# Auditory Device Voice Activity Detection Based on Statistical Likelihood-Ratio Order Statistics
## 6 Conclusions  
We presented a solution for reducing the false rejection error of an LRT-based VAD in terms of auditory device speech-processing performance. The proposed LR order statistics consider that false rejections are linked to the sparseness of speech and additive noise signals. Accordingly, a spectral LRT-based VAD employing the proposed method was developed for a uniform polyphase DFT filter bank to satisfy auditory device hearing aid requirements regarding low computational cost and algorithm processing delay. Our experimental results confirmed that the LRT-based VAD having the  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{\
\begin{tabular}{c} **Noise** \\ **Types** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **SNR** \\ **(dB)** \\ \end{tabular} } & \multicolumn{2}{c}{**Conventional (\(M=100\%\))**} & \multicolumn{2}{c}{**Proposed (\(M=25\%\))**} & \multicolumn{1}{c}{**RDER**} \\  & & **FRP (\%)** & **FAP (\%)** & **FRP (\%)** & **FAP (\%)** & **(\%)** \\ \hline \multirow{6}{*}{**White**} & 20 & 15.81 & 11.31 & 10.17 & 12.00 & 18.25 \\  & 15 & 16.74 & 3.38 & 11.00 & 4.07 & 25.10 \\  & 10 & 16.92 & 6.28 & 12.25 & 4.55 & 27.59 \\  & 5 & 18.49 & 3.59 & 13.08 & 6.48 & 11.41 \\  & 0 & 19.79 & 8.76 & 15.90 & 12.00 & 2.28 \\ \hline \multirow{6}{*}{**Babble**} & 20 & 15.35 & 11.93 & 10.36 & 13.03 & 14.26 \\  & 15 & 15.40 & 4.76 & 7.49 & 6.62 & 30.01 \\ \cline{1-1}  & 10 & 14.89 & 11.10 & 8.41 & 9.66 & 30.47 \\ \cline{1-1}  & 5 & 21.22 & 9.86 & 14.15 & 11.17 & 18.53 \\ \cline{1-1}  & 0 & 24.60 & 15.45 & 20.99 & 14.48 & 11.44 \\ \hline \multirow{6}{*}{**Volvo**} & 20 & 14.93 & 11.52 & 8.88 & 13.38 & 15.84 \\  & 15 & 14.75 & 4.07 & 8.60 & 7.03 & 16.95 \\ \cline{1-1}  & 10 & 14.70 & 4.55 & 10.03 & 5.66 & 18.49 \\ \cline{1-1}  & 5 & 14.89 & 4.83 & 9.85 & 6.14 & 18.91 \\ \cline{1-1}  & 0 & 14.98 & 5.17 & 10.96 & 5.45 & 18.56 \\ \hline \hline \end{tabular}
\end{table}
Table 2: FRP, false acceptance probability (FAP), and relative detection error reduction rate (RDER) (%) of a likelihood-ratio-test (LRT)-based VAD with and without proposed LR order statistics under various noise types and SNR conditions.  
Figure 4: Detection error tradeoff curves for two noise types under the 5 dB SNR condition: (**a**) white noise and (**b**) babble noise.  
proposed LR order statistics relatively reduced the average detection error rate by 15.8% compared to a conventional VAD, with only minimal change in the false acceptance probability under all tested noise conditions in the tested SNR range between 0 and 20 dB.  
[PERSON] contributed to the research idea and the framework of this study. [PERSON] also contributed ideas on how to formulate LR order statistics for VAD and performed the experiments for the activity detection of voice in noisy environments. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIT) (No. 2019R1F1A1063325).  
The author declares no conflict of interest.