# A Wearable Microphone Array Helmet for Automotive Applications
## 2 Materials and Methods
### Acoustics Characterization of the Array Helmet  
Once assembled, the helmet was characterized in the acoustics laboratory at the University of Parma, Parma (Italy), with the dimensions 5 \(\times\) 3 \(\times\) 8 m (W \(\times\) H \(\times\) L). The measurement procedure made use of a two-axis turntable and a loudspeaker (studio monitor type 8351a, by Genelec, Iisalmi, Finland) in a fixed position (Figure 2). Since the helmet must be used in a small environment, the measurement was performed at a very short distance, \(d\) = 0.5 m, to consider the near-field effect provided by the curvature of the sound waves. In fact, the commonly employed analytical beamformers rely on the plane wave hypothesis, which is only true in a far field condition, as demonstrated in [48]. This assumption is not true inside a car cockpit, due to its limited size compared to the wavelengths interested in an ANC system. The near-field beamforming [49,50] allows us to overcome the far field limitation of analytical beamformers. The test signal employed for the measurement was an Exponential Sine Sweep (ESS) [51], pre-equalized for flatting the spectrum and to reduce the time domain impulse response (IR). Since the loudspeaker was positioned in the center of the laboratory, the time of arrival \(t_{1}\) of the first reflections (floor and ceilings) can be easily calculated as  
\[t_{1}=\frac{\sqrt{H^{2}+d^{2}}}{c} \tag{3}\]  
where \(H\) = 3 m is the height of the room, \(d\) = 0.5 m is the distance between the microphone array and the loudspeaker, and c = 343 m/s is the sound celerity in air at 20 \({}^{\circ}\)C. Note that the numerator of (3) is the total travel path of the first reflections, which is about 3.04 m, and hence \(t_{1}\cong 8.9\) ms or 427 samples at the standard audio sampling frequency \(f_{s}\) = 48 kHz. As can be seen in Figure 3, the effective number of samples between the direct sound (first peak of the IR, occurring after 70 samples) and the first reflections (second peak of the IR, occurring after 491 samples) corresponds almost exactly to the analytically calculated time of flight. Therefore, the entire direct sound can be isolated before the first reflections occur, and this technique is referred as a \"pseudo-anechoic chamber\" [52]. It can also be seen that the delay of the first peak in samples, \(s_{d}\), perfectly matches the source-microphone distance, as follows:  
\[s_{d}=\frac{d}{f_{s}}\cdot c \tag{4}\]  
with \(d\) = 0.5 m, \(f_{s}\) = 48 kHz, and \(c\) = 343 m/s, it results in \(s_{d}\) = 70 samples, as expected. Figure 2: Side view of the array helmet after assembling the capsules (**left**). A view of the array helmet mounted on the two-axis turntable while performing the acoustic characterization (**right**). In Figure 4, the spectrum of the IR direct sound is shown in the frequency range of interest, that is 20 Hz-1 kHz. Taking the lowest IR level in this range as an acceptance threshold, i.e., 85.6 dB, we can assess that the measurement can be used above 40 Hz (black dot in Figure 4). However, this can be further improved by measuring the array in a true anechoic chamber, where the IR can be kept longer thanks to the absence of reflections. In that case, without the pre-equalization filter, the lower limit would be given by the frequency response of the loudspeaker (32 Hz according to manufacturer's datasheet). At each repetition of the measurement, the helmet is automatically rotated by the turntable in a specific direction, and the test signal is recorded by the \(N\) capsules of the array. This procedure also addresses the problem of spatial sampling of a sphere, since the choice of the measurement directions has a strong impact on the quality of the beamforming filters. This problem was already treated by one of the same authors in [53], where it is shown that a nearly uniform sampling is again a wise choice. A set of \(D=240\) directions was used to characterize the acoustic response of the array helmet, corresponding to a spherical design of degree \(t=21\).