Bias Allocation and Precoding for Tricolor Visible Light Communications with Signal-dependent Noise

Wavelength-domain multiplexing enables near parallel transmission for visible light communications (VLC). In this paper, we investigate an optimal bias allocation problem for the tri-color VLC channel when there is no color cross-talk (CoC), and propose a joint precoding and bias allocation algorithm when CoC exists. The optimization problems are formulated considering both lighting and communication requirements. The color constraint is depicted using the MacAdam ellipses on the chromaticity diagram, as an effective relaxation from a fixed point restriction. Also, for practical concerns, the addressed system is affected by signal-dependent noise (SDN). The bias allocation problem under SDN and related constraints is shown to be non-convex, thus a convex-concave procedure is utilized in this paper for convexification. The joint design problem is also non-convex, and an iterative optimization procedure is adopted, where the decoder is of Wiener filter form. Simulation results are given to show the impacts of SDN, CoC, and steps of MacAdam ellipses on system performance.