel. The RF link can be modeled by Rayleigh [8; 9], Nakagami-m [10; 11; 12], generalized \(K-\mu\)[13], and \(K\) distribution [14], and the FSO link can be characterized by Gamma Gamma [8; 9; 12; 15], \(\mathcal{M}\)[16], exponentiated Weibull [10; 13], and so on. In [8], the AF relay is used for a mixed RF/FSO relaying system, in which the RF and FSO link are described by Rayleigh distribution and Gamma-Gamma distribution, respectively. In [10], it is supposed that the RF link is modeled by Nakagami-m distribution and the FSO link follows exponentiated Weibull fading, in which a fixed-gain relay scheme and variable-gain relay scheme are utilized. A dual-hop mixed RF/FSO system is provided in [11], and the RF and FSO links follow Nakagami-m and double generalized Gamma distribution, respectively. An asymmetric dual-hop AF relaying system is considered in [12], and the RF and FSO links are modeled by Nakagami-m fading and Gamma-Gamma fading, respectively. The performance of a mixed RF-FSO system based on DF relay is analyzed in [13], in which RF hop follows \(K-\mu\) shadowed fading and FSO hop adopts the exponentiated Weibull distribution. In [14], a mixed RF/FSO two-way relay (TWR) communication system is investigated, where the fading on the RF and FSO links is modeled using \(\mathcal{K}\)-distribution and the double Gamma turbulence model, respectively. The physical-layer security for a mixed RF/FSO system is investigated in [16], and the \(\alpha-\mu\) distribution is used in the RF link and the FSO link experiences \(\mathcal{M}\) fading with pointing error. Considering multiple variable-gain relays, the outage probability of a mixed RF/FSO system has been studied, in which the channel is modeled by Rayleigh fading and \(\mathcal{M}\) fading with pointing errors for RF and FSO links, respectively [17]. [PERSON] et al. present the performance analysis of mixed RF/FSO systems with an AF relaying scheme in a Nakagami-m and exponentiated Weibull distributed channel [18]. A comprehensive performance analysis is presented in [19], where the RF link is modeled by \(\eta-\mu\) fading with multiuser diversity and the FSO link follows \(\mathcal{M}\)-distribution fading. [PERSON] et al. research a cooperative system with variable-gain relay, in which multiple antennas and multiple apertures are considered in source and destination [20].