## 2 Experiment Setup  
Figure 1 shows a diagram of experimental 640 Gbps 16-QAM CO-OFDM transmission over 800 km fiber with a mid-link OPC. Likewise, the same optical simulation system as the laboratory experimental system described in Figure 1 is implemented on the \"OPTISYSTEM 15.0\" optical simulation platform [21]. In the transmitter, two signal streams are loaded into two parallel arbitrary waveform generators (AWG, M8195A: Keysight, Penang, Malaysia) running at 64 GS/s and modulated with a pair of parallel dual-drive Mach-Zehnder modulators (MZM) with opposite polarity, respectively. The signal laser has 193.1 THz (1552.52 nm) central frequency and 0.3 MHz linewidths. At the output of MZM, there are in-phase optical 16-QAM and quadrature-phase optical 16-QAM, respectively, in which each signal stream is composed of 80 sub-carriers. Two optical 16-QAM signal streams, orthogonal to each other, are coupled into a 16-QAM CO-OFDM stream at a bit rate of 640 Gbps. The detailed parameters of the experiment are shown in Table 1.  
The fiber link is implemented by 16 spans of 50 km standard single-mode fiber SMF-28e+ (SSMF, Corning) and an erbium-doped fiber amplifier (EDFA, AEDFA-18-B-FA: Amonics, Hong Kong, China) of 10 dB gain per span. Variable optical attenuators (VOAs, VOAA-15-40-S/FA: OptoQuest, Saitama Prefecture, Japan) are employed at the input of each fiber span to ensure the optical signal power symmetry throughout the system [16]. Band-pass filter (BPF, WSS-1000s: Finisar, Sydney, Australia) with bandwidth 0.32 nm is used to minimize the amplified spontaneous emission (ASE) noise. Alternatively, a dispersion compensated fiber (DCF) with group velocity dispersion (GVD) of \(-98\ ps/nm/km\) and attenuation of 0.16 \(dB/km\) is implemented as a bypass route to evaluate the effect of \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline Bit rate & 640 Gbps \\ Maximum possible sub-carriers & 128 \\ Number of sub-carriers & 80 \\ Number of prefix points & 10 \\ Number of training symbols & 10 \\ Number of pilot symbols & 6 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The experiment parameters. Figure 1: A diagram of 16-QAM coherent-optical orthogonal frequency-division multiplexing (CO-OFDM) transmission with mid-link optical phase conjunction (OPC) compensation. fiber nonlinearity on 16-QAM CO-OFDM signal without OPC, where an EDFA to provide 20 dB gain in signal power and an optical BPF of 0.32 nm to minimize the ASE noise are included for comparing with the case of using OPC under the same conditions. The mid-link OPC has two inputs, including dual pump laser signals at 193.14 THz (1552.20 nm) and the 16-QAM CO-OFDM signal at 193.1 THz (1552.52 nm). A polarization beam combiner (PBC) provides orthogonal polarization for the pumps to achieve polarization-insensitive operation. To prevent useless idles generated by two different pump frequencies, two pumps with the same frequency of 193.14 THz are utilized to improve the phase conjugation efficiency and polarization insensitivity [4]. The optical phase conjugation occurs at a center frequency 193.18 THz (1551.88 nm) based on FWM which benefits from HNLF [13]:  
\[\lambda_{con}=2\lambda_{pump}-\lambda_{sig} \tag{1}\]  
At the receiver end, the 16-QAM CO-OFDM signal into 90\({}^{\circ}\) hybrid coherent detection which consisting of a Kylia optical hybrid and balanced photodiodes to down-convert the optical signal. A real-time sampling oscilloscope (DSO-X 92804A Infiniium: Agilent, Penang, Malaysia) running at 80 GS/s was used as the analog to digital converter (ADC). Clearly, when 16-QAM CO-OFDM signal is given, the design of OPC involves the selection of HNLF length and the optimization of signal power and pump signal power that inputs into OPC, which are highly related to the characteristics of HNLF. Hence four different types of HNLFs, as illustrative examples, are considered to study how to select suitable OPC parameters based on the HNLF characteristics.