## 3 Comparison and Discussion
### Noise Reduction Performance Analysis  
Three different indexes, MSE, SegSNR, and PESQ, were selected as the measurements of the noise reduction performance. The SegSNR is averaged over all time frames and is given by [15]:  
\[\text{SegSNR}=\frac{1}{L}\sum\
olimits_{l=1}^{\text{L}}10 log_{10}\frac{\sum \
olimits_{k=1}^{\text{K}}\left|S(k,l)\right|^{2}}{\sum\
olimits_{k=1}^{ \text{K}}\left|\left|Z_{i}(k,l)-S(k,l)\right|^{2}}, \tag{41}\]  
PESQ is the most common and subjective metric for evaluating speech quality, which can be used in a wide range of end to end measurement applications with live and simulated networks [24]. PESQ is a more complex metric for capturing a wider range of distortions. Its value varies from \(-0.5\) to \(4.5\), and a higher value means the better performance. Here, PESQ was introduced to measure the quality of enhanced bird vocalization. The detailed calculation method can be seen in [24].  
\begin{table}
\begin{tabular}{c c c} \hline
**Algorithm** & **Node 4** & **Node 5** \\ \hline DDSB & 15 & 5 \\ DMVDR & 11 & 4 \\ IDMVDR & 6 & 2 \\ \hline \end{tabular}
\end{table}
Table 1: The numbers of iterations when converging in the WASN with \(N_{d}\) = 5.  
\begin{table}
\begin{tabular}{c c c} \hline
**Algorithm** & **Node 8** & **Node 5** \\ \hline DDSB & 37 & 28 \\ DMVDR & 49 & 43 \\ IDMVDR & 10 & 6 \\ \hline \end{tabular}
\end{table}
Table 4: The number of iterations when converging in the WASN with \(N_{d}\) = 20.  
\begin{table}
\begin{tabular}{c c c} \hline
**Algorithm** & **Node 1** & **Node 5** \\ \hline DDSB & 35 & 33 \\ DMVDR & 38 & 30 \\ IDMVDR & 19 & 11 \\ \hline \end{tabular}
\end{table}
Table 2: The number of iterations when converging in the WASN with \(N_{d}\) = 10.  
\begin{table}
\begin{tabular}{c c c} \hline
**Algorithm** & **Node 8** & **Node 2** \\ \hline DDSB & 95 & 45 \\ DMVDR & 64 & 22 \\ IDMVDR & 51 & 19 \\ \hline \end{tabular}
\end{table}
Table 3: The number of iterations when converging in the WASN with \(N_{d}\) = 15.  
Also, the four WASNs in Section 3.1 were applied for simulation. One bird vocalization and ten types of noises were selected as audio sources for each experiment. Here, bird vocalizations were high SNR, and selected from Freesound [25], xeno-canto [26], or our laboratory. The ten types of noises contained five independent white Gaussian noise signals and five independent other noise signals, including three types of noise from the Aurora2 database [27], namely Babble, Restaurant, and Street. In all the experiments, the input SNR of node 1 was set to 1 dB. Ten experiments with different audio sources were performed for all three methods, and the final results are the average of multiple experiments.  
Tables 5 and 6 show the MSEs and SegSNRs of the distributed beamformers, respectively. It was found that the noise reduction performance of IDMVDR was better than that of DMVDR and DDSB, which means that the proposed PSD estimation algorithm of IDMVDR is more efficient.  
Table 7 shows the PESQs of the beamformer's output. It was observed that the PESQs of the IDMVDR and DMVDR are obviously better than that of DDSB. This is reasonable, since the MVDR beamformer generally had better speech quality and intelligibility than the DDSB algorithm when the noise signals of the microphones were correlated [15]. Meanwhile, the bird vocalization quality of IDMVDR was slightly better than that of DMVDR.