Free Space Optical (FSO) communication systems are easily affected by atmospheric turbulence effects. In order to reduce the Bit Error Rate (BER) of the system under saturated turbulence condition, and considering the requirement of maximum diversity gain under limited Signal Noise Ratio (SNR) in practical engineering, it is necessary to study the diversity performance of the system to obtain the relationship between diversity gain and parameters such as SNR and system link number. This article uses Multiple-Input-Multiple-Output (MIMO) technology to design a MIMO-FSO system based on Quadrature Amplitude Modulation (QAM). The performance of the system in a negative exponential distribution channel model is analyzed, and the BER calculation formula and closed form expressions of diversity gain related parameters (such as Diversity Order (DO), Incremental Diversity Order (IDO), and speed of convergence (SOC)) are derived. Simulation experiments are conducted using mathematical software such as Matlab to verify the accuracy of the derived formula through Monte Carlo simulation. The simulation results show that MIMO the technology can significantly reduce the BER of FSO systems without increasing the transmission power and receiving aperture area. Moreover, in saturated turbulent channels, when the number of system links increases or the turbulence intensity decreases, the diversity order increases to the theoretical maximum with the SNR at a faster rate. The MIMO technology effectively suppresses the negative impact of atmospheric turbulence on the system and significantly improves system performance. When conditions are satisfied, using more transmitters and receivers can achieve higher diversity gain in the system under limited SNR. However, it is also necessary to consider the deployment cost and installation difficulty in actual engineering to choose the appropriate number of links.