Analytical QoT estimator of dual-polarization coherent systems with non-integer fractionally-spaced MIMO equalizers

We present a comprehensive and computationally efficient analytical framework to estimate the performance of linear dual-polarization coherent optical systems employing finite-length multiple input multiple output (MIMO) equalizers. By adopting a formulation based on Block-Toeplitz matrices, our model extends prior art by uniquely capturing the complex interplay between optical filtering, chromatic dispersion (CD), distributed polarization impairments, namely polarization mode dispersion (PMD) and polarization dependent loss (PDL), distributed and colored noise, and fractional sampling regimes (e.g., 3/2, 4/3 samples-per-symbol (SpS)) in coherent optical transmission systems. Unlike traditional asymptotic models, we explicitly quantify the impact of limited equalizer memory and colored noise statistics on the post-equalization signal-to-noise-ratio (SNR), which can directly lead to bit error ratio (BER) degradation. Extensive validation against time-domain decision-directed (DD)-least mean square (LMS) simulations, using probabilistic shaping (PS)-16-QAM format, demonstrates the model's accuracy, showing an average estimation error up to 0.3 dB even under severe impairment scenarios with an SNR penalty ≲15 dB. Furthermore, we leverage the model to highlight the advantages of fractional sampling, showing that 3/2 SpS and 4/3 SpS architectures yield superior performance compared to standard 2 SpS solutions given the same equalizer complexity (i.e., same number of taps) once converging. Notably, this framework offers a dramatic reduction in computational time, by orders of magnitude, compared to traditional time-domain simulations, making it a pivotal tool for the design and optimization of future reconfigurable optical networks.