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OFDM symbol is given by [5] 

<img src='content_image/307454.jpg'>

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 

<img src='content_image/307455.jpg'>

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 

<img src='content_image/307458.jpg'>

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, 

