# Auditory Device Voice Activity Detection Based on Statistical Likelihood-Ratio Order Statistics
## 1 Introduction  
The goal of voice activity detection (VAD) is to detect the presence or absence of speech in a sound signal. VAD is increasingly difficult in noisy situations, especially for nonstationary noise such as babble noise. VAD has steadily gained research interest in the speech community in recent years, especially for applications such as selectively encoding and transmitting data in telecommunications, estimating noise statistics in speech enhancement, and detecting endpoints in speech recognition [1; 2; 3]. We focus on VAD's function in auditory hearing aid speech processing. Individuals with hearing impairment have difficulty understanding relevant speech content in their daily lives. Attempts have been made to address this problem using auditory devices such as hearing aids, which are widely used to compensate for hearing loss and match the dynamic range [4]. However, many individuals avoid using hearing aids, often because of noise contamination of the speech signal entering the ear; only 23% of hearing-impaired people use hearing aid auditory devices [5; 6; 7]. This has motivated progress to improve complex speech perception for hearing aid users by reducing the effects of background noise on the targeted speech signal. This improvement is usually accomplished by preserving the characteristics of speech using short-term spectral amplitude (STSA) analysis, for which statistical speech enhancement techniques including Wiener filters and minimum mean square error (MMSE) estimation have been widely used [8; 9]. These techniques are strongly dependent on the a priori signal-to-noise ratio (SNR) obtained by noise power spectral densities (PSDs), which can be reliably estimated in noise-only intervals [10; 11]. Eventually, in the coupled systems of speech enhancement, a priori SNRs, PSDs, and noise-only intervals, the speech-enhancing performance is strongly dependent on accurate noise-only interval estimation. Thus, the auditory hearing aid mustuse reliable VAD algorithms to obtain accurate noise-only interval information, even when target speech is corrupted by nonstationary noise such as babble noise [10; 11]. VAD algorithms commonly use features such as energy levels, zero-crossing rates, entropy, and likelihood ratios (LRs) [3; 12; 13]. LRs produce few detection errors when the estimated global (the averaged value over all frequency bins) log LR in a frame is compared to a decision threshold [12; 13]--referred to as a likelihood-ratio test (LRT) [11; 12; 13]. The decision threshold can be determined by minimizing the detection error rate and combining the false rejection probability (FRP) and the false acceptance probability (FAP). Several strategies have been suggested to improve the accuracy of the statistical-model-based LRT [13; 14; 15]; however, although false rejections do frequently arise in VAD with optimized decision thresholds, they have not been investigated systematically. We argue that the false rejection rate is linked to the sparseness characteristics of the noisy speech signal because the speech activity decision is based on the global LR magnitude relative to the decision threshold. However, empty frequency bins (independent of whether speech is active) reduce the global LR, which in turn causes false rejections. We demonstrate that the existing statistical LRT-based VAD can be improved by including false rejection measures based on the sparseness characteristics of the noisy speech. In other words, this paper proposes a method for reducing the FRP of a conventional statistical LRT-based VAD based on the sparseness characteristics of speech and noise, which is performed using LR order statistics over all frequency bins. In the last decade, as part of efforts to identify more efficient solutions via speech-processing algorithms such as speech enhancement and VAD, the research focus of the speech algorithm community has turned to deep neural network (DNN) methods, with less attention to the previously described approaches [16; 17; 18; 19].