  MIMO processing techniques in fiber optical communications have been proposed
as a promising approach to meet increasing demand for information throughput.
In this context, the multiple channels correspond to the multiple modes and/or
multiple cores in the fiber. In this paper we characterize the distribution of
the mutual information with Gaussian input in a simple channel model for this
system. Assuming significant cross talk between cores, negligible
backscattering and near-lossless propagation in the fiber, we model the
transmission channel as a random complex unitary matrix. The loss in the
transmission may be parameterized by a number of unutilized channels in the
fiber. We analyze the system in a dual fashion. First, we evaluate a
closed-form expression for the outage probability, which is handy for small
matrices. We also apply the asymptotic approach, in particular the Coulomb gas
method from statistical mechanics, to obtain closed-form results for the
ergodic mutual information, its variance as well as the outage probability for
Gaussian input in the limit of large number of cores/modes. By comparing our
analytic results to simulations, we see that, despite the fact that this method
is nominally valid for large number of modes, our method is quite accurate even
for small to modest number of channels.
