Average Worst-Case PEP Optimality of Repetition Coding Among Rate-1 DC-Offset STBCs for MIMO Optical Intensity Channels

Abstract

An optical wireless intensity-modulation direct-detection multiple-input multiple-output communication system is considered. The performance of $M$ -PAM rate-1 direct current offset space-time block codes is studied in terms of average worst-case pairwise error probability (WC-PEP) in quasi-static channels. It is shown that within this code class, the average WC-PEP is minimized by repetition coding (RC) under both electrical and optical individual power constraints, irrespective of channel statistics. This agrees with previously published results related to ON–OFF keying RC. This is further extended to sum power constraints, where it is shown that spatial beamforming minimizes the average WC-PEP within this code class, which simplifies to RC if the channel matrix has independent and indentically distributed columns and a sum electrical power constraint. Under a sum optical power constraint, this also holds true at high signal-to-noise ratio (SNR), but not at low SNR. Generally, the time dimension of this code class is redundant from an average WC-PEP perspective. Numerical results are provided to support the theoretical findings and to show that the average WC-PEP leads to a good approximation of the actual error probability at high SNR.