# A Wearable Microphone Array Helmet for Automotive Applications
showed a portable array with 512 MEMS microphones [33]. The layout of the capsules over the surface of the array is at least as important. A heuristic approach was used for planar arrays in [34], while several mathematical approaches were developed for SMA, with the aim of optimizing the spatial sampling over the sphere, as well treated in [35]. In the case of equiangular sampling, the number \(N\) of required microphones is given by (1), while in the case of nearly uniform sampling, it is given by (2)  
\[N=4(O+1)^{2} \tag{1}\]  
\[N=1/2(O+1)^{2} \tag{2}\]where \(O\) is the Ambisonics order. The Ambisonics theory, consisting of a Spherical Harmonics (SHs) expansion of the sound field at the recording point, was first presented by [PERSON] in 1975 [36; 37] and nowadays is widely employed for delivering spatial audio. More on the SH can be found in [38], while an exhaustive discussion of SH decomposition with SMA can be found in [39]. In the case of nearly uniform sampling, a mathematical approach called Spherical Design is commonly employed to optimize the distribution of the capsules over the surface of a rigid SMA. A spherical design is a finite set of \(N\) points on the d-dimensional unit sphere \(S_{d}\) such that the average value of any polynomial \(f\) of degree \(t\) or less equals the average value of \(f\) on the whole sphere [40; 41; 42]. Such a set is often also called the Spherical T-design. In [43; 44], many spherical designs and their properties are presented. Other interesting distributions of points are based on regular polyhedrons, such as tetrahedron, dodecahedron, and icosahedron, with \(N\) = 4, 12, and 20, respectively. Eigenmike32, widely recognized as the reference system of the last decade and employed as a comparative target also in the presented work, features 32 capsules arranged in a truncated icosahedron over a rigid sphere of 84 mm diameter. When selecting the type of capsule, the choice is between analog and digital transducers. Analog transducers can provide high-quality audio signals, but they come with some drawbacks, such as cumbersome wiring and susceptibility to noise interference, especially when long cables are used to connect the capsules to the Analog-to-Digital (A/D) converters. Affordable digital MEMS microphones are less affected by electrical interference, though this often comes at the expense of lower acoustic performance, such as reduced dynamic range and signal-to-noise ratio. A review of MEMS microphones can be found in [45]. In this work, a wearable microphone array is presented for the development and performance assessment of ANC systems installed on vehicles. The array solves a common limitation encountered in measuring automotive ANC systems with microphone arrays: the presence of the driver in the front left seat during road tests. The array was built by using a normal rigid helmet as a frame. The dimension of the helmet, which is larger than the microphone arrays currently available on the market, allows for shifting the frequency range of beamforming toward low frequencies, where ANC systems are mostly effective. With the shape of the helmet being almost spherical, the nearly uniform sampling theory was applied to optimize the distribution of the capsules over the surface of the array. A Spherical Design of degree \(t\) = 7 with \(N\) = 32 points was employed. The proposed solution features electret capsules connected to a miniaturized A/D converter incorporated in the helmet. The A/D converter also integrates an A\({}^{2}\)B transceiver (see Section 2.3), allowing it to deliver digital signals over an Ethernet cable, thus ensuring immunity to electromagnetic disturbances, which are always present in a car cabin. The proposed solution is flexible and can be used in many scenarios, such as internal combustion engines or electric vehicles, different road conditions (smooth, rough, very rough asphalt, with/without bumps are common tests performed by car makers), and speed.