# Post-FEC Performance of Pilot-Aided Carrier Phase Estimation over Cycle Slip
## 3 Experimental Results and Discussion
When the OSNR is 10.5 dB, 12.1 dB, and 15.4 dB, the CPE filter lengths required to achieve \(1\times 10^{-6}\) are 32, 16, 8 for CPE scheme and 20, 6, 2 for CPE + PAPU scheme. As shown in Figure 4, the probability of CS is decreasing and the performance of PRE-FEC BER is improving with the increasing of OSNR, thus the difference between the required CPE filter lengths to achieve \(1\times 10^{-6}\) for two CPE schemes is small with high OSNR. With the lower OSNR, CPE + PAPU scheme is less sensitive to CPE filter length which may reduce the complexity of DSP. Figure 4: (**a**) Probability of cycle slips versus optical signal noise ratio (OSNR) for the CPE scheme and the CPE + PAPU scheme; (**b**) PRE-forward error correction (FEC) bit error rate (BER) versus OSNR for the CPE scheme and the CPE + PAPU scheme. The PRE-FEC BER and POST-FEC BER versus OSNR curves under different CPE filter lengths are shown in Figure 6b. Different CPE filter lengths are shown in the label. As is shown, the CPE + PAPU scheme outperforms the CPE scheme by about 3 dB at PRE-FEC BER of \(2\times 10^{-2}\) with CPE filter length less than 16. It can be easily observed that slight degeneration of PRE-FEC BER may lead to rapid deterioration of POST-FEC BER due to CS. Figure 6b also depicts the POST-FEC BER performance of CPE and CPE + PAPU scheme indicated by square and circle connected with solid lines, respectively. The results prove that the CPE + PAPU scheme achieves about 3 dB, 1 dB, and 0.5 dB POST-FEC OSNR gain compared with the CPE scheme under the CPE filter length of 8, 16, and 20. The CPE + PAPU scheme outperforms the CPE scheme under shorter filter length benefitting from its effectively CS mitigation. Figure 5: (**a**) Probability of cycle slips versus CPE filter length for the CPE scheme and the CPE + PAPU scheme; (**b**) PRE-FEC BER versus CPE filter length for the CPE scheme and the CPE + PAPU scheme, with OSNR equivalent to 10.5 dB, 12.1 dB, and 15.4 dB. Figure 6: (**a**) BER versus CPE filter length curves of CPE and CPE + PAPU, with OSNR equivalent to 10.5 dB, 12.1 dB, and 15.4 dB; (**b**) BER versus OSNR curves of CPE and CPE + PAPU with different CPE filter lengths (W and WO respectively present the CPE +PAPU scheme and the CPE scheme). Figure 7 shows the relationship between POST-FEC BER and PRE-FEC BER on the CPE + PAPU scheme and the CPE scheme. The AWGN theory curve is represented by dark hollow circle. Apparently, CPE filter length has no significant effect on the BER transfer characteristic for CPE + PAPU scheme. When the CPE filter lengths are respectively equivalent to 8, 16, 20, and 48, the CPE + PAPU scheme successfully decodes signals with \(1.4\times 10^{-2}\), \(1.8\times 10^{-2}\), \(1.9\times 10^{-2}\), and \(2.0\times 10^{-2}\) PRE-FEC BER and the CPE scheme fails to decode signals above \(2.5\times 10^{-3}\), \(8.9\times 10^{-3}\), \(1.6\times 10^{-2}\), and \(2.0\times 10^{-2}\) PRE-FEC BER. As shown in Figure 4a, the CPE + PAPU scheme still present some independent CS, however, these CS can be effectively corrected by FEC. The continuous CS induced by inappropriate PU and amplifier spontaneous-emission (ASE) noise cannot be corrected by FEC. Comparing with the CPE scheme, the CPE + PAPU scheme seems to be less sensitive to CPE filter length. This might be attributed to the fact that the CPE + PAPU scheme effectively mitigates continuous CS induced by phase noise and inappropriate PU.