Convergence Analysis of Diffusion Adaptive Networks Working Through Free Space Optical Communication Channels

Our endeavour in this paper is about studying the performance of adaptive networks with the communication links between nodes that are based on free space optical (s) communications technology. In this case the communication links between nodes are assumed to suffer from turbulence induced fading along with Gaussian noise. The effects of FSO channels are represented by irradiance coefficients that follow Log-normal and Gamma-Gamma distributions. The log-normal distribution is used for modelling weak and moderate turbulence regimes and the Gamma-Gamma distribution is mainly used for modelling strong turbulence cases. We study the steady-state behaviour of the diffusion adaptive network under the FSO channel conditions and derive closed-form relations for mean square deviation (MSD) and excess mean square error for the diffusion network. The results of our simulations for implementing adaptive networks with wireless optical communication technology show the perfect match with derived theoretical outcomes that are presented based on MSD measurements. We conclude that the performance of adaptive network in FSO environment, depends directly on the mean and second order moment of the assumed channel distribution and as expected, for the channels with strong turbulence regimes, the convergence errors of adaptive networks becomes higher.