Tight Bounds on Channel Capacity for Dimmable Visible Light Communications

In this paper, the upper and lower bounds for the channel capacity of dimmable visible light communications(VLC) systems are investigated. Because the information is modulated into the instantaneous optical intensity, the transmitted optical intensity is represented by a nonnegative input that is corrupted by an additive white Gaussian noise. Considering the illumination support in a VLC system, the transmitted optical intensity signal must satisfy the illumination constraint, i.e., the average transmitted optical intensity is constrained by a target illumination intensity, which is determined by the nominal optical intensity of the light source devices and dimming target. An upper bound on the channel capacity is derived based on the signal space geometry via a sphere packing argument. A lower bound on the channel capacity is derived by maximizing the mutual information between the channel input and output. Both the upper and lower bounds are presented in closed forms. Furthermore, a closed-form optimal intensity distribution of the transmitted optical signal is obtained. The numerical results show that the presented bounds are very tight at the application zone of dimmable VLC links.