Modified Cramér–Rao Bound for Clock Recovery in the Presence of Self-Phase Modulation

We investigate the effect of nonlinear self-phase modulation (SPM) on clock recovery in long-haul coherent optical communication systems with low to moderate baud rates. We consider dual-polarization, multilevel quadrature amplitude modulation, and evaluate conventional timing estimators as well as a modified Cramér-Rao bound. As the latter is hard to compute in the presence of nonlinear channel impairments, we derive an approximate closed-form expression. Contrary to linear channel impairments, the nonlinear impairments can degrade the performance for higher input powers. In addition, the bounds exhibit oscillatory behavior due to the oscillations in the signal spectrum in the presence of SPM.