## 4 Conclusions  
In this paper, taking into consideration the highly time-variable noises in nature and the limited energy, calculation ability, and communication ability of wireless sensor nodes, the IDMVDR beamforming method for bird audio enhancement in WASNs was proposed. The continuous spectrum update algorithm was used to estimate the noise PSD, and the average metropolis weight consensus algorithm was introduced to fasten the convergence rate of each node herein. To validate the advantages of the proposed method, the audio enhancement experiments in four WASNs with different network topologies were simulated in MATLAB. Compared with DDSB and DMVDR, the average MSE, SegSNR,  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**WASN of Different \(N_{d}\)** & **DDSB** & **DMVDR** & **IDMVDR** \\ \hline
5 & \(-\)5.56 dB & \(-\)5.44 dB & \(-\)3.05 dB \\
10 & \(-\)6.49 dB & \(-\)6.45 dB & \(-\)3.31 dB \\
15 & \(-\)7.12 dB & \(-\)6.67 dB & \(-\)3.24 dB \\
20 & \(-\)6.98 dB & \(-\)6.32 dB & \(-\)4.67 dB \\ Ave & \(-\)6.54 dB & \(-\)6.22 dB & \(-\)3.68 dB \\ \hline \hline \end{tabular}
\end{table}
Table 6: The noise reduction performance of different \(N_{d}\) in terms of SegSNR.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**WASN of Different \(N_{d}\)** & **DDSB** & **DMVDR** & **IDMVDR** \\ \hline
5 & 1.89 & 2.47 & 2.67 \\
10 & 1.55 & 2.11 & 2.50 \\
15 & 1.56 & 2.14 & 2.49 \\
20 & 1.58 & 2.18 & 2.48 \\ Ave & 1.65 & 2.22 & 2.54 \\ \hline \hline \end{tabular}
\end{table}
Table 7: The noise reduction performance of different \(N_{d}\) in terms of PESQ.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**WASN of Different \(N_{d}\)** & **DDSB** & **DMVDR** & **IDMVDR** \\ \hline
5 & \(-\)10.74 dB & \(-\)12.56 dB & \(-\)13.17 dB \\
10 & \(-\)7.49 dB & \(-\)9.99 dB & \(-\)11.13 dB \\
15 & \(-\)6.63 dB & \(-\)10.00 dB & \(-\)11.21 dB \\
20 & \(-\)6.89 dB & \(-\)10.63 dB & \(-\)10.87 dB \\ Ave & \(-\)7.94 dB & \(-\)10.79 dB & \(-\)11.85 dB \\ \hline \hline \end{tabular}
\end{table}
Table 5: The noise reduction performance of different \(N_{d}\) in terms of MSE.  
and PESQ of the enhanced signals obtained by the proposed method were best. Additionally, the proposed algorithm presented a faster convergence rate, which provides the capability of reducing the iteration time and communication cost of the network. Thanks to the above better performances, the proposed IDMVDR method is more suitable for practical utilization in WASNs with variable topology. Through the proposed method, better quality bird audio files can be achieved in bird audio monitoring, which is more advantageous for improving the accuracy of bird species identification. However, there was a simplifying assumption in our current research: only one bird audio source was considered. In nature, there is always more than one bird singing or vocalizing at the same time. In this complex situation, we need to do further research on audio enhancement.  
[PERSON] and [PERSON] proposed the algorithm and designed the experiments; [PERSON] and [PERSON] provided and processed the sound data; [PERSON] and [PERSON] performed the experiments; [PERSON] and [PERSON] analyzed the data; all the authors participated in the paper writing.  
The paper is supported by \"Science and Technology Project of State Grid Corporation of China (SGGR0000 WLJS1801082)\" and \"the Fundamental Research Funds for the Central Universities (No. 2016 ZCQ08 & No. 2015 ZXQ-GX-04)\".  
The authors declare no conflict of interest.