Capacity and Optimum Signal Constellations for VLC Systems

In this paper, the capacity of the point-to-point VLC system is investigated by means of functional analysis subject to amplitude constraint and average intensity constraint. It is proved that the capacity can be achieved by a unique probability density function (PDF). The necessary and sufficient condition for the capacity-achieving PDF is derived by the functional optimization theorem. Moreover, the capacity-achieving PDF is proved to be discrete and finite. Based on these properties, the capacity-achieving constellation optimization problems under amplitude constraint and average intensity constraint is formulated and an algorithm is proposed to solve the corresponding problem. To apply simple adaptive modulation in practical VLC systems, constellation optimization problem subject to an additional equal probability constraint is formulated and solved by maximizing the mutual information as well.