Performance Analysis of Free-Space Optical Links Over Lognormal-Shadow Rician ((M)over-tilde-$) Turbulence Channels With Generalized Pointing Errors

In this paper, we propose the use of the (M) over tilde $ distribution that is the product of Lognormal and Shadow Rician to describe the atmospheric turbulence-induced scintillation in free space optical communication systems. By approximating the moment generating function of Lognormal distribution with Hermite polynomial, the probability density function of (M) over tilde $ distribution is obtained in an approximately analytical form. It is shown that the proposed model yields a best fit to experimental and simulation data over a wide range of channel conditions when compared with the other widely used turbulence models. With resect to the pointing error model, we introduce a singular value decomposition method to transform the correlated sways to be independent and find that it is equivalent to the coordinate rotation method proposed before. To efficiently approximate the Beckmann distribution by the modified Rayleigh distribution, we present a new variance estimation method by using the Kullback-Leibler divergence and find that the derived new variance can reduce the computational cost of the gain parameter. Moreover, Kolmogorov-Smirnov goodness-of-fit statistical test results show that the derived new variance leads to a better approximation in most scenarios when compared with the two other estimates derived with the moment matching method in literature. To investigate the outage probability, bit error rate performance, and the ergodic capacity performance, an unifying probability density function of signal-to-noise ratio (SNR) under the combined effects of atmospheric turbulence and pointing errors for heterodyne detection and intensity modulation and direct detection techniques is derived. The simulation results verify the accuracy of the approximately analytical results and indicate that the derived new variance provides the best approximation accuracy in the performance of ergodic capacity in the whole SNR regime.