Low-Complexity Second-Order Volterra Equalizer for DML-Based IM/DD Transmission System

Volterra nonlinear equalizers (VNLEs) are known to be effective in compensating for nonlinear distortions. However, the major drawback of these equalizers is the huge implementation and computation complexity. In this article, we propose and demonstrate low-complexity quadratic VNLEs specifically designed for directly modulated laser (DML)-based intensity-modulation/direct-detection (DD) systems. We first derive an analytical expression of the quadratic Volterra model for DML/DD systems and then identify the nonlinear distortion terms mainly contributing to the system performance. We show that the interplay between the DML's adiabatic frequency chirp and fiber chromatic dispersion produces the quadratic beating between the signal and the sum of time-sampled signals, which, in turn, makes the coefficients of some beating terms in Volterra series similar. Based on these findings, we reduce the number of coefficients to be determined in the quadratic VNLEs by grouping those beating terms. The performance of the proposed VNLEs is evaluated experimentally on a 56-Gb/s 4-ary pulse amplitude modulation link implemented by using a 1.55-μm DML. We measure the bit-error ratio performance of various equalizers, including feedforward equalizer, polynomial nonlinear equalizer, diagonally-pruned (DP) VNLE, and proposed quadratic VNLE, and compare them in terms of receiver sensitivity and implementation complexity. The results show that the proposed VNLE outperforms the DP-VNLE, although the implementation complexity of the two equalizers is similar. Also presented in this article is an algorithm for optimizing the parameter required in the proposed VNLE.