In this paper, an analytical time-domain model is presented to analyze the radio over free space optical (RoFSO) systems under two turbulence channels, the log-normal and the exponential channel. This analytical model uses general cases of a dual-drive Mach-Zehnder modulator (DD-MZM) and photodetector (PD) for typical optical double sideband (ODSB) and single sideband (OSSB) signals under turbulence channels. This results in output current after a PD as a function of the summation of each frequency component in time domain. Additionally, we derive a closed-form average BER performance under turbulence channels. The numerical result shows that as the scintillation index increases from 0.25 to 0.75 under the log-normal channel, the average BER decreases almost 5.6 dB at the signal power of -30 dBm for ODSB.