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The propagation performance of a free-space optical (FSO) communication system in an atmospheric environment is restricted and degraded due to the influence of atmospheric turbulence. In this paper, both the lognormal and Gamma–Gamma channel models are employed to characterize this turbulence under weak-to-strong conditions. In addition, the average bit error rate and average channel capacity of an FSO communication system under the influence of background noise, thermal noise and quantum noise (resulting from the environment, the device, manual operation, etc.) are considered. Moreover, the comparison of system performance under different turbulence conditions and various noises are conducted. Simulation results reveal that thermal noise has a dominant effect on the FSO system. In addition, both the channel parameters and the system parameters have a significant influence on the performance of an FSO communication system.