Large-aperture receiving is one of the effective approaches to overcome the impact of turbulence on atmospheric optical communications. Based on the irradiance fluctuation theory for finite apertures,the relationship between the average signal-to-noise ratio and the quantities of the signal-to-noise ratio without turbulence,the aperture averaging factor and the irradiance fluctuation variance was mathematically modeled,and the formula of bit error rate (BER) was derived. The curves of relationship between the aperture diameter and the signal-to-noise ratio without turbulence at a given BER with various turbulence parameters were obtained numerically.