###### Abstract
The limited accuracy of beacon detectors has been analyzed in terms of the noise equivalent angle, known as the random centroid error [20; 21; 22], particularly in the field of adaptive optics to evaluate the Shack-Hartmann wavefront sensors [23; 24; 25; 26; 27]. However, the intensity fluctuations resulting from atmospheric turbulence were not taken into consideration in these reports to precisely assess the centroid error. Over the years, many mathematical models have been proposed to describe the turbulence-induced scintillation in terms of probability density functions including the log-normal, K-channel, negative exponential, and gamma-gamma models [28; 29; 30; 31; 32]. Specifically, the log-normal and gamma-gamma models are widely used due to their simplicity and good agreement between the  
Figure 1: Block diagram of the optical communication terminal with monostatic architecture. theoretical and experimental data. Consequently, they have been found to be suitable for weak-to-moderate and moderate-to-strong turbulence conditions, respectively [33]. An accurate centroid estimation is critical to the beacon tracking system to point the optical beam toward the partner terminal, so that sufficient optical power is received to meet the data rate and bit error rate performance requirements. This makes it essential, when evaluating the pointing capability of a PAT system, to analyze the centroid error intrinsic to noise sources and the finite delay time under atmospheric turbulence. Korea has a plan to conduct an optical downlink experiment employing a CubeSat that requires not only the use available commercial off-the-shelf (COTS) components for a reduction in development costs, but also accurate pointing and tracking capabilities under the size, weight, and power constraints for a reliable communication link. Thus, the beacon tracking system onboard a CubeSat should be designed through a trade-off between two requirements for COTS components as well as pointing and tracking capabilities over fade channels. In this study, the SNR formula of position-sensitive detectors was given in terms of the received photoelectron count depending heavily on the exposure time, which also includes shot noise, background noise, dark current, and thermal noise. Taking into account the log-normal tracking channels, the closed-form models were derived for two metrics, average centroid error and fade probability in the function of the received photoelectron count. For practical applications, the received photon count was estimated by considering turbulence-induced beam spreading and atmospheric attenuation due to atmospheric constituents and cirrus clouds. We analyzed the angular positioning performance of an uplink beacon system for two metrics in terms of exposure time and atmospheric turbulence strength using CMOS and QAPD detectors. We found from numerical simulations that an optimal exposure time exists, which minimizes the centroid error resulting from noise sources and the exposure time latency. However, fade probabilities decreased rapidly as the exposure time was extended and atmospheric turbulence became strong. These characteristics should be taken into account in a trade-off of the design of the beacon tracking system requiring high bandwidth and high positioning accuracy.