## 3 Vehicle-Embedded Speech Recognition Front-End for Multi-UAV Control
### Noise Reduction for UAV Environments
#### 3.2.2 MMSE Enhancement Based on Spectral Energy Variation for Noise Reduction in UAV Environments  
User devices that control UAVs may be exposed to various background noises when users operate UAVs in outdoor environments. Generally, noise components in outdoor environments are non-stationary noises that change rapidly and continuously in the time and frequency domains. In contrast, indoor environments generally produce stationary noises, e.g., the operating sounds of home appliances. Figure A2 in Appendix A compares the two types of noises via a 2-dimensional spectrogram. Stationary noises can be reduced easily by most conventional noise reduction methods because the noise components estimated in non-speech regions are preserved in speech regions without variation. In contrast, non-stationary noises provide inefficient conditions for noise reduction because it is difficult to classify speech and non-speech regions, and each region has different noise characteristics. Among conventional approaches, the MMSE method can provide stable noise reduction performance in terms of spectral analysis. It analyzes speech and noise characteristics in each frequency bin of both speech and non-speech regions, whereas other methods consider the overall spectral characteristics in non-speech regions. Thus, the MMSE method is not dependent on classifying speech and non-speech regions. On the other hand, other approaches require detection of non-speech regions to estimate noise components but may fail to detect non-speech regions in speech contaminated by non-stationary noises. Thus, this study concentrates on the MMSE method to handle non-stationary noises in outdoor environments. Generally, the noise-contaminated speech signal \(y(n)\) can be described as \(\mathrm{x}(n)+w(n)\), where \(\mathrm{x}(n)\) and \(w(n)\) denote the clean speech signal and noise signal, respectively. In the frequency domain, it can be transformed to \(\left|Y(\omega)\right|=\left|\mathrm{X}(\omega)\right|+\left|\mathrm{W}(\omega)\right|\), where \(\left|\mathrm{X}(\omega)\right|=S(\omega)e^{\mathrm{i}p(\omega)}\) and \(\left|\mathrm{Y}(\omega)\right|=R(\omega)e^{\mathrm{i}p(\omega)}\). The main objective of the MMSE method is to estimate de-noised speech \(\hat{S}(\omega)\) such that \(\left(S(\omega)-\hat{S}(\omega)\right)^{2}\) is minimized. The MMSE describes \(\hat{S}(\omega)\) as follows:  
\[\hat{S}(\omega)=G(\omega)R(\omega) \tag{3}\]  
where \(G(\omega)\) is a gain function used to adjust the noise-contaminated speech to a clean speech signal. If speech components are dominant in the frequency bin \(\omega\), \(G(\omega)\) approaches 1, thereby maintaining \(R(\omega)\). Otherwise, the function proceeds to 0, thereby decreasing \(R(\omega)\). Conventional studies introduced several ways to estimate the gain function. However, the following approximation is considered an efficient method in terms of correctness and computational intensity [28; 29]:  
\[G(\omega)=\frac{\wedge(\omega)}{1+\wedge(\omega)}\approx 1-q(\omega) \tag{4}\]  
where \(\wedge(\omega)\) is a likelihood ratio between speech and non-speech components in frequency bin \(\omega\). As described in (4), \(G(\omega)\) can be approximated using \(q(\omega)\), i.e., the speech absence probability (SAP). The SAP of the \(l\)-th frame in frequency bin \(\omega\) is estimated as follows:  
\[q_{l}(\omega)=\alpha\cdot q_{l-1}(\omega)+(1-\alpha)\cdot I_{l}(\omega) \tag{5}\]  
where \(\alpha\) is a constant value between 0 and 1, and \(I_{l}(\omega)\) is a hard-decision parameter that determines whether speech is present in the corresponding frequency bin. Here, the decision is made using the posteriori signal-to-noise ratio (SNR) (\(\gamma_{u}^{l}\)) and threshold (\(\gamma_{TH}\)) as follows:  
\[I_{l}(\omega)= \begin{cases}0&(\gamma_{\omega}^{l}\geq\gamma_{TH})\\ 1&(\gamma_{\omega}^{l}<\gamma_{TH})\end{cases} . \tag{6}\]  
If \(I_{l}(\omega)\) is determined to be 0, the frequency region is considered a speech-present bin.