In order to investigate the effects of PMD, numerical simulations were performed using five polarization multiplexed QPSK Nyquist WDM signals (central channel $193.1\,THz$) over a transmission link comprising thirty two 80 km spans of standard single mode fiber using various numbers of ideal optical phase conjugation devices, distributed uniformly along the link. The transmitter and transmission link were implemented in $VPI~TransmissionMaker9.3$ simulated with $2^4$ bits per symbol per polarisation ($\approx$ 0.9 THz simulation bandwidth). Ideal lossless Raman amplification and zero dispersion slope are assumed to allow the results to focus on the detrimental impact of PMD without being obscured by power-dispersion symmetry. To increase accuracy of the parametric noise amplification, which is dependent on the point at which amplified spontaneous emission is generated, noise was added every $2.5~km$ assuming a nonlinear coefficient of $1.13$. Other fibre parameters are dispersion of $-16 ps/(km~nm)$ and a background loss of $0.046~km^{-1}$. The correlation length of the fiber birefringence was set to $50\,m$.In the transmitter 28 Gbaud Nyquist signals with a roll off factor of 0.01 were simulated, with $2^{10}$ bits per polarization and per wavelength (33 GHz Nyquist spaced wavelengths). An ideal model of the inline optical phase conjugator was used with practical realisation impairments, such as excess losses and crosstalk, neglected also to enable us to focus on the impact of PMD. The iPCs were implemented by reversing the sign of the imaginary field components using a $Matlab~2015b$ cosimulation. The iPCs were placed at intervals of 16,8,6,2 and 1 spans. By using an odd number of uniformly spaced iPCs the signals were received without net wavelength conversion and the dispersion compensation block in the receiver DSP could be bypassed. Ten simulation runs per point were performed with different random number seeds for each 2.5 km section determining both polarisation rotation and for each spontaneous emission noise. After coherent detection, the receiver DSP was implemented in Matlab. The received signal was down-sampled to $2$ samples per bit and filtered using a matched filter. For reference uncompensated transmission, chromatic dispersion was first compensated using a fixed frequency domain equalizer. The signal was then polarization demultiplexed using a $5$ tap butterfly filter, optimized using a constant modulus algorithm. % and providing at least 76\% more DSP memory than the mean DGD anticipated for the highest level of PMD simulated.
Phase recovery was performed using a Viterbi-Viterbi algorithm with a averaging window of $21$. Performance is illustrated by the $Q^{2}$-factor of the central channel estimated from the constellation diagram\cite{ECOC:Carena2010}.