The Hermitian Jacobi process: simplified formula for the moments and application to optical fibers MIMO channels

TL;DR

This paper derives a simplified formula for the moments of the Hermitian Jacobi process using symmetric functions, and applies it to model optical fiber MIMO channels, including capacity calculations.

Contribution

It introduces a more straightforward moment formula for the Hermitian Jacobi process and applies it to optical fiber MIMO channel modeling and capacity analysis.

Findings

Simpler moment formula for the Hermitian Jacobi process.

Application to optical fiber MIMO channel capacity.

Expression of moments as balanced hypergeometric series.

Abstract

Using a change of basis in the algebra of symmetric functions, we compute the moments of the Hermitian Jacobi process. After a careful arrangement of the terms and the evaluation of the determinant of an `almost upper-triangular' matrix, we end up with a moment formula which is considerably simpler than the one derived in \cite{Del-Dem}. As an application, we propose the Hermitian Jacobi process as a dynamical model for optical fibers MIMO channels and compute its Shannon capacity for small enough power at the transmitter. Moreover, when the size of the Hermitian Jacobi process is larger than the moment order, our moment formula may be written as a linear combination of balanced terminating ${}_4F_3$-series evaluated at unit argument.