DSP-based Mode-dependent Loss and Gain Estimation in Coupled SDM Transmission

Abstract

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 6mode 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.

MDG and SNR Estimation in SDM Transmission Based on Artificial Neural Networks

“…iLMS and σ mdg . The LMS-based correction factor methods applies the correction factor proposed and validated in [12], [14], [15] to the DSP-estimated eigenvalues before estimating σ mdg . The ANN estimator uses the same structure and training data as in the long-haul case study in Section V. The results are shown in Fig.…”

“…(2) and (3) indicate that the accuracy of the conventional method that estimates σ mdg based on the DSP-estimated eigenvalues, λ 2 i,MMSE , is clearly affected by the optical SNR [12]. In coupled SDM transmission, the MMSE equalizer is usually implemented by means of semi-supervised or supervised adaptive schemes, such as the well-known least mean square (LMS) algorithm.…”

“…In the recent literature, MDG has been estimated by digital signal processing (DSP) using the transfer function of multiple-input multiple-output (MIMO) [4], [5], [10], [11] equalizers. However, we show in [12] that, as adaptive MIMO equalizers typically use the minimum mean square error (MMSE) criterion [13], the DSP-based estimation accuracy is affected by noise. We show that the accumulated MDG is underestimated for high levels of MDG and low optical SNRs 2 .…”

Experimental validation of MDL emulation and estimation techniques for SDM transmission systems

“…At a component level, MDL can be characterized by means of an optical vector network analyzer (OVNA) [4], [5] or digital holography techniques [6], [7] , while at a system level, the MDL is usually estimated from the channel transfer function obtained by the multiple-input multiple-output (MIMO) equalizer. In [8], we showed that the MDL estimation based on minimum mean square error (MMSE) MIMO equalizers depends on the signalto-noise ratio (SNR), resulting in an underestimation of the MDL at low SNR. We also proposed a correction factor that improves the estimation process for moderate levels of MDL.…”

“…The correction factor that improves the MDL estimation was initially proposed in [8] and experimentally validated in [10] for a back-to-back and single span transmission scheme using an MDL emulator at the transmitter side. In this work, we extend the experimental validation and show that the correction factor reduces the MDL estimation error both for the case of MDL emulation at the transmitter side, as well as for the in-span MDL emulation scenario.…”