The first-order (FO) perturbation theory-based nonlinearity compensation (PB-NLC) technique has been widely investigated to combat the detrimental effects of intra-channel Kerr in polarization-multiplexed (Pol-Mux) optical fiber communication systems. However, NLC performance FO-PB-NLC is significantly limited highly nonlinear regimes Pol-Mux long-haul transmission In this paper, we extend FO t...