As a power- and bandwidth-efficient modulation scheme, the optical spatial modulation (SM) technique has recently drawn increased attention in the field of visible light communications (VLC). To guarantee the number of bits mapped by the transmitter's index at each timeslot is an integer, the number of transmitters (i.e., light-emitting diodes) in the SM-based VLC system is often set be a power of two. To break the limitation on the required number of transmitters and provide more design flexibility, this paper investigates the SM-based VLC with an arbitrary number of transmitters. Initially, a channel-adaptive bit mapping (CABM) scheme is proposed, which includes three steps: bit mapping in the space domain, bit mapping in the signal domain, and channel adaptive mapping. The proposed CABM scheme allows operation with an arbitrary number of transmitters, and is verified to be an efficient scheme through numerical results. Based on the CABM scheme, the information-theoretical aspects of the SM-based VLC are analyzed. The theoretical expression of the mutual information is first analyzed. However, it is very hard to evaluate system performance. To obtain more insights, a lower bound of the mutual information is derived, which is in closed form. Both theoretical analysis and numerical results show that the gap between the mutual information and its lower bound is small. Finally, to further improve the system performance, the precoding scheme is proposed for the SM-based VLC. Numerical results show that the system performance improves dramatically when using the proposed precoding scheme.
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