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

New Lower Bound on the Ergodic Capacity of Optical MIMO Channels