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

Rémi Bonnefoi (1) , Kevin Nadaud (1, 2)

1 IETR - Institut d'Électronique et des Technologies du numéRique
2 SCEE - Signal, Communication et Electronique Embarquée

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 × 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.

Mots clés: MIMO; optical fiber; multi-core/multi-mode; Ergodic Capacity; Christoffel-Darboux kernel; lower-bound

Domaines: Traitement du signal et de l'image [eess.SP]; Réseaux et télécommunications [cs.NI]; Théorie de l'information [cs.IT]

Rémi Bonnefoi, Kevin Nadaud. A New Lower Bound on the Ergodic Capacity of Optical MIMO Channels. 2017 IEEE International Conference on Communications (ICC), May 2017, Paris, France. ⟨10.1109/icc.2017.7996690⟩. ⟨hal-01486625⟩