MCRB for timing, phase and frequency estimation in presence of self-phase modulation for low-rate optical communication

In this paper we derive the theoretical lower bound, namely Modified Cramér-Rao bound (MCRB) for symbol timing, phase and frequency offset in presence of nonlinear self-phase modulation (SPM) in a dispersion compensated long-haul coherent fiber link. The system model considers multiple span of fiber each associated with optical amplifier. Dual polarization multilevel quadrature amplitude modulation is opted for data transmission to support the data rate lower than 10 Gigabaud. We find that SPM induces underdamped oscillation on the MCRB bounds depending on the pulse shapes (symmetric and asymmetric) utilized. In presence of realistic low-pass filter at the receiver front end, the MCRB degrades significantly due to SPM. We also show the effect of SPM on symbol error rate degradation. Simulation is carried out with symmetric return-to-zero pulse with duty cycles of 33, 67 % and self-generated asymmetric pulse to verify the theoretical results.