A Novel Approach to Approximating Generalized Pointing Errors Modeled by Beckmann Distribution in FSO Communication Systems

Abstract

In this paper, we introduce a new and accurate approximation for the Beckmann distribution, a widely employed model for describing generalized pointing errors in the context of free-space optical (FSO) communication systems. More specifically, this four-parameter distribution, which considers distinct jitter variances along horizontal and vertical displacements and accounts for nonzero boresight errors at the receiver, is approximated using a Gamma distribution with shape and scale parameters. By applying this approximation to the generalized pointing error model and incorporating angle-of-arrival (AOA) variations, we present novel analytical equations for the cumulative distribution function and the probability density function of the composite Gamma-Gamma turbulence channel. These unified formulations are applicable to intensity modulation with direct detection and heterodyne detection methods, and are expressed using the generalized Meijer's-G function. Utilizing these results, we provide expressions for the moments, the ergodic capacity, the average bit-error rate for several modulations, and the outage probability. Additionally, employing a moments-based approach, we derive a highly accurate asymptotic approximation for the ergodic capacity for high signal-to-noise ratio (SNR) regimes using simple functions. All analytical expressions are validated using Monte-Carlo simulations.