## 2 Materials and Methods
### STI Measurements  
In the context of the STI, the interference to intelligibility related to a reduction in temporal modulation caused by the transmission system can be represented by the modulation transfer function [52; 55]. The modulation transfer function was distributed in 14 modulation frequencies \(F_{l}\), ranging from 0.63 to 12.5 Hz, and seven octave bands, with center frequencies \(f_{k}\) ranging from 125 Hz to 8 kHz. To reduce the measurement time and improve repeatability, an indirect single-impulse-response measurement approach was developed by [PERSON] [56] and then improved by [PERSON] [57]. In the indirect method, the modulation transfer function \(m_{T}(f_{k},F_{l})\) calculated from the reverberation can be expressed as follows:  
\[m_{T}(f_{k},F_{l})=\frac{\int_{0}^{\infty}h^{2}(f_{k},t)\exp(-j2\pi F_{l}t)dt} {\int_{0}^{\infty}h^{2}(f_{k},t)dt}, \tag{1}\]  
where \(k\) is the sequence number of the octave band, \(l\) is the sequence number of the modulation frequency, and \(t\) is time in seconds. The transmission function \(h(f_{k},t)\) was obtained from the BRIR \(h(t)\) through octave filtering at the center frequencies \(f_{k}\). Because the influence of noise on intelligibility is not normally included in the BRIR, an additional modulation transfer function \(m_{N}(f_{k},F_{l})\) that is independent of the modulation frequency \(F_{l}\) was used:  
\[m_{N}(f_{k},F_{l})=\frac{1}{1+10^{-SNR(f_{k})/10}}, \tag{2}\]  
where \(SNR(f_{k})\) is the SNR at the frequency \(f_{k}\) of the octave band. Usually, the levels of the noise and speech signal must be measured separately [52]. Binaural speech signals were indirectly obtained by auralization technology [22], and a stationary noise source, specifically pink noise, was taken into consideration as the background noise with the same sound pressure level in each frequency band. First, a pink-noise signal was created, and the spectrum was filtered and adjusted in accordance with GB/T 7347-1987 [58] to generate a monaural speech sample. Next, by convolving the monaural speech sample \(E_{0}\) with the corresponding BRIRs obtained, as described in Section 2.1, the binaural speech signals were obtained. The SNRs can be indirectly derived for different conditions using the stationary noise and binaural speech signals. Then, \(SNR(f_{k})\) was computed as  
\[SNR(f_{k})=10\lg(\frac{1}{T_{0}}\int_{0}^{T_{0}}(E_{0}(t)h(f_{k},t))^{2}dt)-L _{noise}(f_{k}), \tag{3}\]  
where \(T_{0}\) is the length of the speech signal and \(L_{noise}\) is the sound pressure level of the noise at frequency \(f_{k}\) of the octave band. In this way, the combined modulation transfer function \(m(f_{k},F_{l})\) can be calculated as the product of \(m_{T}(f_{k},F_{l})\) and \(m_{N}(f_{k},F_{l})\). It includes the combined effects of background noise and the transfer function. The \(MTF(f_{k},F_{l})\) for each condition was produced as a \(7\times 14\) matrix, which was subsequently transformed into the apparent SNR as follows:  
\[X(f_{k},F_{l})=10\times\log_{10}\biggl{(}\frac{m(f_{k},F_{l})}{1-m(f_{k},F_{l}) }\biggr{)}. \tag{4}\]  
After being cropped into the range from \(-15\) to \(+15\) dB, each apparent SNR will correlate linearly with the STI, which ranges from 0 to 1. Consequently, the transmission index \(TI(f_{k},F_{l})\) can be expressed as  
\[TI(f_{k},F_{l})=\left\{ \begin{array}{cc}0,&\text{if }X(f_{k},F_{l})<-15\\ \frac{X(f_{k},F_{l})+15}{30},&\text{if }X(f_{k},F_{l})>15\end{array} \right. \tag{5}\]  
which means that if the SNR is less than -15 dB, then the STI in the cabin is deemed absolutely unacceptable, and vice versa. In this way, the modulation transfer index \(MTI(f_{k},F_{l})\) at each octave can be obtained as the average value at different modulation frequencies:  
\[MTI(f_{k})=\frac{1}{14}\sum_{l=1}^{14}TI(f_{k},F_{l}). \tag{6}\]  
Then, we calculated the overall STI from a weighted sum:  
\[STI=\sum_{k=1}^{7}\lambda_{k}MTI(f_{k}), \tag{7}\]  
where \(\lambda_{k}\) are the weighting coefficients for the octave bands from 125 Hz to 8 kHz [52].