Optical MIMO communication with unequal power allocation to channels

TL;DR

This paper derives exact and approximate statistical characterizations of mutual information in optical MIMO systems with unequal power allocation, extending previous work that assumed equal power per mode, and validates results with simulations.

Contribution

It provides new determinant-based formulas for the mutual information distribution under arbitrary covariance, addressing unequal power allocation in optical MIMO channels.

Findings

Exact MGF for MI derived for arbitrary covariance matrices

Gaussian and Weibull approximations for MI distribution

Analytical results match Monte Carlo simulations

Abstract

Multiple input multiple output (MIMO) approach in fiber optical communication has emerged as an effective proposition to address the ever increasing demand for information exchange. In the ergodic case, the multiple channels, associated with multiple modes or cores or both in the optical fiber, is modeled by the Jacobi ensemble of random matrices. A key quantity for assessing the performance of MIMO systems is the mutual information (MI). We focus here on the case of an arbitrary transmission covariance matrix and derive exact determinant based results for the moment generating function (MGF) of mutual information (MI), and thereby address the scenario of unequal power per excited mode. The MGF is used to obtain Gaussian- and Weibull-distribution based approximations for the probability density function (PDF), cumulative distribution function (CDF) or, equivalently, the outage probability, and also the survival function (SF) or reliability function. Moreover, a numerical Fourier inversion approach is implemented to obtain the PDF, CDF, and SF directly from the MGF. The MGF is further used to investigate the ergodic capacity, which is the first moment (mean) of the mutual information. The analytical results are found to be in excellent agreement with Monte Carlo simulations. Our study goes beyond the earlier investigations where covariance matrix proportional to identity matrix has been considered which corresponds to equal power allocation per excited mode.