  Timing recovery is critical for synchronizing the clocks at the transmitting
and receiving ends of a digital coherent communication system. The core of
timing recovery is to determine reliably the current sampling error of the
local digitizer so that the timing circuit may lock to a stable operation
point. Conventional timing phase detectors need to adapt to the optical fiber
channel so that the common effects of this channel, such as chromatic
dispersion (CD) and polarization mode dispersion (PMD), on the timing phase
extraction must be understood. Here we exploit the cyclostationarity of the
optical signal and derive a model for studying the CD and PMD effect. We prove
that the CD-adjusted cyclic correlation matrix contains full information about
timing and PMD, and the determinant of the matrix is a timing phase detector
immune to both CD and PMD. We also obtain other results such as a completely
PMD-independent CD estimator, etc. Our analysis is supported by both
simulations and experiments over a field implemented optical cable.
