# A Wearable Microphone Array Helmet for Automotive Applications
## 4 Discussion  
The SC and LD charts of Figures 7 and 8 can be used to precisely define the frequency limits of beamforming at each Ambisonics order. This is obtained by applying the previously stated thresholds, SC > 0.9 and LD > \(-1\) dB. Each of them intersects the chart for each Ambisonics order in two points, thus identifying a low and a high acceptable frequency. These results are shown in Table 3, where it can be seen that the LD is always more restrictive at low frequency, while the SC is at high frequency. Therefore, the frequency limits provided by the two metrics must be combined, taking the most restrictive condition at low and at high frequency for each Ambisonics order (Table 4). The maximum beamforming frequency for the array helmet is 1 kHz at all orders. Despite being lower than the Eigenmike32 (10 kHz at 1 st order, 9 kHz at 2 nd and 8 kHz at 3 rd), it is still acceptable for ANC applications. As referred to in [28] by [PERSON], the maximum theoretical beamforming frequency, \(f_{max}\), can be calculated as  
\[f_{max}=\frac{1}{2}.\frac{c}{d_{min}} \tag{10}\] \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Eigenmike32**} & \multicolumn{4}{c}{**Array Helmet**} \\ \cline{2-9}  & \multicolumn{2}{c}{**SC**} & \multicolumn{2}{c}{**LD**} & \multicolumn{2}{c}{**SC**} & \multicolumn{2}{c}{**LD**} \\ \hline
**Ambisonics** & **Low Freq.** & **High Freq.** & **Low Freq.** & **High Freq.** & **Low Freq.** & **High Freq.** & **Low Freq.** & **High Freq.** \\
**Order** & **[Hz]** & **[Hz]** & **[Hz]** & **[Hz]** & **[Hz]** & **[Hz]** & **[Hz]** & **[Hz]** \\ \hline
1 & - & 10,000 & 45 & 10,100 & - & 1050 & - & 1100 \\
2 & 100 & 9000 & 170 & 9100 & 35 & 1050 & 40 & 1100 \\
3 & 380 & 7950 & 700 & 8050 & 120 & 1050 & 220 & 1100 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Acceptable low and high frequency limits at various Ambisonics orders for SC and LD metrics. Figure 9: Sound color map analysis of a pink noise source located in (\(0^{\circ}\); \(0^{\circ}\)) at various octave bands. where \(c\) = 343 m/s is the celerity of the sound wave and \(d_{min}\) is the minimum distance between the capsules of the array. The results shown in Table 5 are obtained by replacing the value of \(d_{min}\) in (10) for the Eigenmike32 and for the array helmet. The main advantage offered by the proposed solution consists of a significant shift in the beamforming capability toward low frequencies, as follows:  
* First order Ambisonics at 20 Hz (array helmet) instead of 45 Hz (Eingemike32);
* Second order Ambisonics at 40 Hz (array helmet) instead of 170 Hz (Eingemike32);
* Third order Ambisonics at 220 Hz (array helmet) instead of 700 Hz (Eingemike32). Usually, the comparison between microphone arrays is also performed in terms of octave bands. As can be seen in Table 6, the array helmet allowed gaining one Ambisonics order at the octave bands from one to five. The two solutions have the same performance at the sixth octave band (centered at 1 kHz), while only the Eigenmike32 operates at the octave bands centered at 2, 4, and 8 kHz. A particularly useful improvement for ANC applications is obtained at the first octave band (centered at 31.5 Hz), at which the Eigenmike32 does not provide any beamforming, while the array helmet offers a first order localization. The second laboratory experiment, related to the localization of a noise source through sound color mapping, is now analyzed. The acoustic center of noise source was positioned coincident with the optical center of the panoramic camera. Therefore, in polar coordinates \begin{table}
\begin{tabular}{c c c} \hline \hline
**Octave Bands Center** & \multicolumn{2}{c}{**Highest Available Ambisonics Order**} \\ \cline{2-3}
**Frequency [Hz]** & **Eigenmike32** & **Array Helmet** \\ \hline
31.5 & - & 1 \\
63 & 1 & 2 \\
125 & 1 & 2 \\
250 & 2 & 3 \\
500 & 2 & 3 \\
1000 & 3 & 3 \\
2000 & 3 & - \\
4000 & 3 & - \\
8000 & 3 & - \\
16,000 & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Ambisonics orders at different octave bands.