Enabling Equalization and Soft Decision by k-Means for VCSEL-Based PAM-4 Optical Interconnection

As for vertical-cavity surface-emitting lasers (VCSEL)-based optical pulse amplitude modulation (PAM) interconnection system, apart from the universal signal distortions like Gaussian noise and fiber dispersion, direct modulation of VCSEL specially induces level nonlinearity and level-dependent noise. To mitigate these two specific distortions in VCSEL-based link, a k-means assisted PAM-4 signal receiver including equalization and soft decision (SD) is proposed. Based on learned mean values and standard deviations for individual levels through k-means approach, probability density function of nonlinearly distorted PAM-4 symbols can thus be approximated more precisely than conventional SD, leading to improved decision performance. In addition, depending on k-means result, least means square (LMS) equalization with adapted levels can converge to a lower error value than conventional LMS, thanks to level nonlinearity mitigation. Consequently, by using proposed k-means equalization and SD, improved signaling performance can be obtained by mitigating the level nonlinearity and level-dependent noise. Both simulation and experiment are performed for evaluating the proposed method in a 100-Gb/s VCSEL-MMF PAM-4 optical interconnection system, by comparing with conventional means.