# A Wearable Microphone Array Helmet for Automotive Applications
## 3 Results  
At first, the beamforming capability of the proposed array helmet was compared to the Eigenmike32. The comparison was made by using a well-established metric for microphone array assessment [60], which consists of evaluating the deviation of the directivity \(\mathbf{A^{\prime}}\) with respect to the ideal directivity defined by \(\mathbf{A}\). This can be performed by relying on two parameters, the Spatial Correlation (SC), which sets the limit of the beamforming at high frequency and is the defined in (8), and the Level Difference (LD), which sets the limit of the beamforming at low frequency and is defined in (9) as follows:  
\[\text{SC}=\frac{\sum_{d}(A^{\prime})^{T}\cdot A}{\sum_{d}\biggl{(}\sqrt{\left(A ^{\prime}\right)^{T}\cdot A^{\prime}}\cdot\sqrt{A^{T}\cdot A}\biggr{)}} \tag{8}\]  
\[\text{LD}=\frac{1}{D}\sum_{d}\frac{A^{2}}{A^{\prime}\cdot\left(A^{\prime} \right)^{n}}\cdot\left[\text{dB}\right] \tag{9}\]  
The parameters are calculated for each frequency, each direction, and each virtual microphone; then, the \(D\) directions are summed, while the virtual microphones are averaged among those belonging to the same Ambisonics order. Hence, from 1 to 4 in the first order, from 5 to 9 in the second order, and from 10 to 16 in the third order. In the ideal case of perfect reconstruction of the SH, it will be SC = 1 and LD = 0 dB. However, a certain amount of deviation is always present in the real case; hence, the upper and lower frequency limits of the beamforming are usually defined by considering two thresholds: SC > 0.9 and LD > \(-\)1 dB. The results are shown in Figure 7 for Eigenmike32 and in Figure 8 for the array helmet.  
\begin{table}
\begin{tabular}{c c} \hline \hline \multicolumn{1}{c}{**A/D Characteristics**} & \multicolumn{1}{c}{**Value**} \\ \hline Number and type of input channels & 4-channels, analog \\ Dynamic range & 123 dB \\ Total harmonic distortion + noise (THD + N) & \(-\)98 dB \\ Input voltage range & 2 Vrms \\ Sample rate & 8 to 768 kHz \\ Power consumption & 9.2 mW/ch @ 48 kHz \\ Audio serial data interface & TDM or l\({}^{2}\)S \\ \hline
**D/A Characteristics** & **Value** \\ \hline Number of output channels & 16-channels, single ended \\ Resolution & 24 bits \\ Dynamic range & 110 dB (A) \\ Total harmonic distortion + noise (THD + N) & \(-\)97 dB \\ Sample rate & 32 to 192 kHz \\ \hline \hline \end{tabular}
\end{table}
Table 2: A/D (TLV320 ADC6140) and D/A (ADAU1966) converter specification.  
Then, a localization test was performed in the acoustic laboratory at the University of Parma, Parma (Italy), using the sound color mapping technique [61,62]. The array helmet was mounted on a microphone stand, in front of the Genelec studio monitor 8351a playing pink noise. A 30 s signal was recorded and converted into Ambisonics third order. Then, the array helmet was replaced with a dual lenses camera to take a 360\({}^{\circ}\) picture of the environment, which is used as the background of the sound color maps. The analysis was performed in the octave bands centered at 31.5 Hz, 63 Hz, 125 Hz, 250 Hz, 500 Hz, and 1 kHz. The quantity being mapped is the Sound Pressure Level (SPL), calculated with a resolution of 1 degree. The pseudo-color maps are generated through graphical interpolation, with a color scale that goes from blue (lowest SPL value) to red (highest SPL value). The results are shown in Figure 9.  
Figure 8: SC (**left**) and LD (**right**) calculated for the array helmet.  
Figure 7: SC (**left**) and LD (**right**) calculated for the Eigenmike32.  
Figure 9: _Cont._