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

We investigate upper bounds for single-channel and multi-channel digital back-propagation (BP) in fully loaded wavelength-division multiplexed 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 to 256-ary quadrature amplitude modulation. In typical scenarios, the potential benefit of singlechannel BP is limited to ~0.5 dB in terms of the peak signal-tonoise ratio, and to ~1 and ~1.2 dB in the case of joint threeand five-channel BP. The additional gain from increasing the number of jointly back-propagated channels beyond five is limited to ~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 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.