# New Lower Bound on the Ergodic Capacity of Optical MIMO Channels

## TL;DR

This paper derives a new analytical lower bound and approximation for the ergodic capacity of optical MIMO channels modeled as sub-matrices of Haar-distributed unitary matrices, supported by numerical validation.

## Contribution

It introduces a novel lower bound and capacity approximation for optical MIMO channels using random matrix theory and eigenvalue analysis.

## Key findings

- Derived a closed-form lower bound for ergodic capacity
- Provided an approximation for low-SNR regimes
- Numerical results validate the analytical expressions

## Abstract

In this paper, we present an analytical lower bound on the ergodic capacity of optical multiple-input multiple-output (MIMO) channels. It turns out that the optical MIMO channel matrix which couples the mt inputs (modes/cores) into mr outputs (modes/cores) can be modeled as a sub-matrix of a m x m Haar-distributed unitary matrix where m > mt,mr. Using the fact that the probability density of the eigenvalues of a random matrix from unitary ensemble can be expressed in terms of the Christoffel-Darboux kernel. We provide a new analytical expression of the ergodic capacity as function of signal-to-noise ratio (SNR). Moreover, we derive a closed-form lower-bound expression to the ergodic capacity. In addition, we also derive an approximation to the ergodic capacity in low-SNR regimes. Finally, we present numerical results supporting the expressions derived.