## 8 Recent Experiments of SDM Transmission Using FMFs  
Last but not least, a couple of topical experimental verifications are assessed facilitating a higher transmission capacity for short, medium, and long distances in this section, utilizing FMFs and/or MCFs, along with the progressive maturity of the SDM amplifier, spatial mode coupler, and digital MIMO equalizers to safeguard higher capacity and spectral efficiency. For instance, [PERSON] et al. conducted an experiment in 2018 for a MIMO-based 36-mode (two polarization modes) transmission over a 2-km-long 50-\(\upmu\)m graded-index multimode fiber (MMF) with a spectral efficiency of 72 bit/s/Hz, as denoted in Figure 32 along with the close-ups of the heterodyne  
Figure 31: BER vs. OSNR for MCF-based SDM transmission system using the joint DSP scheme [45]. Figure 30: A joint DSP approach for multicore fiber (MCF)-based SDM transmission system with master–slave phase recovery [44]. receiver arrangement and multimode acousto-optic modulator, as well as the spectrum of the test signal and location of the heterodyne filters and local oscillator [46]. The results were attained using a 72 \(\times\) 72 coherent MIMO-DSP, with five 15-Gbaud dual-carrier PDM-QPSK signals with a channel spacing of 50 GHz transmitted. Figure 33 denotes the experimental set-up of an MIMO-based 45-mode (two polarization modes) MDM transmission over a 26.5-km-long 50-\(\upmu\)m graded-index MMF over 20 wavelength channels resulting in a total capacity of 101 Tb/s and a spectral efficiency of 202/bit/s/Hz. The received 90-degree complex amplitude signals were processed by a 90 \(\times\) 90 MIMO-FDE with 300 symbol-spaced taps, whereas the initial convergence of the equalizer was obtained using the data-aided FD-LMS algorithm with CMA used after that. Then, the carrier-phase recovery and BER counting were performed, while the Q-factors were computed by evaluating an inverse Q function of the BER [47]. The corresponding plots also include the Q-factors of 90 spatial tributaries for QPSK and 16 QAM transmission in line with the mode groups, sorted by the performance within the mode group in Figure 33b, with the intensity-averaged impulse response attained from channel estimation over the MMF in Figure 33c, and the intensity transfer matrix showing the coupling between the mode groups in Figure 33d, along with the average Q-factor for QPSK and 16 QAM as a function of wavelength in Figure 33e. The error bars within the plots signify the best and the worst spatial tributaries. In another example, a 138 Tbit/s coherent transmission over six spatial modes plus two polarizations, and 120 wavelength channels carrying 120 Gbit/s mapped 16 QAM signals over a 65 km FMF12 fiber are shown in Figure 34, where low insertion and MDL mode-selective photonic lanterns are used along with a coherent 12 \(\times\) 12 MIMO equalization using a data-aided FD-LMS algorithm for resolving the modal mixing [48]. The FMF12 fiber is a special FMF designed to have low attenuation for the first 12 spatial channels, while having sufficiently high losses for the higher-order modes to guarantee an effective cut-off. At the receiver side, optical front-end impairment, CD, and frequency-offset compensation is performed, while the carrier phase recovery is performed before calculating performance metrics over 8 million bits per spatial channel. Moreover, the Q-factors versus the launch power averaged for 15 WDM channels, as well as for 120 WDM channels after 650-km transmission are shown in Figure 35, where the gradient of the shaded areas  
Figure 32: **(a) Setup of a 72 \(\times\) 72 MIMO-based transmission; (b) heterodyne receiver arrangement; (c) spectrum of the test signal and location of the heterodyne filters and local oscillator; (d) multimode acousto-optic modulator [46]. **  
in WDM channel performance [48]. In addition, the larger performance variations on the edges of the spectrum, and the singular values for each WDM channel averaged, corresponding to the measured MDL, are depicted in Figure 35c,d, respectively.