Inter-aperture correlation in MIMO free space optical systems

We present a unified framework for determining the inter-aperture separations in multiple-input-multiple-output (MIMO) free space optical (FSO) systems such that the transmitter-receiver paths are resolvable. The analysis framework is also useful in determining the amount of spatial correlation for a given set of system configuration parameters and aperture separations. It is applicable to both point apertures and also apertures with larger diameters and can be used at both transmit and receive arrays. We show that the results obtained via theoretical derivations are in good agreement with those in the literature obtained via measurements or simulations. The theoretical calculations reveal that even under strong turbulence conditions and very long link distances, aperture separations at the order of a few tens of centimeters are sufficient to have resolvable paths with independent fading gains. Furthermore, the channel correlations increase relatively slowly with decreasing inter-aperture separations which are below these values. We also provide design guidelines to obtain resolvable paths for several commonly used system configurations.