Derivation and Analysis of Probability Distribution of Visible-Light Channel Gain Difference Based on Lambertian Radiation

Abstract

The distribution of channel gain difference (CGD) is important for maximizing system capacity and implementing user cooperation. However, its analysis in visible light communication has not been extensively studied thus far. In this study, we investigate the probability distribution of visible-light CGD based on Lambertian radiation. First, owing to the difficulties in direct analysis, we derive the approximate expression for CGD of visible light based on the Lambertian model. Second, when user distribution is uniform, we derive the probability density function and cumulative distribution of the CGD based on visible-light channel. Third, we provide the closed form of optimal lighting angle for the visible-light cell, leading to the high probability of CGD. Furthermore, we analyze the relationship between the CGD and other parameters in lighting deployment. Finally, the simulation results demonstrate the approximation between theoretical and actual distributions of CGD, and the numerical results offer the insight between CGD and lighting deployment based on visible-light channels.