## 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
In this region, \(q_{l}(\omega)\) indicates a small value reaching 0 according to Equation (5), and the gain function approaches 1 according to Equation (4). In contrast, in speech-absent bins, \(I_{l}(\omega)\) becomes 1, thus increasing the SAP but decreasing \(G_{l}(\omega)\). As described above, the hard-decision parameter \(I_{l}(\omega)\) plays an import role in determining the SAP and gain function, which is a main factor in estimating de-noised speech \(\hat{S}(\omega)\) in the MMSE estimator. In other words, an incorrect decision of \(I_{l}(\omega)\) may induce errors in MMSE-based noise reduction. However, the conventional method of determining this parameter has some drawbacks. First, the posteriori SNR (\(\gamma_{u}^{l}\)) used to determine the parameter may be incorrect for non-stationary noises in which spectral characteristics continuously change over time and frequency. The next problem is related to threshold (\(\gamma_{TH}\)), i.e., the conventional method is highly dependent on this threshold, which is maintained as a fixed value. Thus, it is equally applied in every speech frame and frequency bin, and therefore, it may incorrectly operate for non-stationary noises. To handle the hard-decision parameter carefully, we concentrate on the spectral tendency in terms of energy variation in the time domain. As shown in Figure 11, spectral energy in speech-present frequency bins indicates higher variation than in speech-absent frequency bins in a short period. This tendency is also observed in non-stationary noises because noise components are added to speech-present and speech-absent bins identically during a given period. To observe the tendency for non-stationary noises, we investigated spectral energy variation for each frequency bin over time, using several frames of speech contaminated by outdoor noises. The variation was calculated as the variance of spectral energy of each frequency bin for a certain number of consecutive frames. Figure 5 shows the result. In this experiment, we attempted to classify each frequency bin into speech-present and speech-absent bins using a criterion value (100). Frequency bins greater than 100 are shown in orange, and other bins are shown in blue. Regions indicating higher values are shown in darker colors. As shown in Figure 5, frame sequences 5 to 7 can be determined as speech regions in which both speech-present and speech-absent bins are observed. Other sequences colored by blue can be regarded as non-speech regions where only noise components are observed. This classification result based on spectral energy variation corresponds approximately to the speech data used in this experiment. To derive the hard-decision parameter using a mathematical formula, we first define the energy variation of each frequency bin over time. To observe the variation during a given period, we divide input signals as a 20-ms frame unit (Section 3.1) and designate a certain number of consecutive frames as the analysis window. Here, the size of the analysis window is limited to five to ten frames because more frames may fail to detect exact speech regions. In addition, the next window begins from the second frame of the current window, thereby providing overlap between two consecutive windows. First, the mean spectral energy value is calculated for each frequency bin belonging to a given analysis window as follows:  
\[\mu_{I}(\omega)=\frac{1}{F}\sum_{f=1}^{F}\left|Y_{l,f}(\omega)\right|, \tag{7}\]  
where \(F\) is the number of frames an analysis window covers, and \(\left|Y_{l,f}(\omega)\right|\) is the spectral energy of frequency bin \(\omega\) of the \(f\)-th frame of the \(l\)-th analysis window. Then, the spectral energy variance is obtained as follows:  
\[\sigma_{l}{}^{2}(\omega)=\frac{1}{F}\sum_{f=1}^{F}\left(\left|Y_{l,f}(\omega) \right|-\mu_{I}(\omega)\right)^{2}. \tag{8}\]  
Finally, we define a new hard-decision parameter to substitute the conventional method described in Equation (6).