## 1 Introduction  
The optical network demands to have a transmission capacity of over 1000 Gbps, so coherent-optical orthogonal frequency-division multiplexing (CO-OFDM) as an advanced modulation scheme is currently under investigation to support both high spectral efficiency and long transmission distance. The advantage of CO-OFDM includes seamlessly multi-plexed sub-carriers which not only offer a high spectral efficiency but also enable efficient channel estimation and dynamic allocation of carrier number and data rate at negligible hardware cost. In 2016, [PERSON] et al. demonstrated a single-wavelength 400 Gbps OFDM experimental system [1]. However, due to the relatively high peak-to-average power ratio, the long-haul transmission of CO-OFDM is constrained by self-phase modulation (SPM), cross-phase modulation (XPM), and four-wave-mixing (FWM), which become significant under a high signal launched power [2]. From this point of view, if high launched power is used to improve the optical signal-to-noise ratio (OSNR) and transmission distance, the nonlinear mitigation is indispensable. There are many approaches of nonlinear compensation available in the literature. [PERSON] et al. proposed an adaptive modulation technique to mitigate fiber nonlinear effects [3]. Optical phase conjugation (OPC) is an approach for nonlinear compensation in long haul transmission over optical fiber, where the signal formats and bit rates are heterogeneous and agnostic [4; 5]. OPC based on FWM benefits from the uniqueness of signal-transparent, multichannel-adaptive, wide bandwidth, and effective in simultaneous compensation of linear dispersion and nonlinear impairments [6; 7]. OPC combined with wavelength division multiplexing (WDM) to transmit intensity-modulated and phase-modulated signals were tested in the laboratory [6]. Likewise, OPC is also utilized in a long-haul transmission based on multichannel and agnostic modulation-format/bitrate operations [7; 8; 9]. Recently, CO-OFDM has become increasingly popular owing to its capability to retrieve complex signals [10; 11]. Whilst considering long haul transmission, linear dispersion and nonlinear effect in fiber can distort the signal [11; 12]. There are a number of digital OPC solutions, including a semiconductor optical amplifier (SOA) [13], periodically-poled lithium-niobate (PPLN)-based guard-band-less optical phase conjugation [14], and silicon waveguide-based OPC [15]. However, such OPC solutions are inefficient for multiple sub-channel operations in real-time due to the limited available bandwidth of the components. Besides, the nonlinear distortion compensation requires a large computing resource. In practice, mid-link OPC, also named mid-span spectral inversion (MSSI), is utilized to enhance the transmission quality over long haul fiber [1], where the key element for optical phase conjugation is HNLF [2] through XPM and FWM effects. For example, mid-link OPC compensation is employed in 2\(\times\), 4\(\times\), and 8 \(\times\) 28 Gbps PM-QPSK over 100 km fiber [8] and 3 \(\times\) 20 Gbps PAM4 over 360 km fiber [9]. The numerical results demonstrate that OPC compensates 90% of the signal nonlinear interference, equivalent to 2.3 dB Q-factor gain [10]. Furthermore, mid-link OPC implemented by wavelength shift-free technique [11] shows that 0.7 dB gain in Q-factor can be obtained in the transmission of 8 \(\times\) 200 Gb/s polarization division multiplexed 16-QAM over 1.6 Tb/s fiber for 800 km. Regarding to WDM employed in long haul fiber transmission, a 64-QAM signal over 400 km is equipped with mid-link OPC [16]. The numerical results show that Q-factor gain up to 2.5 dB can be achieved. Nonlinear distortion mitigation in OPC can also be implemented by introducing backward-pumped Raman amplifier that allows a lower input signal power of 2 dB compared with direct transmission.