Error-Controlled Iterative Algorithms for Digital Linearization of IMDD-Based Optical Fibre Transmission Systems

In intensity-modulation and direct-detection (IMDD) single-mode fibre (SMF) transmission systems, the nonlinear operation of square-law detection causes signal-signal beating interference (SSBI) that considerably limits the signal transmission capacity versus reach performance of the systems. To address this challenge, an error-controlled iterative algorithm (ECIA) with extra decision thresholds is proposed to digitally linearize the IMDD transmission systems. In the ECIA, instead of amplitude errors used in previously reported algorithms, the
${{\boldsymbol{Q}}}^{ - 2}$
factor is utilized as an objective function, along with the proposed stochastic gradient descent (SGD) optimization of the thresholds for symbol decision. The thresholds can be adaptively adjusted to reduce decision errors during iterations. To improve the algorithm's adaptivity to various system operation conditions, new constraints are also introduced including maximum step size and/or sign of threshold variation. By making use of the identified optimum key parameters of the ECIA, numerical investigations are conducted of the effectiveness of the proposed scheme in supporting 100 Gb/s 4-level pulse amplitude modulation (PAM4) transmissions over 80 km standard SMFs. Results show that compared with the previously reported decision-directed data-aided iterative algorithm (DD-DIA), the ECIA significantly reduces the power/optical signal-to-noise ratio (OSNR) penalty, required minimum number of iterations (convergence rate) and improves the wavelength drift tolerance. For the ECIA, an OSNR penalty of ≤3.8 dB (10% overhead) and a minimum iteration count of 50 are observed for up to 400 km SMF transmissions, showing its robustness to accumulated dispersions of long fibres. More importantly, a pilot-free operation (0% overhead) is also feasible at a cost of a slightly increased OSNR penalty of ≤0.5 dB.