## 3 MMPD Design for DB PAM4  
DB PAM-4 is a seven-level signal, and it cannot meet the needs of phase-detection only by the voltage threshold \"0\" judgment [14], and at least six-voltage threshold judgments are required in all levels. The MM phase-detection algorithm realizes phase-detection at the edge of data conversion. The eye diagram of the 3 UI of DB PAM-4 is shown in the Figure 3.  
Compared with 3 UI PAM-4, DB PAM-4 has an increase in data conversion edge from 64 cases to 175 cases, while only 37 objects need to be discriminated in BBPD mode [16], the complexity of phase-detection process increases significantly, mainly in the space complexity. To solve the complex phase-detection problem of DB PAM-4, the waveform sifting technology used to transform the phase-detection object into five types of judgment processes based on trends, which significantly reduces the space complexity of the phase-detection logic process. The reduction in space complexity lies in a significant reduction in the amount of auxiliary data and basic devices in the process. The MMPD of DB PAM-4 consists of a Data Sampler, Waveform Selector, Error Sampler, and Phase Detector, as shown in Figure 4, with the core of waveform sifting, error judgment, and phase judgment. The waveform sifting process of DB PAM-4 divides the waveforms into five categories according to the relative relationship between D\({}_{n-2}\), D\({}_{n-1}\) and D\({}_{n}\), as shown in Table 1, including Up, Down, Keep-Jump, Jump-Keep, No-Decision, as shown in Figure 5. The operation principle is as follows: The D\({}_{n}\)[7:0] obtained by the 8-bit data ADC is compared with the six judgment thresholds in Figure 3 through the data sampler, and the 3-bit data d\({}_{n}\)[2:0] as shown in Figure 4, then input to the waveform selector, according to the relative relationship of the three continuous data in Table 1 to get the work mode mode[2:0]; It corresponds to 001, Down corresponds to 100, Keep-Jump corresponds to 110, Jump-Keep corresponds to 011, and No-Decision corresponds to 000. After waveform sifting, Up, Down, Keep-Jump, and Jump-Keep are used as phase-detection objects, and the phase-detection waveform is reduced from 175 to 114. The waveform selector consists of comparator and selector. By adding quantization processing, the waveform selector input is reduced from 24 bit to 9 bit, the comparator input is reduced from 8 bit to 3 bit, and the circuit size is reduced by 5/8. While three data samplers  
Figure 3: Eye diagram of DB PAM-4 with 3 UI. add some space, they reduce the amount of auxiliary data during computation. After digital synthesis, the look-up table (LUT) and FIFO structures that occupy the most data space are reduced from 56 to 44, which is equivalent to reducing the data space by 21.4%. This PD can provide phase-detection information in 50% of the data transitions in PAM-4, and the phase-detection density is 50%, which is the same as the typical density \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Classification** & **Relative Relation** & **Number** & **Probability** \\ \hline Up & D\({}_{n-2}\) \(<\) D\({}_{n-1}\) \(<\) D \({}_{n}\) & 27 & 9/64 \\ Down & D\({}_{n-2}\) \(>\) D\({}_{n-1}\) \(>\) D\({}_{n}\) & 27 & 9/64 \\ Keep-Jump & D\({}_{n-2}\) = D\({}_{n-1}\) \(\
eq\) D\({}_{n}\) & 30 & 3/16 \\ Jump-Keep & D\({}_{n-2}\) \(\
eq\) D\({}_{n-1}\) = D\({}_{n}\) & 30 & 3/16 \\ No-Decision & Other & 61 & 11/32 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Waveform classification of DB PAM-4. Figure 4: MMPD architecture of DB PAM-4. Figure 5: Waveform classification of DB PAM-4, (**a**) Up, (**b**) Down, (**c**) Keep-Jump, and (**d**) Jump-Keep. under NRZ data [8]; the phase-detection density of PAM-4 MMPD [11] is about 43.75%. The phase-detection density of DB PAM-4 is about 65% and 25% with BBPD [16]. As shown in Table 2, DB PAM-4 improves the phase by about 30% compared to 50% of the classical phase-detection density and 160% compared to BBPD.