Outage Capacity for the Optical MIMO Channel

TL;DR

This paper analyzes the capacity of optical MIMO channels modeled as random unitary matrices, providing exact and asymptotic formulas for outage probability and mutual information, validated by simulations.

Contribution

It introduces a novel analytical framework using the Coulomb gas method to evaluate outage probability and mutual information in optical MIMO systems with small to moderate channel numbers.

Findings

Closed-form outage probability for small matrices

Asymptotic formulas for large number of channels

Analytical results closely match simulations

Abstract

MIMO processing techniques in fiber optical communications have been proposed as a promising approach to meet increasing demand for information throughput. In this context, the multiple channels correspond to the multiple modes and/or multiple cores in the fiber. In this paper we characterize the distribution of the mutual information with Gaussian input in a simple channel model for this system. Assuming significant cross talk between cores, negligible backscattering and near-lossless propagation in the fiber, we model the transmission channel as a random complex unitary matrix. The loss in the transmission may be parameterized by a number of unutilized channels in the fiber. We analyze the system in a dual fashion. First, we evaluate a closed-form expression for the outage probability, which is handy for small matrices. We also apply the asymptotic approach, in particular the Coulomb gas method from statistical mechanics, to obtain closed-form results for the ergodic mutual information, its variance as well as the outage probability for Gaussian input in the limit of large number of cores/modes. By comparing our analytic results to simulations, we see that, despite the fact that this method is nominally valid for large number of modes, our method is quite accurate even for small to modest number of channels.