  The capacity in space division multiplexing (SDM) systems with coupled
channels is fundamentally limited by mode-dependent loss (MDL) and
mode-dependent gain (MDG) generated in components and amplifiers. In these
systems, MDL/MDG must be accurately estimated for performance analysis and
troubleshooting. Most recent demonstrations of SDM with coupled channels
perform MDL/MDG estimation by digital signal processing (DSP) techniques based
on the coefficients of multiple-input multiple-output (MIMO) adaptive
equalizers.
  Although these methods provide a valid indication of the order of magnitude
of the accumulated MDL/MDG over the link, MIMO equalizers are usually updated
according to the minimum mean square error (MMSE) criterion, which is known to
depend on the channel signal-to-noise ratio (SNR). Therefore, MDL/MDG
estimation techniques based on the adaptive filter coefficients are also
impaired by noise. In this paper, we model analytically the influence of the
SNR on DSP-based MDL/MDG estimation, and show that the technique is prone to
errors. Based on the transfer function of MIMO MMSE equalizers, and assuming a
known SNR, we calculate a correction factor that improves the estimation
process in moderate levels of MDL/MDG and SNR. The correction factor is
validated by simulation of a 6-mode long-haul transmission link, and
experimentally using a 3-mode transmission link. The results confirm the
limitations of the standard estimation method in scenarios of high additive
noise and MDL/MDG, and indicate the correction factor as a possible solution in
practical SDM scenarios.
