On the Ergodic Capacity of MIMO Free-Space Optical Systems over Turbulence Channels

The free-space optical (FSO) communications can achieve high capacity with huge unlicensed optical spectrum and low operational costs. The corresponding performance analysis of FSO systems over turbulence channels is very limited, especially when using multiple apertures at both transmitter and receiver sides. This paper aim to provide the ergodic capacity characterization of multiple-input multiple-output (MIMO) FSO systems over atmospheric turbulence-induced fading channels. The fluctuations of the irradiance of optical channels distorted by atmospheric conditions is usually described by a gamma-gamma ($ΓΓ$) distribution, and the distribution of the sum of $ΓΓ$ random variables (RVs) is required to model the MIMO optical links. We use an $α$-$μ$ distribution to efficiently approximate the probability density function (PDF) of the sum of independent and identical distributed $ΓΓ$ RVs through moment-based estimators. Furthermore, the PDF of the sum of independent, but not necessarily identically distributed $ΓΓ$ RVs can be efficiently approximated by a finite weighted sum of PDFs of $ΓΓ$ distributions. Based on these reliable approximations, novel and precise analytical expressions for the ergodic capacity of MIMO FSO systems are derived. Additionally, we deduce the asymptotic simple expressions in high signal-to-noise ratio regimes, which provide useful insights into the impact of the system parameters on the ergodic capacity. Finally, our proposed results are validated via Monte-Carlo simulations.