  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.
