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.
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