Mode-dependent Loss and Gain Estimation in SDM Transmission Based on MMSE Equalizers

Ruby S.B. Ospina (Corresponding author), Menno Van den Hout, Juan Carlos Alvarado-Zacarias, Jose Enrique Antonio-Lopez, Marianne Bigot-Astruc, Adrian Amezcua-Correa, Pierre Sillard, Rodrigo Amezcua Correa, Chigo Okonkwo, Darli A.A. Mello

Research output: Contribution to journalArticleAcademicpeer-review

9 Citations (Scopus)


The capacity of 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.

Original languageEnglish
Article number9291436
Pages (from-to)1968-1975
Number of pages8
JournalJournal of Lightwave Technology
Issue number7
Early online date11 Dec 2020
Publication statusPublished - 1 Apr 2021


  • mode-dependent gain
  • Mode-dependent loss
  • optical fiber communications
  • space division multiplexing


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