A Two-Dimensional Maximum Likelihood Parameter Estimation of Distribution for Free Space Optical Channels with Weak Turbulence Conditions

We present an approach for maximum likelihood (ML) parameter estimation of the Gamma-Gamma (?-?) 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 ?-? parameter estimation (1DML) method proposed in [1]. To achieve the 2D estimation, an explicit closed form expression between the ?-? 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 2DML outperforms modified MOM/CVX in terms of the mean square error of the estimation and the variance of the estimators. Moreover, the convergence rate of the 2DML method is high and not sensitive to the starting points.