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With fairness consideration, optimal linear precoding designs for multi-color, multi-user visible light communication (VLC) systems are presented in this paper. Utilizing both the spatial and multi-color resources, the precoding designs are proposed to mitigate the impact of the multi-user interference (MUI) and the multi-color crosstalk. With the constraints of chromaticity, luminance, and signal range, the precoding designs are formulated to achieve the max-min fairness and the maximum sum-rate. Since the closed-form expression for the capacities is not available, the lower and upper bounds are chosen as the performance criterions. To make the optimization problems be easy to be solved by using standard optimization packages, the non-convex problems are cast into convex ones. Subsequently, algorithms are developed to find optimal solutions. Extensive simulation results indicate that the proposed precoding schemes outperform the conventional pseudo inverse method.

Optimal Linear Precodings for Multi-Color, Multi-User Visible Light Communication System with Fairness Considerations