Optical MISO IM/DD channels: Optimality of spatial repetition codes among DC-offset STBCs

In this paper, an optical wireless multiple-input single-output communication system employing intensity-modulation direct-detection is considered. Subject to a per transmit-aperture power constraint, the performance of direct current (DC) offset space-time block codes (STBC) is studied in terms of pairwise error probability (PEP). It is shown that among the class of DC-STBCs, the worst case PEP, i.e., the one corresponding to the minimum distance between two codewords, is minimized by repetition coding (RC) for any channel state. Therefore, it follows that among all DC-STBCs, RC is optimal in terms of worst case PEP under any turbulence statistics. This result agrees with previously published numerical results showing the superiority of RC in such systems. It also agrees with previously published analytical results on this topic under lognormal turbulence and further extends it to arbitrary turbulence statistics. Numerical results provided to verify this indicate that RC is not only optimal in terms of worst case PEP, but also in terms of average error probability.