A Perturbation-Aided Residual Bidirectional GRU Nonlinear Equalizer for DP-16QAM Optical Communication Systems

Residual Kerr-induced nonlinear distortion after linear digital signal processing remains a major performance limitation in long-haul dual-polarization 16-QAM (DP-16QAM) coherent optical transmission. To address this issue, a perturbation-aided residual bidirectional gated recurrent unit (Bi-GRU) nonlinear equalizer is proposed. First-order perturbation theory is employed to extract impairment-related features as physical priors. Following PCA-based feature decorrelation and compact nonlinear projection, a two-layer Bi-GRU captures the bidirectional temporal dependencies associated with dispersion-coupled nonlinear inter-symbol interference, while a residual prediction head estimates the remaining nonlinear I/Q distortion. Numerical simulations of a 1200 km, 100 Gb/s DP-16QAM transmission link demonstrate that the proposed equalizer achieves a lower BER than linear DSP, digital backpropagation, pure Bi-GRU, a parameter-matched perturbation-aided CNN, and a perturbation-aided unidirectional GRU around the optimum launch power. Specifically, the proposed Bi-GRU achieves a mean BER of 8.785×10−5, compared with 1.079×10−4 for the parameter-matched CNN. Its BER is also comparable to the 8.976×10−5 obtained by the perturbation-aided Bi-LSTM, while requiring 19.7% fewer trainable parameters. These results indicate that the physical perturbation prior and bidirectional temporal modeling improve nonlinear impairment compensation without introducing a substantial computational burden, enabling the proposed equalizer to achieve a favorable performance–complexity trade-off.