  We analyze coherent wave transport in a new physical setting associated with
multimode wave systems where reflection is completely suppressed and
mode-dependent losses together with mode-mixing are dictating the wave
propagation. An additional physical constraint is the fact that in realistic
circumstances the access to the scattering (or transmission) matrix is
incomplete. We have addressed all these challenges by providing a statistical
description of wave transport which fuses together a free probability theory
approach with a Filtered Random Matrix ensemble. Our theoretical predictions
have been tested successfully against experimental data of light transport in
multimode fibers.
