On the Optimality of Repetition Coding among Rate-1 DC-offset STBCs for MIMO Optical Wireless Communications
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AbstractIn this paper, an optical wireless multiple-input multiple-output communication system employing intensity-modulation direct-detection is considered. The performance of direct current offset space-time block codes (DC-STBC) is studied in terms of pairwise error probability (PEP). It is shown that among the class of DC-STBCs, the worst case PEP corresponding to the minimum distance between two codewords is minimized by repetition coding (RC), under both electrical and optical individual power constraints. It follows that among all DC-STBCs, RC is optimal in terms of worst-case PEP for static channels and also for varying channels 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 analytic results on this topic under log-normal turbulence and further extends it to arbitrary turbulence statistics. This shows the redundancy of the time-dimension of the DC-STBC in this system. This result is further extended to sum power constraints with static and turbulent channels, where it is also shown that the time dimension is redundant, and the optimal DC-STBC has a spatial beamforming structure. Numerical results are provided to demonstrate the difference in performance for systems with different numbers of receiving apertures and different throughput.
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