  We consider multi-input multi-output (MIMO) communications over multi-mode
fibers (MMFs). Current MMF standards, such as OM3 and OM4, use fibers with core
radii of 50 \mu m, allowing hundreds of modes to propagate. Unfortunately, due
to physical and computational complexity limitations, we cannot couple and
detect hundreds of data streams into and out of the fiber. In order to
circumvent this issue, we present input-output coupling schemes that allow the
user to couple and extract a reasonable number of signals from a fiber with
many modes. This approach is particularly attractive as it is scalable; i.e.,
the fibers do not have to be replaced every time the number of transmitters or
receivers is increased, a phenomenon that is likely to happen in the near
future.
  We present a statistical channel model that incorporates intermodal
dispersion, chromatic dispersion, mode dependent losses, mode coupling, and
input-output coupling. We show that the statistics of the fiber's frequency
response are independent of frequency. This simplifies the computation of the
average Shannon capacity of the fiber. We also provide an input-output coupling
strategy that leads to an increase in the overall capacity. This strategy can
be used whenever channel state information (CSI) is available at the
transmitter. We show that the capacity of an Nt by Nt MIMO system over a fiber
with M>>Nt modes can approach the capacity of an Nt-mode fiber with no
mode-dependent losses. We finally present a statistical input-output coupling
model in order to quantify the loss in capacity when CSI is not available at
the transmitter. It turns out that the loss, relative to Nt-mode fibers, is
minimal (less than 0.5 dB) for a wide range of signal-to-noise ratios (SNRs)
and a reasonable range of MDLs.
