## 1 Introduction  
Nonlinearities in long-haul fiber-optic communication systems present an obstacle to the capacity increase of optical transport networks [1]. Nonlinear compensation methods (digital or optical) have been extensively studied in recent years [2]. Digital equalization techniques can provide mitigation of both linear and nonlinear effects in coherent optical communication systems and fall into two main categories [3]: (a) pre-compensation methods that create a more resilient signal to fiber nonlinearities prior to fiber propagation [4; 5]; and (b) post-compensation techniques, which are applied on the distorted signal after propagation. The latter category includes nonlinear equalizers (NLEs) based on perturbation solutions of the coupled nonlinear Schrodinger equations (CNLSE) [6; 7; 8], the digital back-propagation (DBP) based on the split-step Fourier (SSF) method [9; 10; 11], and Volterra transfer function series-based NLEs [12; 13], using either 3 rd-order [14; 15; 16; 17] or 5 th order-kernels [18; 19]. The last few years, interesting studies have been published on the 3 rd-order Volterra-based NLEs [14; 15; 16; 17]. For this category of NLEs, the linear and nonlinear compensation is performed in parallel, rendering them more suitable for real-time implementation. One of these published works investigates the performance of a Volterra series intra-channel NLE, based on an analytical closed-form solution for the 3 rd-order Volterra kernel, in the frequency domain [14]. This Volterra-NLE is tested in a single-channel optical system using a 20 Gbaud, non-return-to-zero (NRZ)-quadrature phase shift keying (QPSK) signal after 1600 km of both SSMF and non-zero dispersion shifted fiber [14]. The results reveal a \(\sim\)2 dB \(Q^{2}\)-factor improvement on the nonlinear tolerance relatively to the multistep-per-span DBP-SSF method when 2 samples per symbol (SpS) are used for the equalization process [14]. Even though the equalization performance of the 3 rd-order Volterra-based NLEs can compete with the widely-used DBP-SSF method, the increasing need for reduced computational complexity has triggered more in-depth studies on this topic [15]. One of them is the numerical study of the performance of a simplified Volterra NLE, which showed reduction of the total computational complexity by a factor of \(\sim\)3 compared to the full Volterra NLE [15], when tested on a long-haul 224 Gb/s dual-polarization (DP), 16-ary quadrature amplitude modulation (QAM) transmission system [15]. Then, a 3 rd-order inverse Volterra series transfer function (IVSTF)-NLE was studied via simulations in [16], on a single-channel transmission system using a 256 Gb/s DP, 16 QAM signal after 1024 km of an SSMF, revealing a 1 dB \(Q^{2}\)-factor improvement and a 50% reduction in the computational complexity by lowering the processing rate. Later, the performance of a variant of the 3 rd-order IVSTF-NLE was studied in a coherent orthogonal frequency division multiplexing (OFDM) single-channel system of the same total rate and transmission distance [17] showing a \(Q^{2}\)-factor improvement of 2 dB, i.e., 1 dB higher compared to the study of [16]. Up to date and to the best of our knowledge, no experimental work has been published on investigating the potential of a 3 rd-order IVSTF-NLE in a long-haul wavelength division multiplexing (WDM) system consisting of high-bit rate super-channels, as high as 400 Gb/s, which are necessary, nowadays, to meet the requirements of high-speed transmission [20]. Therefore, there is a gap in the available literature which should be covered. A very appealing version of a super-channel is based on a DP, multi-band OFDM signal offering greater spectral efficiency and increased nonlinear tolerance compared to the single-carrier case, mostly due to the splitting of high-baud-rate, single-carrier signals into multiple multiplexed low-baud-rate subcarriers [21].