In this paper, we propose a statistical adaptive derivative equalizer (SADE) in order to reduce an optical beat interference (OBI) noise in an optical access link. The proposed SADE generates an output signal similar to the shape of the input pulse amplitude modulation (PAM)-4 signal waveform, which is implemented as an adaptive total variation that responds to the shape of the multi-step signal waveform with the weighting function considering the Lorentzian characteristics of the OBI noise. We implement a 20-km optical link and measure the bit error rate (BER) and signal to noise ratio (SNR) to see if the OBI noise was reduced using the proposed technique. A 1.5-dB SNR gain was observed over the overall SNR range of received PAM-4 signal than that without the use. A power penalty in the case of using only SADE was improved by 1.5 dB at 7% forward error correction (FEC) limit compared to that without the SADE. Furthermore, when the proposed SADE and matched filter were applied simultaneously, about 2.5-dB power penalty was observed at the 7% FEC limit.