  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.
