## 4 Experimental Results and Analysis  
### The Parameters Affecting Equalizer Performance  
After determining the optimal MZM bias voltage for the equalizer in this system, we explored the parameters affecting the performance of the PA-DFE and MA-DFE in the case of BtB transmission, at an ROP of \(-20\) dBm. Figure 5a shows the effect of the number of  
Figure 4: (**a**) Experimentally measured MZM transfer function. (**b**) Effect of MZM bias voltage on equalizer performance (BtB, ROP \(=-22\) dBm, (80,10) represents (feedforward taps: 80, feedback taps: 10), The red dashed line represents the soft decision threshold \(1\times 10^{-2}\)). PAM4 constellation diagram with the bias point at (**c**) Q1 and (**d**) Q2. feedforward taps on the performance of the equalizer when the number of feedback taps is 0 and 10. It can be seen that they have a similar decreasing trend, with the equalizer containing 10 feedback taps having a lower BER. After the number of feedforward taps exceeded 80, all equalizers achieved stable BER performance. Figure 5b shows the effect of the number of feedback taps on the performance when feedforward taps are fixed at 85, and the BER can be significantly decreased as the feedback taps increase. When the feedback taps exceed 15, the BER almost reaches stability. Considering that increasing the number of taps raises computational complexity, the number of taps should be constrained while seeking the optimal equalizer performance. Then, we investigated the convergence properties of the PA-DFE and MA-DFE (see Figure 6a,b). It can be observed that the forgetting factor \(\lambda\) in the RLS algorithm affects both the convergence speed and stability from the figure. For \(\lambda=1\), the convergence curves of the PA-DFE and MA-DFE are similar, requiring 1000 iterations for the MSE to stabilize. When \(\lambda=0.98\), the convergence is faster and only 500 iterations are needed, but this leads to larger residuals and less stable equilibrium. We also investigate the effect of tap configuration on convergence properties. From the curves, it is observed that their variations are almost the same for tap configurations of (85, 16) and (45, 6). Therefore, it can be concluded that the effect of the number of taps on the convergence rate is relatively weak. When analyzing the computational complexity of an equalizer, since multipliers require more computational resources compared to adders, we meas  
Figure 5: The effect of the number of taps on equalizer performance: (**a**) feedforward, (**b**) feedback (BtB transmission, ROP = \(-20\) dBm). Figure 6: The convergence properties of (**a**) PA-DFE and (**b**) MA-DFE for different \(\lambda\) and tap configurations (BtB transmission, ROP = \(-20\) dBm). complexity by calculating the number of multiplications per output symbol [23]. It is important to note that we did not include the computational complexity of the training process, as once the equalizer converges, the tap training is completed and the equalizer no longer updates. According to the equalizer output expression in Equation (1), in the feedforward section, given that the number of feedforward taps is \(N\), and both the tap coefficients \(w_{p}^{F}\) and the received PAM4 signal \(x(k)\) are complex numbers, multiplying two complex numbers involves four multiplication operations. Therefore, the computational complexity of the feedforward equalization is \(4N\). Similarly, in the feedback section, given that the number of taps is \(M\), the tap coefficients \(w_{q}^{B}\) are complex numbers, the phase \(e^{\beta(k-q)}\) is a complex number, and the decision value \(d(k)\) is a real number, the computational complexity of the feedback equalization is \(4M+2M=6M\). Thus, the overall computational complexity of the equalizer can be expressed as:  
\[C_{PA/MA-DFE}=4N+6M \tag{13}\]  
In order to balance the equalizer's performance and computational complexity, we tested the BER performance and computational complexity for different tap combinations.