title: An upper bound for the directivity index of superdirective acoustic vector sensor arrays.
abstract: Approximate analytical expressions of the white noise gain (WNG) for two superdirective acoustic vector sensor arrays are provided, which disclose the strong dependence of the tradeoff between the WNG and the directivity index (DI) on the highest order of the modes for the pattern synthesis. The considered arrays are a uniform linear array and a uniform circular array. A condition on the WNG that ensures a high array gain in the two-dimensional homogeneous and isotropic noise field is deduced. Using this condition, an upper bound on the highest order of the modes for the pattern synthesis can be derived, and hence the maximum DI can be determined. The presented results are not strictly limited to the two array geometries considered herein, and can be extended to other superdirective acoustic array designs.
authors.affiliation: Key Laboratory of Ocean Acoustics and Sensing (Northwestern Polytechnical University), Ministry of Industry and Information Technology, Xi'an 710072, Chinaxguo@nwpu.edu.cn.
authors.forename: Xijing
authors.initials: X
authors.lastname: Guo
authors.affiliation: Université de Lorraine, Centre de Recherche en Automatique de Nancy, Unité Mixte de Recherche 7039, Vandœuvre-lès-Nancy, F-54506, France sebastian.miron@univ-lorraine.fr.
authors.forename: Sebastian
authors.initials: S
authors.lastname: Miron
authors.affiliation: Key Laboratory of Ocean Acoustics and Sensing (Northwestern Polytechnical University), Ministry of Industry and Information Technology, Xi'an 710072, China yxyang@nwpu.edu.cn.
authors.forename: Yixin
authors.initials: Y
authors.lastname: Yang
authors.affiliation: College of Underwater Acoustic Engineering, Harbin Engineering University, 145 Nantong Street, 150001 Harbin, China yangshie@hrbeu.edu.cn.
authors.forename: Shi'e
authors.initials: S
authors.lastname: Yang