Novel Approximate Distribution of the Generalized Turbulence Channels for MIMO FSO Communications

In this article, we develop an innovative series representation for the sum of Rician non-zero boresight pointing error random variates based on the ${\bm{\kappa }} - {\bm{\mu \ }}$ distribution, which is suitable for multiple-input multiple-output (MIMO) transmission for the first time. Then, using this new representation, we introduce a novel closed-form probability density function (PDF) approximation for the sum of Gamma-Gamma random variates with generalized pointing errors and atmospheric attenuation of MIMO free-space optical (FSO) communications. Statistical Kolmogorov-Smirnov tests confirm the accuracy of this approximation over a wide range of channel conditions. The significance of this approximation is emphasized by deriving closed-form expressions for the ergodic capacity, outage probability, and average bit error rate (BER) using Meijer's G-function. This article provides a comprehensive analysis of the performance of MIMO FSO systems utilizing the equal gain combining (EGC) diversity technique under various conditions, such as different numbers of transmitter and receiver, turbulence intensities, the effects of non-zero boresight pointing errors, and path attenuation. The results show that using MIMO technology with more transmitters and receivers significantly improves the performance of FSO communication compared to other diversity techniques, including single input single output (SISO), and multiple input single output (MISO) systems. Detailed evaluations of the ergodic capacity, outage probability, and average BER performance at high signal-to-noise ratios provide additional insights. Monte-Carlo simulation results demonstrate the accuracy of the proposed approach.