Optimal Design of Linear Space Code for MIMO Optical Wireless Communications

Abstract

In this paper, the design of linear full-diversity space code (FDSC) is considered for an intensity-modulated direct-detection multiple-input-multiple-output optical wireless communication (IM/DD MIMO-OWC) system, in which the channel suffers from log-normal fading and different links have different variances. Utilizing our recently established error performance criterion for the design of FDSC with a maximum-likelihood detector, we formulate the design problem of optimizing both large-scale diversity gain and small-scale diversity into a max-min optimization problem with continuous-discrete mixed design variables. We propose the use of the Farey sequence in number theory as a powerful tool to solve this kind of optimization problem. By taking advantage of some available properties and by developing some new interesting properties on the Farey sequence, a closed-form solution is attained for IM/DD MIMO-OWC equipped with two transmitters and multiple receivers. This optimal design shows that a repetition code with an optimal power allocation is optimal.

Keywords

• Intensity modulation with direct detection (IM/DD)
• large-scale diversity
• fading channels
• maximum likelihood (ML) detection
• multiple-input-multiple-output (MIMO)
• optical wireless communication (OWC)