Digital monitoring and compensation of MDL based on higher-order Poincaré spheres

We present a digital technique able to monitor and compensate for the mode-dependent losses (MDL) in space-division multiplexing (SDM) transmission systems. The working principle of the technique is based on the analysis of the received signal samples in the higher-order Poincaré spheres (HoPs). When an arbitrary pair of tributaries is represented in the respective HoPs, the effect of the MDL can be modeled as a simple shift of the constellation points in a such sphere. Therefore, the MDL can be estimated by computing those shifts over all the HoPs and the induced signal distortions can be compensated by re-centering all the constellations in the respective HoPs. It should be highlighted that the proposed technique is scalable with an arbitrary number of spatial channels, modulation format agonistic and free of training sequences. The HoPs-based MDL monitoring (compensation) technique allows the MDL estimation (compensation) up to values of ≈ 6 dB. The proposed technique can partially compensate the MDL distortion, making a MDL sensitive algorithm in an insensitive one. When the proposed technique assists a HoPs-based space-demultiplexing algorithm, it provides signal-to-noise ratio (SNR) enhancements of 2, 4 and 8 dB for PM-QPSK, PM-16QAM and PM-64QAM signals, respectively, for the particular case of a SDM-based transmission system with a spatial diversity of 2 and 2 dB of MDL.