## 4 Results and Comparison
### PNR-TDNN Experiments
#### 4.2.5 Discussion of Other SNR's Situations  
The SNR used in previous sections to characterize the noise level ranges from 0 to 0.5 dB, which is a very narrow range. This means that through repeated training, the network may cleverly avoid the influence of noise (in Section 2.1, we found that noise energy is more easily dispersed than speech energy). Therefore, we supplemented the comparative experiments with a larger range of SNR. In the production of noisy speech, the SNR is in narrow (0 to 0.5 dB) and wide (\(-5\) to 3 dB) ranges. The SNR was chosen at random, i.e., in the form of a uniform distribution. More than 60% of these speeches were in the negative SNR condition, and less than 40% were in the lower positive SNR. These conditions are closer to the complex and challenging real sound field, and we list the experimental results in Table 9.  
On dataset A, the larger Hu + EC + FAM has the best EER, with an improvement of 12.6% with respect to CAM++, while both S-Hu + EC + FAM and T-Hu + EC + FAM also present a stronger performance than CAM++. This phenomenon suggests that the larger the pre-trained model is, the better the adaptation to the back-end task. As for dataset B and C, the EER of Hu + EC + FAM improves 5.2%/6.12% relative to RedimNet, while the performance of CAM++ is not stable enough to be used as a baseline. Furthermore, the EER of S-Hu + EC + FAM and T-Hu + EC + FAM are both slightly weaker than RedimNet.  
In narrow-range SNR, due to the weakening of the noise by fusion Res2 net and SE-attentive mean, it is very likely that the noise effect will be ignored by implicit noise suppression. However, smaller Hu + EC + FAM can easily outperform the baseline for milder general acoustic field environments, but the large pre-trained model still has a significant advantage when faced with the challenge of noise intensity greater than speech intensity and a very wide range of SNR.  
When exposed to stronger noise energy and a wide range of SNR, the large pre-trained model is still able to extract more feature information about a particular speaker through its deeper network parameters; this finding is significantly different from the experimental results obtained for the narrow-range SNR.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Noise** & **Methodology** & \multicolumn{2}{c}{**Dataset A**} & \multicolumn{2}{c}{**Dataset B**} & \multicolumn{2}{c}{**Dataset C**} \\
**Sources** & **EER (\%)** & **MinDCF** & **EER (\%)** & **MinDCF** & **EER (\%)** & **MinDCF** \\ \hline \multirow{8}{*}{ESC50/CnCeleb} & EC & 9.42/8.89 & 0.200/0.203 & 9.41/9.45 & 0.193/0.195 & 7.31/7.08 & 0.170/0.170 \\  & CAM++ & 8.21/7.68 & 0.197/0.198 & 8.83/10.43 & 0.193/0.197 & 8.58/8.30 & 0.174/0.177 \\  & MFA-Conformer & 8.95/10.52 & 0.204/0.203 & 9.91/9.81 & 0.194/0.192 & 6.96/7.03 & 0.171/0.167 \\  & Wespeaker & 13.3/13.3 & 0.209/0.207 & 13.2/13.6 & 0.197/0.197 & 11.0/11.8 & 0.176/0.174 \\  & RedimNet & 9.11/8.39 & 0.209/0.208 & 8.67/8.89 & 0.194/0.195 & 10.63/9.15 & 0.176/0.171 \\  & Gemini & 8.76/9.14 & 0.207/0.205 & 9.37/9.70 & 0.194/0.194 & 8.69/9.36 & 0.175/0.175 \\ \cline{2-8}  & Hu + EC & 7.61/7.43 & 0.199/0.195 & 8.35/8.95 & 0.191/0.194 & 7.11/6.84 & 0.160/0.160 \\  & Hu + EC + FAM & 7.41/7.27 & 0.196/0.192 & 8.12/8.71 & 0.190/0.190 & 6.80/6.63 & 0.162/0.156 \\  & **S-Hu + EC + FAM** & **5.87**/**5.79** & **0.191**/**0.188** & **7.27**/**6.98** & **0.187**/**0.185** & **5.25**/**4.19** & **0.155**/0.146 \\  & **T-Hu + EC + FAM** & 6.26/6.44 & 0.200/0.190 & 8.35/7.63 & 0.188/**0.185** & 6.51/5.39 & 0.168/**0.145** \\ \hline \end{tabular}
\end{table}
Table 8: PNR-TDNN’s best EER and MinDCF in ESC50 and Cnceleb noise situations (Note:EC = ECAPA-TDNN, Hu = HuBERT, S-Hu = small HuBERT, T-Hu = tiny HuBERT, FAM = fusion Res2 net + SE-attentive mean + multi-head attentive statistics pooling).