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We present an approach for maximum likelihood (ML) parameter estimation of the Gamma-Gamma (Γ-Γ) distribution in the weak turbulence conditions of the free space optical (FSO) channels. A two-dimensional ML (2DML) estimation approach is deployed to extend our one-dimensional Γ-Γ parameter estimation (1DML) method proposed in . To achieve the 2D estimation, an explicit closed form expression between the Γ-Γ parameters is extracted, where the constant factors of the expression are obtained using genetic algorithm (GA). The proposed 2DML estimation is compared with the modified method of moments based on a convex optimization (modified MOM/CVX). The numerical results demonstrate that the 2DML outperforms the modified MOM/CVX in terms of the mean square error of the estimation.