## 5 Conclusions  
This paper proposes PNR-TDNN, a speaker verification method designed to handle challenging conditions such as strong noise and reverberation interference. This study improves upon the current model by applying a new training strategy to the SSL model, introducing multi-head attentive statistics pooling, cross-channel fusion of residuals, and non-average full-channel mechanisms into the embedded extraction units, such as the pooling layer and SE-Res2 block of ECAPAP-TDNN, respectively. A miniaturization method for PNR-TDNN is also proposed and tested. The proposed method has been tested on several datasets characterized by strong noise and reverberation interference. The exper  
Figure 14: Best EERs of the four baseline models and the T-Hu+EC+FAM model (blue for cnceleb_v2-B, red for VoxCeleb1-B). \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **VoxCeleb1-A/B** & **VoxCeleb1-A/B** & **cnceleb\_v2-A/B** & **cnceleb\_v2-A/B** \\
**Methodology** & **(Noise)** & **(Noise and Reverb)** & **(Noise)** \\
**EER (\%)** & **HmDCF** & **EE (\%)** & **MinDCF** & **EER (\%)** & **MinDCF** \\ \hline EC & 6.87/13.5 & 0.250/0.331 & 18.0/23.3 & 0.308/0.509 & 12.6/8.68 & 0.201/0.334 & 14.1/14.0 & 0.241/0.438 \\ CAM++ & 15.9/15.5 & 0.306/0.409 & 34.7/59.7 & 0.403/0.930 & 13.8/7.52 & 0.235/0.310 & 16.2/13.6 & 0.241/0.426 \\ MFA-Conformer & 17.1/15.5 & 0.329/0.421 & 19.3/24.2 & 0.356/0.573 & 13.4/11.9 & 0.241/0.504 & 15.8/18.7 & 0.255/0.560 \\ Wespeaker & 13.9/25.7 & 0.319/0.582 & 22.2/34.7 & 0.351/0.624 & 16.6/20.3 & 0.246/0.768 & 18.0/27.3 & 0.270/0.818 \\ RedimNet & 13.9/15.1 & 0.306/0.412 & 16.4/25.6 & 0.335/0.580 & 14.8/10.3 & 0.236/0.369 & 17.2/16.5 & 0.241/0.579 \\ Gemini & 17.0/18.9 & 0.351/0.468 & 20.5/22.4 & 0.329/0.545 & 16.7/12.1 & 0.255/0.493 & 19.9/16.9 & 0.266/0.620 \\ \hline Hu + EC & 4.62/9.96 & 0.247/0.212 & 17.21/2.7 & **0.304**/0.536 & 12.27/1.5 & 0.203/0.309 & 14.2/13.2 & 0.244/0.445 \\
**Hu + EC + FAM** & 3.30/9.27 & 0.208/**0.205** & 15.8/20.9 & 0.296/0.523 & 11.9/6.73 & **0.197**/0.281 & 13.8/12.8 & 0.240/0.414 \\
**S-Hu + EC + FAM** & **3.06**/9.78 & **0.195**/0.275 & **15.0/19.2** & 0.307/**0.505** & 10.9/**4.87** & 0.240/**0.258** & **12.9/11.9** & **0.233/0.408** \\
**T-Hu + EC + FAM** & 4.39/**9.19** & 0.219/0.244 & 16.5/20.5 & 0.313/0.542 & **9.69**/5.26 & 0.221/0.266 & 14.5/13.3 & 0.241/0.449 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: VoxCeleb1-A/B and cn-celeb_v2-A/B setup (percentage: refers to the proportion to the original unlabeled speech(VoxCeleb1-S or cn-celeb_v2-S)). imental results demonstrate varying levels of reduction in EER, thereby confirming the effectiveness of the PNR-TDNN approach. Further research is anticipated to extend the application of PNR-TDNN to the domain of speaker identification. Conceptualization, X.Z. ; methodology, X.Z. and C.S. ; software, X.Z. ; validation, X.Z. and C.S. ; formal analysis, X.Z. and C.S. ; investigation, X.Z. and C.S. ; resources, J.T. and J.L. ; data curation, X.Z. and C.S. ; writing--original draft preparation, X.Z. ; writing--review and editing, X.Z., C.S., H.C. and C.W. ; visualization, X.Z. ; supervision, J.T. and J.L. ; project administration, C.S. ; funding acquisition, J.L., J.T., C.S., C.W. and H.C. All authors have read and agreed to the published version of the manuscript. This work was partially supported by Innovative Research Group Project of National Natural Science Foundation of China (Nos. 51821003), the Excellent Youth foundation of Shanxi Province (Nos. 202103021222011), the Key research and development project of Shanxi Province (Nos. 202202020101002), the fundamental research program of Shanxi Province (Nos. 202230302121150), the Aviation Science Foundation (Nos. 2022Z0220U0002), the Shanxi province key laboratory of quantum sensing and precision measurement (Nos. 201905D121001), 173 Foundation (Nos. 2021 XXXX0668), ZBZJDJCYJKT (Nos. 51405 XX01). Not applicable.