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A novel method for the estimation of nonlinear interference (NLI) penalties in optical networks is presented. Its theoretical derivation is grounded in linear least squares (LLS) longitudinal power monitoring (LPM), an algorithm capable of estimating the absolute power evolution of a signal along the link. We demonstrate that closed-form NLI estimation is inherently integrated into LPM. However, this method does not account for the cross-channel interference (XCI) contribution to NLI, since the receiver typically lacks knowledge of other WDM channels. To address this limitation, simple analytical expressions to compensate for the bias originating from neglecting XCI are proposed for the scenario of homogenous WDM combs. These formulas are derived from closed-form NLI models (e.g., the GN-model) and require only limited information about the signal configuration. The effectiveness of the proposed approach is validated through a wide range of realistic numerical simulations and experiments, including C-band transmissions over 300-km and 1100-km EDFA-amplified optical links. The obtained results confirm the reliability of the method, yielding nonlinear SNR estimates with a maximum absolute error consistently below 0.97 dB when compared to well-established analytical NLI models or measured values. The mean absolute errors in simulation and experiments are 0.3 dB and 0.5 dB, respectively. Additionally, a practical demonstration of transmit power optimization is provided, leveraging the values obtained through the proposed method.
Andrenacci et al. (Mon,) studied this question.