## 1 Introduction  
Free-space optical (FSO) communication has attracted considerable attention due to its advantages of lower cost, higher data rates, and higher security for many wireless communication applications [1, 2]. FSO communication is therefore considered a promising technology that will play a significant role in research on fifth-generation and even sixth-generation communication [3, 4]. However, an FSO communication system is hampered by several challenges when an optical wave propagates in atmospheric turbulence [5]. The intensity of the optical signal fluctuates during this period, in a process referred to as scintillation, since the refractive index of the atmosphere turbulence changes randomly as a result of variations in the atmospheric temperature and atmospheric pressure [6, 7]. Recently, several probability distribution functions (PDFs) have been proposed for various channel models to characterize the fading process of the optical signal in atmospheric turbulence. For turbulence under weak condition, the lognormal fading model is employed, as the signal obeys a lognormal distribution [8, 9]. In view of the influence of atmospheric turbulence under the weak conditions on an optical signal, the performance metrics of the FSO system with maximum-likelihood detection are investigated under the weak turbulence with a lognormal model [10]. In addition, a negative exponential model has been proposed, and has been shown to be a suitable model for strong and even saturation scintillation [11]. In [12], the negative exponential distribution was employed to model FSO links with fading statistics, and the outage probability and the average capacity of the communication system were studied under some limited conditions for the practical applications. Derived from the lognormal model, the \(K\) turbulence channel model has also been proposed for strong turbulence conditions [13]. A study of the propagation of laser light with \(K\) distribution was carried out in [14; 15]. In addition, [PERSON] et al. proposed exact expressions for the bit error rate (BER) and channel capacity for an FSO communication system under both lognormal and \(K\) distribution conditions. In order to investigate atmospheric turbulence under moderate-to-strong conditions, the Gamma-Gamma distribution was proposed in [16]. The performance of an FSO system in terms of the outage probability, average BER, and ergodic capacity in various communication scenarios, such as an unmanned aerial vehicle (UAV)-based optical communication, inter-satellite/satellite-ground laser communication, and underwater optical communication, has been extensively studied [17; 18; 19]. In addition to atmospheric turbulence, noise (such as thermal noise, background noise, quantum noise, etc.) also has a significant influence on the FSO communication system. During the transmission process with high symbol rates, heating emerges on the device [20; 21]. Therefore, a variation in temperature can be produced, giving rise to thermal noise [22; 23]. Due to the wave-particle duality of optical signals, this type of transmission is also called quantum transmission. At the receiving end, a photodetector receives these quanta of light. The change in phase arising from various factors such as jitter at the detector results in a decline in the number of photons received, an effect which is known as quantum noise [24]. In addition to effects created by devices, background noise from manual operation and environmental noise also need to be considered [25]. Recently, several works have investigated the influence of various types of noise on FSO communication system. For instance, the effects of both an avalanche photodiode (APD) and thermal noise on an optical system with binary phase-shift keying (BPSK) subcarrier-intensity modulation over weak-to-strong turbulence channels are discussed in [6]. The effects of both pointing errors and phase noise on the terrestrial-FSO link have also been studied for a subcarrier phase-shift keying (PSK) modulation scheme [26].