Joint beamformer and offset design for multi-color visible light communications

In this paper, we propose a new joint beamformer and offset design method for visible light communication (VLC) with multiple red/green/blue light emitting diodes (RGB LED). We take into account key practical lighting constraints including optical power, color illumination, non-negativeness, CRI and LER, and formulate a non-convex optimization problem to minimize the system mean squared error (MSE). We resort to approximation methods to relax a non-convex constraint into a convex one, and propose a way to relax the original problem into a simple version, which is solvable by the standard water-filling method. Simulation results are provided to illustrate performance of the proposed method for different color illumination scenarios. Also, the relationship between channel cross-talks and optimized offset allocation is observed.