Reconstruction of probability density function of intensity fluctuations relevant to free-space laser communications through atmospheric turbulence

A new method of reconstructing and predicting an unknown probability density function (PDF) characterizing the statistics of intensity fluctuations of optical beams propagating through atmospheric turbulence is presented in this paper. The method is based on a series expansion of generalized Laguerre polynomials ; the expansion coefficients are expressed in terms of the higher-order intensity moments of intensity statistics. This method generates the PDF from the data moments without any prior knowledge of specific statistics and converges smoothly. The utility of reconstructed PDF relevant to free-space laser communication in terms of calculating the average bit error rate and probability of fading is pointed out. Simulated numerical results are compared with some known non-Gaussian test PDFs: Log-Normal, Rice-Nakagami and Gamma-Gamma distributions and show excellent agreement obtained by the method developed. The accuracy of the reconstructed PDF is also evaluated.