## 2 System Configuration  
The typical system configuration for short-reach optical links based on PAM4 modulation is presented in Figure 1. The origin data generated by pseudorandom binary sequence (PRBS) is first encoded by a forward error correction (FEC) encoder and then mapped to the PAM4 symbol. After resampling and pulse shaping, the digital signal is pre-equalized through a finite impulse response (FIR) filter to pre-compensate for the limited bandwidth and nonlinearity of the transmitter. The processed signal is then loaded into a digital-to-analog converter (DAC) in order to obtain the baseband electrical signal. Afterward, the DAC output signals are amplified by a linear driver and then fed into a modulator for the generation of optical PAM4 signal. The laser can be a vertical cavity surface-emitting laser (VCSEL), a directly modulated laser (DML) or an electro-absorption modulator integrated with distributed feedback laser (EML). A comparison between different kinds of transmitter is summarized in Table 1. Generally, the directly-modulated lasers like VCSEL and DML reach a bandwidth barrier to operate beyond 25 GBaud [54], despite many research efforts made to achieve higher speed transmission [55; 56]. EML generally have high bandwidth at the expense of high cost. Since the electrical signals of VCSEL and DML are directly applied to their laser cavity, larger frequency chirps will exist rather than EML, which can induce severe nonlinear distortions and lead to the serious degradation of transmission performance [57; 58]. However, the adiabatic chirp of DML causes frequency modulation (FM) of the optical signal, which is able to fundamentally mitigate the first power fading dip incurred by CD [59]. Note that the Mach-Zehnder modulator (MZM) based on Lithium Niobate (LiNbO\({}_{3}\)) is out of consideration due to a large footprint and high cost. For optical links below 300 m, the multi-mode fiber (MMF) combined with VSCEL is widely used at present. When the transmission distance increases, the modal dispersion in the MMF will distort the signal and the standard single-mode fiber (SSMF) becomes the common choice.  
At the receiver, the signal is directly detected by PD or avalanche photodiode (APD). To improve receiver sensitivity, a TIA is generally cascaded behind to amplify the electrical signal. An alternative solution is using the combination of an optical amplifier (OA) and an optical band-pass filter (OPBF) before PD to amplify received optical signal and remove out-of-band noise. The comparison of different receivers is presented in Table 2, where OA + PD has the highest sensitivity due to the use of high-cost OA. The gain of APD results in relative higher SNR, which makes it more suitable for longer reach links compared to traditional PD [26]. After being processed by an analog-to-digital converter (ADC), the signal is resampled to an expected sampling rate for subsequent steps. Synchronization is achieved to eliminate sampling clock offset (SCO) and depress timing jitter. Then, various DSP techniques are utilized to equalize the received signal for the performance improvement of the transmission system. Finally, after de-mapping and FEC decoding, the received data is obtained and the bit error rate (BER) can be calculated.  
However, due to the limitation of cost, all transmitters and receivers mentioned above can induce different degree distortions for high-speed PAM4 transmission. Therefore, equalization is one of the most DSP components to eliminate impairments in short-reach optical links. As is shown in Figure 1, the equalization technologies can be utilized both in the transmitter as pre-equalization and in the receiver as post-equalization. The distortions induced by low cost and the different equalization technologies will be introduced specifically in the following sections.