Average achievable rate of spatial diversity MIMO-FSO over correlated Gamma–Gamma fading channels

This paper studies the average achievable rate (AAR) of spatial diversity multiple-input multiple-output (MIMO) free-space optical (FSO) communications over correlated Gamma–Gamma (G-G) fading channels. In particular, we derive the AAR for two different combining techniques at the receiver, namely equal gain combining (EGC) and maximal ratio combining (MRC). Based on atmospheric fading correlation analysis and by employing an approximation method for the sum of correlated G-G random variables (RVs), closed-form expressions for AAR are derived for the EGC scheme. For the case of the MRC technique, we first derive the joint probability distribution of correlated G-G RVs with the arbitrary correlation coefficient. The AAR is then computed based on the use of the moment generating function. Numerical results with practical channel correlation coefficients are presented to demonstrate the negative impact of channel correlation on the system performance. Monte Carlo simulations are also performed to validate the analytical results, and an excellent agreement between the analytical and simulation results is confirmed.