On the Limits of Digital Back-Propagation in Fully Loaded WDM Systems

We investigate upper bounds for single- and multichannel digital back-propagation (BP) in fully loaded wavelengthdivision multiplexed (WDM) systems. Using the time-domain model for nonlinear interference noise, we expand previous estimates of BP gains to accurately cover a wide range of system configurations, including a variety of modulation formats from quadrature phase shift keying (QPSK) to 256-ary quadrature amplitude modulation (256-QAM). In typical scenarios the potential benefit of single-channel BP is limited to about 0.5 dB in terms of the peak signal-to-noise ratio (SNR), and to about 1 and 1.2 dB in the case of joint 3- and 5-channel BP. The additional gain from increasing the number of jointly backpropagated channels beyond 5 is limited to about 0.1 dB per additional back-propagated channel. We also study the role of BP for receivers that separately compensate for nonlinear phase and polarization rotation noise (PPRN) and show that while the additional gain provided by BP does not change significantly in long-haul systems, it holds the promise of being notably higher in short-reach ultra-high-capacity systems.