# Auditory Device Voice Activity Detection Based on Statistical Likelihood-Ratio Order Statistics
## 5 Experiments and Results  
We evaluated the proposed algorithm by counting detection errors and comparing it with conventional VAD under various noise types and SNR conditions. Speech utterances of approximately 57 s in duration were obtained from four speakers (two males and two females) from the TIMIT database (DB) [28] and mixed with three noises (white, babble, and Volvo noise) from the NOISEX-92 DB [29]. Based on the clean signals, 65.7% of the samples in the speech material were marked as active (49.3% voiced and 16.4% unvoiced). The noise signals were then artificially mixed additively with SNRs ranging from 0 to 20 dB with 5 dB steps. Signals were segmented using the 128-point LPF window in [27] and overlapped with each previous segment by one-eighth. We implemented the statistical LRT-based VAD method proposed in [12] with a conventional hang-over scheme to investigate how much the proposed LR order statistics approach reduced the detection error rate. Moreover, we set the \(\alpha=0.97\) in Equation (8) and \(\beta=0.98\) in Equation (10) for the experiments, which were empirically determined. Figure 2a illustrates an example waveform of male speech at 5 dB SNR in babble noise, and Figure 2b illustrates the conventional \(\log\Lambda_{k}\) and the proposed descending version of \(\log\Lambda_{k}\), \(\Psi_{k}\), at close to 0.6 s (a voiced interval) of this waveform. The proposed \(\Psi_{k}\) illustrated a concentration at low frequencies and is less distributed than \(\log\Lambda_{k}\). Figure 2c illustrates the global log LR curves obtained from the local LRs of \(\log\Lambda_{k}\) and \(\Psi_{k}\). To quantize the tuning parameter \(\widetilde{K}^{\prime}\) in Equation (17), the value was converted to a percentage: \(M=100\times\widetilde{K}^{\prime}/\widetilde{K}(\%)\). The proposed method (at \(M=25\%\)) produced higher log LRs than the conventional method. At \(M=100\%\) (or \(\widetilde{K}^{\prime}=\widetilde{K}\)), the proposed method was identical to the conventional VAD in Equation (11). For investigating the effect of the control constant \(K^{\prime}\) in Equation (17) in detail, the FRP was measured by comparing the detection results of the proposed method to true voice activity intervals (Figure 3). The ground truth voice activity intervals were determined manually by the author. The figure illustrates FRP histograms for white noise (left) and babble (right) noise environments at 5 dB SNR for three different values of \(M\). The FRPs decreased considerably with decreasing \(M\) for both white noise and babble noise. The optimal value of \(M=25\%\) was adopted for the subsequent experiments. Figure 2: Step-by-step illustration of (**a**) waveform of babble noisy speech at 5 dB signal-to-noise ratio (SNR), (**b**) local likelihood ratio (LR) estimates of the frequency, and (**c**) global log LR estimates of the time. We measured the FAP to investigate further the effectiveness of the proposed LR order statistics in an LRT-based VAD method. Figure 4 depicts the results of the comparison between the proposed and conventional methods. The results are presented in the form of a detection error tradeoff graph, similar to receiver operating characteristic (ROC) curves. Depicted are the results of the conventional method with \(M=100\%\) and the proposed method with \(M=25\%\) for speech in white noise and babble noise at 5 dB SNR. The detection error tradeoff curve of the proposed method was always closer to the bottom-left corner than that of the conventional VAD for both noise conditions, demonstrating that the proposed method is more robust against false detection than the conventional method. Finally, we compared the relative detection error reduction rate (RDER) of the proposed method (\(M=25\%\)) to that without under variable noise and SNR conditions. The detection error rate was defined as (FAP + FRP)/2. The decision threshold was explicitly determined to minimize the detection error under each noise and SNR condition.