MCRB for Timing and Phase Offset for Low-Rate Optical Communication with Self-Phase Modulation

We derive the modified Cramer-Rao bound (MCRB) for symbol timing and phase offset estimation in the presence of nonlinear self-phase modulation (SPM) in a dispersion compensated long-haul optical fiber link with coherent detection at data rates below 10 Gigabaud. In the presence of a low-pass filter at the receiver front-end, we find that SPM degrades the MCRB. Moreover, depending on the pulse shape, SPM induces underdamped oscillation on the bounds.