Three-dimensional 32QAM constellation design based on a lattice in visible light communication systems

In this Letter, we propose and experimentally demonstrate a novel, to the best of our knowledge, three-dimensional 32-quadrature amplitude modulation (3D-32QAM) constellation for visible light communication systems. The 3D-32QAM constellation is constructed by solving the optimal lattice that maximizes the fundamental coding gain. The constellation points of the resulting 3D-32QAM are arranged in a triangular manner within the spherical boundary. Compared with the traditional cross-shaped 3D-32QAM and two-dimensional 32QAM constellations, the minimum Euclidean distance of the proposed 3D-32QAM constellation is increased by 8.6% and 62.0%, respectively. Further, the superiority of the proposed scheme is verified by experiments. Considering the 7% pre-forward error correction bit error rate threshold of 3.8 × 10^-3, the available ranges of the bias current and driving peak-to-peak voltage are significantly improved.