Analytical Evaluation of Practical DBP-Based Intra-Channel Nonlinearity Compensators

We derive an analytical expression for the transmission performance of intra-channel nonlinearity compensated and dispersion unmanaged orthogonal frequency-divison multiplexing (OFDM) systems using practical digital back propagation (DBP) with span-length step size. The analytical expression is verified by numerical simulations with evaluation inaccuracy less than 0.4 dB for 1000-km 16-QAM modulated polarization division multiplexed-OFDM transmissions. Using the derived theory, the dependence of performance and optimum nonlinear compensation coefficient on system parameters is identified. The limitation of processing bandwidth on the performance improvement using practical intra-channel DBP is also investigated. Analytical results show that for achieving 1-dB improvement on maximum $Q^{2}$ factor, the processing signal bandwidth of span-length step size DBP should be within 55 GHz for 2000-km SSMF transmissions over 62.5-km spans.