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Considering the influence of more random atmospheric turbulence, worse pointing errors and highly dynamic link on the transmission performance of mobile multiple-input multiple-output (MIMO) free space optics (FSO) communication systems, this paper establishes a channel model for the mobile platform. Based on the combination of Alamouti space-time code and time hopping ultra-wide band (TH-UWB) communications, a novel repetition space-time coding (RSTC) method for mobile 2×2 free-space optical communications with pulse position modulation (PPM) is developed. In particular, two decoding methods of equal gain combining (EGC) maximum likelihood detection (MLD) and correlation matrix detection (CMD) are derived. When a quasi-static fading and weak turbulence channel model are considered, simulation results show that whether the channel state information (CSI) is known or not, the coding system demonstrates more significant performance of the symbol error rate (SER) than the uncoding. In other words, transmitting diversity can be achieved while conveying the information only through the time delays of the modulated signals transmitted from different antennas. CMD has almost the same effect of signal combining with maximal ratio combining (MRC). However, when the channel correlation increases, SER performance of the coding 2×2 system degrades significantly.