  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 space domain, bit mapping in signal domain, and the 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 closedform. 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.
