In recent years, short-reach optical links have attracted much more attention and have come to constitute a key market segment due to the rapid development of data-center applications and cloud services. Four-level pulse amplitude modulation (PAM4) is a promising modulation format to provide both a high data rate and relatively low cost for short-reach optical links. However, the direct detector and low-cost components also pose immense challenges, which are unforeseen in coherent transmission. To compensate for the impairments and to truly meet data rate requirements in a cost-effective manner, various digital signal processing (DSP) technologies have been proposed and investigated for short-reach PAM4 optical links. In this paper, an overview of the latest progress on DSP equalization technologies is provided for short-reach optical links based on PAM4 modulation. We not only introduce the configuration and challenges of the transmission system, but also cover the principles and performance of different equalizers and some improved methods. Moreover, machine learning algorithms are discussed as well to mitigate the nonlinear distortion for next-generation short-reach PAM4 links. Finally, a summary of various equalization technologies is illustrated and our perspective for the future trend is given.

The POST-forward error correction (FEC) bit error rate (BER) performance and the cycle-slip (CS) probability of the carrier phase estimation (CPE) scheme based on Viterbi–Viterbi phase estimation (VVPE) algorithm and the VV cascaded by pilot-aided-phase-unwrap (PAPU) algorithm have been experimentally investigated in a 56 Gbit/s quadrature phase-shift keying (QPSK) coherent communication system. Experimental results show that, with 0.78% pilot overhead, the VVPE + PAPU scheme greatly improves the POST-FEC performance degraded by continuous CS, maintaining a low CS probability with less influence of filter length. Comparing with the VVPE scheme, the VVPE + PAPU scheme can respectively obtain about 3.1 dB, 1.3 dB, 0.6 dB PRE-FEC optical signal noise ratio (OSNR) gains at PRE-BER of 1.8 × 10⁻². Meanwhile, the VVPE + PAPU scheme respectively achieves about 3 dB, 1 dB, and 0.5 dB POST-FEC OSNR gain and improves the FEC limit from 2.5 × 10⁻³ to 1.4 × 10⁻², from 8.9 × 10⁻³ to 1.8 × 10⁻², and from 1.6 × 10⁻² to 1.9 × 10⁻² under the CPE filter length of 8, 16, and 20.

We propose to relax the requirement of carrier-to-signal power ratio in Kramers-Kronig receiver by probabilistically shaping the constellation to avoid destroying minimum phase condition. About 1.5-dB reduction in optimal carrier-to-signal power ratio are observed.