New statistical model for atmospheric optical scintillation and its application

A generic statistical model, termed Málaga, or M distribution has been proposed recently for the irradiance fluctuations. Based on this model, the irradiance has been written as a product of one term that model large-scale turbulent effects by a second term that represents the statistically independent small-scale turbulent effects. The distribution of the small-scale fluctuations has been derived in terms of the confluent hypergeometric function. The large-scale fluctuations is widely accepted to be a log-normal (LN) amplitude, however, to derive a closed-form expression for the probability density function of the M distribution, it has been modelled by Gamma distribution. It is well-known that the Gamma distribution is not a good approximation for LN distribution. Hence, in this paper, the inverse Gaussian distribution is proposed, as an alternative to the LN model. It is demonstrated that this substitution gives birth to a new statistical model, termed S distribution, which can be written in a closed-form expression and makes it possible to model accurately the irradiance fluctuations. To give an application, the performance of a wireless optical heterodyne communication system is investigated over S-distributed turbulence channel and closed-form expression is derived for the average bit error rate of the system.