Novel approximate distribution of the sum of Gamma–Gamma variates with pointing errors and applications in MIMO FSO links

Abstract

In this work, a novel approximate closed-form probability density function for the sum of Gamma–Gamma random variates with Rayleigh pointing errors is derived by means of the well-known Jensen’s inequality. We employ the Kolmogorov–Smirnov goodness-of-fit statistical tests to verify the accuracy of the proposed approximation. The test results demonstrate that an exact distribution can be efficiently approximated by this derived approximate expression over a wide range of channel conditions. Also, the analysis of the approximation error is presented to indicate that a higher approximation accuracy can be achieved for small pointing errors. The series representation of this approximate expression is also developed, which enables us to avoid dealing with the integration. To reveal the importance of proposed approximation, new approximate closed-form expressions of the average bit error rate (BER) and ergodic capacity are derived. The performance for multiple-input multiple-output (MIMO) free-space optical (FSO) systems with equal gain combining (EGC) diversity technique are analyzed with different parameters, including the number of transmit and receive apertures, strength of atmospheric turbulence, and presence of pointing errors. It is observed that the pointing errors significantly degrade the performance of MIMO FSO systems. The numerical results and simulation are further utilized to illustrate the accuracy of the proposed approach.