# Upper and Lower Bounds for the Ergodic Capacity of MIMO Jacobi Fading Channels

## TL;DR

This paper derives new analytical bounds and closed-form expressions for the ergodic capacity of MIMO Jacobi-fading channels, relevant for optical fiber communications, validated through simulations.

## Contribution

It provides the first tight bounds and closed-form formulas for ergodic capacity in Jacobi-fading MIMO channels, enhancing understanding of optical fiber channel limits.

## Key findings

- Derived tight lower bounds on ergodic capacity.
- Established analytical upper bounds at any SNR.
- Validated expressions with simulation results.

## Abstract

In multi-(core/mode) optical fiber communication, the transmission channel can be modeled as a complex sub-matrix of the Haar-distributed unitary matrix (complex Jacobi unitary ensemble). In this letter, we present new analytical expressions of the upper and lower bounds for the ergodic capacity of multiple-input multiple-output Jacobi-fading channels. Recent results on the determinant of the Jacobi unitary ensemble are employed to derive a tight lower bound on the ergodic capacity. We use Jensen's inequality to provide an analytical closed-form upper bound to the ergodic capacity at any signal-to-noise ratio (SNR). Closed-form expressions of the ergodic capacity, at low and high SNR regimes, are also derived. Simulation results are presented to validate the accuracy of the derived expressions.