OFDM symbol is given by [5] where φ is a common phase error (CPE) noise owing to the phase noises that varies for different OFDM symbols. In (1) Φ$_{D}$( f$_{m}$ ) is the phase dispersion owing to CD and given by H$_{m}$ = e $^{jφ}$ej Φ$_{D}$( f$_{m}$ $^{)}$T$_{m}$ , (1) Φ$_{D}$( f$_{m}$ ) = πcDLf 2 m f 2 c , with f$_{m}$ = m − 1 t$_{s}$ . (2) where t$_{s}$ is the actual time duration of one DFT-spread OFDM symbol not including the cyclic prefix; c is the speed of the light; D is the CD parameter in unit of ps/pm/km; L is the total length of the multi-span fiber link; and f$_{c}$ is the carrier frequency of the laser. Here we assume that the periodic dispersion map is employed and the CD is completely compensated for at each span. Hence T$_{m}$ in (1) is the Jones matrix with the dispersion compensation fiber (DCF) inserted at each stage, given by where k$_{l}$ denotes the attenuation factor of PDL; τ$_{l}$ is the differential group de- lay (DGD); θ$_{l}$ is the uniformly random rotation angle [6]. For each span, the DGD is a random variable following the Maxwellian distribution. However, T$_{m}$ = n$_{E}$ ∏ l =1 e − j Φ D ( f m ) n E    1 0 0 k$_{l}$    ·    e jπ ( f$_{c}$ + f$_{m}$ ) τ$_{l}$ 0 0 e − jπ ( f$_{c}$ + f$_{m}$ ) τ$_{l}$    ·    cos θ$_{l}$ sin θ$_{l}$ − sin θ$_{l}$ cos θ$_{l}$    , (3) 6