Spatial correlation for transmitters in spatial MIMO optical wireless links with Gaussian-beam waves and aperture effects

The spatial correlation between signals arising from a pair of constituent transmitters in a spatial multiple-input–multiple-output (MIMO) system is investigated. General formulations for the spatial correlation functions considering Gaussian-beam waves and receiver aperture effects are given under weak turbulence condition. Based on the analytical expressions, we find that spatial correlation decreases with separation distance, but increases with receiver aperture sizes, turbulence strength and wavelengths. In particular, receiver aperture averaging effects can evidently increase the correlation. It is also shown that decreasing the beam widths can generally reduce the spatial correlation, and convergent beams have lower spatial correlation than their collimated counterparts. It is found that Gaussian beams with the Fresnel ratios larger than 1 have advantages in reducing both the spatial correlation and the beam scintillations.