Design of two-dimensional signal constellations for visible light communication

This paper investigates a two-dimensional signal space for visible light communication (VLC) by taking into account some practical constraints. We first present the relationship between the signal space and basis functions, and then find the basis function yielding the largest signal space. Besides, to improve the symbol error rate (SER) performance of the system, we design the constellations by maximizing the minimum Euclidean distance among all constellation pairs. The original optimization problem is non-convex and relaxed to a convex one through a linear approximation method. Simulation results show that the optimized design provides significant signal-to-noise ratio gain (up to 6 dB at the SER of 10−4 for half-illumination target) over the heuristic design.