Modal beamforming for small circular arrays of particle velocity sensors

Vector sensors are directional receivers that measure the vectorial particle velocity associated with an acoustic wave rather than the scalar pressure. Therefore, arrays of vector sensors possess some desirable directional properties compared to conventional arrays of pressure sensors. In this paper, a modal beamformer for circular arrays of 1-D acoustic vectors sensors are presented. Arrays of both radially and circumferentially oriented vector sensors are considered. It is shown that the highly directional modes of the acoustic velocity field can be extracted from the sensor measurements using the spatial Fourier transform. These modes are weighted and combined to form narrow steerable beams. The highest order of mode that can be extracted is limited by the number of vector sensors utilized in the array. Theoretical analysis and numerical simulations indicate that the proposed modal beamformer attains the same directivity performance as that of circular pressure sensor array beamformers but outperforms them in terms of white noise gain. In addition, it uses half the number of sensors to achieve the same directivity performance of a circular vector sensor array modal beamformer reported previously in the literature. The proposed method is suitable for in-air and underwater low frequencies array processing applications.