  A joint frame and carrier frequency synchronization algorithm for coherent
optical systems, based on the digital computation of the fractional Fourier
transform (FRFT), is proposed. The algorithm utilizes the characteristics of
energy centralization of chirp signals in the FRFT domain, together with the
time and phase shift properties of the FRFT. Chirp signals are used to
construct a training sequence (TS), and fractional cross-correlation is
employed to define a detection metric for the TS, from which a set of equations
can be obtained. Estimates of both the timing offset and carrier frequency
offset (CFO) are obtained by solving these equations. This TS is later employed
in a phase-dependent decision-directed least-mean square algorithm for adaptive
equalization. Simulation results of a 32-Gbaud coherent polarization division
multiplexed Nyquist system show that the proposed scheme has a wide CFO
estimation range and accurate synchronization performance even in poor optical
signal-to-noise ratio conditions.
