###### Abstract  
Optical satellite communication has received considerable attention as a promising alternative to radio frequency communication because of its potential advantages including higher data rates and license free spectrum. Many studies have conducted performance analyses of optical communication channels, but few have investigated beacon tracking channels under atmospheric turbulence. The centroid accuracy of beacon tracking channels is limited by not only noise sources, but also a finite delay time, which also fluctuates due to atmospheric turbulence. Consequently, the centroid error is an important figure of merit when evaluating the performance of a beacon tracking system. In this study, the closed-form expressions were derived for average centroid error and fade probability, based on received photoelectron counts depending on exposure time, taking into account the log-normal tracking channels. We analyzed the angular positioning performance of beacon tracking detectors onboard small satellites in the presence of atmospheric turbulence, in terms of centroid error and fade probability. We found that an optimal exposure time exists, which minimizes the centroid error, and that fade probability is inversely proportional to the exposure time. These are significant properties to consider in the design of beacon tracking systems. satellite optical communication; beacon tracking; centroid error; fade probability; log-normal tracking channel 2021131931[[https://doi.org/10.3390/rs13101931](https://doi.org/10.3390/rs13101931)]([https://doi.org/10.3390/rs13101931](https://doi.org/10.3390/rs13101931)) 10. The FPA detector provides not only more precise and faster LOS alignment, but also a narrower steering angle. To accomplish this, it employs a fast steering mirror and a position-sensitive detector such as quadrant PIN photodiode (QPD) or quadrant avalanche photodiode (QAPD). The position-sensitive detectors have several advantages over classical image sensors including better positioning accuracy, a faster response time, and very simple signal conditioning circuits [9]. The CPA have to be able to control several-centimeter-class telescopes within a pointing accuracy of sub-micro radians for planetary missions, or several micro radians for Earth orbiting missions, and its bandwidth should also be larger than 1 kHz to accommodate the pointing jitters caused by the satellite platform vibration and atmospheric turbulence [4; 8; 10; 11; 12]. Because of the relative velocity of the two terminals and the finite speed of light, an angular offset exists between the transmitting and received beams, the so-called point-ahead angle. The magnitude of angular offset is achievable with the help of known ephemeris data, up to 70 micro radians for inter-satellite links and as much as 500 micro radians for interplanetary links [13; 14; 15]. The PAA compensates the point-ahead angle by controlling the fast steering mirror if the angle is comparable to or larger than the transmitting beamwidth. Figure 1 shows the block diagram of the optical communication terminal including the PAT system with two types of actuators: gimbal and fast steering mirror (FSM). When a beacon beam propagates through the atmosphere, it can be adversely affected by atmospheric turbulence including atmospheric scintillation such as intensity and phase fluctuations, angle of arrival fluctuations, beam spot wandering, and spatial beam spreading [16; 17; 18]. The beacon image follows the point spread function of the imaging optics since the uplink beacon can be regarded as a point source rather than an extended object [19], which can be distorted and blurred by atmospheric turbulence. Therefore, the centroid error of beacon images on a beacon detector depends on atmospheric turbulence as well as the exposure time, which plays a great role in the signal-to-noise ratio (SNR).