Full Large-Scale Diversity Space Codes for MIMO Optical Wireless Communications

TL;DR

This paper develops a criterion for designing full large-scale diversity space codes in MIMO optical wireless communications suffering from log-normal fading, demonstrating that positive entries in the coding matrix are essential for maximum likelihood detection.

Contribution

It introduces a general design criterion for FLDSC in MIMO-OWC systems and provides a closed-form linear FLDSC for 2x2 systems using number theory, revealing the optimality of repetition codes.

Findings

FLDSC outperforms spatial multiplexing in diversity gain.

Repetition code is optimal for linear FLDSC.

Space-only transmission suffices for full diversity in MIMO-OWC.

Abstract

In this paper, we consider a multiple-input-multiple-output optical wireless communication (MIMO-OWC) system suffering from log-normal fading. In this scenario, a general criterion for the design of full large-scale diversity space code (FLDSC) with the maximum likelihood (ML) detector is developed. Based on our criterion, FLDSC is attained if and only if all the entries of the space coding matrix are positive. Particularly for $2\times 2$ MIMO-OWC with unipolar pulse amplitude modulation (PAM), a closed-form linear FLDSC satisfying this criterion is attained by smartly taking advantage of some available properties as well as by developing some new interesting properties on Farey sequences in number theory to rigorously attack the continuous and discrete variables mixed max-min problem. In fact, this specific design not only proves that a repetition code (RC) is the best linear FLDSC, but also uncovers a significant difference between MIMO radio frequency (RF) communications and MIMO-OWC that space-only transmission is sufficient for a full diversity achievement. Computer simulations demonstrate that FLDSC substantially outperforms spatial multiplexing with the same total optical power and spectral efficiency and the latter obtains only the small-scale diversity gain.