Digital Signal Processing for MDG Estimation in Long-Haul SDM Transmission

In space-division multiplexing (SDM) transmission, mode-dependent gain (MDG) can be estimated by digital signal processing (DSP) from the transfer matrix of the multiple-input multiple-output (MIMO) equalizer. However, previous works have shown that the estimation performance using MIMO equalizers based on the minimum mean square error (MMSE) is significantly degraded, particularly at low SNRs. In this paper, we experimentally assess DSP-based MDG estimation techniques in long-haul SDM transmission. Besides the intrinsic MDG of the optimized setup configuration, an additional power imbalance between modes is artificially introduced to generate a controlled amount of MDG. Two approaches for MDG estimation employing MMSE MIMO equalization are discussed. The direct method readily computes the channel eigenvalues from the MIMO equalizer coefficients. Conversely, the reverse method requires equalizer training dedicated for MDG estimation, which is suitable for laboratory experiments but, eventually, overly computationally expensive for real-time DSP. Moreover, an ANN model is evaluated as an ML-based technique for MDG estimation. The results corroborate previous works showing that the direct method saturates the estimated MDG for high values of accumulated MDG. The reverse method offers accurate results for an increased range of MDG values, confirming its suitability for experimental works. Finally, the ANN-based method tends to overestimate the MDG for high accumulated values but has promising prospects for real-time operation considering its low complexity.