Linear space codes for indoor MIMO visible light communications with ML detection

In this paper, we consider the optimal design of linear space codes for an indoor multiple input multiple output (MIMO) visible light communication (VLC) system with maximum-likelihood (ML) detection, where we assume that the full knowledge of channel state information (CSI) is available at both the transmitter and the receiver. For such a system with on-off-keying (OOK) modulation, an optimal closed-form linear space code that maximizes the minimum Euclidean distance for ML detection is attained for the scenario with two transmitters and multiple receivers. Our results reveal the fact that when the channel is good, the optimal code has either a diagonal or an anti-diagonal structure, and when the channel is bad, the optimal code is to diagonalize the channel matrix first, then, optimally distribute the total transmission power into each eigen-subchannel, and then, follow a repetition coding (RC) scheme. Computer simulations verify both the accuracy and the validity of our theoretical analysis, and show that our newly proposed linear space code provides significant error performance gains over currently available space modlution (SM) and RC in literature without CSI at the transmitter.