MCRB for synchronization parameters offset in the presence of self-phase modulation in coherent optical communication

In this paper we derive the Modified Cramér-Rao Bound (MCRB) for symbol timing, phase and frequency offset in presence of non-linear self-phase modulation (SPM) in a dispersion compensated long-haul coherent fiber link. We consider dual polarization multilevel quadrature amplitude modulation and multiple span of fiber each associated with optical amplifier. In presence of a realistic low pass filter (LPF) at the receiver front end, we find that SPM degrades the MCRB significantly. Moreover, SPM induces underdamped oscillation on the bounds. Simulation is carried out with self-generated asymmetric pulse to verify the theoretical results.