Superposed probabilistically shaped QAM constellation design based on nonlinear coding for MIMO visible light communication systems

In this study, we propose a superposed probabilistically shaped (PS) quadrature amplitude modulation (QAM) constellation scheme for multiple-input multiple-output visible light communication systems. PS QAM signals are generated from a nonlinear coding equation that converts uniformly distributed 8-level signals into PS 9- or 10-level signals, which are then mapped into PS 9QAM or 10QAM signals. Square-shaped 9QAM and trapezoid-shaped 10QAM constellations are introduced to maximize the minimum Euclidean distance (MED) of the superposed constellation. Finally, the PS 9QAM and 10QAM signals are superposed with the 4QAM signals in a flipped manner to obtain PS 36QAM or 40QAM signals at the receiver, respectively. To exploit the temporal correlation of the resulting signal from nonlinear coding, we developed a detection algorithm based on Viterbi decoding. Experimental results confirmed the superiority of the proposed schemes by achieving a higher MED and stronger ability to resist nonlinearity. Compared with the traditional scheme, the peak-to-peak voltage dynamic ranges of the superposed 36QAM and 40QAM constellation schemes were improved by 52% and 48%, respectively.