Free-space optical communication (FSO) is a wireless communication technology that uses light to transmit data in free space. The main advantages of FSO are higher bandwidth, low maintenance costs, low power consumption, flexibility, a license-free frequency band, high speed, and security. However, its performance is limited due to geometric loss, atmospheric attenuation, and atmospheric turbulence, which deteriorate the performance of the link. To alleviate this problem, a multiple-input multiple-output (MIMO) system is used. Additionally, a coherent receiver with digital signal processing (DSP) algorithms is used to improve channel capacity, receiver performance, and link range. In this thesis, the performance of a gray-coded dual polarization-16 quadrature amplitude modulation (DP-16 QAM)-based MIMO FSO link using coherent detection and DSP operating at a data rate of 120 Gbps and a symbol rate of 15 GBaud is investigated. The performance of the system is evaluated by constellation diagrams, RF and optical power spectra, bit error rate (BER), and error vector magnitude (EVM). It is observed that before DSP, the constellation diagrams are distorted, whereas after DSP, distinct constellation symbols are observed. In clear air conditions, as a result of gray code, a link range improvement of 0.08 km, 0.1 km, 0.14 km, and 0.15 km for SISO-strong, SISO-weak, 4x4 MIMO-strong, and 4x4 MIMO-weak turbulence levels, respectively, are achieved. The longest link range to attain the acceptable BER limit is achieved under 4x4-MIMO weak turbulence levels in clear air conditions, which is 11.55 km, while the shortest is achieved under SISO-strong turbulence levels in light fog conditions, which is 0.895 km. An OSNR penalty of 8.64 dB, 1.816 dB, 1.48 dB, and 0.495 dB is observed for SISO-strong, SISO-weak, 4x4 MIMO-strong, and 4x4 MIMO-weak turbulence levels, respectively, as compared to the back-to-back (B-2-B) case in medium rain conditions. The system possesses a spectral efficiency of around 4.62 b/s/Hz and 5.871 b/s/Hz for DP-16 QAM and DP-32 QAM modulation formats, respectively. However, in wet snow conditions, a maximum link range of 2.145 km and 2.548 km for DP-32 QAM and DP-16 QAM modulation formats, respectively, is achieved in a 4x4 MIMO link under weak turbulence levels. After the channel impairments are mitigated by DSP, the simulation results show that the MIMO link outperforms the SISO link in all scenarios. Keywords: Coherent detection, DP-16 QAM, DSP, FSO, Gray code, MIMO