Semi-Supervised and Supervised Nonlinear Equalizers in Fiber-FSO Converged System

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We leverage the supervised and semi-supervised Volterra nonlinear equalizers (VNLE) to mitigate the system nonlinearity. Two methods are employed to estimate the coefficients: ordinary least square (OLS) estimator and the least absolute shrinkage and selection operator (Lasso). Due to the additional coupling loss and higher propagation loss in bad weather conditions, FSO-fiber link requires a more stringent power budget. Higher modulation depth and transmitter output power can improve the link budget but need to make nonlinearity correction. Thus, we comprehensively perform a proof-of-concept demonstration in a fiber-FSO converged link with pulse amplitude modulation (PAM). Compared with conventional supervised VNLE using OLS, the coefficients estimated from Lasso require a smaller training symbol overhead. In both the 50-Gbaud PAM4 (at the 1.22 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−2</sup> threshold) and 35-Gbaud PAM8 (at the 2 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−2</sup> threshold) cases, when the labeled data proportion is 5%, supervised VNLE using Lasso exhibits a received optical power (ROP) improvement up to 3 dB, compared to supervised VNLE using OLS. Moreover, the semi-supervised method can utilize the unlabeled data and further improve the performance without adding signal overhead to the system. In our 50-Gbaud PAM4 experiment, with 60% unlabeled data, the semi-supervised VNLE based on the soft decision (SD) and Lasso demonstrates up to 3-dB sensitivity gain at the BER threshold of 4.5 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−3</sup> compared with the supervised VNLE using Lasso. The semi-supervised VNLE using SD and Lasso also demonstrates a line rate improvement >100% at the 4.5 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−3</sup> Pre-FEC BER threshold over the conventional supervised VLNE using OLS.