Optimal Constellation Design for Indoor $2\times 2$ MIMO Visible Light Communications

Owing to the line-of-sight characteristics in indoor visible light communication (VLC) systems, different geometrical locations of transmitters and receivers provide distinct channel correlations, thus bringing various impacts on the conventional multiple-input multiple-output (MIMO) techniques. In this letter, by taking full advantage of the channel state information (CSI) available at both the transmitter and the receiver, we present an optimal constellation for the 2 × 2 MIMO-VLC system, where the signal vectors are selected to maximize the minimum Euclidean distance under a total optical power constraint. Simulation results verify both the accuracy and the validity of our analytical derivation, and show its significant error performance gains over repetition coding (RC) and space shift keying (SSK) for mobile receivers, respectively.