## 1 Introduction  
In recent years, phenomenal growth in the demand for bandwidth has been witnessed due to the progress in cloud computing, high-definition video streaming, and the internet of things. The surge in the increasing data requirements has inspired the expansion of telecommunication networks by developing better modulation and coding techniques. Optical networks have provided support to match the high-bandwidth requirements from short-haul to the long-haul transmission links. Single-mode fibers (SMFs) are preferred for long-distance optical systems due to their low dispersion properties and low signal attenuation. Despite the availability of degrees of freedom such as time, wavelength, or polarization, the capacity of an SMF is rapidly reaching [PERSON]'s limit [1, 2, 3]. Furthermore, the small core diameter of an SMF causes sub-micron alignment tolerances. Multi-mode fibers (MMFs) consist of a larger core (50 \(\upmu\)m or 62.5 \(\upmu\)m) and hence have higher alignment margins. Due to the larger core diameter, the MMF core can support multiple parallel data channels using up to 100 transverse spatial mode groups [4; 5; 6]. The orthogonality between different mode groups is only preserved for a short distance. In an intensity modulation/direct detection (IM/DD) system for short-reach optical links, an MMF is preferred over an SMF due to higher spectral efficiency, cost-effectiveness and simple implementation. However, MMFs adversely affect the available bandwidth distance product as a result of intermodal dispersion and mode-dependent losses such as mode scrambling [6; 7; 8]. The technique for creating multiple parallel data channels using the transverse spatial extent of an MMF is known as space-division multiplexing (SDM) [9]. Offset light-launching conditions excite two or more parallel data streams in the SDM technique. The considerable enhancement in the data rates and the mitigation of mode scrambling are handled by incorporating the multiple-input and multiple-output (MIMO) signal-processing technique [6; 7]. Moreover, the spectral efficiency of the transmission link is boosted using the higher-order modulation (HOM) formats, where the constellation size is more than two. In particular, in an IM/DD system, the pulse-amplitude modulation (PAM) formats are preferred over subcarrier modulation (SCM) [10], carrier-less amplitude modulation (CAP) [11], or discrete multitone (DMT) [12; 13] in terms of simple implementation and better sensitivity regarding the received optical power. However, an MMF channel is severely impaired by intermodal dispersion compared to an SMF link [8]. Dispersion compensation mechanisms include physical components, such as dispersion-shifted fibers or fiber Bragg gratings, and digital mitigation using equalization. In an IM/DD system, when a trade-off between complexity and cost-effectiveness is considered, digital dispersion compensation mechanisms, especially linear MIMO equalizers, are preferred. On the other hand, the performance of non-linear MIMO equalizers surpasses most optimal linear MIMO equalizers based on the minimum mean-squared error (MMSE) principle [14; 15; 16; 17]. However, a linear MMSE-based equalizer is selected because of comprehensive implementation, simple realization and analytical traceability [3; 18]. Additionally, a further boost in the system performance is evident in the presence of a transceiver equalization compared to the equalization applied either at the transmitter or the receiver [14; 15; 19]. According to the literature, the zero-forcing (ZF) principle is commonly adapted for the design of the pre-equalizer. Moreover, a separate equalization principle is utilized to calculate the post-equalization coefficients [16; 17; 20; 21]. Additionally, the performance evaluation of these pre- and post-equalization (PPE) schemes is validated either on the single-input and single-output (SISO) system model or over an SMF fiber [16; 17; 21; 22].