We evaluate the performances of 25.78-Gb/s signals modulated in on-off keying and four-level pulse amplitude modulation (PAM4) formats in the 12.2-km long multi-mode fiber (MMF) transmission system implemented by using the mode-field matched center-launching technique, which is realized simply by fusion-splicing the single-mode fiber (SMF)-pigtailed transceivers to the transmission MMF. The results show a serious bit-error rate (BER) fluctuation as well as a large power penalty for the PAM4 signal after the 12.2-km long MMF transmission. We identify that the power penalty and BER fluctuations are caused by the signal-to-interference beat noise generated in the SMF-pigtailed receiver, resulting from the small portion of the signal (similar to 5%) unwantedly carried by the high-order modes of MMF. However, we can suppress this beat noise by replacing the SMF-pigtailed receiver with the MMF-pigtailed one since all modes are orthogonal in MMF. For example, when we utilize this proposed method, the power penalty of the 25.78-Gb/s PAM4 signal measured after the transmission over 12.2 km of MMF is reduced from 3.9 to 0.9 dB (@ BER = 5x10(-5)). We also demonstrate the transmission of the 56-Gb/s PAM4 signal over 2.3 km of MMF by using this method.