3.6 Conclusion 73 link. In this case, digital back-propagation [118,119], which reversely solves the nonlinear Schro dinger equation at the receiver through DSP, can be applied. Digital ¨ backward propagation can also be implemented at the transmitter [120]. However, digital backward propagation requires multiple back-propagation steps, each step requiring a DSP load similar to that of a generic digital coherent receiver, so the needed DSP resource and power are much increased. In WDM transmission, inter-channel cross-phase modulation (XPM) and FWM also cause nonlinear penalty. These penalties can be substantially compensated by using digital back-propagation, but this requires the receiver to jointly process the sampled fields of the interacting wavelength channels, which further increases the needed computational load [121]. For compensating inter-channel FWM, the phase relationship among the interacting channels also needs to be obtained, and this causes additional hardware complexity, e.g., by requiring phase locking between the transmitter laser and the optical local oscillator and/or higher receiver sampling bandwidth. Nevertheless, future advances in DSP circuits and in nonlinear compensation/mitigation methods may help relax the nonlinear Shannon limit. 3.5.6 Spatial multiplexing