On the correlated Gamma–Gamma distribution and coherent detection performance of optical spatial modulation

The performance of optical spatial modulation (OSM) is severely damaged by correlated atmospheric turbulence (AT) channels for coherent free-space optical (FSO) communication systems. In this paper, we assume correlated AT channels comply with Gamma–Gamma distribution and present a coherent FSO-OSM system model. Based on this, we derive the closed-form approximated expressions of average symbol error probability (ASEP), and discuss the interaction of signal constellation diagram and spatial constellation diagram of the OSM under different conditions. We further illustrate relations of the ASEP caused by signal constellation and spatial constellation to AT strength and correlation. In addition, we explore the impact trends of the correlation coefficients respectively resulted from large-scale and small-scale eddies on the performance of system under different AT conditions. Through simulations, we prove theoretical results and demonstrate that the rise of AT severity and correlation coefficients can degrade the performance of coherent OSM.