On the Optimality of Spatial Repetition Coding for MIMO Optical Wireless Communications

As a spatial diversity transmission scheme, repetition code (RC) is conjectured to be optimal in the sense of error performance for an intensity modulated direct detection multi-input-multi-output optical wireless communication (IM/DD MIMO-OWC) over log-normal fading channels. Despite the fact that all the experimental evidences thus far have strongly demonstrated that this hypothesis is indeed true, its mathematical proof remains a long-standing open problem mainly due to the lack of an explicit signal design criterion like MIMO radio frequency communications. In this letter, subject to two commonly used power constraints, we prove the optimality of RC under a much weaker condition in the sense of maximizing both large-scale and small-scale diversity gains for any space signalling using the recently established pair-wise error probability design criterion for a maximum likelihood (ML) detector.