## 1 Introduction  
Nowadays, the majority of the transmitted digital data is carried by optical fibre cables, forming the major part of the telecommunications infrastructure worldwide. However, due to the explosive growth of the Internet and a number of bandwidth-hungry new services such as online gaming, 3D or high-definition TV and cloud computing, this infrastructure will eventually fail to satisfy future capacity needs. As Gartner Research states: \"4.9 billion connected things in use in 2015, and will reach 20.8 billion by 2020\". This growing demand for more capacity will lead to an imminent capacity crunch, should we not be successful in presenting innovative solutions to faster data transmission [1; 2]. Current optical networks are based on conventional single-mode fibre (SMF) cables and high-order modulation formats such as 16-quadrature amplitude modulation (16-QAM) where more digital information can be carried. This could form the most plausible alternative towards the desirable bandwidth capacity increase. However, the reason why we have not adopted this solution so far lies in the very cause of the capacity crunch itself which originates from the optical fibre Kerr effect [3]. The Kerr effect is a nonlinear phenomenon which causes distortion to the propagated optical signal and it is proportional to its power [4], resulting in the deceleration of the data transmission [5]. Few-mode fibers (FMFs) are naturally more prominent to nonlinearity due to the increasing crosstalk distortionsbetween the spatial modes, compared to the SMFs. On the other hand, the drive towards higher-order modulation formats, such as 16-QAM, and spectral-efficient techniques, such as orthogonal frequency division multiplexing (OFDM), lead to greater transmission impairments, reducing the maximum distance over which increased capacity can be provided. More specific, denser constellation diagrams render higher-order modulation formats are more susceptible to circularly-symmetric Gaussian noise as generated by Erbium-doped fiber amplifiers (EDFAs) along the transmission link [6]. Even though the launch power per wavelength channel can be increased to improve the signal-to-noise ratio (SNR) at the receiver, transmission is limited by nonlinear distortions due to the Kerr effect, which have a more severe impact on higher-order modulation formats and spectral-efficient modulation schemes [5; 7]. Moreover, the transmission of more than two signal wavelengths (wavelength-division multiplexing, WDM) through an optical fibre generates four-wave mixing (FWM), a process caused by the power dependence of the refractive index of the optical fibre [3]. FWM is related to fibre nonlinearity and gives rise to new wavelengths which significantly degrade the signal quality especially at high optical powers and when signals are spectrally close to each other. FWM is one of the most dominant nonlinear effects in optical networks and a primary root of the capacity crunch [3]. Since nonlinear noise such as FWM is highly correlated to signals themselves, nonlinearity can be mitigated by performing special treatment of the signals or conducting post-transmission digital signal processing (DSP) on received signals [5; 7]. On the other hand, coherent optical OFDM (CO-OFDM) [8] has attracted a lot of interest in optical fiber communications due to its simplified DSP units, high spectral-efficiency, flexibility, and tolerance to linear impairments. However, CO-OFDM's high peak-to-average power ratio (PAPR) imposes high vulnerability to fiber-induced nonlinearities [8]. Attempts to combat nonlinearities in CO-OFDM have been performed by deterministic nonlinearity compensators which take advantage of the fact that light scattering within a fibre is a deterministic process. Key techniques towards nonlinearity compensation (NLC) include mid-span optical phase conjugation (MS-OPC) [9], phase-conjugated subcarrier-coding (PCSC) [10], digital back-propagation (DBP) [11; 12], and inverse-Volterra series-transfer function (IVSTF) [13].