Approximation to the Sum of Two Correlated Gamma-Gamma Variates and its Applications in Free-Space Optical Communications

Abstract

Abstract-The Gamma-Gamma (ΓΓ) distribution is popularly accepted for modeling the received intensity fluctuations in the near-ground free-space optical (FSO) communication. We consider in this letter the case of dual space diversity FSO systems when the fading coefficients corresponding to the two sub-channels are correlated. In order to evaluate the receiver performance analytically, we propose to approximate the sum of correlated ΓΓ random variables by an α-µ distribution. We show that there is a good match between the performance obtained by simulated data based on the ΓΓ channel model and that obtained from analytical calculation based on the approximate α-µ model.

Performance evaluation of receive-diversity free-space optical communications over correlated Gamma–Gamma fading channels

“…However, it is not obvious how to do this decomposition, since mathematically there are an infinite number of solutions. Some previous work has assumed that the fading correlation arises only from large-scale turbulence, e.g., [19,21]. But to the best of our knowledge, no detailed study has been performed so far on the accuracy and correctness of this assumption.…”

Fading correlation and analytical performance evaluation of the space-diversity free-space optical communications system

“…Also, a multivariate ΓΓ model with the exponential correlation was proposed in [16], but this correlation model is not suitable for most FSO system configurations. In a recent work [17], we proposed the α-µ approximation to the sum of two correlated ΓΓ RVs for evaluating the performance of a dual-diversity FSO system.…”

“…Afterwards, we propose an analytical approach to investigate the impact of fading correlation on the system BER. For this purpose, we extend the α-µ approximation method proposed in [17] to the case of multiple diversity by approximating the sum of arbitrarily correlated multiple ΓΓ RVs by an α-µ distribution. As a matter of fact, the proposed method in [17] was based on the joint moments of Gamma-distributed RVs.…”

“…For this purpose, we extend the α-µ approximation method proposed in [17] to the case of multiple diversity by approximating the sum of arbitrarily correlated multiple ΓΓ RVs by an α-µ distribution. As a matter of fact, the proposed method in [17] was based on the joint moments of Gamma-distributed RVs. Therein, we could only find the joint moments of two correlated Gamma RVs in a closedform formula.…”

MIMO techniques for high data rate free space optical communication system in log-normal channel

“…Optical turbulence arises as a result of random fluctuations in the refractive index of the atmosphere which are directly dependent on fluctuating atmospheric temperature and pressure [2]. The refractive-index fluctuations cause detrimental effects on the optical beam such as beam spreading, irradiance fluctuation and loss of spatial coherence [3,4].…”