# Post-FEC Performance of Pilot-Aided Carrier Phase Estimation over Cycle Slip
## 2 Experimental Setup and Principles  
A 28 Gbaud single-polarization (SP)-QPSK experiment has been conducted to investigate the POST-FEC performance and the CS probability of the previous proposed CPE + PAPU scheme [27]. Figure 1 illustrates the block diagram of the experimental setup. A DFB laser with 300-kHz line-width, centered at 1550 nm, is used as the transmitter laser. The independent pseudo-random binary sequences (PRBS) are encoded in sequence by outer encoder, Reed Solomon (RS) (255,239), and inner encoder LDPC. Inner encoder uses the most commonly used soft-decision code, DVB-S2 (LDPC), with 11.1% overhead [26] and its maximum decoder iteration number is 50. Pilot symbols with known information of 0.78% [27] overhead are inserted periodically per 127 symbols at the transmitter side and the phase estimated by the pilot symbols are used as a reliable reference in the CPE phase unwrap process at the receiver side. Pilot inserted data are loaded to pulse pattern generator (PPG) and then modulated by a double balanced modulator (IQ modulator) to generate 56 Gbit/s QPSK signals. An erbium-doped optical fiber amplifier (EDFA) cascaded by a variable optical attenuator (VOA) are used as noise source. An optical coupler (OC) with coupling ratio of 1:99 splits the output optical signals. One of branch is sent to the coherent receiver for signal processing, the other is used to detect optical signal noise ratio (OSNR). Agilent optical modulation analyzer with sampling rate of 80 GSa/s and bandwidth of 33 GHz is used as coherent receiver and off-line DSP. The key physical parameters in the experimental setup are specified and summarized in Table 1.  
In the offline DSP, the signals are firstly processed by Gram-Schmidt orthogonalization procedure (GSOP) [28] to compensate in-phase (I) and quadrature (Q) imbalance. Then, the Gardner algorithm [29] is adopted to recovery clock and M-power frequency offset estimation (FOE) algorithm [30] is used to compensate frequency offset. Following the FOE, two different algorithms are employed to estimate the carrier phase. The first scenario is the traditional CPE based on VVPE, and the CPE + PAPU is adopted as the second scenario. The principle of the CPE scheme and the CPE + PAPU scheme are respectively shown in Figure 2a,b. The key point of the CPE + PAPU scheme, as shown in Figure 2b, is the pilot-symbols-aided phase unwrapping (PAPU), which does CS detection and correction in a completely forward way and combine itself with the usual phase unwrapping. Without loss of generality, we use VVPE as the CPE, and PAPU is implemented as the following procedure. After carrier phase recovery, LDPC decoder and RS decoder are conducted. Finally, the BER is calculated using 10 M bits data.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline Symbol Rate & 28-Gbaud \\ Wavelength & 1550-nm \\ Linewidth & 300-kHz \\ Bandwidth of Modulator & 40-GHz \\ Bandwidth of Receiver & 33-GHz \\ Sampling Rate & 80-GSa/s \\ \hline \hline \end{tabular}
\end{table}
Table 1: Summary of the key physical parameters in experimental setup.  
Figure 1: Experimental setup.  
Figure 2: Fourth-power carrier phase recovery with (**a**) usual-phase unwrap, (**b**) pilot-symbol-aided phase unwrap.