## 1 Introduction  
With the new trends in technology such as cloud computing, Internet of Things and 5G fronthaul, the capacity of optical systems based on single-mode fiber (SMF) transmission links has reached their limit [1]. Hence, the development of cutting-edge communication links, which subjects to address the incessant demand for higher data capacity and cost-effectiveness, is crucially required. By utilizing the transverse spatial extent of a multi-mode fiber (MMF) core, parallel individual data channels can be created over non-overlapping subsets of excited mode groups [2]. This approach is named as space-division multiplexing (SDM) in which an MMF is essential, as these fibers support up to 100 transverse spatial modes that can be translated as parallel data channels [1; 2]. SDM also provides the higher spectral efficiency to cope up with the bandwidth-intense applications. The capacity crunch due to the SMFs is eliminated by using the MMFs with SDM. Moreover, for short reach optical links, intensity modulation/direct detection (IM/DD) systems with an MMF provides a cost-effective solution. The consequences of employing the MMFs are mode scrambling and inherent inter-modal dispersion, which are limiting factors for the maximum achievable data rates [3]. By applying multiple-input and multiple-output (MIMO) techniques, the adverse effects of the mode scrambling are mitigated and higher data capacity is achieved [4; 5; 6]. Additionally, the higher spectral efficiency can be boosted by utilizing higher-order modulation (HOM) formats which include pulse-amplitude modulation (PAM) schemes. These HOM formats, PAM-\(M\), provide larger constellation sizes, \(M>2\), which offer efficient use of the bandwidth. The main challenges are to excite a particular mode group and extraction of them at the receiver due to strong temporal broadening of the light from the MMF channel. The countermeasures to mitigate the dispersive-induced impairments are by using the physical optical components such as dispersion-shifted fibers or fiber Bragg gratings [7]. Most prevalent dispersion compensation mechanisms include the use of digital signal processing such as equalization. Conventionally, when the trade-off between cost-effectiveness and complexity is taken into account, a linear MIMO equalizer is preferred. The non-linear equalizers, such as Viterbi equalizer or Tomlinson-Harishima precoder, perform better than a linear equalizer such as minimum mean-squared error (MMSE). However, the mathematical traceability and comprehensive implementation of a linear equalizer is chosen in comparison to the complex realization of the non-linear equalizer [1,8]. From the literature, it is evident that the equalizer present at both the transmitter and the receiver offers better performance than the equalization which is only limited to either the transmitter or the receiver [9,10]. Few studies have explored the usefulness of pre- and post-equalization (PPE) schemes, and these schemes have been tested on optical systems based on SMF, which is impaired with chromatic dispersion only [11, 12, 13]. The joint design and optimization of a PPE filter with HOM formats for an MMF-based optical MIMO system has not been established yet. Against this background, the novelty of this work is improvement in the bit-error rate (BER) using the joint-PPE scheme while employing HOM formats in an IM/DD system. The competency of the joint-PPE scheme is provided over an optical (\(2\times 2\)) MIMO system based on an MMF channel, which is critically impaired with inter-symbol interference (ISI) and inter-channel interference (ICI). The coefficients of the PPE are mutually computed and optimized using a numerical optimization algorithm in presence of the frequency-selective channel. This work also provides a cost-effective and low complexity solution by using a parallel frame synchronization (PFS) experimental setup.