Performance analysis of decode-and-forward dual-hop optical spatial modulation with diversity combiner over atmospheric turbulence

Dual-hops transmission is a growing interest technique that can be used to mitigate against atmospheric turbulence along the Free Space Optical (FSO) communication links. This paper analyzes the performance of Decode-and-Forward (DF) dual-hops FSO systems in-conjunction with spatial modulation and diversity combiners over a Gamma-Gamma atmospheric turbulence channel using heterodyne detection. Maximum Ratio Combiner (MRC), Equal Gain Combiner (EGC) and Selection Combiner (SC) are considered at the relay and destination as mitigation tools to improve the system error performance. Power series expansion of modified Bessel function is used to derive the closed form expression for the end-to-end Average Pairwise Error Probability (APEP) expressions for each of the combiners under study and a tight upper bound on the Average Bit Error Rate (ABER) per hop is given. Thus, the overall end-to-end ABER for the dual-hops FSO system is then evaluated. The numerical results depicted that dual-hops transmission systems outperformed the direct link systems. Moreover, the impact of having the same and different combiners at the relay and destination are also presented. The results also confirm that the combination of dual hops transmission with spatial modulation and diversity combiner significantly improves the systems error rate with the MRC combiner offering an optimal performance with respect to variation in atmospheric turbulence, change in links average received SNR and link range of the system.