Using space as an additional degree of freedom is one possible solution to cope with future bandwidth issues. In free-space optics (FSO), spatial multiplexing of structured light modes is limited by the impact of the atmospheric turbulence. Therefore, beating the effects of turbulence is a major problem for structured light-based FSO communication. Here, we model the propagation of Laguerre-Gaussian beams using a modified von Kármán turbulence model with time-dependent turbulence phase screens. We equally investigate the performance of a zero-forcing pre-coding technique to mitigate the effects of turbulence in a full-duplex Laguerre-Gaussian mode based FSO. In the modeling, we account for various limiting factors, including phase estimation errors, noise, imperfect, and outdated channel-state information on the pre-coding approach.